
DU B.SC.(H) PHYSICS, SEMIV: NUMERICAL ANALYSIS  RANJANA MEHTA 

Cover Price : Rs 225.00

Imprint : Ane Books Pvt. Ltd. ISBN : 9789382127475 YOP : 2016

Binding : Paperback Total Pages : 124 CD : No


About the Book :
This book is useful for various graduate and postgraduate courses in Mathematics, Physics, Computer Science. The book covers the syllabus for B.Sc(Hons.) Physics, IInd Year, SemesterIV for the paper16,PHHT414.
This text has a student friendly approach with an easy to read writing style and a perfect blend of theory and numerical. It presents all the basic material in one place and gives an opportunity to understand the topic in the most easy and comfortable way. A large number of examples are used to explain the concepts. The book contains number of exercises to help build confidence in students.
Contents :
1. Errors and Iterative Methods
2. Solution of Algebraic Transcendental Equations
3. Matrices and Linear System of Equations
4. Interpolation
5. Least Square Approximation
6. Numerical Differentiation
7. General Quadrature Formula
8. Solution of Initial Value Problems
References
About the Author :
Dr. Ranjna Mehta is an Associate Professor in the Department of Mathematics at Sri Venkateswara College. She has over 36 years of teaching experience at the undergraduate level. Her area of interest are Numerical Analysis, Calculus, Geometry (two and three dimensional), Algebra, Functional Equations. She did her Ph.D entitled "Functional Equations on Algebraic Structures" from University of Delhi in 1982. Four of her research papers have been published in Indian and Foreign journals. She attended one science conference in Bombay in 1976. She attended various workshops held in North and South Campus in the Department of Mathematics. Recently, She has published one book entitled "Numerical Methods and Programming" from Ane Books Pvt.Ltd.




Algebra : Fields and Galois Theory  Falko Lorenz 

Cover Price : Rs 695.00

Imprint : Springer ISBN : 8181289803 YOP : 2008

Binding : Paperback Total Pages : 304 CD : No


About the Book :
Algebra : Fields and Galois Theory
The present textbook is a lively, problemoriented and carefully written introduction to classical modern algebra. The author leads the reader thorough interesting subject matter while assuming only the background provided by a first course in linear algebra.
The book focuses of field extensions. Galois theory and its applications are treated more thoroughly than in most texts. It also covers basic applications to number theory, ring extensions and algebraic geometry.
This book contain numerous exercises and can be used as a textbook for advanced undergraduate students.
From Reviews of the German version :
This is a charming textbook, introduction the reader to the classical parts of algebra. The exposition is admirably clear and lucidly written with only minimal prerequisites from linear algebra. The new concepts are, at least in the first part of the book, defined in the framework of the development of carefully selected problems.
 Stefan Porubsky, Mathematical Reviews
Contents :
Foreword
1 Constructibility with Ruler and Compass
2 Algebraic Extensions
3 Simple Extensions
4 Fundamentals of Divisibility
5 Prime Factorization in Polynomial Rings. Gauss’s Theorem
6 Polynomial Splitting Fields
7 Separable Extensions
8 Galois Extensions
9 Finite Fields, Cyclic Groups and Roots of Unity
10 Group Actions
11 Applications of Galois Theory to Cyclotomic Fields
12 Further Steps into Galois Theory
13 Norm and Trace
14 Binomial Equations
15 Solvability of Equations
16 Integral Ring Extensions
17 The Transcendence of ð
18 Transcendental Field Extensions
19 Hilbert’s Nullstellensatz
Appendix: Problems and Remarks
Index of Notation
Index.




Algebra  Volume I  B. L. van der Waerden 
Author 
B. L. van der Waerden


Cover Price : Rs 595.00

Imprint : Springer ISBN : 8181288868 YOP : 2008

Binding : Paperback Total Pages : 272 CD : No


About the Book :
...This beautiful and eloquent text served to transform the graduate teaching of algebra, not only in Germany, but elsewhere in Europe and the United States. It formulated clearly and succinctly the conceptual and structural insights which Noether had expressed so forcefully. This was combined with the elegance and understanding with which Artin had lectured...Its simple but austere style set the pattern for mathematical texts in other subjects, from Banach spaces to topological group theory...It is, in my view, the most influential text in algebra of the twentieth century.
 Saunders MacLane, Notices of the AMS
How exciting it must have been to hear Emil Artin and Emmy Noether lecture on algebra in the 1920's, when the axiomatic approach to the subject was amazing and new! Van der Waerden was there, and produced from his notes the classic textbook of the field. To Artin's clarity and Noether's originality he added his extraordinary gift for synthesis. At one time every wouldbe algebraist had to study this text. Even today, all who work in Algebra owe a tremendous debt to it; they learned from it by second or third hand, if not directly. It is still a firstrate (some would say, the best) source for the great range of material it contains.
 David Eisenbud, Mathematical Sciences Research Institute
Van der Waerden's book Moderne Algebra, first published in 1930, set the standard for the unified approach to algebraic structures in the twentieth century. It is a classic, still worth reading today.
 Robin Hartshorne, University of California, Berkeley
Contents :
1. Numbers and Sets; 2. Groups; 3. Rings and Fields; 4. Vector Spaces and Tensor Spaces; 5. Polynomials; 6. Theory of Fields; 7. Continuation of Group Theory; 8. The Galois Theory; 9. Ordering and Well Ordering of Sets; 10. Infinite Field Extensions; 11. Real Fields; Index.




Applied Numerical Analysis  Gerald 

Cover Price : Rs 295.00

Imprint : PG / Addison Wesley ISBN : 8178085674 YOP : Edition :

Binding : Paperback Total Pages : 0 CD : No


Mathematics / Management 
ANE 



Introduction to Linear Algebra, 2016  Inder K. Rana 

Cover Price : Rs 350.00

Imprint : Ane Books Pvt. Ltd. ISBN : 9789380156965 YOP : 2016

Binding : Paperback Total Pages : 288 CD : No


About the Book
There are two aspects of linear algebra: abstract and applied. Both these aspects play important role in diverse branches of mathematics, physics, engineering, economics, and so on. The aim of this book is to present both these aspects of linear algebra. We shall try to show how abstract concepts arise out of applications and physical needs, and how abstract concepts can be applied in various problems.
Normally, students are taught matrices and determinants in the first introductory course in linear algebra. We shall assume familiarity with the concept of matrices only. However, we do give a brief introduction of matrices in chapter 2. We will relate the origin and use of these concepts in linear algebra.
The book contains a moderate set of exercises.
We intend to bring out an interactive eversion of the book in a CDROM. A preview of the same is available on the website www.math4all.in.
Contents
1. From Geometry to AlgebraI: The Euclidean Space R3, 2. Systems of Linear Equations, 3. Linear Independence and Dependence of Vectors, 4. Determinants, 5. Vector Spaces, 6. Linear Transformations, 7. From Geometry to AlgebraII: Inner Product Spaces, 8. Orthogonal Projections and Orthogonal Basis, 9. Isometries and Orthogonal Matrices, 10. Diagonalization and the Spectral Theorem, 11. Applications of Diagonalization, Answers, Index
About the Author
Dr. Inder K. Rana is Professor at the Department of Mathematics, I.I.T. Bombay, with a teaching experience of more than 30 years. He was awarded the “C.L.C. Chandana award for the year 2000” for excellence in teaching and research in Mathematics, and also awarded the “Excellence in Teaching award for the year 2004” by I.I.T. Bombay. Other books authored by him include “An Introduction to Measure and Integration” published by American Mathematical Society, and “From Numbers to Analysis” published by World Scientific Press. 



Experimental Number Theory  Fernando Rodriguez Villegas 
Author 
Fernando Rodriguez Villegas


Cover Price : Rs 595.00

Imprint : Oxford University Press ISBN : 0199548729 YOP : 2008

Binding : Paperback Total Pages : 232 CD : No


About the Book :
This graduate text, based on years of teaching experience, is intended for first or second year graduate students in pure mathematics. The main goal of the text is to show how the computer can be used as a tool for research in number theory through numerical experimentation. The book contains many examples of experiments in binary quadratic forms, zeta functions of varieties over finite fields, elementary class field theory, elliptic units, modular forms, along with exercises and selected solutions. Sample programs are written in GP, the scripting language for the computational package PARI, and are available for download from the author's website.
Contents :
Preface
1. Basic examples
2. Reciprocity
3. Positive definite binary quadratic forms
4. Sequences
5. Combinatorics
6. padic numbers
7. Polynomials
8. Remarks on selected exercises
References
Index.
About the Author :
Fernando Rodriguez Villegas, Department of Mathematics, University of Texas at Austin. 



Calculus 2nd ed, Reprint  J.P. Singh 

Cover Price : Rs 395.00

Imprint : Ane Books Pvt. Ltd. ISBN : 9789382127260 YOP : 2015

Binding : Paperback Size : 5.50" X 8.50" Total Pages : 688 CD : No


About the Book
The second edition of this book is the result of the enthusiastic reception given to the earlier edition received from the students and teachers, who are the end users of this book.
The book covers the complete syllabus of BCA semesterI of GGSIP University. It introduces calculus and its techniques at undergraduate level in a simplified manner.
Salient features:
Text is selfexplanatory and the language is vivid and lucid
Contains numerous examples that illustrate the basic as well as high level concepts of the concerned topics
Additional questions provided in all the chapters for practice
Most of the questions conform to the trend in which the questions appear in GGSIP University
Contents
1. Matrices and Determinants 2. Eigen Values and Eigen Vectors 3. Limits 4. Continuous Functions 5. Differentiation 6. Successive Differentiation 7. General Mean Value Theorems 8. Indeterminate Forms and L' Hôpital Rule 9. Maxima and Minima 10. Asymptotes 11. Integration and its Techniques 12. Reduction Formulae 13. Beta and Gamma Functions, End Term Examination Papers, Some Useful Trigonometric Results/Identities
About the Author
J.P. Singh is a professor in Department of Mathematics at Jagan Institute of Management Studies, Rohini (Affiliated to GGSIP University), Delhi. He has more than 14 years of teaching experience and has taught at various affiliated Institutes of GGSIP University. He has undergone rigorous training from IIT Delhi in Financial Mathematics. He is a certified Six Sigma Green Belt from Indian Statistical Institute, Delhi.
He is a lifetime member of Indian Mathematical Society and Ramanujan Mathematical Society. His areas of interest include Stochastic Process, Discrete Mathematics, Mathematical Statistics, Numerical Methods, Number Theory and Theory of Computation.




Algebra  Volume II  B. L. van der Waerden 
Author 
B. L. van der Waerden


Cover Price : Rs 595.00

Imprint : Springer ISBN : 8181288875 YOP : 2008

Binding : Paperback Total Pages : 296 CD : No


About the Book :
...This beautiful and eloquent text served to transform the graduate teaching of algebra, not only in Germany, but elsewhere in Europe and the United States. It formulated clearly and succinctly the conceptual and structural insights which Noether had expressed so forcefully. This was combined with the elegance and understanding with which Artin had lectured...Its simple but austere style set the pattern for mathematical texts in other subjects, from Banach spaces to topological group theory...It is, in my view, the most influential text in algebra of the twentieth century.
 Saunders MacLane, Notices of the AMS
How exciting it must have been to hear Emil Artin and Emmy Noether lecture on algebra in the 1920's, when the axiomatic approach to the subject was amazing and new! Van der Waerden was there, and produced from his notes the classic textbook of the field. To Artin's clarity and Noether's originality he added his extraordinary gift for synthesis. At one time every wouldbe algebraist had to study this text. Even today, all who work in Algebra owe a tremendous debt to it; they learned from it by second or third hand, if not directly. It is still a firstrate (some would say, the best) source for the great range of material it contains.
 David Eisenbud, Mathematical Sciences Research Institute
Van der Waerden's book Moderne Algebra, first published in 1930, set the standard for the unified approach to algebraic structures in the twentieth century. It is a classic, still worth reading today.
 Robin Hartshorne, University of California, Berkeley
Contents :
12. Linear Algebra; 13. Algebras; 14. Representation Theory of Groups and Algebras; 15. General Ideal Theory of Commutative Rings; 16. Theory of Polynomial Ideas; 17. Integral Algebraic Elements; 18. Fields with Valuations; 19. Algebraic Functions of One Variable; 20. Topological Algebra; Index.




Short Calculus  Serge Lang 

Cover Price : Rs 595.00

Imprint : Springer ISBN : 8181289742 YOP : 2008

Binding : Paperback Total Pages : 272 CD : No


About the Book :
This is a reprint of A First Course in Calculus, which has gone through five editions since the early sixties. It covers all the topics traditionally taught in the firstyear calculus sequence in a brief and elementary fashion. As sociological and educational conditions have evolved in various ways over the past four decades, it has been found worthwhile to make the original edition available again. The audience consists of those taking the first calculus course, in high school or college. The approach is the one which was successful decades ago, involving clarity, and adjusted to a time when the students background was not as substantial as it might be. We are now back to those times, so it is time to start over again. There are no epsilondeltas, but this does not imply that the book is not rigorous. Lang learned this attitude from Emil Artin, around 1950.
Contents :
Numbers and Functions * Graphs and Curves * The Derivative * Sine and Cosine * The Mean Value Theorem * Sketching Curves * Inverse Functions * Exponents and Logarithms * Integration * Properties of the Integral * Techniques of Integration * Some Substantial Exercises * Applications of Integration * Taylor's Formula * Series * Appendix 1. Epsilon and Delta * Appendix 2. Physics and Mathematics * Answers * Index. 



Business Mathematics for BBA, 2014  J.P. Singh 

Cover Price : Rs 350.00

Imprint : Ane Books Pvt. Ltd. ISBN : 9789382127826 YOP : 2014

Binding : Paperback Total Pages : 640 CD : No


About the Book
This book has been written for undergraduate students pursuing Business Mathematics as their subject. The book primarily aims at students preparing for BBA, Semester I examination conducted by GGSIP University. This book consists of twelve chapters. All the chapters have been supplied by numerous solved examples and exercises along with their answers. The main objective of this book is to provide useful selfstudy material for the students which will not only enhance students' understanding of the concept discussed but will also prepare them for examination.
Salient features:
1. It covers the complete syllabus of BBA Semester I of GGSIPU.
2. The text material is selfexplanatory and the language is vivid and lucid. It can be used for sophomorelevel course in Business Mathematics.
3. More than 415 solved examples of different types and different levels have been included.
4. Most of the questions conform to trend questions appearing in GGSIPU.
Contents
1. Permutation and Combinations 2. Mathematical Induction 3. Sequence and Series 4. Matrices and Determinants 5. Applications of Matrices to Business and Economics 6. Differentiation 7. Applications of Differentiation 8. Partial Differentiation and its Applications 9. Integrations 10. Applications of Integration in Business and Economics 11. Differential Equation and its Applications 12. Vectors
About the Author
J.P. Singh is a Professor in Department of Mathematics at Jagan Institute of Management Studies, Rohini (Affiliated to GGSIP University), Delhi. He has more than 14 years of teaching experience and has taught at various affiliated Institutes of GGSIP University. He has undergone rigorous training from IIT Delhi in Financial Mathematics. He is a Certified Six Sigma Green Belt from Indian Statistical Institute, Delhi.
He is a lifetime member of the Indian Mathematical Society and Ramanujan Mathematical Society. His areas of interest include Stochastic Process, Discrete Mathematics, Mathematical Statistics, Numerical Methods, Number Theory and Theory of Computation.




Classical Algebra  Roger Cooke 

Cover Price : Rs 2,995.00

Imprint : Wiley ISBN : 9788126553624 YOP : 2015

Binding : Hardback Total Pages : 218 CD : No


Classical Algebra provides a complete and contemporary perspective on classical polynomial algebra through the exploration of how it was developed and how it exists today. With a focus on prominent areas such as the numerical solutions of equations, the systematic study of equations, and Galois theory, this book facilitates a thorough understanding of algebra and illustrates how the concepts of modern algebra originally developed from classical algebraic precursors.
This book successfully ties together the disconnect between classical and modern algebra and provides readers with answers to many fascinating questions that typically go unexamined, including:
What is algebra about?
How did it arise?
What uses does it have?
How did it develop?
What problems and issues have occurred in its history?
How were these problems and issues resolved?
The author answers these questions and more, shedding light on a rich history of the subject—from ancient and medieval times to the present. Structured as eleven "lessons" that are intended to give the reader further insight on classical algebra, each chapter contains thoughtprovoking problems and stimulating questions, for which complete answers are provided in an appendix.
Complemented with a mixture of historical remarks and analyses of polynomial equations throughout, Classical Algebra: Its Nature, Origins, and Uses is an excellent book for mathematics courses at the undergraduate level. It also serves as a valuable resource to anyone with a general interest in mathematics.
Contents
Preface
Part 1. Numbers and Equations.
Lesson 1. What Algebra Is.
1. Numbers in disguise.
1.1. Classical and modern algebra.
2. Arithmetic and algebra.
3. The environment of algebra: Number systems.
4. Important concepts and principles in this lesson.
5. Problems and questions.
6. Further reading.
Lesson 2. Equations and Their Solutions.
1. Polynomial equations, coefficients, and roots.
1.1. Geometric interpretations.
2. The classification of equations.
2.1. Diophantine equations.
3. Numerical and formulaic approaches to equations.
3.1. The numerical approach.
3.2. The formulaic approach.
4. Important concepts and principles in this lesson.
5. Problems and questions.
6. Further reading.
Lesson 3. Where Algebra Comes From.
1. An Egyptian problem.
2. A Mesopotamian problem.
3. A Chinese problem.
4. An Arabic problem.
5. A Japanese problem.
6. Problems and questions.
7. Further reading.
Lesson 4. Why Algebra Is Important.
1. Example: An ideal pendulum.
2. Problems and questions.
3. Further reading.
Lesson 5. Numerical Solution of Equations.
1. A simple but crude method.
2. Ancient Chinese methods of calculating.
2.1. A linear problem in three unknowns.
3. Systems of linear equations.
4. Polynomial equations.
4.1. Noninteger solutions.
5. The cubic equation.
6. Problems and questions.
7. Further reading.
Part 2. The Formulaic Approach to Equations.
Lesson 6. Combinatoric Solutions I: Quadratic Equations.
1. Why not set up tables of solutions?.
2. The quadratic formula.
3. Problems and questions.
4. Further reading.
Lesson 7. Combinatoric Solutions II: Cubic Equations.
1. Reduction from four parameters to one.
2. Graphical solutions of cubic equations.
3. Efforts to find a cubic formula.
3.1. Cube roots of complex numbers.
4. Alternative forms of the cubic formula.
5. The \irreducible case.
5.1. Imaginary numbers.
6. Problems and questions.
7. Further reading.
Part 3. Resolvents.
Lesson 8. From Combinatorics to Resolvents.
1. Solution of the irreducible case using complex numbers.
2. The quartic equation.
3. Viµete's solution of the irreducible case of the cubic.
3.1. Comparison of the Viète and Cardano solutions.
4. The Tschirnhaus solution of the cubic equation.
5. Lagrange's reflections on the cubic equation.
5.1. The cubic formula in terms of the roots.
5.2. A test case: The quartic.
6. Problems and questions.
7. Further reading.
Lesson 9. The Search for Resolvents.
1. Coefficients and roots.
2. A unified approach to equations of all degrees.
2.1. A resolvent for the cubic equation.
3. A resolvent for the general quartic equation.
4. The state of polynomial algebra in 1770.
4.1. Seeking a resolvent for the quintic.
5. Permutations enter algebra.
6. Permutations of the variables in a function.
6.1. Twovalued functions.
7. Problems and questions.
8. Further reading.
Part 4. Abstract Algebra.
Lesson 10. Existence and Constructibility of Roots.
1. Proof that the complex numbers are algebraically closed.
2. Solution by radicals: General considerations.
2.1. The quadratic formula.
2.2. The cubic formula.
2.3. Algebraic functions and algebraic formulas.
3. Abel's proof.
3.1. Taking the formula apart.
3.2. The last step in the proof.
3.3. The verdict on Abel's proof.
4. Problems and questions.
5. Further reading.
Lesson 11. The Breakthrough: Galois Theory.
1. An example of a solving an equation by radicals.
2. Field automorphisms and permutations of roots.
2.1. Subgroups and cosets.
2.2. Normal subgroups and quotient groups.
2.3. Further analysis of the cubic equation.
2.4. Why the cubic formula must have the form it does.
2.5. Why the roots of unity are important.
2.6. The birth of Galois theory.
3. A sketch of Galois theory.
4. Solution by radicals.
4.1. Abel's theorem.
5. Some simple examples for practice.
6. The story of polynomial algebra: a recap.
7. Problems and questions.
8. Further reading.
Epilogue: Modern Algebra.
1. Groups.
2. Rings.
2.1. Associative rings.
2.2. Lie rings.
2.3. Special classes of rings.
3. Division rings and fields.
4. Vector spaces and related structures.
4.1. Modules.
4.2. Algebras.
5. Conclusion.
Appendix: Some Facts about Polynomials.
Answers to the Problems and Questions.
Subject Index.
Name Index.
Roger Cooke, PhD, is Emeritus Professor of Mathematics in the Department of Mathematics and Statistics at the University of Vermont. Dr. Cooke has over forty years of academic experience, and his areas of research interest include the history of mathematics, almostperiodic functions, uniqueness of trigonometric series representations, and Fourier analysis. He is also the author of The History of Mathematics: A Brief Course, Second Edition (Wiley).




ADVANCES IN PDE MODELING AND COMPUTATION  S. SUNDAR 

Cover Price : Rs 1,195.00

Imprint : Ane Books Pvt. Ltd. ISBN : 9789383656042 YOP : 2014

Binding : Hardback Total Pages : 324 CD : No


About the Book
This book on "Advances in PDE Modeling and Computation" is a collection of invited articles from active established researchers who are working in the area of PDE modeling and PDE computing.
There are 22 articles in this book given as Invited Talks at the International Workshop on PDE Modeling and Computation held at IIT Madras during October 2125, 2013. These selected articles showcasing the importance and challenges of PDE based mathematical modeling, analysis and computing. Covering a wide spectrum of applications, this Book is aimed at Masters and Ph.D. students aspiring to take up some challenges. Each article is carefully written, self contained and supported with up to date references.
Contents
 Mesh free method for numerical solution of the eikonal equation
 A spline collection method for pricing options under the jumpdiffusion model
 An alebased finite element method for the simulation of an impinging droplet on a hot surface
 Multilevel augmentation method for parameter identification
 StaRMAP a second order staggered grid method for radiative transfer: application in radiotherapy
 Exact controllability in domains with oscillating boundaries: homogenization
 AC0 interior penalty method for an optimal control problem governed by the biharmonic operator
 A multilevel finite element discretization for efficient solution of multidimensional population balance system
 Meshfree numerical scheme for time dependent problems in fluid and continuum mechanics
 On the wave equations of kirchhoff narasimha and carrier
 Micromechanical modeling on non linear behaviour of 13 type piezocomposite
 A meshfree approach for the numerical solution of straight fiber equations
 Finite pointset method (FPM) for gas flows in slip regime
 Comparison of RBF and hermiteRBF local schemes with variable (optimized) shape parameter
 On the construction of dual gabor frame generators
 Analysis of heatlines and entropy generation during natural convection within tilted square cavities
 Modeling heat flow through glass fibre insulators
 Evolutionary games and replicator dynamics
 Deterministic ordinary differential equation models in population ecology, with special reference to indirect mutualism
 Effect of surface piercing barriers on membrane coupled gravity waves
 Evolution of a prelens tear film after a blink
 On enforcement of discrete maximum principle for coherence enhancing diffusion
About the Author
Prof. Dr. S. Sundar, Professor of Mathematics at the prestigious Indian Institute of Technology Madras is a DAAD Fellow and one of the four recipients of the Award “Alumni Ambassador of the City Kaiserslautern, Germany” and “Distinguished Alumni of Technical Universitaet Kaiserslautern, Germany” in the year 2012. Prof. Sundar is well known for his contribution in the broad field of Mathematical Modelling and Numerical Simulation. He has on his credit over 50 publications in high impact factor journals. He has guided over 10 Ph.D. students and several M.Tech./M.Sc. projects. Many of his Ph.D. and Masters students are in holding leading positions at various Industries across the World.
Prof. Sundar is a Member of Department of Science and Technology (DST), Government of India – Programme Advisory Committee (Mathematical Sciences), Editorial Board Member of Journal of Indian Academy of Mathematics, Member of IIT Mandi Academic Council, Member of Board of Studies in several universities across India, to name a few.




Mathematical Logic  Ian Chiswell 
Author 
Ian Chiswell Wilfrid Hodges


Cover Price : Rs 595.00

Imprint : Oxford University Press ISBN : 0199548743 YOP : 2008

Binding : Paperback Total Pages : 260 CD : No


About the Book :
 Based on the authors' extensive teaching on the subject
 Practical examples are given for each idea as it is introduced
 Methods and concepts are introduced intuitively in terms of actual mathematical practice, but then developed rigorously
 Extensive exercises are presented along with selected solutions
Assuming no previous study in logic, this informal yet rigorous text covers the material of a standard undergraduate first course in mathematical logic, using natural deduction and leading up to the completeness theorem for firstorder logic. At each stage of the text, the reader is given an intuition based on standard mathematical practice, which is subsequently developed with clean formal mathematics. Alongside the practical examples, readers learn what can and can't be calculated; for example the correctness of a derivation proving a given sequent can be tested mechanically, but there is no general mechanical test for the existence of a derivation proving the given sequent. The undecidability results are proved rigorously in an optional final chapter, assuming Matiyasevich's theorem characterising the computably enumerable relations. Rigorous proofs of the adequacy and completeness proofs of the relevant logics are provided, with careful attention to the languages involved. Optional sections discuss the classification of mathematical structures by firstorder theories; the required theory of cardinality is developed from scratch. Throughout the book there are notes on historical aspects of the material, and connections with linguistics and computer science, and the discussion of syntax and semantics is influenced by modern linguistic approaches. Two basic themes in recent cognitive science studies of actual human reasoning are also introduced. Including extensive exercises and selected solutions, this text is ideal for students in Logic, Mathematics, Philosophy, and Computer Science.
Contents :
Preface
1. Prelude
2. Informal natural deduction
3. Propositional logic
4. First interlude: Wason's Selection Task
5. Quantifierfree logic
6. Second interlude: The Linda Problem
7. Firstorder logic
8. Postlude
A. The natural deduction rules
B. Denotational semantics
C. Solutions to some exercises
Index.
About the Authors :
Ian Chiswell, Queen Mary, University of London and
Wilfrid Hodges, Queen Mary, University of London.




Mathematical Methods in Survival Analysis, Reliability and Quality of Life  Catherine Huber 
Author 
Catherine Huber Nikolaos Limnios Mounir Mesbah Mikhail Nikulin


Cover Price : Rs 5,995.00

Imprint : Wiley ISBN : 9788126553617 YOP : 2015

Binding : Hardback Total Pages : 370 CD : No


Reliability and survival analysis are important applications of stochastic mathematics (probability, statistics and stochastic processes) that are usually covered separately in spite of the similarity of the involved mathematical theory involved.
This book aims to redress this situation: it includes 21 chapters divided into four parts: Survival analysis, Reliability, Quality of life, and Related topics. Many of these chapters are based on papers that were presented at the European Seminar on Mathematical Methods for Survival Analysis, Reliability and Quality of Life in 2006.
Contents
Preface
PART I
Chapter 1. Model Selection for Additive Regression in the Presence of RightCensoring
Elodie BRUNEL and Fabienne COMTE
1.1. Introduction
1.2. Assumptions on the model and the collection of approximation spaces
1.2.1. Nonparametric regression model with censored data
1.2.2. Description of the approximation spaces in the univariate case
1.2.3. The particular multivariate setting of additive models
1.3. The estimation method
1.3.1. Transformation of the data
1.3.2. The meansquare contrast
1.4. Main result for the adaptive meansquare estimator
1.5. Practical implementation
1.5.1. The algorithm
1.5.2. Univariate examples
1.5.3. Bivariate examples
1.5.4. A trivariate example
1.6. Bibliography
Chapter 2. Nonparametric Estimation of Conditional Probabilities, Means and Quantiles under Bias Sampling
Odile PONS
2.1. Introduction
2.2. Nonparametric estimation of p
2.3. Bias depending on the value of Y
2.4. Bias due to truncation on X
2.5. Truncation of a response variable in a nonparametric regression model
2.6. Double censoring of a response variable in a nonparametric model
2.7. Other truncation and censoring of Y in a nonparametric model
2.8. Observation by interval
2.9. Bibliography
Chapter 3. Inference in Transformation Models for Arbitrarily Censored and Truncated Data
Filia VONTA and Catherine HUBER
3.1. Introduction
3.2. Nonparametric estimation of the survival function S
3.3. Semiparametric estimation of the survival function S
3.4. Simulations
3.5. Bibliography
Chapter 4. Introduction of Withinarea Risk Factor Distribution in Ecological Poisson Models
Lea FORTUNATO, Chantal GUIHENNEUCJOUYAUX, Dominique LAURIER,Margot TIRMARCHE, Jacqueline CLAVEL and Denis HEMON
4.1. Introduction
4.2. Modeling framework
4.2.1. Aggregated model
4.2.2. Prior distributions
4.3. Simulation framework
4.4. Results
4.4.1. Strong association between relative risk and risk factor, correlated withinarea means and variances (meandependent case)
4.4.2. Sensitivity to withinarea distribution of the risk factor
4.4.3. Application: leukemia and indoor radon exposure
4.5. Discussion
4.6. Bibliography
Chapter 5. SemiMarkov Processes and Usefulness in Medicine
Eve MATHIEUDUPAS, Claudine GRASAYGON and JeanPierre DAURES
5.1. Introduction
5.2. Methods
5.2.1. Model description and notation
5.2.2. Construction of health indicators
5.3. An application to HIV control
5.3.1. Context
5.3.2. Estimation method
5.3.3. Results: new indicators of health state
5.4. An application to breast cancer
5.4.1. Context
5.4.2. Age and stagespecific prevalence
5.4.3. Estimation method
5.4.4. Results: indicators of public health
5.5. Discussion
5.6. Bibliography
Chapter 6. Bivariate Cox Models
Michel BRONIATOWSKI, Alexandre DEPIRE and Ya’acov RITOV
6.1. Introduction
6.2. A dependence model for duration data
6.3. Some useful facts in bivariate dependence
6.4. Coherence
6.5. Covariates and estimation
6.6. Application: regression of Spearman’s rho on covariates
6.7. Bibliography
Chapter 7. Nonparametric Estimation of a Class of Survival Functionals
Belkacem ABDOUS
7.1. Introduction
7.2. Weighted local polynomial estimates
7.3. Consistency of local polynomial fitting estimators
7.4. Automatic selection of the smoothing parameter
7.5. Bibliography
Chapter 8. Approximate Likelihood in Survival Models
Henning LAUTER
8.1. Introduction
8.2. Likelihood in proportional hazard models
8.3. Likelihood in parametric models
8.4. Profile likelihood
8.4.1. Smoothness classes
8.4.2. Approximate likelihood function
8.5. Statistical arguments
8.6. Bibliography
PART II
Chapter 9.Cox Regression with Missing Values of a Covariate having a Nonproportional Effect on Risk of Failure
JeanFrancois DUPUY and Eve LECONTE
9.1. Introduction
9.2. Estimation in the Cox model with missing covariate values: a short review
9.3. Estimation procedure in the stratified Cox model with missing stratum indicator values
9.4. Asymptotic theory
9.5. A simulation study
9.6. Discussion
9.7. Bibliography
Chapter 10.Exact Bayesian Variable Sampling Plans for Exponential Distribution under TypeI Censoring
ChienTai LIN, YenLung HUANG and N. BALAKRISHNAN
10.1. Introduction
10.2. Proposed sampling plan and Bayes risk
10.3. Numerical examples and comparison
10.4. Bibliography
Chapter 11. Reliability of Stochastic Dynamical Systems Applied to Fatigue Crack Growth Modeling
Julien CHIQUET and Nikolaos LIMNIOS
11.1. Introduction
11.2. Stochastic dynamical systems with jump Markov process
11.3. Estimation
11.4. Numerical application
11.5. Conclusion
11.6. Bibliography
Chapter 12. Statistical Analysis of a Redundant System with One Standby Unit
Vilijandas BAGDONAVIC¡ IUS, Inga MASIULAITYTE and Mikhail NIKULIN
12.1. Introduction
12.2. The models
12.3. The tests
12.4. Limit distribution of the test statistics
12.5. Bibliography
Chapter 13.A Modified Chisquared Goodnessoffit Test for the ThreeparameterWeibull Distribution and its Applications in Reliability
Vassilly VOINOV, Roza ALLOYAROVA and Natalie PYA
13.1. Introduction
13.2. Parameter estimation and modified chisquared tests
13.3. Power estimation
13.4. NeymanPearson classes
13.5. Discussion
13.6. Conclusion
13.7. Appendix
13.8. Bibliography
Chapter 14.Accelerated Life Testing when the Hazard Rate Function has Cup Shape
Vilijandas BAGDONAVIC¡ IUS, Luc CLERJAUD and Mikhail NIKULIN
14.1. Introduction
14.2. Estimation in the AFTGW model
14.2.1. AFT model
14.2.2. AFTWeibull, AFTlognormal and AFTGW models
14.2.3. Plans of ALT experiments
14.2.4. Parameter estimation: AFTGW model
14.3. Properties of estimators: simulation results for the AFTGW model
14.4. Some remarks on the second plan of experiments
14.5. Conclusion
14.6. Appendix
14.7. Bibliography
Chapter 15. Point Processes in Software Reliability
James LEDOUX
15.1. Introduction
15.2. Basic concepts for repairable systems
15.3. Selfexciting point processes and blackbox models
15.4. Whitebox models and Markovian arrival processes
15.4.1. A Markovian arrival model
15.4.2. Parameter estimation
15.4.3. Reliability growth
15.5. Bibliography
PART III
Chapter 16. Likelihood Inference for the Latent Markov Rasch Model
Francesco BARTOLUCCI, Fulvia PENNONI and Monia LUPPARELLI
16.1. Introduction
16.2. Latent class Rasch model
16.3. Latent Markov Rasch model
16.4. Likelihood inference for the latent Markov Rasch model
16.4.1. Loglikelihood maximization
16.4.2. Likelihood ratio testing of hypotheses on the parameters
16.5. An application
16.6. Possible extensions
16.6.1. Discrete response variables
16.6.2. Multivariate longitudinal data
16.7. Conclusions
16.8. Bibliography
Chapter 17. Selection of Items Fitting a Rasch Model
JeanBenoit HARDOUIN and Mounir MESBAH
17.1. Introduction
17.2. Notations and assumptions
17.2.1. Notations
17.2.2. Fundamental assumptions of the Item Response Theory (IRT)
17.3. The Rasch model and the multidimensional marginally sufficient Rasch model
17.3.1. The Rasch model
17.3.2. The multidimensional marginally sufficient Rasch model
17.4. The Raschfit procedure
17.5. A fast version of Raschfit
17.5.1. Estimation of the parameters under the fixed effects Rasch model
17.5.2. Principle of Raschfitfast
17.5.3. A model where the new item is explained by the same latent trait as the kernel
17.5.4. A model where the new item is not explained by the same latent trait as the kernel
17.5.5. Selection of the new item in the scale
17.6. A small set of simulations to compare Raschfit and Raschfitfast
17.6.1. Parameters of the simulation study
17.6.2. Results and computing time
17.7. A large set of simulations to compare Raschfitfast, MSP and HCA/CCPROX
17.7.1. Parameters of the simulations
17.7.2. Discussion
17.8. The Stata module “Raschfit”
17.9. Conclusion
17.10.Bibliography
Chapter 18. Analysis of Longitudinal HrQoL using Latent Regression in the Context of Rasch Modeling
Silvia BACCI
18.1. Introduction
18.2. Global models for longitudinal data analysis
18.3. A latent regression Rasch model for longitudinal data analysis
18.3.1. Model structure
18.3.2. Correlation structure
18.3.3. Estimation
18.3.4. Implementation with SAS
18.4. Case study: longitudinal HrQoL of terminal cancer patients
18.5. Concluding remarks
18.6. Bibliography
Chapter 19. Empirical Internal Validation and Analysis of a Quality of Life Instrument in French Diabetic Patients during an Educational Intervention
Judith CHWALOW, Keith MEADOWS, Mounir MESBAH, Vincent COLICHE and Etienne MOLLET
19.1. Introduction
19.2. Material and methods
19.2.1. Health care providers and patients
19.2.2. Psychometric validation of the DHP
19.2.3. Psychometric methods
19.2.4. Comparative analysis of quality of life by treatment group
19.3. Results
19.3.1. Internal validation of the DHP
19.3.2. Comparative analysis of quality of life by treatment group
19.4. Discussion
19.5. Conclusion
19.6. Bibliography
19.7. Appendices
PART IV
Chapter 20. Deterministic Modeling of the Size of the HIV/AIDS Epidemic in Cuba
Rachid LOUNES, Hector DE ARAZOZA, Y.H. HSIEH and Jose JOANES
20.1. Introduction
20.2. The models
20.2.1. The k2X model
20.2.2. The k2Y model
20.2.3. The k2XY model
20.2.4. The k2 XYX+Y model
20.3. The underreporting rate
20.4. Fitting the models to Cuban data
20.5. Discussion and concluding remarks
20.6. Bibliography
Chapter 21.Some Probabilistic Models Useful in Sport Sciences
Leo GERVILLEREACHE, Mikhail NIKULIN, Sebastien ORAZIO, Nicolas PARIS and Virginie ROSA
21.1. Introduction
21.2. Sport jury analysis: the GaussMarkov approach
21.2.1. GaussMarkov model
21.2.2. Test for nonobjectivity of a variable
21.2.3. Test of difference between skaters
21.2.4. Test for the less precise judge
21.3. Sport performance analysis: the fatigue and fitness approach
21.3.1. Model characteristics
21.3.2. Monte Carlo simulation
21.3.3. Results
21.4. Sport equipment analysis: the fuzzy subset approach
21.4.1. Statistical model used
21.4.2. Sensorial analysis step
21.4.3. Results
21.5. Sport duel issue analysis: the logistic simulation approach
21.5.1. Modeling by logistic regression
21.5.2. Numerical simulations
21.5.3. Results
21.6. Sport epidemiology analysis: the accelerated degradation approach
21.6.1. Principle of degradation in reliability analysis
21.6.2. Accelerated degradation model
21.7. Conclusion
21.8. Bibliography
Appendices
A. European Seminar: Some Figures
A.1. Former international speakers invited to the European Seminar
A.2. Former meetings supported by the European Seminar
A.3. Books edited by the organizers of the European Seminar
A.4. Institutions supporting the European Seminar (names of colleagues)
B. Contributors
Index
Catherine Huber is an Emeritus professor at Université de Paris René Descartes, France.
Nikolaos Limnios is a professor at the University of Technology of Compiègne, France.
Mounir Mesbah is a professor at the Université Victor Segalen, Bordeaux 2, France.




Probability Theory  Yuan Shih Chow 
Author 
Yuan Shih Chow Henry Teicher


Cover Price : Rs 695.00

Imprint : Springer ISBN : 8181281373 YOP : 2004 Edition : 2004

Binding : Paperback Total Pages : 490 CD : No


DESCRIPTION
Comprising the major theorems of probability theory and the measure theoretical foundations of the subject, the main topics treated here are independence, interchangeability, and martingales. Particular emphasis is placed upon stopping times, both as tools in proving theorems and as objects of interest themselves. No prior knowledge of measure theory is assumed and a unique feature of the book is the combined presentation of measure and probability. It is easily adapted for graduate students familiar with measure theory using the guidelines given. Special features include: A comprehensive treatment of the law of the iterated logarithm * The MarcinklewiczZygmund inequality, its extension to martingales and applications thereof * Development and applications of the second moment analogue of Walds equation * Limit theorems for martingale arrays; the central limit theorem for the interchangeable and martingale cases; moment convergence in the central limit theorem * Complete discussion, including central limit theorem, of the random casting of r balls into n cells * Recent martingale inequalities * Cram rL vy theorem and factorclosed families of distributions.
CONTENTS
Classes of Sets, Measures,and Probability Spaces. Binomial Random Variables. Independence. Integration in a Probabilty Space. Sums of Independent Random Variables. Measure Extensions, LebesgueStieltjes Measure, Kolmogorov Consistency Theorem. Conditional Expectation, Conditional Independence, Introduction to Martingales. Distribution Functions and Characteristic Functions. Central Limit Theorems. Limit Theorems for Independent Random Variables. Martingales. Infinitely Divisible Laws.




Probability and Numerical Methods,3rd ed.  J. P. Singh 

Cover Price : Rs 275.00

Imprint : Ane Books Pvt. Ltd. ISBN : 9789382127512 YOP : 2015

Binding : Paperback Total Pages : 408 CD : No


About the Book
The third edition of probability and Numerical Methods is the result of the enthusiastic reception given to the earlier edition received from students and teachers, who are the end users of this book.
The book covers the complete syllabus of BCA, Semester IV of GGSIP University. It introduces Probability and Numerical Methods at undergraduate level in a simplified manner.
Salient features
• Text is selfexplanatory and the language is vivid and lucid.
• Contains numerous examples that illustrate the basic as well as high level concepts of the concerned topic.
• Additional questions provided in all the chapters for practice.
• Most of the questions conform to the trend in which the questions appear in GGSIP University.
Contents
0.Elementary Concepts 1. Combinatorics: Permutation, Combination and Binomial Theorem 2. ProbabilityI 3. ProbabilityII 4. Random Variable and Mathematical Expectations 5. Discrete Probability Distributions 6. Normal Distribution 7. Finite Difference 8. Interpolation 9. Solution of Algebraic and Transcendental Equations 10. Solution of Linear Simultaneous Equations 11. Numerical Differentiation and Integration Tables,End Term Examination
About the Author
J.P. Singh is Professor in Department of Mathematics at Jagan Institute of Management Studies (Affiliated to GGSIP University), Delhi. He has been teaching experience of 14 years and has taught at various affiliated Institutes of GGSIP University. He has undergone rigorous training from IIT Delhi in Financial Mathematics. He is a Certified Six Sigma Green Belt from Indian Statistical Institute, Delhi.
His areas of interest include Mathematical Statistics, Stochastic Process, Numerical Methods, Number Theory, Discrete Mathematics and Theory of Computation.




GUIDE TO ABSTRACT ALGEBRA  CAROL WHITEHEAD 

Cover Price : £ 8.99

Imprint : Palgrave / Macmillan ISBN : 0230574182 YOP : 2007 Edition : 2007

Binding : Paperback Total Pages : 224 CD : No


DESCRIPTION:
Guide to Abstract Algebra is a comprehensive and accessible text covering the basic topics of an introductory abstract algebra course. New concepts are introduced gradually and illustrated by a variety of worked examples.
New features in this second edition are:
· Two new chapters on Number Systems and Polynomials
· Proofs by induction are introduced through a new section on sequences and recurrence relations
· Fully updated to reflect the needs of today's first year undergraduate students
This book is ideal for first year undergraduate courses in Mathematics or Computer Science.
CONTENTS:
Glossary of symbols
Preface to the second edition
1. Sets
2. Relations
3. Mappings
4. The Integers
5. Number Systems
6. Polynomials
Suggestions for Further Reading
Index.
ABOUT THE AUTHOR:
CAROL WHITEHEAD has considerable experience of teaching mathematics at higher education level and is the author of a number of research papers in discrete mathematics.




Pattern Recognition Algorithms for Data Mining  Sankar K. Pal, Pabitra Mitra 
Author 
Sankar K. Pal Pabitra Mitra


Cover Price : Rs 1,995.00

Imprint : CRC Press ISBN : 9781498797764 YOP : 2016

Binding : Hardback Total Pages : 272 CD : No


Reviews:
Pattern Recognition Algorithms in Data Mining is a book that commands admiration. Its authors, Professors S.K. Pal and P. Mitra are foremost authorities in pattern recognition, data mining, and related fields. Within its covers, the reader finds an exceptionally wellorganized exposition of every concept and every method that is of relevance to the theme of the book. There is much that is original and much that cannot be found in the literature. The authors and the publisher deserve our thanks and congratulations for producing a definitive work that contributes so much and in so many important ways to the advancement of both the theory and practice of recognition technology, data mining, and related fields. The magnum opus of Professors Pal and Mitra is mustreading for anyone who is interested in the conception, design, and utilization of intelligent systems.
 from the Foreword by Lotfi A. Zadeh, University of California, Berkeley, USA.
The book presents an unbeatable combination of theory and practice and provides a comprehensive view of methods and tools in modern KDD. The authors deserve the highest appreciation for this excellent monograph.
 from the Foreword by Zdzislaw Pawlak, Polish Academy of Sciences, Warsaw.
This volume provides a very useful, thorough exposition of the many facets of this application from several perspectives. I congratulate the authors of this volume and I am pleased to recommend it as a valuable addition to the books in this field.
 from the Forword by Laveen N. Kanal, University of Maryland, College Park, USA.
About the Book:
Pattern Recognition Algorithms for Data Mining addresses different pattern recognition (PR) tasks in a unified framework with both theoretical and experimental results. Tasks covered include data condensation, feature selection, case generation, clustering/classification, and rule generation and evaluation. This volume presents various theories, methodologies, and algorithms, using both classical approaches and hybrid paradigms. The authors emphasize large datasets with overlapping, intractable, or nonlinear boundary classes, and datasets that demonstrate granular computing in soft frameworks. Organized into eight chapters, the book begins with an introduction to PR, data mining, and knowledge discovery concepts. The authors analyze the tasks of multiscale data condensation and dimensionality reduction, then explore the problem of learning with support vector machine (SVM). They conclude by highlighting the significance of granular computing for different mining tasks in a soft paradigm.
Contents:
Foreword. Preface. List of Tables. List of Figures. Introduction. Multiscale data condensation. Unsupervised feature selection. Active learning using support vector machine. Roughfuzzy case generation. Roughfuzzy clustering. Rough selforganizing map. Classification, rule generation and evaluation using modular roughfuzzy MLP. Appendices. References. Index. About the Authors. 



Textbook of Graph Theory  R. Balakrishnan 
Author 
R. Balakrishnan K. Ranganathan


Cover Price : Rs 695.00

Imprint : Springer ISBN : 9781493975174 YOP : 2017

Binding : Paperback Total Pages : 240 CD : No


About the Book:
Graph theory has experienced a tremendous growth during the 20th century. One of the main reasons for this phenomenon is the applicability of graph theory in other disciplines such as physics, chemistry, psychology, sociology, and theoretical computer science.
This book aims to provide a solid background in the basic topics of graph theory. It covers Dirac's theorem on kconnected graphs, HararyNashwilliam's theorem on the hamiltonicity of line graphs, ToidaMcKee's characterization of Eulerian graphs, the Tutte matrix of a graph, Fournier's proof of Kuratowski's theorem on planar graphs, the proof of the nonhamiltonicity of the Tutte graph on 46 vertices and a concrete application of triangulated graphs. The book does not presuppose deep knowledge of any branch of mathematics, but requires only the basics of mathematics. It can be used in an advanced undergraduate course or a beginning graduate course in graph theory.
Contents:
Basic Results. Directed Graphs. Connectivity. Trees. Independent Sets and Matchings. Eulerian and Hamiltonian Graphs. Graph Colourings. Planarity. Triangulated Graphs. Applications.




Functional Analysis  Kosaku Yosida 

Cover Price : Rs 895.00

Imprint : Springer ISBN : 9783662559291 YOP : 2017

Binding : Paperback Total Pages : 504 CD : No


TABLE OF CONTENTS
Preliminaries. Seminorms. Applications of the BaireHausdorff Theorem. The Orthogonal Projection and F. Riesz' Representation Theorem. The HahnBanachTheorems.Strong Convergence and Weak Convergence. Fourier Transform and Differential Equations. Dual Operators. Resolvent and Spectrum. Analytical Theory of Semigroups. Compact Operators. Normed Rings and Spectral Representation. Other Representation Theorems in Linear Spaces. Ergodic Theory and Diffusion Theory. The Integration of the Equations of Evolution.
ABOUT THE AUTHOR
Kôsaku Yosida (7.2.190920.6.1990) was born in Hiroshima, Japan. After studying mathematics a the University of Tokyo he held posts at Osaka and Nagoya Universities before returning to the University of Tokyo in 1955. Yosida obtained important and fundamental results in functional analysis and probability. He is best remembered for his joint work with E. Hille which brought forth a theory of semigroups of operators successfully applied to diffusion equations, Markov processes, hyperbolic equations and potential theory. His famous textbook on functional analysis was published in 6 distinct editions between 1965 and 1980.




CLASSIC ALGEBRA , INDIAN REPRINT  P.M. COHN (EX) 

Cover Price : Rs 3,995.00

Imprint : Wiley India ISBN : 9788126540679 YOP : 2013

Binding : Hardback Total Pages : 442 CD : No


Fundamental to all areas of mathematics, algebra provides the cornerstone for the students development. The concepts are often intuitive, but some can take years of study to fully absorb. For over twenty years, the authors classic threevolume set, Algebra, has been regarded by many as the most outstanding introductory work available. This work, Classic Algebra, combines a fully updated Volume 1 with the essential topics from Volumes 2 and 3, and provides a selfcontained introduction to the subject.
In addition to the basic concepts, advanced materials is introduced, giving the reader an insight into more advanced algebraic topics. The clear presentation style gives this book the edge over others on the subject.
Undergraduates studying first courses in algebra will benefit from the clear exposition and perfect balance of theory, examples and exercises. The book provides a good basis for those studying more advanced algebra courses.
• Complete and rigorous coverage of the important basic concepts
• Topics covered include sets, mappings, groups, matrices, vector spaces, fields, rings and modules
• Written in a lucid style, with each concept carefully explained
• Introduces more advanced topics and suggestions for further reading
• Contains over 800 exercises, including many solutions
"There is no better textbook on algebra than the volumes by Cohn"  Walter Benz, Universität Hamburg, Germany
Contents
1. Sets and Mappings.
2. Integers and Rational Numbers.
3. Groups.
4. Vector Spaces and Linear Mappings.
5. Linear Equations.
6. Rings and Fields.
7. Determinants.
8. Quadratic Forms.
9. Further Group Theory.
10.Rings and Modules.
11.Normal Forms for Matrices.
Appendices.
Solutions to the Exercises.
Further Reading.
Some Frequently Used Notations.
Index. 



GUIDE TO MECHANICS  Phil Dyke 
Author 
Phil Dyke Roger Whitworth


Cover Price : £ 8.99

Imprint : Palgrave / Macmillan ISBN : 0230574168 YOP : 2007 Edition : 2007

Binding : Paperback Total Pages : 360 CD : No


DESCRIPTION:
A sound knowledge of Mechanics is fundamental to an understanding of much of physics and engineering. This book takes the reader through the fundamentals of the subject in as informal a manner as possible, without sacrificing mathematical rigour.
The second edition has new material on orbits, rigid body mechanics and non linear dynamics to produce a more comprehensive text that serves the needs of undergraduate students of mathematics, physics and engineering.
CONTENTS:
Preface to Second Edition
Kinematics
Forces
Forces as a Vector
Collisions
Motion Under Gravity
Circular Motion
Rotating Axes
Vibrations
Orbits
Introduction to Rigid Body Dynamics
Variable Mass Problems
Nonlinear Dynamics
Answers
Index.
ABOUT THE AUTHORS:
PHILIP P.G.DYKE is an experienced author with over 40 publications, including 8 textbooks ranging from mathematics and mechanics to marine science. He has over 30 years' lecturing experience in higher education, and has taught students across the ability range. Since 1985 he has been Professor of Applied Mathematics and Head of the School of Mathematics and Statistics at the University of Plymouth.
ROGER WHITWORTH is Head of Mathematics at Droitwich High School. 



An Introduction to Number Theory  Graham Everest 
Author 
Graham Everest Thomas Ward


Cover Price : Rs 595.00

Imprint : Springer ISBN : 8181288035 YOP : 2007

Binding : Paperback Total Pages : 302 CD : No


DESCRIPTION:
An Introduction to Number Theory provides an introduction to the main streams of number theory. Starting with the unique factorization property of the integers, the theme of factorization is revisited several times throughout the book to illustrate how the ideas handed down from Euclid continue to reverberate through the subject.
In particular, the book shows how the Fundamental Theorem of Arithmetic, handed down from antiquity, informs much of the teaching of modern number theory. The result is that number theory will be understood, not as a collection of tricks and isolated results, but as a coherent and interconnected theory.
A number of different approaches to number theory are presented, and the different streams in the book are brought together in a chapter that describes the class number formula for quadratic fields and the famous conjectures of Birch and SwinnertonDyer. The final chapter introduces some of the main ideas behind modern computational number theory and its applications in cryptography.
Written for graduate and advanced undergraduate students of mathematics, this text will also appeal to students in cognate subjects who wish to learn some of the big ideas in number theory.
CONTENTS:
A Brief History of Prime. Diophantine Equations. Quadratic Diophantine Equations. Recovering the Fundamental Theorem of Arithmetic. Elliptic Curves. Elliptic Functions. Heights. The Riemann Zeta Function. The Functional Equation of the Riemann Zeta Function. Primes in an Arithmetic Progression. Converging Streams. Computational Number Theory. References. Index.




Essential Mathematical Biology  Nicholas F Britton 
Author 
Nicholas F Britton


Cover Price : Rs 695.00

Imprint : Springer ISBN : 8181281810 YOP : 2004

Binding : Paperback Total Pages : 336 CD : No


DESCRIPTION
Essential Mathematical Biology is a selfcontained introduction to the fastgrowing field of mathematical biology. Written for students with a mathematical background, it sets the subject in its historical context and then guides the reader towards questions of current research interest, providing a comprehensive overview of the field and a solid foundation for interdisciplinary research in the biological sciences.
A broad range of topics is covered including: Population dynamics, Infectious diseases, Population genetics and evolution, Dispersal, Molecular and cellular biology, Pattern formation, and Cancer modelling.
This book will appeal to 3rd and 4th year undergraduate students studying mathematical biology. A background in calculus and differential equations is assumed, although the main results required are collected in the appendices. A dedicated website at www.springer.co.uk/britton/ accompanies the book and provides further exercises, more detailed solutions to exercises in the book, and links to other useful sites.
TABLE OF CONTENTS
Single Species Population Dynamics Population Dynamics of Interacting Species
Infectious Diseases
Population Genetics and Evolution Biological Motion. Molecular and Cellular Biology. Pattern Formation Tumour Modelling. Further Reading
Some Techniques for Difference Equations
Some Techniques for Ordinary Differential Equations
Some Techniques for Partial Differential Equations
Nonnegative Matrices
Hints for Exercises
Index.
WRITTEN FOR
3rd and 4th year undergraduate students of mathematics / mathematical biology, lecturers, postgraduate students, researchers, mathematically literate biologists
KEYWORDS
Cancer modelling
Mathematical biology
Mathematical modelling
Molecular and cellular biology
Pattern formation
Population dynamics
Population genetics and evolution 



Linear Algebra  Klaus Janich 

Cover Price : Rs 695.00

Imprint : Springer ISBN : 818128187X YOP : 2004

Binding : Paperback Total Pages : 206 CD : No


DESCRIPTION
This book covers the material of an introductory course in linear algebra: sets and maps, vector spaces, bases, linear maps, matrices, determinants, systems of linear equations, Euclidean spaces, eigenvalues and eigenvectors, diagonalization of selfadjoint operators, and classification of matrices. The book is written for beginners. Its didactic features (the "book within a book" and multiple choice tests with commented answers) make it especially suitable for selfstudy.
TABLE OF CONTENTS
1. Sets and Maps
2. Vector Spaces
3. Dimension
4. Linear Maps
5. Matrix Calculus
6. Determinants
7. Systems of Linear Equations
8. Euclidean Vector Spaces
9. Eigenvalues
10. The Principal Axes Tranformation
11. classification of Matrices
12. Answer to the tests
References
Index.




A Beginner's Guide to Finite Mathematics  W D Wallis 

Cover Price : Rs 595.00

Imprint : Springer ISBN : 8181282175 YOP : 2004

Binding : Paperback Total Pages : 356 CD : No


DESCRIPTION
This concise text takes a distinctly applied approach to finite mathematics at the freshman and sophomore level. Topics are presented sequentially: the book opens with a brief review of sets and numbers, followed by an introduction to data sets, histograms, means and medians. Counting techniques and the Binomial Theorem are covered, which provides the foundation for elementary probability theory; this, in turn, leads to basic statistics. Graph theory is defined, with particular emphasis on its use in mathematical modeling. Matrices and vectors are discussed, along with several elementary commercial applications. The book concludes with an introduction to linear programming, including the simplex method and duality. Ample examples and illustrations are provided throughout; each section contains two sets of problems, with solutions provided for the first set. Requiring little mathematical background beyond high school algebra, the text will be especially useful for business and liberal arts majors. Its straightforward treatment of the essential concepts in finite mathematics will appeal to a wide audience of students and teachers.
CONTENTS
Preface
Numbers and Sets
Counting
Probability
Relations and Functions
Graph Theory
Matrices
Linear Programming
Bibliography
Answers to Group A Exercises
Index.




Differential and Integral Equations  Peter J. Collins 

Cover Price : Rs 795.00

Imprint : Oxford University Press ISBN : 0195695828 YOP : 2008

Binding : Paperback Total Pages : 384 CD : No


About the Book :
Differential and integral equations involve important mathematical techniques, and as such will be encountered by mathematicians, and physical and social scientists, in their undergraduate courses. This text provides a clear, comprehensive guide to first and secondorder ordinary and partial differential equations, whilst introducing important and useful basic material on integral equations. Readers will encounter detailed discussion of the wave, heat and Laplace equations, of Green's functions and their application to the SturmLiouville equation, and how to use series solutions, transform methods and phaseplane analysis. The calculus of variations will take them further into the world of applied analysis.
Providing a wealth of techniques, but yet satisfying the needs of the pure mathematician, and with numerous carefully worked examples and exercises, the text is ideal for any undergraduate with basic calculus to gain a thorough grounding in 'analysis for applications'.
Contents :
Preface
How to use this book
Prerequisites
1. Integral equations and Picard's method
2. Existence and uniqueness
3. The homogeneous linear equation and Wronskians
4. The nonhomogeneous linear equation: Variations of parameters and Green's functions
5. Firstorder partial differential equations
6. Secondorder partial differential equations
7. The diffusion and wave equations and the equation of Laplace
8. The Fredholm alternative
9. HilbertSchmidt theory
10. Iterative methods and Neumann series
11. The calculus of variations
12. The SturmLiouville equation
13. Series solutions
14. Transform methods
15. Phaseplane analysis
Appendix: The solution of some elementary ordinary differential equations
Bibliography
Index.
About the Author :
Peter Collins has taught differential and integral equations for 40 years and has held posts in universities in the United Kingdom, United States, France and New Zealand. He is currently Senior Research Fellow of St Edmund Hall, Oxford, and Head of the Analytic Topology Research Group at Oxford University's Mathematical Institute. 



GUIDE TO MATHEMATICAL METHODS  JOHN GILBERT 
Author 
JOHN GILBERT CAMILLA JORDAN


Cover Price : £ 9.99

Imprint : Palgrave / Macmillan ISBN : 0230574144 YOP : 2007 Edition : 2007

Binding : Paperback Total Pages : 440 CD : No


DESCRIPTION
A second edition of this text for science and engineering undergraduates which introduces the mathematical techniques and tools needed to solve the mathematical problems they will face on the first year of their course. Updated and revised by Camilla Jordan, the book now has additional examples and 'Aims and Objectives' sections. As with other titles in the Mathematical Guides series, this book is designed to enable students to acquire confidence and provides a solid foundation for further study.
CONTENTS
Preface
Symbols, notation and Greek letters
Preliminaries
Functions
Differentiation
Further Functions
Applications of Differentiation
Integration
Further Integration
Linear Equations and Matrices
Vectors
Functions of Two Variables
Line Integrals
Double Integrals
Complex Numbers
Differential Equations.
ABOUT THE AUTHORS
JOHN GILBERT is Senior Lecturer in Mathematics at Lancaster University.
CAMILLA JORDAN is a Staff Tutor in the Mathematics and Computing Faculty of the Open University. 



Theory and Applications of Partial Functional Differential Equations  Jianhong Wu 

Cover Price : Rs 595.00

Imprint : Springer ISBN : 8181283198 YOP : 2005

Binding : Paperback Total Pages : 443 CD : No


DESCRIPTION
Abstract semilinear functional differential equations arise from many biological, chemical, and physical systems which are characterized by both spatial and temporal variables and exhibit various spatiotemporal patterns. The aim of this book is to provide an introduction of the qualitative theory and applications of these equations from the dynamical systems point of view. The required prerequisites for that book are at a level of a graduate student. The style of presentation will be appealing to people trained and interested in qualitative theory of ordinary and functional differential equations.
CONTENTS
Introduction. Preliminaries. Existence and compactness of solution semiflows. Generators and decomposition of state spaces for linear systems. Nonhomogenous systems and linearized stability. Invariant manifolds of nonlinear systems. Hopf Bifurcations.Small and large diffusivity. Invariance, comparison, lower and upper solutions. Convergence, monotononicity and contracting rectangles. Dispativeness, exponential growth and invariance principles. Travelling wave solutions. References. Index.




Basic Principles of the Finite Element Method  K M Entwistle 

Cover Price : Rs 695.00

Imprint : Woodhead ISBN : 190265353X YOP : 2005

Binding : Paperback Total Pages : 204 CD : No


DESCRIPTION
The objective of this book is to provide and introductory text that lays out the basic theory of the finite element method in a form that will be comprehensible to materials scientists. It presents the basic ideas in a sequential and measured fashion, avoiding the use of specialist vocabulary that is not clearly defined. The basic principles are illustrated by a diversity of examples that serve to reinforce the particular aspects of the theory.
CONTENTS
About matrices; The stiffness matrix; Onedimensional finite element analysis; Energy principles in finite element analysis; Finite elements that form part of a continuum; Finite element analysis using higher order elements; Worked examples applying the theory of section 7.2 to calculate the stresses in a loaded tapered sheet; A cautionary epilogue.




Structure Determination of Organic Compounds : Tables of Spectral Data  E. Pretsch 
Author 
E. Pretsch P. Buhlmann C. Affolter


Cover Price : Rs 895.00

Imprint : Springer ISBN : 818128383X YOP : 2006

Binding : Paperback Total Pages : 460 CD : Yes


DESCRIPTION
This volume presents in the form of texts, tables, charts and graphs a modern compilation of spectroscopic reference data for IR, UV/Vis, 1H and 13CNMR, MS (incl. prototype spectra of almost every important class of organic compounds and spectra of MALDI and FAB matrix materials) and is intended as a short textbook and a handson guide for interpreting experimental spectral data and elucidating the chemical structure of the respective compound behind it. The concise texts include special chapters on fragmentation rules in mass spectrometry and on currently used multipulse and 2D NMR techniques. The book is primarily designed for students to be used during courses and exercises. The use of the book requires only basic knowledge of spectroscopic techniques, but is structured in such a way that it will support practitioners routinely faced with the task of interpreting such spectral information, and it will serve as data reference for specialists in the fields.
CONTENTS
1 Introduction
2.Summary Tables
3.Combination Tables
4.13C NMR Spectroscopy
5.1H NMR Spectroscopy
6.IR Spectroscopy
7. Mass Spectroscopy
8.UV/Vis Spectroscopy
Subject Index.




Introductory Complex Analysis  Richard A. Silverman 
Author 
Richard A Silverman


Cover Price : $ 17.95

Imprint : Dover ISBN : 9780486946862 YOP : 2016

Binding : Paperback Total Pages : 400 CD : No


About the Book
Introductory Complex Analysis is a scaleddown version of A. I. Markushevich's masterly threevolume "Theory of Functions of a Complex Variable." Dr. Richard Silverman, the editor and translator of the original, has prepared this shorter version expressly to meet the needs of a oneyear graduate or undergraduate course in complex analysis. In his selection and adaptation of the more elementary topics from the original larger work, he was guided by a brief course prepared by Markushevich himself.
The book begins with fundamentals, with a definition of complex numbers, their geometric representation, their algebra, powers and roots of complex numbers, set theory as applied to complex analysis, and complex functions and sequences. The notions of proper and improper complex numbers and of infinity are fully and clearly explained, as is stereographic projection. Individual chapters then cover limits and continuity, differentiation of analytic functions, polynomials and rational functions, Mobius transformations with their circlepreserving property, exponentials and logarithms, complex integrals and the Cauchy theorem , complex series and uniform convergence, power series, Laurent series and singular points, the residue theorem and its implications, harmonic functions (a subject too often slighted in first courses in complex analysis), partial fraction expansions, conformal mapping, and analytic continuation.
Elementary functions are given a more detailed treatment than is usual for a book at this level. Also, there is an extended discussion of the SchwarzChristolfel transformation, which is particularly important for applications.
There is a great abundance of workedout examples, and over three hundred problems (some with hints and answers), making this an excellent textbook for classroom use as well as for independent study. A noteworthy feature is the fact that the parentage of this volume makes it possible for the student to pursue various advanced topics in more detail in the threevolume original, without the problem of having to adjust to a new terminology and notation .
In this way, IntroductoryComplex Analysis serves as an introduction not only to the whole field of complex analysis, but also to the magnum opus of an important contemporary Russian mathematician.
About the Author
Richard A. Silverman: Dover's Trusted Advisor
Richard Silverman was the primary reviewer of our mathematics books for well over 25 years starting in the 1970s. And, as one of the preeminent translators of scientific Russian, his work also appears in our catalog in the form of his translations of essential works by many of the greatest names in Russian mathematics and physics of the twentieth century. These titles include (but are by no means limited to): Special Functions and Their Applications (Lebedev); Methods of Quantum Field Theory in Statistical Physics (Abrikosov, et al); An Introduction to the Theory of Linear Spaces, Linear Algebra, and Elementary Real and Complex Analysis (all three by Shilov); and many more.
During the Silverman years, the Dover math program attained and deepened its reach and depth to a level that would not have been possible without his valuable contributions. 



Theory of Transforms with Applications  Vinod Mishra 

Cover Price : Rs 1,995.00

Imprint : Ane Books Pvt. Ltd. ISBN : 9789385462603 YOP : 2017

Binding : Hardback Size : 6.25" X 9.50" Total Pages : 368 CD : No


About the Book
Mathematical transforms play an important role in solving ordinary and partial differential equations, integral and integrodifferential equations, difference equations and problems arising in applied science and engineering. Bulk of these problems are solved using Fourier, Laplace, Mellin and Hankel transforms. Many of the problems unresolved by existing classical techniques due to the nature and complexities involved. In such a scenario, implementation of the approximation or numerical techniques as Discrete and Fast Fourier transform and numerical inversion of Laplace transform become a necessity. Z transform is best suited for analyzing electrical signals. Little known Legendre transform plays significant role in thermodynamics and classical mechanics.
This book peeps into continuous and discrete version of Fourier and Laplace transforms. Mellin, Hankel and Legendre transforms in continuous version have been placed next; while the Z transform occupies the last chapter. Each transform is related to one or more of these transforms. A wide range of applications and problems are covered in physical, engineering and medical world including Dirichlet boundary value problem, SturmLiouville problem, transfer function, classical, statistical and quantum mechanics, state space equations, electrical signals, heat, wave and steady state equations, Poisson equation, probability density function and thermodynamics. The case studies include problems from mechanics, population dynamics, seismology, elasticity and medicine.
The book presented with a view of philosophy of learning helps the readers to have access to advanced concepts through theory and varied applications in pedagogical way. Certain numerical inversion of Laplace transform and Legendre transform are distinctive. Historical development would not only provide the origin and growth of the concept but also excitement and insight of great scholars providing beautiful tools and perhaps could be inspirational factor to the readers. Lucid style of presentation and rigorous mathematical approach are the key features. Proofs of theorems and lemmas have been presented wherever necessary. Few case studies and examples of significance have been included to make the concept understandable.
The book is suitable for both UG/PG and B.Tech./M.Tech. students of Mathematics and Physics, practitioners, teachers and research scholars in the field of mathematics, physics and engineering.
Contents
Chapter 1: Fourier Series
Chapter 2: Continuous Fourier Transform
Chapter 3: Discrete and Fast Fourier Transform
Chapter 4: Laplace Transform
Chapter 5: Numerical Inverse Laplace Transform
Chapter 6: Mellin Transform
Chapter 7: Hankel Transform
Chapter 8: Legendre Transform
Chapter 9: Z Transform
About the Author
Currently, a Professor (former Head) at the Department of Mathematics, at Sant Longowal Institute of Engineering and Technology (Deemed University established by MHRD, Govt. of India), Longowal, Punjab, he has been active member of Senate and Board of Studies at the same institute and is associated with various mathematical societies in India and abroad. He is also the ‘Fellow’ of prestigious Indian Institute of Advanced Study based at Shimla where he submitted a research monograph also.
He enjoys nearly twenty three years of regular teaching experience of undergraduate and postgraduate courses in higher education in science, technology and research at the grassroot and advanced levels of mathematical science and has brought innumerable publications in the field of history & education of mathematics, wavelet analysis of numerical problems and numerical inverse Laplace transforms. He has chaired eight technical sessions and delivered twelve invited lectures during national and international conferences in India and overseas.




Introduction to Mathematics for Life Scientists 3/ed  E. Batschelet, Reprint 2015, Best Seller 

Cover Price : Rs 995.00

Imprint : Springer ISBN : 9788181280848 YOP : 2015

Binding : Paperback Total Pages : 662 CD : No


DESCRIPTION
The book is suitable both for use as a classroom textbook and for self teaching. This third edition includes more problems and solutions as well as many worked examples. The chapters on calculus and linear algebra have been particularly expanded and the work has been amended throughout following suggestions from leading biomathematicians.
Practical applications include: electrocardiogram, biological rhythm, flow of blood in blood vessels, psychophysical scaling and various problems from genetics and systems analysis.
From a review: "For research workers in the biomedical field who feel a need for freshening up their knowledge in mathematics, but so far have always been frustrated by either too boring textbooks, there is now exactly what they would like to have: an easy to read introduction. This book is highly motivating for practical workers because only those mathematical techniques are offered for which there is an application in the life sciences. The reader will find it stimulating that each tool described is immediately exemplified by problems from latest publications.
CONTENTS
Chapter 1. Real Numbers
Chapter 2. Sets and Symbolic Logic
Chapter 3. Relations and Functions
Chapter 4. The Power Function and related functions
Chapter 5. Periodic Functions
Chapter 6. Exponential and Logarithmic
Functions I
Chapter 7. Graphical Methods
Chapter 8. Limits
Chapter 9. Differential and Integral Calculus
Chapter 10. Exponential and Logarithmic Functions II
Chapter 11. Ordinary Differential Equations
Chapter 12. Functions of Two or more Independent Variables
Chapter 13. Probability
Chapter 14. Matrices and Vectors
Chapter 15. Complex Numbers
Appendix (Tables A to K)
Solutions to odd Numbered Problems
References
Author and Subject Index.




Optimization : Linear Programming 2015  B. N. Mishra 
Author 
B. N. Mishra B. K. Mishra


Cover Price : Rs 395.00

Imprint : Ane Books Pvt. Ltd. ISBN : 9788180521256 YOP : 2017

Binding : Paperback Total Pages : 318 CD : No


About the Book Optimization is a comprehensive textbook which has grown out of the collective experience of the authors in teaching the course over the years. The introductory text provides undergraduate and graduate students with a concise and practical introduction to the primary concepts and techniques of optimization. With a strong emphasis on basic concepts and techniques throughout, the book explains the theory behind each technique as simply as possible, along with illustrations and worked examples.
Salient Features
• A rigorous discussion on linear programming and its duality including model formulation. Additional solved examples and multi choice objective questions included at the last. • Theory of convex sets discussed. • Formulation of Transportation problem and methods of solution discussed, including optimality test. • Assignment problem formulated and discussed. • Emphasis on Degeneracy and game theory.
Pedagogical Features
• Simple, lucid and easily retainable language. • Illustrative examples • Unsolved problems. • More real life applications • Detailed index.
CONTENTS
Preface, 1. Linear Programming, 2. Simplex Method, 3. Convex Sets, 4. Transportation, 5. Assignment Problems, 6. Theory of games, 7. Duality Theory, 8. Degeneracy.
About the Author
Dr. B.N.Mishra has retired as a University Professor and Head Department of Mathematics, Vinoba Bhave University, Hazaribag, Jharkhand. His research areas are in the field of Fluid Mechanics, BioMathematics, and Vedic Mathematics. He has published several research papers in the journals of national as well as international repute. He has produced 20 Ph.D.'s and one D.Sc. He has a vast experience in teaching undergraduate and postgraduate students. He has taught the course Operations Research for more than 25 years. He has also published several books.
Dr. Bimal Kumar Mishra is an Assistant Professor in the Mathematics Group, Birla Institute of Technology and Science, Pilani, Rajasthan. He got his M.Sc. Degree in Operational Research from University of Delhi and also M.Sc. Degree in Mathematics .He has published more then thirty five research papers in journals of national and international repute. His research areas are in the field of Mathematical Modeling on Blood Flow, Environmental Pollution, Population Dynamics and Computer Viruses.




Topology, Reprint 2011  Klaus Janich 

Cover Price : Rs 495.00

Imprint : Springer ISBN : 8181284984 YOP : 2011

Binding : Paperback Total Pages : 200 CD : No


DESCRIPTION
This is an intellectually stimulating, informal presentation of those parts of point set topoloty that are of importance to the nonspecialist . In his presentation and through many illustrations, the author strongly appeals to the intuition of the reader, presenting many examples and situations where the understanding of elementary topological questions will lead to much deeper and more advanced problems in topology and geometry.
CONTENTS
Introduction
Chapter 1
Fundamental Concepts
Chapter 2
Topological Vector Spaces
Chapter 3
The Quotient Topology
Chapter 4
Completion of Metric Spaces
Chapter 5
Homotopy
Chapter 6
The Two Countability Axioms
Chapter 7
CW – Complexes
Chapter 8
Construction pf Continuous Functions on Topological Spaces
Chapter 9
Covering Prices
Chapter 10
The Theorem of Tychonoff
Last Chapter
Set Theory
References
Table of Symbols
Index




Mathematical Modeling : Application, Issues and Analysis  Bimal K. Mishra 
Author 
Bimal K. Mishra Dipak K. Satpathi


Cover Price : Rs 795.00

Imprint : Ane Books Pvt. Ltd. ISBN : 8180521273 YOP : 2009

Binding : Paperback Total Pages : 464 CD : No


Reprinted in 2008 
About the Book :
Mathematical Modeling is a discipline, which helps in solving real life problems by shaping them into mathematical models. Process of Mathematical Modeling can be divided into three steps.
1. Defining the problem
2. Simplifying the problem by introducing certain assumptions and converting the problem into the
mathematical equations.
3. Solving the mathematical equations and interpretation of the results.
National Conference on Mathematical Modeling and Analysis provides discussions and insights of leading scientists, engineers and technocrats from all over the country. It includes papers in the areas of
• Drug Design
• Biological systems
• Environmental Pollution
• Fluid Mechanics
• Applied Analysis
With this coverage, the book would serve as a useful reference for scientists, engineers, technocrats and researchers.
Contents :
Preface
List of Contributors
Section I: Drug Design
Section II: Biological Systems
Section III: Industrial Mathematics
Section IV: Environmental Pollution
Section V: Fluid Mechanics
Section VI: Applied Analysis
About the Editors
Dr. Bimal Kumar Mishra is an Assistant Professor in the Mathematics Group, Birla Institute of Technology and Science, Pilani. He has published more then thirty research papers in journals of national and international repute. His research areas are in the field of Mathematical Modeling on Blood Flow, Environmental Pollution, Population Dynamics and Computer Viruses.
Dr. Dipak Kumar Satpathi is an Assistant Professor in Mathematics Group, Birla Institute of Technology and Science, Pilani. He earned his Ph.D. degree from IIT Kanpur and his area of research is in the field of
Biomechanics.




Calculus of One Variable  M.Thamban Nair, 2016 

Cover Price : Rs 395.00

Imprint : Ane Books Pvt. Ltd. ISBN : 9789383656950 YOP : 2015

Binding : Paperback Total Pages : 320 CD : No


About the Book:
The book is meant for a onesemester introductory course on Calculus of One Variable at the Bachelors levels of Science and Engineering programs. It provides clear understanding of the basic concepts of differential and integral calculus, and also introduces slightly advanced topics such as power series and Fourier series. The introduction of sequences and series as the first chapter of the book helps a great deal in the discussion of various other concepts in the later chapters.
Key features:
· Precise definitions of basic concepts are given.
· Several motivating examples are provided for understanding the concepts and also for illustrating the results.
· Proofs of theorems are given with sufficient motivation – not just for the sake of proving them alone.
· Remarks in the text supply additional information on the topics under discussion.
· Exercises are interspersed within the text for making the students attempt them while the lectures are in progress.
· Large number of problems at the end of each chapter are meant as homeassignments.
The student friendly approach of the exposition of the book would definitely be of great use not only for students, but also for the teachers of the course.
About the Author:
Dr. M. Thamban Nair, Professor of Mathematics at IIT Madras, is a Research Mathematician as well as a teacher for more than 25 years at the Post Graduate and Under Graduate level courses in mathematics. He taught Calculus courses to B.Tech students of IIT Madras many times since 1995. He has won the prestigious C.L. Chandana Award for Distinguished and Outstanding Contributions to Mathematics Research and Teaching in India for the year 2003. He was also a Post Doctor Fellow at University of Grenoble (France), Visiting Fellow/Professor at Australian National University (Australia), University of Kasiserslautern (Germany) and Sun Yatsen University, Guangzhou (China). He published more than 65 research papers in national international journals, and also author of two books, one on Functional Analysis for M.Sc level and another on Linear Operator Equations for PostMSc level. He gave several invited talks at various conferences in India and abroad, and also a mentor of INSPIRE program of DST. 



ALGEBRA I (A BASIC COURSE)  ASHA GAURI SHANKAR 
Author 
ASHA GAURI SHANKAR


Cover Price : Rs 395.00

Imprint : Ane Books Pvt. Ltd. ISBN : 9789382127888 YOP : 2015

Binding : Paperback Total Pages : 448 CD : No


About the Book
This book is designed as a textbook for the Undergraduate students. It meets the curriculum requirements of the Course I.2 Algebra I (DCI) of the University of Delhi. This book is useful for students of any other University also who would like to study the topics covered in this book. It focuses on the introductory aspects of the course, supporting the theory with numerous Examples and Solved Problems. The text starts with equivalence relations, and goes on to functions. It explains the Principle of Mathematical Induction and also proves the Fundamental Theorem of Arithmetic. Complex numbers in polar form have also been introduced and the nth roots of unity have been explained in detail. Linear equations, linear transformations, matrices, eigenvalues and eigenvectors and vector spaces have also been covered.
A unique feature is the glossary of the terms used in the text and summary of the chapters.
The salient features of the book are:
Learning objectives given at the beginning of each chapter.
Concepts illustrated with examples.
Stepwise Proofs of Theorems and Solution of problems.
Emphasis on techniques of problem solving through numerous solved problems.
Graded Exercises.
Concepts reinforced by true/false questions.
Chapterwise summary for ready reference.
Glossary of the terms used in the text.
Index for ready reference.
Answers to all the exercises and hints to difficult questions.
About the Author
Dr. Asha Gauri Shankar, earned her Ph.D. in Numerical Analysis from Imperial College of Science, Technology and Medicine, University of London as a Commonwealth Scholar. She also earned her Ph.D. in Topology from Chaudhary Charan Singh University.
For over 4 decades, she has taught undergraduate and postgraduate students at the University of Delhi; Imperial College of Science, Technology and Medicine, London and the Institute of Advanced Studies, Meerut. She has to her credit research papers in national and international journals, several popular articles, a research level book “Numerical Integration of Differential Equations”, and three books for university students “Algebra I”, Pearson Education(2012); “Complex Numbers and Theory of Equations”, Anthem Press(2012), and “Group Theory ”, Pearson Education(2013). Her research interest is in Mathematics Education and Numerical Analysis.
In September 2009, she was awarded “Teacher of Excellence” by the University of Delhi. She has also been awarded “Bharat Excellence Award ” and “Mahila Sree Award” by FFI and the Shiksha Rattan Puraskar by IIFS.
Dr. Asha Gauri Shankar is currently an Associate Professor in the Department of Mathematics in Lakshmibai College, University of Delhi.




GUIDE TO ANALYSIS  MARY HART 

Cover Price : £ 8.99

Imprint : Palgrave / Macmillan ISBN : 0230574113 YOP : 2007 Edition : 2007

Binding : Paperback Total Pages : 304 CD : No


DESCRIPTION
This new edition aims to guide undergraduate students through the first year of their mathematics course. It provides a rigorous introduction to Analysis, which takes into account the difficulties students often face when making the transition from Alevel mathematics to this higher level. Plenty of examples are provided, some of which have full, detailed solutions, and others which encourage the student to discover and investigate the ideas themselves. Hints are provided, but the book aims to build confidence and understanding in all topics.
This second edition has two new substantial chapters, covering integration and powere series, and is updated throughout, taking into account changes in notation.
CONTENTS
Preface
Introduction
Numbers and Number Systems
Sequences
Infinite Series
Functions
Differentiable Functions
Integration
Power series
Index
ABOUT THE AUTHOR
MARY HART is a lecturer in Pure Mathematics at Sheffield University. 



GUIDE TO SCIENTIFIC COMPUTING  PETER R. TURNER 

Cover Price : £ 8.99

Imprint : Palgrave / Macmillan ISBN : 0230574175 YOP : 2007 Edition : 2007

Binding : Paperback Total Pages : 312 CD : No


DESCRIPTION
This book is a gentle and sympathetic introduction to many of the problems of scientific computing, and the wide variety of methods used for their solutions. It is ideal for students taking a first course in numerical mathematics who need a low level entry to the subject. It gives an appreciation of the need for numerical methods for the solution of different types of problem, and discusses basic approaches. For each of the problems, at least some mathematical justification and examples provide both practical evidence and motivations for the reader to follow. Practical justification of the methods is presented through computer examples and exercises. The book also includes an introduction to MATLAB, but the code used is not intended to exemplify sophisticated or robust pieces of software; it is purely illustrative of the methods under discussion.
☻ Includes appendix covering MATLAB basics
☻ Classtested at the US Naval Academy and University of Lancaster
☻ No prior mathematical knowledge assumed beyond calculus
CONTENTS
Number Representations and Errors
Iterative Solution of Equations
Approximate Evaluation of Functions
Interpolation
Numerical Calculus
Differential Equations
Linear Equations
MATLAB Basics
Answers to Exercises .
ABOUT THE AUTHORS
PETER TURNER is a Professor in the Department of Mathematics at the US Naval Academy in Annapolis.
He was awarded his PhD from the University of Sheffield and has extensive undergraduate teaching experience at the Universities of Sheffield, Lancaster and Maryland as well as at the US Naval Academy, where he has been responsible for introductory courses in scientific computing for more than a decade. 



Advanced Graph Theory  S.K. Yadav 

Cover Price : Rs 350.00

Imprint : Ane Books Pvt. Ltd. ISBN : 9789385462634 YOP : 2017

Binding : Paperback Size : 6.25" X 9.50" Total Pages : 302 CD : No


About the Book
This book is designed to meet the syllabus requirements of the students of B.Sc. (H) (Math/Computer Sc./Physcial Sc), B.C.A/M.C.A., B.Tech.(Computer Sc., E.C.E., I.T.,), M.Tech(C.S.E./ I.T.), M.Sc.(Mathematics/C.S./Electronics) and other professional courses of various universities/institutions at home and abroad. The students of open and distance education courses will find the book most useful.
Contents
1. Basics of Graph Theory
2. Trees
3. Planar Graphs
4. Directed Graphs
5. Matching and Covering
6. Colouring of Graphs
7. Colouring of Graphs
8. Enumeration and Pölya’s Theorem
9. Spectral Properties of Graphs
10. Spectral Properties of Graphs
About the Author
Dr. Santosh Kumar Yadav has been associated with academic and research activities for more than 25 years. He has been an active and dynamic administrator as Director (Academic and Research) at J.J.T. University, Rajasthan. As an academician he has taught under graduates and post graduate classes in different premire institutions including various colleges of Delhi University in different capacities.
As a researcher, Dr. Yadav has guided more than 70 research scholars of different universities at home and abroad. As an author he has written 38 books and more than a century of selflearning materials of different universities. Dr.Yadav is editor of six well reputed international journals of research and life member of 26 reputed professional apex bodies of academics and research.




CONCRETE INTRODUCTION TO HIGHER ALGEBRA 2ND ED  Lindsay N. Childs (EX) 

Cover Price : Rs 595.00

Imprint : Springer ISBN : 9788181284136 YOP :

Binding : Paperback Total Pages : 544 CD : No


About the Book :
This book is an informal and readable introduction to higher algebra at the postcalculus level. The concepts of ring and field are introduced through study of the familiar examples of the integers and polynomials. A strong emphasis on congruence classes leads in a natural way to finite groups and finite fields. The new examples and theory are built in a wellmotivated fashion and made relevant by many applications  to cryptography, error correction, integration, and especially to elementary and computational number theory. The later chapters include expositions of Rabin's probabilistic primality test, quadratic reciprocity, the classification of finite fields, and factoring polynomials over the integers. Over 1000 exercises, ranging from routine examples to extensions of theory, are found throughout the book; hints and answers for many of them are included in an appendix.
Contents :
Numbers. Induction. Euclid's Algorithm. Unique Factorization. Congruence. Congruence Classes. Rings and Fields. Matrices and Codes. Fermat's and Euler's Theorems. Applications of Fermat's and Euler's Theorems. Groups. The Chinese Remainder Theorem. Polynomials. Unique Factorization. The Fundamental Theorem of Algebra. Polynomials in Q[x]. Congruences and the CRT. Fast Polynomial Multiplication. Cyclic Groups and Cryptography. Carmichael Numbers.. Quadratic Reciprocity. Quadratic Applications. Congruence Classes Modulo a Polynomial. Homomorphism and Finite Fields. BCH Codes. Factoring in Z[x]. Irreducible Polynomials. Answers and Hints to the Exercises. References. Index. 



A Friendly Guide to Wavelets  Gerald Kaiser 

Cover Price : Rs 995.00

Imprint : Springer ISBN : 8181283818 YOP : 2008

Binding : Paperback Total Pages : 320 CD : No


Reviews :
"I wholeheartedly recommend this book for a solid and friendly introduction to wavelets, for anyone who is comfortable with the mathematics required of undergraduate electrical engineers. The book's appeal is that it covers all the fundamental concepts of wavelets in an elegant, straightforward way. It offers truly enjoyable (friendly!) mathematical exposition that is rich in intuitive explanations, as well as clean, direct, and clear in its theoretical developments. I found Kaiser's straightforward endofchapter exercises excellent... Kaiser has written an excellent introduction to the fundamental concepts of wavelets. For a book of its length and purpose, I think it should be essentially unbeatable for a long time."
— Proceedings of the IEEE
"It is well produced and certainly readable...This material should present no difficulty for fourthyear undergraduates...It also will be useful to advanced workers in that it presents a different approach to wavelet theory from the usual one."
— Computing Reviews
"I found this to be an excellent book. It is eminently more readable than the books...which might be considered the principal alternatives for textbooks on wavelets."
— Physics Today
"This volume is probably the most gentle introduction to wavelet theory on the market. As such, it responds to a significant need. The intended audience will profit from the motivation and commonsense explanations in the text. Ultimately, it may lead many readers, who may not otherwise have been able to do so, to go further into wavelet theory, Fourier analysis, and signal processing."
— SIAM Review
"The first half of the book is appropriately named. It is a wellwritten, nicely organized exposition...a welcome addition to the literature. The second part of the book introduces the concept of electromagnetic wavelets...This theory promises to have many other applications and could well lead to new ways of studying these topics. This book has a number of unique features which...makes it particularly valuable for newcomers to the field."
— Mathematical Reviews
About the Book :
This volume is designed as a textbook for an introductory course on wavelet analysis and timefrequency analysis aimed at graduate students or advanced undergraduates in science and engineering. It can also be used as a selfstudy or reference book by practicing researchers in signal analysis and related areas. Since the expected audience is not presumed to have a high level of mathematical background, much of the needed analytical machinery is developed from the beginning. The only prerequisites for the first eight chapters are matrix theory, Fourier series, and Fourier integral transforms. Each of these chapters ends with a set of straightforward exercises designed to drive home the concepts just covered, and the many graphics should further facilitate absorption.




Applied Probability  Kenneth Lange 

Cover Price : Rs 595.00

Imprint : Springer ISBN : 8181289544 YOP : 2008

Binding : Paperback Total Pages : 318 CD : No


About the Book :
This textbook on applied probability is intended for graduate students in applied mathematics, biostatistics, computational biology, computer science, physics, and statistics. It presupposes knowledge of multivariate calculus, linear algebra, ordinary differential equations, and elementary probability theory. Given these prerequisites, Applied Probability presents a unique blend of theory and applications, with special emphasis on mathematical modeling, computational techniques, and examples from the biological sciences.
Contents :
Chapter 1 reviews elementary probability and provides a brief survey of relevant results from measure theory. Chapter 2 is an extended essay on calculating expectations. Chapter 3 deals with probabilistic applications of convexity, inequalities, and optimization theory. Chapters 4 and 5 touch on combinatorics and combinatorial optimization. Chapters 6 through 11 present core material on stochastic processes. If supplemented with appropriate sections from Chapters 1 and 2, there is sufficient material here for a traditional semesterlong course in stochastic processes covering the basics of Poisson processes, Markov chains, branching processes, martingales, and diffusion processes. Finally, Chapters 12 and 13 develop the ChenStein method of Poisson approximation and connections between probability and number theory.
About the Author :
Kenneth Lange is Professor of Biomathematics and Human Genetics and Chair of the Department of Human Genetics at the UCLA School of Medicine. He has held appointments at the University of New Hampshire, MIT, Harvard, and the University of Michigan. While at the University of Michigan, he was the Pharmacia & Upjohn Foundation Professor of Biostatistics. His research interests include human genetics, population modeling, biomedical imaging, computational statistics, and applied stochastic processes. SpringerVerlag published his books Numerical Analysis for Statisticians and Mathematical and Statistical Methods for Genetic Analysis Second Edition, in 1999 and 2002, respectively.




Basic Stochastic Processes  Tomasz Zastawniak 
Author 
Tomasz Zastawniak Zdzislaw Brzezniak


Cover Price : Rs 595.00

Imprint : Springer ISBN : 8181283279 YOP : 2005

Binding : Paperback Total Pages : 240 CD : No


About the Book :
This book is a final year undergraduate text on stochastic processes, a tool used widely by statisticians and researchers working in the mathematics of finance. The book will give a detailed treatment of conditional expectation and probability, a topic which in principle belongs to probability theory, but is essential as a tool for stochastic processes. Although the book is a final year text, the author has chosen to use exercises as the main means of explanation for the various topics, and the book will have a strong selfstudy element. The author has concentrated on the major topics within stochastic analysis: martingales in discrete time and their convergence, Markov chains, stochastic process in continuous time, with emphasis on the Poisson process and Brownian motion, as well as Itô stochastic calculus including stochastic differential equations.
The Springer Undergraduate Mathematics Series (SUMS) is a new series of guides, written for undergraduates in the Mathematical Sciences. The books cover the basics of each topic via explanatory text, examples and problems. Students can read and check their understanding of the text against fully worked solutions at the back of each chapter.
Contents :
Preface
1. Review of Probability
2. Conditional Expectation
3. Martingales in Discrete Time
4. Martingale Inequalities and Convergence
5. Markov Chains
6. Stochastic Processes in Continuous Time
7. Itô stochastic Calculus
Index.




Partial Differential Equations : Basic Theory  Michael E. Taylor 

Cover Price : Rs 695.00

Imprint : Springer ISBN : 8181284143 YOP : 2006

Binding : Paperback Total Pages : 584 CD : No


About the Book :
This text provides an introduction to the theory of partial differential equations. It introduces basic examples of partial differential equations, arising in continuum mechanics, electromagnetism, complex analysis and other areas, and develops a number of tools for their solution, including particularly Fourier analysis, distribution theory, and Sobolev spaces. These tools are applied to the treatment of basic problems in linear PDE, including the Laplace equation, heat equation, and wave equation, as well as more general elliptic, parabolic, and hyperbolic equations. Companion texts, which take the theory of partial differential equations further, are AMS volume 116, treating more advanced topics in linear PDE, and AMS volume 117, treating problems in nonlinear PDE. This book is addressed to graduate students in mathematics and to professional mathematicians, with an interest in partial differential equations, mathematical physics, differential geometry, harmonic analysis, and complex analysis.
Contents :
Series Preface
Introduction
1. Basic Theory of ODE and Vector Fields
2. The Laplace Equation and Wave Equation
3. Fourier Analysis, Distributions, and ConstantCoefficient Linear PDE
4. Sobolev Spaces
5. Linear Elliptic Equations
6. Linear Evolution Equations
A. Outline of Functional Analysis
B. Manifolds, Vector Bundles, and Lie Groups
Index.




Complex Analysis  John M. Howie, 2015 

Cover Price : Rs 695.00

Imprint : Springer ISBN : 9788181282965 YOP : 2015

Binding : Paperback Total Pages : 272 CD : No


About the Book :
Complex analysis is one of the most attractive of all the core topics in an undergraduate mathematics course. Its importance to applications means that it can be studied both from a very pure perspective and a very applied perspective. This book takes account of these varying needs and backgrounds and provides a selfstudy text for students in mathematics, science and engineering. Beginning with a summary of what the student needs to know at the outset, it covers all the topics likely to feature in a first course in the subject, including: complex numbers, differentiation, integration, Cauchy's theorem, and its consequences, Laurent series and the residue theorem, applications of contour integration, conformal mappings, and harmonic functions. A brief final chapter explains the Riemann hypothesis, the most celebrated of all the unsolved problems in mathematics, and ends with a short descriptive account of iteration, Julia sets and the Mandelbrot set. Clear and careful explanations are backed up with worked examples and more than 100 exercises, for which full solutions are provided.
Contents :
Preface
1. What Do I Need to Know?
2. Complex Numbers
3. Prelude to Complex Analysis
4. Differentiation
5. Complex Integration
6. Cauchy’s Theorem
7. Some Consequences of Cauchy’s Theorem
8. Laurent Series and the Residue Theorem
9. Applications of Contour Integration
10.Further Topics
11.Conformal Mappings
12.Final Remarks
13.Solutions to Exercises
Bibliography
Index.




Real Analysis  J. P. Singh 

Cover Price : Rs 180.00

Imprint : Ane Books Pvt. Ltd. ISBN : 8180522709 YOP : 2009

Binding : Paperback Total Pages : 368 CD : No


About the Book :
This book 'Real Analysis' is primarily designed for the undergraduate students of GGS Indraprastha University and reflects my understanding of the requirements of students. In addition, this book would be extremely useful for all the students studying Real Analysis at the undergraduate level at other Indian Universities.
Some of the salient features of this book are :
• It covers the entire syllabus of BCA III sem of GGSIPU and many other Indian Universities.
• The text material is selfexplanatory and the language is vivid and lucid.
• For each topic several solved examples, carefully selected to cover all aspects of the topic are covered.
• Most of the questions conform to trend questions appearing in GGSIPU.
Contents :
1. Complex Number, 2. Sequence, 3. Infinite Series, 4. Vector Calculus, 5. Fourier Series, 6. Ordinary Differential Equations, 7. Linear Differential Equation of Higher Order and Special Methods.
About the Author :
J. P. Singh is Professor in Department of Mathematics at Jagan Institute of Management Studies, Rohini, Delhi. He has more than 10 years of rich experience of teaching Real Analysis, Mathematical Statistics, Calculus, Numerical Methods and Discrete Mathematics to the students of MCA and BCA. He has taught at various affiliated Institutes of GGSIPU.
His areas of interest include Mathematical Statistics, Number Theory, Theory of Computation, Numerical Methods, Discrete Mathematics and Real Analysis.




Fields and Galois Theory  John M. Howie 

Cover Price : Rs 595.00

Imprint : Springer ISBN : 8181289834 YOP : 2008

Binding : Paperback Total Pages : 240 CD : No


About the Book :
The pioneering work of Abel and Galois in the early nineteenth century demonstrated that the longstanding quest for a solution of quintic equations by radicals was fruitless: no formula can be found. The techniques they used were, in the end, more important than the resolution of a somewhat esoteric problem, for they were the genesis of modern abstract algebra.
This book provides a gentle introduction to Galois theory suitable for third and fourthyear undergraduates and beginning graduates. The approach is unashamedly unhistorical: it uses the language and techniques of abstract algebra to express complex arguments in contemporary terms. Thus the insolubility of the quintic by radicals is linked to the fact that the alternating group of degree 5 is simple  which is assuredly not the way Galois would have expressed the connection.
Topics covered include :
• rings and fields
• integral domains and polynomials
• field extensions and splitting fields
• applications to geometry
• finite fields
• the Galois group
• equations
Group theory features in many of the arguments, and is fully explained in the text. Clear and careful explanations are backed up with worked examples and more than 100 exercises, for which full solutions are provided.
Contents :
Preface
1. Rings and Fields
2. Integral Domains; Polynomials
3. Field Extensions
4. Applications to Geometry
5. Splitting Fields
6. Finite Fields
7. The Galois Group
8. Equations and Groups
9. Some Group Theory
10. Groups and Equations
11. Regular Polygons
12. Solutions
Bibliography
List of Symbols
Index.




Probability Essentials  Jean Jacod 
Author 
Jean Jacod Philip Protter


Cover Price : Rs 595.00

Imprint : Springer ISBN : 8181289827 YOP : 2008

Binding : Paperback Total Pages : 264 CD : No


About the Book :
This introduction to Probability Theory can be used, at the beginning graduate level, for a onesemester course on Probability Theory or for selfdirection without benefit of a formal course; the measure theory needed is developed in the text. It will also be useful for students and teachers in related areas such as Finance Theory (Economics), Electrical Engineering, and Operations Research. The text covers the essentials in a directed and lean way with 28 short chapters. Assuming of readers only an undergraduate background in mathematics, it brings them from a starting knowledge of the subject to a knowledge of the basics of Martingale Theory. After learning Probability Theory from this text, the interested student will be ready to continue with the study of more advanced topics, such as Brownian Motion and Ito Calculus, or Statistical Inference. The second edition contains some additions to the text and to the references and some parts are completely rewritten.
Contents :
1. Introduction
2. Axioms of Probability
3. Conditional Probability and Independence
4. Probabilities on a Finite or Countable Space
5. Random Variables on a Countable Space
6. Construction of a Probability Measure
7. Construction of a Probability Measure on R
8. Random Variables
9. Integration with Respect to a Probability Measure
10. Independent Random Variables
11. Probability Distributions on R
12. Probability Distributions on R
13. Characteristic Functions
14. Properties of Characteristic Functions
15. Sums of Independent Random Variables
16. Gaussian Random Variables (The Normal and the Multivariate Normal Distributions)
17. Convergence of Random Variables
18. Weak Convergence
19. Weak Convergence and Characteristic Functions
20. The Laws of Large Numbers
21. The Central Limit Theorem
22. L2 and Hilbert Spaces
23. Conditional Expectation
24. Martingales
25. Supermartingales and Submartingales
26. Martingale Inequalities
27. Martingale Convergence Theorems
28. The RadonNikodym Theorem
References
Index.




Survival Analysis : A Self  Learning Text  David G. Kleinbaum 
Author 
David G. Kleinbaum Mitchel Klein


Cover Price : Rs 895.00

Imprint : Springer ISBN : 8184890082 YOP : 2008 Edition : 2008

Binding : Paperback Total Pages : 608 CD : No


About the Book :
This greatly expanded second edition of Survival Analysis A Selflearning Text provides a highly readable description of stateoftheart methods of analysis of survival/eventhistory data. This text is suitable for researchers and statisticians working in the medical and other life sciences as well as statisticians in academia who teach introductory and secondlevel courses on survival analysis. The second edition continues to use the unique "lecturebook" format of the first (1996) edition with the addition of three new chapters on advanced topics:
Chapter 7: Parametric Models
Chapter 8: Recurrent events
Chapter 9: Competing Risks.
Also, the Computer Appendix has been revised to provide stepbystep instructions for using the computer packages STATA (Version 7.0), SAS (Version 8.2), and SPSS (version 11.5) to carry out the procedures presented in the main text.
The original six chapters have been modified slightly
• to expand and clarify aspects of survival analysis in response to suggestions by students, colleagues and reviewers, and
• to add theoretical background, particularly regarding the formulation of the (partial) likelihood functions for proportional hazards, stratified, and extended Cox regression models
Contents :
Introduction to Survival Analysis. KaplanMeier Survival Curves and the LogRank Test. The Cox Proportional Hazards Model and Its Characteristics. Evaluating the Proportional Hazards Assumption. The Stratified Cox Procedure. Extension of the Cox Proportional Hazards Model for TimeDependent Variables. Parametric Survival Models. Recurrent Events Survival Analysis. Competing Risks Survival Analysis.
About the Authors :
David Kleinbaum is Professor of Epidemiology at the Rollins School of Public Health at Emory University, Atlanta, Georgia. Dr. Kleinbaum is internationally known for innovative textbooks and teaching on epidemiological methods, multiple linear regression, logistic regression, and survival analysis. He has provided extensive worldwide shortcourse training in over 150 short courses on statistical and epidemiological methods. He is also the author of ActivEpi (2002), an interactive computerbased instructional text on fundamentals of epidemiology, which has been used in a variety of educational environments including distance learning.
Mitchel Klein is Research Assistant Professor with a joint appointment in the Department of Environmental and Occupational Health (EOH) and the Department of Epidemiology, also at the Rollins School of Public Health at Emory University. Dr. Klein is also coauthor with Dr. Kleinbaum of the second edition of Logistic Regression A SelfLearning Text (2002). He has regularly taught epidemiologic methods courses at Emory to graduate students in public health and in clinical medicine. He is responsible for the epidemiologic methods training of physicians enrolled in Emory’s Master of Science in Clinical Research Program, and has collaborated with Dr. Kleinbaum both nationally and internationally in teaching several short courses on various topics in epidemiologic methods.




Applied Mathematics  Gerald Dennis Mahan 
Author 
Gerald Dennis Mahan


Cover Price : Rs 695.00

Imprint : Springer ISBN : 8184890075 YOP : 2008

Binding : Paperback Total Pages : 376 CD : No


About the Book :
Applied Mathematics is a textbook for a twosemester graduate course in Mathematical Methods in Physics. Most universities give this course, which is often taught jointly with the Engineering or Mathematics Departments. General topics include: group theory, linear equations, matrices, series, functions of complex variables, conformal mapping, special functions, and partial differential equations. Each chapter has numerous homework problems. The section on transforms includes those on Fourier and Laplace, as well as the modern topic of wavelets. The chapters on partial differential equations include: Laplace's, Poisson's, Helmholtz, diffusion, and wave equations. Related topics such as transforms and orthogonal functions are also discussed in depth. The new topic of wavelet transforms is included.
Contents :
1. Determinants. 2. Matrices. 3. Group theory. 4. Complex Variables. 5. Series. 6. Conformal Mapping. 7. Markov Averaging 8. Fourier Transforms. 9. Equations of Physics. 10. One Dimension. 11. Two Dimensions. 12. Three Dimensions. 13. Odds and Ends.
About the Author :
Geralad D. Mahan was born and raised in Portland, Oregon. His degrees in physics include a B.A. from Harvard in 1959 and a Ph.D. from the University of California, Berkeley, in 1964. He worked fulltime at the General Electric Research and Development Center from 19641967, and continued part time and as a consultant until 1995. He had faculty appointments in physics at the University of Oregon (19671973), Indiana University (19731984), and the University of Tennessee (19842001). The latter appointment was held jointly with Oak Ridge National Laboratory. In 2001, he joined the faculty of Pennsylvania State University in University Park. He is a Fellow of the American Physical Society, and a member of the Materials Research Society, and a member of the U.S. National Academy of Sciences.




Mathematical Logic for Computer Science 2/E  Ben Ari 

Cover Price : Rs 695.00

Imprint : Springer ISBN : 9781447173618 YOP : 2017

Binding : Paperback Total Pages : 318 CD : No


About the Book :
Mathematical Logic for Computer Science is a mathematics textbook with theorems and proofs, but the choice of topics has been guided by the needs of computer science students. The method of semantic tableaux provides an elegant way to teach logic that is both theoretically sound and yet sufficiently elementary for undergraduates. To provide a balanced treatment of logic, tableaux are related to deductive proof systems.
The logical systems presented are:
 Propositional calculus (including binary decision diagrams);
 Predicate calculus;
 Resolution;
 Hoare logic;
 Z;
 Temporal logic.
Contents :
Preface. Introduction. Propositional Calculus: Formulas, Models, Tableaux. Propositional Calculus: Deductive Systems. Propositional Calculus: Resolution and BDDs. Predicate Calculus: Formulas, Models, Tableau. Predicate Calculus: Deductive Systems. Predicate Calculus: Resolution. Logic Programming. Programs: Semantics and Verification. Programs: Formal Specification with Z. Temporal Logic: Formulas, Models, Tableaux. Temporal Logic: Deduction and Applications. Appendix: Set Theory; Further Reading; Bibliography; Index of Symbols; Index.
About the Author :
Mordechai BenAri is an associate professor in the Department of Science Teaching of the Weizmann Institute of Science. He has published textbooks on concurrent programming and programming languages. 



Complex Variables (Indian Reprint 2015)  Steven G Krantz 

Cover Price : Rs 1,995.00

Imprint : T & F / Routledge ISBN : 9781584885807 YOP : 2015

Binding : Hardback Total Pages : 440 CD : No


About the Book :
From the algebraic properties of a complete number field, to the analytic properties imposed by the Cauchy integral formula, to the geometric qualities originating from conformality, Complex Variables: A Physical Approach with Applications and MATLAB explores all facets of this subject, with particular emphasis on using theory in practice.
The first five chapters encompass the core material of the book. These chapters cover fundamental concepts, holomorphic and harmonic functions, Cauchy theory and its applications, and isolated singularities. Subsequent chapters discuss the argument principle, geometric theory, and conformal mapping, followed by a more advanced discussion of harmonic functions. The author also presents a detailed glimpse of how complex variables are used in the real world, with chapters on Fourier and Laplace transforms as well as partial differential equations and boundary value problems. The final chapter explores computer tools, including Mathematica®, Maple™, and MATLAB®, that can be employed to study complex variables. Each chapter contains physical applications drawing from the areas of physics and engineering.
Offering new directions for further learning, this text provides modern students with a powerful toolkit for future work in the mathematical sciences.
Contents :
Preface. Basic Ideas. Holomorphic and Harmonic Functions. The Cauchy Theory. Applications of the Cauchy Theory. Isolated Singularities. The Argument Principle. The Geometric Theory. Applications of Conformal Mapping. Harmonic Functions. Transform Theory. PDEs and Boundary Value Problems. Computer Packages. Appendices. Bibliography. Index. 



Guide to Mathematical Modelling  Dilwyn Edards 
Author 
Dilwyn Edards Mike Hamson


Cover Price : £ 8.99

Imprint : Palgrave / Macmillan ISBN : 0230574106 YOP : 2007 Edition : 2007

Binding : Paperback Total Pages : 336 CD : No


About the Book :
A basic introduction to Mathematical Modelling, this book encourages the reader to participate in the investigation of a wide variety of modelling examples. These are carefully paced so that the readers can identify and develop the skills which are required for successful modelling. The examples also promote an appreciation of the enormous range of problems to which mathematical modelling skills can be usefully applied.
Contents :
What is Modelling ?
Getting Started
Modelling Methodology
Modelling Skills
Using Difference Equations
Using Differential Equations
Using Random Numbers
Using data
Example Models
Report Writing and Presentation
About the Book :
DILWYN EDWARDS is Senior lecturer in Mathematics at the University of Greenwich
MIKE HAMSON was formerly Senior Lecturer in Mathematics at the Glasgow Caledonian University.




Linear Algebra : A Pure Mathematical Approach  Harvey E. Rose 

Cover Price : Rs 695.00

Imprint : Springer ISBN : 8181282149 YOP : 2008

Binding : Paperback Total Pages : 264 CD : No


About the Book :
Linear algebra is one of the most important branches of mathematics  important because of its many applications to other areas of mathematics, and important because it contains a wealth of ideas and results which are basic to pure mathematics. This book gives an introduction to linear algebra, and develops and proves its fundamental properties and theorems taking a pure mathematical approach.
A large number of examples, exercises and problems are provided. Answers and/or sketch solutions to all of the problems are given in an appendix. The intended readership is undergraduate mathematicians, also anyone who requires a more than basic understanding of the subject. This book will be most useful for a "second course" in linear algebra, that is for students that have seen some elementary matrix algebra. But as all terms are defined from scratch, the book can be used for a "first course" for more advanced students.
Contents :
Preface
Chapter 1  Algebraic Preamble
Chapter 2  Vector Spaces and Linear Maps
Chapter 3  Matrices, Determinants and Linear Equations
Chapter 4  Cayley Hamilton Theorem and Jordan Form
Chapter 5  Interlude on Finite Fields
Finite Fields
Chapter 6  Hermitian and Inner Product Spaces
Chapter 7  Selected Topics
Appendix A  Set theory
Appendix B  Answers and Solutions to the problems
Bibliography
Index. 



Basic Mathematics for Bca  J.P. Singh 

Cover Price : Rs 295.00

Imprint : Ane Books Pvt. Ltd. ISBN : 9789380618685 YOP : 2011

Binding : Paperback Total Pages : 392 CD : No


About the Book
This book primarily aims at students preparing for BCA II Semester examination conducted by GGSIPU. This book covers the complete syllabus of BCA II Semester of GGSIPU.
Salient features:
1. The text matter is selfexplanatory and the language is vivid and lucid.
2. To simplify the process of conceptual assimilation, problems have been segregated as LOTS (Lower Order Thinking Skills) and HOTS (Higher Order Thinking Skills).
3. Most of the questions conform to the trend questions appearing in GGSIPU.
Contents
1. Set Theory
2. Relations
3. Functions
4. Posets and Lattices
5. Limits and Continuity of Functions of Several Variables
6. Partial Differentiation
7. Multiple Integrals
8. Review of Two Dimensional
9. Solid Geometry
About the Author
J.P. Singh is Professor in Department of Mathematics at Jagan Institute of Management Studies (Affiliated to GGSIP University), Delhi. He has more than 12 years of teaching experience and has taught at various affiliated Institutes of GGSIP University. He has undergone rigorous training from IIT Delhi in Financial Mathematics. He is a Certified Six Sigma Green Belt from Indian Statistical Institute, Delhi.
He is life time member of the Indian Mathematical Society. His areas of interest include Mathematical Statistics, Stochastic Process, Numerical Methods, Number Theory, Discrete Mathematics and Theory of Computation.




Business Mathematics & Statistics Reprint 2016  B. M. Aggarwal 

Cover Price : Rs 495.00

Imprint : Ane Books Pvt. Ltd. ISBN : 9788180522857 YOP : 2015

Binding : Paperback Size : 7.25 Total Pages : 800 CD : No


Salient Features of the Book :
• The book addresses concepts through detailed explanation and short illustrations.
• Has a compilation of a large number of questions of different universities with solved examples.
• Unsolved Questions at the end of each chapter for independent practice are a key feature of the text.
• Very student friendly, it enables to analyse text with self evaluation tests in the form of Multiple Choice and Short Answer Questions.
• Although the book has been made tailor specific for the B. Com IInd year of Delhi University, it can be used as a handy text for all the students preparing for other examinations with this syllabus.
Contents :
Unit I: Business Mathematics 1. Matrices and Determinants 2. Applications of Matrices and Determinants to Business and Economics 3. Functions, Limits and Continuity 4. Differentiation 5. Applications of Integration to Business and Economics 6. Integral Calculus 7. Applications of Integrations to Business and Economics 8. Basic Mathematics of Finance Unit II: Business Statistics 1. Introduction to Statistics 2. Preparation of Frequency Distribution 3. Statistical Averages (Measures of Central Tendency) 4. Measures of Variation 5. Correlation and Regression Analysis 6. Index Numbers 7. Time Series
About the Author :
B. M. Aggarwal graduated with Honors in Mathematics from Punjab University followed by a Masters degree in Mathematics from Meerut University and a degree in Electronics and Telecommunication Engineering from the Institute of Electronics and Telecommunications Engineering, Lodhi Road, New Delhi.
A versatile teacher and a reputed Professor of Mathematics, Statistics and Operations Research the author has served in many reputed Management Institutes in Delhi and NCR. His presentation can be seen through his lucid and logical treatment of the text.




An Introduction to Wavelet Analysis  David F. Walnut 

Cover Price : Rs 995.00

Imprint : Springer ISBN : 8184890204 YOP : 2008

Binding : Paperback Total Pages : 472 CD : No


Review :
"D. Walnut's lovely book aims at the upper undergraduate level, and so it includes relatively more preliminary material . . . than is typically the case in a graduate text. It goes from Haar systems to multiresolutions, and then the discrete wavelet transform . . . The applications to image compression are wonderful, and the best I have seen in books at this level. I also found the analysis of the best choice of basis, and wavelet packet, especially attractive. The later chapters include MATLAB codes. Highly recommended!"
— Bulletin of the AMS
About the Book :
An Introduction to Wavelet Analysis provides a comprehensive presentation of the conceptual basis of wavelet analysis, including the construction and application of wavelet bases.
The book develops the basic theory of wavelet bases and transforms without assuming any knowledge of Lebesgue integration or the theory of abstract Hilbert spaces. The book elucidates the central ideas of wavelet theory by offering a detailed exposition of the Haar series, and then shows how a more abstract approach allows one to generalize and improve upon the Haar series. Once these ideas have been established and explored, variations and extensions of Haar construction are presented. The mathematical prerequisites for the book are a course in advanced calculus, familiarity with the language of formal mathematical proofs, and basic linear algebra concepts.
Features :
* Rigorous proofs with consistent assumptions about the mathematical background of the reader (does not assume familiarity with Hilbert spaces or Lebesgue measure).
* Complete background material on is offered on Fourier analysis topics.
* Wavelets are presented first on the continuous domain and later restricted to the discrete domain for improved motivation and understanding of discrete wavelet transforms and applications.
* Special appendix, "Excursions in Wavelet Theory, " provides a guide to current literature on the topic.
* Over 170 exercises guide the reader through the text.
An Introduction to Wavelet Analysis is an ideal text/reference for a broad audience of advanced students and researchers in applied mathematics, electrical engineering, computational science, and physical sciences. It is also suitable as a selfstudy reference guide for professionals.
Contents :
Preface
Part I: Preliminaries
Functions and Convergence
Fourier Series
The Fourier Transform
Signals and Systems
Part II: The Haar System
The Haar System
The Discrete Haar Transform
Part III: Orthonormal Wavelet Bases
Mulitresolution Analysis
The Discrete Wavelet Transform
Smooth, Compactly Supported Wavelets
Part IV: Other Wavelet Constructions
Biorthogonal Wavelets
Wavelet Packets
Part V: Applications
Image Compression
Integral Operators
Appendix A: Review of Advanced Calculus and Linear Algebra
Appendix B: Excursions in Wavelet Theory
Appendix C: References Cited in the Text
Index.




Mathematics  1 : FOR BCA  Zubair Khan 
Author 
Zubair Khan Shadab Ahmad Khan Qazi Shoeb Ahmad


Cover Price : Rs 295.00

Imprint : Ane Books Pvt. Ltd. ISBN : 8180522946 YOP : 2009

Binding : Paperback Total Pages : 600 CD : No


About the Book :
This book is designed to meet the requirements of I year rather I semester students of B.C.A. The book covers subject matter on complex numbers, trigonometry, matrices and determinants, differential calculus, integral calculus, vector calculus and their applications. Each unit of the book contains a variety of solved examples to explain the relevant concepts. Comprehensive exercises have been given at the end of each unit for practice and self assessment.
This book is very useful for B.C.A. students of Integral University and the various other Universities.
Salient features :
• The subject matter has been presented in a very simple language and lucid manner.
• Stepwise treatment of difficult concepts makes them for easily understable.
• Each chapter contains variety of illustrations to explain the relevant concepts.
• Comprehensive exercises have been given at the end each chapter for practice.
Contents :
Preface 1. Trigonometry and Complex Numbers 2. Matrices and Determinant 3. Differential Calculus 4. Integral Calculus 5. Vector Calculus
About the Authors :
Dr. Zubair Khan is working as Lecturer in Department of Mathematics, Integral University, Lucknow. Dr. Khan has obtained his M.Sc., M.Phil. and Ph.D. degrees in Mathematics from Aligarh Muslim University, Aligarh. He has about four years of teaching experience at graduate and postgraduate levels. Dr. Khan has published a number of research papers in various National and International Journals of repute. The areas of his interest from research point of view are Applied Functional Analysis and Variational Inequalities.
Shadab Ahmad Khan is working as Lecturer in Department of Mathematics, Integral University, Lucknow. Mr. Khan has done M.Sc. in Mathematics from Aligarh Muslim University, Aligarh. He has more than five years of teaching experience at graduate and post graduate levels. He has enrolled himself for Ph.D. degree in Lucknow University, selecting Differential Geometry as the research area.
Dr. Qazi Shoeb Ahmad is working as Assistant Professor in Department of Mathematics, Integral University, Lucknow. Dr. Ahmad has obtained M.Sc. and Ph.D. degrees in Operations Research from Aligarh Muslim University, Aligarh. He has more than eight years of teaching experience at graduate and postgraduate levels. Dr. Ahmad has published a number of research papers in prestigious National and International Journals. His area of research interest includes Integer Programming, Sequencing and Mathematical Programming in Sampling.




VECTOR ANALYSIS AND CARTESIAN TENSORS 3RD ED, INDIAN REPRINT  D.E. BOURNE (EX) 
Author 
D.E. BOURNE P.C. KENDALL


Cover Price : £ 5.99

Imprint : CRC Press ISBN : 9780748754601 YOP : 2014

Binding : Paperback Total Pages : 316 CD : No


This is a comprehensive selfcontained text suitable for use by undergraduate mathematics, science and engineering students following courses in vector analysis. The earlier editions have been used extensively in the design and teaching of many undergraduate courses. Vectors are introduced in terms of Cartesian components, an approach which is found to appeal to many students because the basic algebraic rules of composition of vectors and the definitions of gradient divergence and curl are thus made particularly simple. The theory is complete, and intended to be as rigorous as possible at the level at which it is aimed. More advanced work on tensors is also included. For this edition, the book has been redesigned throughout, with alterations to the notation, and the inclusion of further material on applications, for example, on the existence and nature of angular velocity. There is also a brief introduction to the method of steepest descent.
Dr Bourne and Professor kendall have collaborated over a period of 20 years and are wellknown for their contributions to teaching and mathematics education. Their research, in topics ranging from the flow of molten glass to electromagnetic theory, has been carried out at the Universities of Sheffield, Alaska, Colorado, Keele and London.
Contents
Preface to second edition
1. Rectangular Cartesian coordinates and rotation of axes
2. Scalar and vector algebra
3. Vector functions of a real variable, Differential geometry of curves
4. Scalar and vector fields
5. Line, surface and volume integrals
6. Integral theorems
7. Applications in potential theory
8. Cartesian tensors
9. Representation theorems for isotropic tensor functions
Appendix A Determinants
Appendix B Expressions for grad, div, curl, and V2 in cylindrical and spherical polar coordinates
Appendix C The chain rule for Jacobians
Answers to exercises
Index 



Topology : A Geometric Approach  M. Ganesh 

Cover Price : Rs 180.00

Imprint : Ane Books Pvt. Ltd. ISBN : 8180522407 YOP : 2009

Binding : Paperback Total Pages : 212 CD : No


About the Book :
Topology is a simultaneous generalization of two aspects: (1) the metric spaces (that includes normed linear spaces and inner product spaces and — both finite and infinite dimensional), and (2) the various geometries (Euclidean, affine, and projective). Almost all the books in the market are based on the first view point, ignoring or paying very little attention to the second view point. This book emphasizes more on the second point of view, without losing focus on the first point of view. Moreover, the author has taken great pain in presenting the subject matter in a cogent manner and with enough clarity, so that a student can do selfstudy. At the same time, rigor has not been sacrificed or diluted. This book is an outgrowth of the authors many years of experience in teaching topology at the postgraduate level and, therefore, intended especially for that level. Plenty of worked out examples and problems have been included to benefit both the teachers and the students. Plenty of figures are included as visual aids for enhancing the understanding. Certain topics, which are interesting but may prove to be a digression, have been dealt in appendices at the end of each chapter, giving adequate subjective information. On the whole, this book will be a welcome addition to the existing literature on topology and anticipates all success.
About the Author :
Presently, M. Ganesh is a Professor of Mathematics at the Birla Institute of Technology & Science (BITS), Pilani (Rajasthan). The author received his Ph. D. degree from the University of Madras in the year 1979. Prof. Ganesh already has two books to his credit: the first one is entitled “Introduction to Fuzzy Sets & Fuzzy Logic”, published by Prentice Hall of India and the second is entitled “Basics of Computer Aided Geometric Design: An Algorithmic Approach”, published by I.K. International Publishers. The author has also published several papers in reputed National and International Journals. The areas of his current research interests include applications of fuzzy logic in decision making, computer science, and control theory. His other interests include theory of computability, cryptography and formal methods in program verifications.




Mathematics  II : FOR BCA  Shadab Ahmad Khan 
Author 
Shadab Ahmad Khan Qazi Shoeb Ahmad Zubair Khan


Cover Price : Rs 235.00

Imprint : Ane Books Pvt. Ltd. ISBN : 8180521702 YOP : 2009

Binding : Paperback Total Pages : 384 CD : No


About the Book :
This book is designed to meet the requirements of I year, II semester students of B.C.A. The book covers the topics of Partial Differentiation, Ordinary Differential Equations, Partial Differential Equations, Geometry, Probability, Probability Distributions and Statistics. Each unit contains variety of solved examples to explain the relevant concepts. Comprehensive exercises have been given in each unit for practice.
This book can be useful for B.C.A. students of Integral University and other Indian Universities.
Salient features :
• The subject matter has been presented in a simple and lucid form.
• Comprehensive stepbystep explanations for easier understanding.
• Each chapter contains variety of illustrations to explain the relevant concepts.
• Comprehensive exercises have been given at the end of each chapter for practice.
Contents :
Preface, UnitI : Partial Differentiation and its Applications, UnitII : Ordinary Differential Equations, UnitIII : Partial Differential Equation and Geometry, UnitIV : Probability and Distributions, UnitV : Measures of Central Tendency.
About the Authors :
Shadab Ahmad Khan is working as Lecturer in the department of Mathematics, Integral University, Lucknow. He has done his B.Sc. and M.Sc. in Mathematics from Aligarh Muslim University, Aligarh. He has more than five years of teaching experience at graduate and postgraduate levels. He has enrolled himself as a research scholar in the field of Differential Geometry in Lucknow University. He has already four books to his credit.
Dr. Qazi Shoeb Ahmad is working as Assistant Professor in the department of Mathematics, Integral University, Lucknow. He has done his M.Sc. and Ph.D. in Operations Research from Aligarh Muslim University, Aligarh. He has more than eight years of teaching experience at graduate and postgraduate levels. Dr. Ahmad has published a number of research papers in prestigious national & international journals. His area of research interest includes Integer Programming, Sequencing and Mathematical Programming in Sampling. He has already four books to his credit.
Dr. Zubair Khan is working as Lecturer in the department of Mathematics, Integral University, Lucknow. He has done his M.Sc., M.Phil. and Ph.D. in Mathematics from Aligarh Muslim University, Aligarh. He has about four years of teaching experience at graduate and postgraduate levels. Dr. Khan has published a number of research papers in prestigious national & international journals. His area of research interest is Applied Functional Analysis, Variational Inequalities. He has already one book to his credit.




Business Mathematics & Business Statistics  R.S. Soni and Avneet Kaur Soni 
Author 
R.S. Soni Avneet Kaur Soni


Cover Price : Rs 395.00

Imprint : Ane Books Pvt. Ltd. ISBN : 9788180521577 YOP : 2016

Binding : Paperback Total Pages : 598 CD : No


New Arrival 
About the Book :
This book is intended primarily for students preparing Paper VI for B.Com. Course
(Part II) Examination conducted by the University of Delhi. The book has been written strictly in
accordance with the latest syllabus prescribed by the University of Delhi and other Universities having
similar syllabus. The text has grown from authors long teaching experience of over thirtythree years to
the students of Commerce and Business Economics at different levels.
Salient features of this book are:
œ The book has simple and lucid language.
œ Requires no previous knowledge of the subject.
œ Each chapter starts with chapter outline and learning objectives.
œ Difficult concepts have been explained in a simple and easy manner with examples.
œ Written with a view to present a qualitative understanding of the subject.
œ Contains large number of solved examples for better understanding of concepts.
œ Unsolved problems for selfpractice have been taken from recent examination papers of B.Com
(Hons.) and B.Com (Pass).
œ Answers to all the problems in the form of selfpractice problems are given along with problems or at the
end of selfpractice problems.
Contents
Part A : 1. Matrices and Determinants 2. Applications of Matrices to Business and Economics
3. Functions, Limit and Continuity 4. Differentiation 5. Applications of Derivatives to Business and
Economics 6. Integration 7. Applications of Integration to Business and Economics 8. Mathematics of
Finance Part B : 1. Introduction to Statistics 2. Frequency Distribution 3. Measures of Central Tendency
4. Measures of Variation 5. Correlation Analysis 6. Regression Analysis 7. Index Numbers 8. Analysis of Time Series.
About the Author
Dr. R.S. Soni is a Associate Professor in the Department of Mathematics, Sri Guru Nanak Dev Khalsa
College, Devnagar, University of Delhi, since 1976. Dr. Soni has a brilliant first class academic record. He
obtained his Ph. D degree from the University of Delhi in 1975. Many of his research papers have been
published in Indian and International journals of high repute. He has been teaching Mathematics and
Statistics for over thirtythree years. Dr. Soni is the author of several mathematics textbooks. 



Numerical and Statistical Techniques  Qazi Shoeb Ahmad 
Author 
Qazi Shoeb Ahmad Zubair Khan Shadab Ahmad Khan


Cover Price : Rs 395.00

Imprint : Ane Books Pvt. Ltd. ISBN : 9788180522598 YOP : 2015

Binding : Paperback Total Pages : 448 CD : No


New Arrival 
About the Book :
The book is designed to meet the requirements of B.Tech, B.Tech (Biotech), B.C.A. students of Integral University and its study centers, Lucknow University, Jamia Hamdard and various other Universities.
The book covers the topics of Error and Computer Arithmetic, Solution of Algebraic and Transcendental Equations, Solution of Simultaneous Equations, Finite Differences, Interpolation, Numerical Differentiation and Integration, Solution of Differential Equations, Curve Fitting, Regression Analysis, Time Series and Forecasting, Testing of Hypothesis. Each chapter contains variety of solved examples to explain the relevant concepts. Comprehensive exercises have been given in each chapter for practice.
Salient features:
● The subjectmatter has been presented in a simple and lucid form.
● Comprehensive step by step explanations for easier understanding.
● Each chapter contains variety of illustrations to explain the relevant concepts.
● Comprehensive exercises have been given at the end of each chapter for practice.
Contents
Preface 1. Error and Computer Arithmetic 2. Solution of Algebraic and Transcendental Equations 3. Finite Differences 4. Interpolation 5. Numerical Differentiation and Integration 6. Numerical Solution of Ordinary Differential Equations 7. Curve Fitting 8. Regression Analysis 9. Time Series and Forecasting 10. Test of Significance and Analysis of Variance
Appendix, Index.
About the Author
Dr. Qazi Shoeb Ahmad is working as Assistant Professor in the department of Mathematics, Integral University, Lucknow. He has done his M.Sc. and Ph.D. in Operations Research from Aligarh Muslim University, Aligarh. He has more than eight years of teaching experience at graduate and postgraduate levels. Dr. Ahmad has published a number of research papers in prestigious national and international journals. His area of research interest includes Integer Programming, Sequencing and Mathematical Programming in Sampling. The author already has five books in his credit.
Dr. Zubair Khan is working as Lecturer in the department of Mathematics, Integral University, Lucknow. He has done his M.Sc., M.Phil and Ph.D. in Mathematics from Aligarh Muslim University, Aligarh. He has about five years of teaching experience at graduate and postgraduate levels. Dr. Khan has published a number of research papers in prestigious national and international journals. His area of research interest is Applied Functional Analysis, Variational Inequalities. He has also two books in his credit.
Shadab Ahmad Khan is working as Lecturer in the department of Mathematics, Integral University, Lucknow. He has done his B.Sc. and M.Sc. in Mathematics from Aligarh Muslim University, Aligarh. He has more than five years of teaching experience at graduate and postgraduate levels. He has enrolled himself as a research scholar in the field of Differential Geometry in Lucknow University. The author already has five books in his credit.




Classification of Lipschitz Mappings, Indian Reprint  Lukasz Piasecki (EX) 

Cover Price : Rs 4,995.00

Imprint : CRC Press ISBN : 9781466595217 YOP : 2015

Binding : Hardback Total Pages : 234 CD : No


Deep understanding of the properties of Lipschitzian mappings is important for all levels of study in many branches of mathematics. This book by Lukasz Piasecki is a good choice for achieving such an understanding in the framework of mappings in general metric spaces, in particular, Banach spaces. Moreover, it gives new insight into the theory of Lipschitzian mappings via a study of the mean Lipschitz condition. The book is written in a very clear and readerfriendly way. The author gives many examples illustrating various aspects of presented results.”
—Stanislaw Prus, Marie CurieSklodowska University
"… a selfcontained, readable and precise course on the subject. Besides the presentation of the theory, the true value of the book lies in a collection of cleverly chosen interesting examples. “
—Kazimierz Goebel, Maria CurieSklodowska University
"I strongly recommend this book for advanced undergraduate and graduate students … The reader will find a new classification of this kind of mapping as well as many examples and illustrations designed to help the reader understand the definitions, properties, and results…. I also recommend this book for analysts or mathematicians who are looking for new topics to research."
—Victor PerezGarcia, University of Veracruz
Classification of Lipschitz Mappings presents a systematic, selfcontained treatment of a new, more precise classification of Lipschitz mappings and its application in many topics of metric fixed point theory. The mean Lipschitz condition introduced by Goebel, Japon Pineda, and Sims is relatively easy to check and turns out to satisfy several principles: regulating the possible growth of the sequence of Lipschtz constants k(Tn), Ensuring good estimates for k0(T) and k8(T) and Providing some new results in metric fixed point theory.
Contents
Introduction
The Lipschitz Condition
Nonlinear spectral radius
Uniformly lipschitzian mappings
Basic Facts on Banach Spaces
Convexity
The operator norm
Dual spaces, reexivity, the weak, and weak* topologies
Mean Lipschitz Condition
Nonexpansive and mean nonexpansive mappings in Banach spaces
General case
On the Lipschitz Constants for Iterates of Mean Lipschitzian Mappings
A bound for Lipschitz constants of iterates
A bound for the constant k∞(T)
Moving averages in Banach spaces
A bound for the constant k0(T)
More about k(Tn), k0(T), and k∞(T)
Subclasses Determined by pAverages
Basic definitions and observations
A bound for k(Tn), k∞(T), and k0(T)
On the moving paverages
Mean Contractions
Classical Banach’s contractions
On characterizations of contractions
On the rate of convergence of iterates
Nonexpansive Mappings in Banach Space
The asymptotic center technique
Minimal invariant sets and normal structure
Uniformly nonsquare, uniformly noncreasy, and reflexive Banach spaces
Remarks on the stability of f.p.p.
The case of ℓ1
Mean Nonexpansive Mappings
Some new results of stability type
Sequential approximation of fixed points
The case of n = 3
On the structure of the fixed points set
Mean Lipschitzian Mappings with k > 1
Losing compactness in Brouwer’s Fixed Point Theorem
Retracting onto balls in Banach spaces
Minimal displacement
Optimal retractions
Generalized characteristics of minimal displacement
Bibliography
Index




Elements of Graph Theory  S.K. Yadav 

Cover Price : Rs 270.00

Imprint : Ane Books Pvt. Ltd. ISBN : 9380618487 YOP : 2010

Binding : Paperback Total Pages : 273 CD : No


About the Book
This book is designed to meet the syllabus requirement of the students of B.Tech., M.Tech. (C.S.), M.Sc. (Mathematics), M.Sc. (C.S.), M.Sc. (Electronics), M.C.A., and other professional courses of various national and international universities. The questions asked in various universities and professional courses have also been added. The students of open and distance education courses will find the book very helpful.
Contents
1. The basics of Graph Theory 2. Trees 3. Planar Graphs 4. Directed Graphs 5. Matching and Covering 6. Colouring of Graphs 7. Ramsey Theory for Graphs 8. Emerging Trends in Graph Theory. References, Index
About the Author
Prof. Santosh Kumar Yadav has been associated with academic and research activities for two decades. He did his Masters in Science (Physics, Mathematics, Applied Mathematics and Mathematics with Computer Applications), M.Phil (Mathematics, Computer Science) Ph.D, M.Tech (C.S.E.),M.B.A (Education Management).
Prof. Yadav has Written more than a dozen text and reference books and edited more than a hundred selflearning materials for different Universities. He is the editor for four reputed international journals of research and has supervised more than 70 research scholars. 



Complex Analysis  Anuradha Gupta 

Cover Price : Rs 295.00

Imprint : Ane Books Pvt. Ltd. ISBN : 9789381162248 YOP : 2011

Binding : Paperback Total Pages : 432 CD : No


About the Book
The textbook is a continuation of the study of Calculus, but as the study of functions of complex variables. The first goal in writing this book is to present the theory of analytic functions in a more accessible way in the early stages of his/her complex analysis study.
The second aim of this book is to give the students wide applications of complex variable techniques as complex analysis is a powerful tool in applied mathematics.
The third aim of this book is to provide a comparative study between real variables and complex variables of various topics. Basically those areas where real and complex calculus differ, have been discussed to give the clarity about the concept.
I have also provided lots of examples and have tried very hard to supply all pertinent detail of their solution. The corresponding exercise sets are divided in order to make the study easier.
A multifaceted book written to keep the interest of B.Sc (Hons) Mathematics (Part III), M.Sc.(MathematicsPart I) students of University of Delhi. This book is also useful for those who want to appear in their National eligibility Test for Lecturership in Mathematics.
Contents
1. Complex Number and The Complex Plane 2. Functions of Complex Variable 3. Analytic Functions 4. Elementary Functions 5. Complex Integration 6. Cauchys Integral Formulas and their Consequences 7. Analytic Functions in a Disc 8. Simply Connected Region 9. Isolated Singularities 10. The Calculus of Residues 11. Contour Integration and Summation of Series 12. Conformal Mapings 13. Schwarzs LemmaAn Automorphism of Disc, Appendix, Bibliography, Index
About the Author
Dr. Anuradha Gupta, a PhD from University of Delhi, is an Associate Professor in the Department of Mathematics, Delhi College of Arts and Commerce (University of Delhi). She has more than 20 years of rich experience of teaching Real Analysis, Algebra, Complex Analysis and Discrete Mathematics to the students of undergraduate and postgraduate levels of University of Delhi. Her major areas of interest include Operator theory, Functional Analysis, Calculus, Complex and Real Analysis. There are ten research papers published in national and international journals to her credit. She has also written a book entitled Business Mathematics.




Applied Mathematics  II,  Singh Abhimanyu 

Cover Price : Rs 395.00

Imprint : Ane Books Pvt. Ltd. ISBN : 9789381162798 YOP : 2015

Binding : Paperback Total Pages : 654 CD : No


About the Book
This book covers the complete syllabi of the paper Applied MathematicsII of second semester of B.Tech. course of GGSIP University, Delhi, and first & second semesters of other national and international Engineering and Technological Institutions. The matter is presented in so simple manner that even an average student can have a good command on this difficult subject. The text is equipped with a large number of solved problems with enough unsolved exercises. I hope the book will serve its purpose.
Contents
Unit I: Calculus of Several Variables
1. Partial Differentiation
2. Applications of Partial Differentiation
3. Multiple Integrals
Unit II: Functions of A Complex Variable
4. Functions of a Complex Variable
5. Conformal Transformation
6. Complex Integration
7. Power Series
Unit III: Vector Calculus
8. Vector Differentiation
9. Vector Integration
Unit IV: Laplace Transform
10. Laplace Transformation
11. Inverse Laplace Transforms
About the Author
Abhimanyu Singh is currently working as an Assistant Professor in the Dept of Mathematics, GGSIPU (affiliated institute,)Delhi. He has more than 15 years of experience in teaching Engineering Mathematics to B.E.and B.Tech. students at Delhi Technological University (formerly Delhi College of Engineering) and Guru Gobind Singh Indraprastha University, Delhi.




Discrete Mathematics with Graph Theory  S.K. Yadav 

Cover Price : Rs 495.00

Imprint : Ane Books Pvt. Ltd. ISBN : 9789382127185 YOP : 2016

Binding : Paperback Size : 5.50" X 8.50" Total Pages : 670 CD : No


About the Book
This book has been designed to meet the syllabus requirements of the students of B.Sc.(H)(Math/Computer Sc./Physical Sc.), B.C.A/M.C.A., B.Tech. (C.S.E., E.C.E., I.T.,), M.Tech.(C.S.E./I.T.), M.Sc. (Mathematics/C.S./Electronics) and other professional courses of various Universities/ Institutions at home and abroad. The students of Open and Distance Education courses will find the book most useful.
Contents
1. The Language of Sets 2. Basic Combinatorics 3. Mathematical Logic 4. Relations 5. Functions 6. Lattice Theory 7. Boolean Algebras and Applications 8. Fuzzy Algebra 9. Formal Languages and Automata Theory 10. The Basics of Graph Theory 11. Trees 12. Planar Graphs 13. Directed Graphs 14. Matching and Covering 15. Colouring of Graphs, References, Index
About the Author
Dr.Santosh Kumar Yadav (b1968)has been associated with academic and research activities for more than two decades. He has been an active and dynamic administrator as Director (Academics and Research)at J.J.T. University, Rajasthan. As an academician he has taught undergraduates and postgraduate students in different premier institutions including various colleges of University of Delhi in different capacities.
As a researcher, Dr. Yadav has guided more than 70 research scholars of different universities at home and abroad. As an author he has written more than a dozen books and more than a hundred selflearning materials of different universities. Dr. Yadav is editor of six well reputed International Journals of Research and Life Member of 24 reputed professional apex bodies of academics and research.




DU B.SC (HONS),MATH, SEMIII: MULTIVARIABLE CALCULUS  ANURADHA GUPTA 

Cover Price : Rs 295.00

Imprint : Ane Books Pvt. Ltd. ISBN : 9789382127222 YOP : 2016

Binding : Paperback Total Pages : 326 CD : No


About the Book
Multivariable calculus is the extension of calculus in one variable to calculus in more than one variable where the differentiated and integrated functions involve multivariables rather than just one. This book is written to fulfill the needs of B.Sc. (Maths) IIIrd semester students of University of Delhi so that the students learn the concepts of calculus for the function of several variables thoroughly and apply them in new and novel ways. The theme of the book is that the Calculus is about logical thinking one cannot memorize all. The examples and exercises of the book are meticulously crafted and honed to meet the needs of the students who are keen to know about multivariable calculus. Starting from the basics of vector calculus and covering upto double and triple integrals the book provides the students a deep study of the calculus of functions of more than one variables. The book Multivariable Calculus combines in depth the theory with examples and applications of the concepts related to the functions of several variables.
Contents
1. Functions and Graphs 2. Vectors and Geometry of Euclidean Space 3. VectorValued Functions 4. Partial Differentiation 5. Multiple Integrals 6. Vector Fields, Solutions, Table, Bibliography, Index
About the Author
Dr. Anuradha Gupta is an Associate Professor in the Department of Mathematics, Delhi College of Arts and Commerce, University of Delhi. She has rich teaching experience of more than 21 years. She is actively involved in the research activities in the field of Operator Theory and Functional Analysis. Her research articles have been published in various national and international journals. She has also presented her research papers in several international conferences in India and abroad. She has also written two books “Business Mathematics” and “Complex Analysis” for the undergraduate students of various Universities in India.




B.Com (Hons),Sem3: Business Mathematics  R.S. Soni 
Author 
R.S. Soni Avneet Kaur Soni


Cover Price : Rs 450.00

Imprint : Ane Books Pvt. Ltd. ISBN : 9789382127246 YOP : 2016

Binding : Paperback Total Pages : 698 CD : No


About the Book
This book is intended primarily for students preparing Paper CH 3.1 for B.Com.(Hons.) Course, SemesterIII, Examination conducted by the University of Delhi. The book has been written strictly in accordance with the latest syllabus prescribed by the University of Delhi and other Universities having similar syllabus. The text has grown from authors long teaching experience of over thirtythree years to the students of Commerce and Business Economics at different levels.
Salient features of this book are:
• The book has simple and lucid language.
• Requires no previous knowledge of the subject.
• Each chapter starts with chapter outline and learning objectives.
• Difficult concepts have been explained in a simple and easy manner with examples.
• Written with a view to present a qualitative understanding of the subject.
• Contains large number of solved examples for better understanding of concepts.
• Unsolved problems for selfpractice have been taken from recent examination papers of B.Com (Hons.) and B.Com (Pass).
• Answers to all the problems in the form of selfpractice problems are given along with problems or at the end of selfpractice problems.
Contents
1. Matrices and Determinants 2. Applications of Matrices to Business and Economics 3. Functions, Limit and Continuity 4. Differentiation 5. Applications of Derivatives to Business and Economics 6. Partial Differentiation 7. Applications of Partial Differentiation to Business and Economics 8. Integration 9. Applications of Integration to Business and Economics 10. Mathematics of Finance 11. Mathematics of FinanceII 12. Linear ProgrammingI 13. Linear ProgrammingII (Simplex Method)
About the Authors
Dr. R.S. Soni is an Associate Professor in the Department of Mathematics, Sri Guru Nanak Dev Khalsa College, Devnagar, University of Delhi, since 1976. Dr. Soni has a brilliant first class academic record. He obtained his Ph.D. degree from the University of Delhi in 1975. Many of his research papers have been published in Indian and International journals of high repute. He has been teaching Mathematics and Statistics for over thirtythree years. Dr. Soni is the author of several mathematics textbooks.
Avneet Kaur Soni has obtained B.Com (Hons.) degree from Delhi University, M.Com. degree from IGNOU and BCA degree from DOEACC 'A' Level. At present, she is pursuing Ph.D. 



B.Sc(Hons), Math, SemIII: Numerical Methods and Programming  Ranjna Mehta 
Author 
Ranjna Mehta Seema Paliwal


Cover Price : Rs 175.00

Imprint : Ane Books Pvt. Ltd. ISBN : 9789382127192 YOP : 2016

Binding : Paperback Total Pages : 182 CD : No


About the Book
This book is useful for various graduate and postgraduate courses in Mathematics, Physics, Computer Science. The book covers the syllabus for B.SC (Hons.) Mathematics IInd year (IIIrd Semester) for the paper entitled III. 2, Numerical Method and Programming.
This text has a student friendly approach with an easy to read writing style and a perfect blend of theory and numerical. It presents all the basis material in one place and gives an opportunity to understanding the topic in the most easy and comfortable way. A large number of examples are used to explain the concepts. The book contains number of exercises to help build confidence in students.
Contents
1. Algorithm and Convergence, 2. Finite Differences and Interpolations,
3. Interpolation and Approximation, 4. Polynomial and Transcendental Equations,
5. System of Linear Algebraic Equations, 6. Numerical Differentiation and Numerical Integration, 7. Numerical Rule, 8. C++ Programming, Practice Problems, Reference, Question Paper
About the Author
Ranjna Mehta is an Associate Professor in the Department of Mathematics at Sri Venkateswara College. She did her Ph.D from University of Delhi in 1982. Four of her research papers have been published in Indian and Foreign journals
Seema Paliwal is an Assistant Professor in the Department of Mathematics at Hindu College. She has over 12 years of teaching experience at the undergraduate level. Her area of interest are Numerical Analysis, Calculus, Analysis (Real & Complex), and Operator Theory.




Discrete Mathematics for Undergraduates , Revised & Updated  J.P. Singh 

Cover Price : Rs 350.00

Imprint : Ane Books Pvt. Ltd. ISBN : 9789381162910 YOP : 2018

Binding : Paperback Total Pages : 340 CD : No


About the Book
This book has been written for undergraduate students pursuing Discrete Mathematics as their subject. The book primarily aims at students preparing for BCA, Semester II examination conducted by GGSIP University. This book consists of eight chapters. All the chapters have been supplied by numerous solved examples and exercises along with their answers. The main objective of this book is to provide useful selfstudy material for the students. Clear diagrams have been drawn, text headings have been specified that helps students to grasp this subject easily. This will not only enhance students' understanding of the concepts discussed but will also prepare them for the examination.
Salient features:
1. The text matter is selfexplanatory and the language is vivid and lucid.
2. To simplify the process of conceptual assimilation, problems have been segregated as LOTS (Lower Order Thinking Skills) and HOTS (Higher Order Thinking Skills).
3. Most of the questions conform to the trend questions appearing in GGSIPU.
4. Clear diagrams are provided in support of text.
5. Symbols with their meanings are provided for the help of students.
Contents
1. Set Theory 2. Relations 3. Functions 4. Posets and Lattices 5. Mathematical Logic 6. Graph Theory 7. Paths and Circuits 8. Graph Coloring
About the Author
J.P. Singh is a Professor in Department of Mathematics at Jagan Institute of Management Studies, Rohini (Affiliated to GGSIP University), Delhi. He has more than 13 years of teaching experience and has taught at various affiliated Institutes of GGSIP University. He has undergone rigorous training from IIT Delhi in Financial Mathematics. He is a Certified Six Sigma Green Belt from Indian Statistical Institute, Delhi.
He is a lifetime member of the Indian Mathematical Society and Ramanujan Mathematical Society. His areas of interest include Stochastic Process, Discrete Mathematics, Mathematical Statistics, Numerical Methods, Number Theory and Theory of Computation. 



MODERN ADVANCED MATHEMATICS FOR ENGINEERS, WILEY INDIA , INDIAN REPRINT  VLADIMIR V. MITIN (EX) 
Author 
VLADIMIR V. MITIN DMITRI A. RAMANOV MICHAEL P. POLIS


Cover Price : Rs 3,995.00

Imprint : Wiley India ISBN : 9788126539185 YOP : 2013

Binding : Hardback Total Pages : 326 CD : No


Almost every discipline in electrical and computer engineering relies heavily on advanced mathematics. Modern Advanced Mathematics for Engineers builds a strong foundation in modern applied mathematics for engineering students, and offers them a concise and comprehensive treatment that summarizes and unifies their mathematical knowledge using a system focused on basic concepts rather than exhaustive theorems and proofs.
The authors provide several levels of explanation and exercises involving increasing degrees of mathematical difficulty to recall and develop basic topics such as calculus, determinants, Gaussian elimination, differential equations, and functions of a complex variable. They include an assortment of examples ranging from simple illustrations to highly involved problems as well as a number of applications that demonstrate the concepts and methods discussed throughout the book. This broad treatment also offers
• Key mathematical tools needed by engineers working in communications, semiconductor device simulation, and control theory
• Concise coverage of fundamental concepts such as sets, mappings, and linearity
• Thorough discussion of topics such as distance, inner product, and orthogonality
• Essentials of operator equations, theory of approximations, transform methods, and
• partial differential equations
• A treatment that is adaptable for use with computer systems
Modern Advanced Mathematics for Engineers gives students a strong foundation in modern applied mathematics and the confidence to apply it across diverse engineering disciplines. It makes an excellent companion to less general engineering texts and a useful reference for practitioners.
Contents
Dedication.
Preface.
The Basic of Set Theory.
Relations and Mappings.
Mathematical Logic.
Algebraic Structures: Group Through Linear Space.
Linear Mappings and Matrices.
Metrics and Topological Properties.
Banach and Hilbert Spaces.
Orthonormal Bases and Fourier Series.
Operator Equations.
Fourier and Laplace Transforms.
Partial Differential Equations.
Topic Index.
VLADIMIR V. MITIN and DMITRI A. ROMANOV are both Professors in the Department of Electrical and Computer Engineering at Wayne State University.
MICHAEL P. POLIS is Professor in the School of Engineering and Computer Science at Oakland University in Michigan.




PARTIAL DIFFERENTIAL EQUATIONS AND THE FINITE ELEMENT METHOD, INDIAN REPRINT  PAVEL SOLIN (EX) 

Cover Price : Rs 3,995.00

Imprint : Wiley India ISBN : 9788126537570 YOP : 2013

Binding : Hardback Total Pages : 490 CD : No


Partial Differential Equations and the Finite Element Method provides a muchneeded, clear, and systematic introduction to modern theory of partial differential equations (PDEs) and finite element methods (FEM). Both nodal and hierachic concepts of the FEM are examined. Reflecting the growing complexity and multiscale nature of current engineering and scientific problems, the author emphasizes higherorder finite element methods such as the spectral or hpFEM.
A solid introduction to the theory of PDEs and FEM contained in Chapters 14 serves as the core and foundation of the publication. Chapter 5 is devoted to modern higherorder methods for the numerical solution of ordinary differential equations (ODEs) that arise in the semidiscretization of timedependent PDEs by the Method of Lines (MOL). Chapter 6 discusses fourthorder PDEs rooted in the bending of elastic beams and plates and approximates their solution by means of higherorder Hermite and Argyris elements. Finally, Chapter 7 introduces the reader to various PDEs governing computational electromagnetics and describes their finite element approximation, including modern higherorder edge elements for Maxwell's equations.
The understanding of many theoretical and practical aspects of both PDEs and FEM requires a solid knowledge of linear algebra and elementary functional analysis, such as functions and linear operators in the Lebesgue, Hilbert, and Sobolev spaces. These topics are discussed with the help of many illustrative examples in Appendix A, which is provided as a service for those readers who need to gain the necessary background or require a refresher tutorial. Appendix B presents several finite element computations rooted in practical engineering problems and demonstrates the benefits of using higherorder FEM.
Numerous finite element algorithms are written out in detail alongside implementation discussions. Exercises, including many that involve programming the FEM, are designed to assist the reader in solving typical problems in engineering and science.
Specifically designed as a coursebook, this studenttested publication is geared to upperlevel undergraduates and graduate students in all disciplines of computational engineeringand science. It is also a practical problemsolving reference for researchers, engineers, and physicists.
Contents
List of Figures.
List of Tables.
Preface.
Acknowldegments.
1. Partial Differential Equations.
2. Continuous Elements for 1D Problems.
3. General Concept of Nodal Elements.
4. Continuous Finite Elements for 2D Problems.
5. Transient Problems and ODE Solvers.
6. Beam and Plate Bending Problems.
7. Equations of Electrimagnetics.
Appendix A: Basics of Functional Analysis.
Appendix B: Software and Examples.
References.
Index.
PAVEL SOLÍN, PhD, is Associate Professor in the Department of Mathematical Sciences at The University of Texas at El Paso. Prior to this appointment, Dr. Solin was a postdoctoral research associate at the Johannes Kepler University (Linz, Austria), The University of Texas at Austin, and Rice University (Houston, Texas). He received his PhD from the Charles University in Prague, Czech Republic, in 1999. Dr. Sol?n is a coauthor of the monograph HigherOrder Finite Element Methods.




Applied Mathematics 1  Abhimanyu Singh 

Cover Price : Rs 325.00

Imprint : Ane Books Pvt. Ltd. ISBN : 9789380156323 YOP : 2010

Binding : Paperback Total Pages : 518 CD : No


About the Book
This book is written to completely fulfil the requirement of first semester students of B. Tech. of GGSIPU, Delhi; and to partially fulfil the requirement of first semester students of Delhi Technological University, Delhi; Jamia Miliya Islamiya University, Delhi, and other Indian and Foreign Engineering and Technological Institutions.
Contents
Preface
Syllabus
1. Complex Numbers
2. Infinite Series
3. Successive Differentiation
4. Expansion of Functions and Approximate Calculations
5. Asymptotes
6. Curvature
7. Curve Tracing
8. Integration
9. Area of Plane Curves (Quadrature)
10.Rectification
11.Volume and Surface of Solids of Revolutions
12.Matrices
13.Differential Equations
About the Author
Abhimanyu Singh has more than 13 years of teaching experience Engineering Mathematics to B.E. and B.Tech. Students at Delhi Technological University (formerly Delhi College of Engineering) and Guru Gobind Singh Indraprastha University, Delhi.




ENGINEERING MATHEMATICS  I  ABHIMANYU SINGH 

Cover Price : Rs 395.00

Imprint : Ane Books Pvt. Ltd. ISBN : 9789381162392 YOP : 2012

Binding : Paperback Total Pages : 584 CD : No


About the Book
This book covers a wide range of first and second semester syllabus in mathematics of various Indian Technological Universities and International Engineering and Technological Institutions. This book will provide a foundation in mathematical principles, which will enable students to solve mathematical, scientific and engineering problems. The text, has been presented in a simple and lucid manner, includes a large number of solved and unsolved problems.
Contents
UNITI: DIFFERENTIAL CALCULUSI
1. Successive Differentiation
2. Expansion of Functions and Approximate Calculations
3. Asymptotes
4. Curve Tracing
5. Partial Differentiation
UNITII : DIFFERENTIAL CALCULUS–II
6. Jacobians
7. Approximate Calculations of One and Two Variable Functions
8. Maxima/Minima
UNITIII : MATRICES
9. Matrices
UNITIV : MULTIPLE INTEGRALS
10.Double and Triple Integrals
11.Beta and Gama Functions, Dirichlet Integrals and Applications
UNITV : VECTOR CALCULUS
12.Vector Calculus
13.Integration of Vector Functions
Examination Paper 2007–11
About the Author
Abhimanyu Singh is currently working as an Assistant Professor in the Department of Mathematics, GGSIPU (affiliated institute), Delhi. He has more than 15 years of experience in teaching Engineering Mathematics to B.E. and B.Tech. students at Delhi Technological University (formerly Delhi College of Engineering) and Guru Gobind Singh Indraprastha University, Delhi. 



MATHEMATICAL ANALYSIS, INDIAN REPRINT  BERND S.W. SCHRODER (EX) 
Author 
BERND S.W. SCHRODER


Cover Price : Rs 3,495.00

Imprint : Wiley ISBN : 9788126542376 YOP : 2013

Binding : Hardback Total Pages : 578 CD : No


Mathematical Analysis: A Concise Introduction presents the foundations of analysis and illustrates its role in mathematics. By focusing on the essentials, reinforcing learning through exercises, and featuring a unique "learn by doing" approach, the book develops the reader's proof writing skills and establishes fundamental comprehension of analysis that is essential for further exploration of pure and applied mathematics. This book is directly applicable to areas such as differential equations, probability theory, numerical analysis, differential geometry, and functional analysis.
Mathematical Analysis is composed of three parts:
Part One presents the analysis of functions of one variable, including sequences, continuity, differentiation, Riemann integration, series, and the Lebesgue integral. A detailed explanation of proof writing is provided with specific attention devoted to standard proof techniques. To facilitate an efficient transition to more abstract settings, the results for single variable functions are proved using methods that translate to metric spaces.
Part Two explores the more abstract counterparts of the concepts outlined earlier in the text. The reader is introduced to the fundamental spaces of analysis, including Lp spaces, and the book successfully details how appropriate definitions of integration, continuity, and differentiation lead to a powerful and widely applicable foundation for further study of applied mathematics. The interrelation between measure theory, topology, and differentiation is then examined in the proof of the Multidimensional Substitution Formula. Further areas of coverage in this section include manifolds, Stokes' Theorem, Hilbert spaces, the convergence of Fourier series, and Riesz' Representation Theorem.
Part Three provides an overview of the motivations for analysis as well as its applications in various subjects. A special focus on ordinary and partial differential equations presents some theoretical and practical challenges that exist in these areas. Topical coverage includes NavierStokes equations and the finite element method.
Mathematical Analysis: A Concise Introduction includes an extensive index and over 900 exercises ranging in level of difficulty, from conceptual questions and adaptations of proofs to proofs with and without hints. These opportunities for reinforcement, along with the overall concise and wellorganized treatment of analysis, make this book essential for readers in upperundergraduate or beginning graduate mathematics courses who would like to build a solid foundation in analysis for further work in all analysisbased branches of mathematics.
Contents
Preface.
PART I. ANALYSIS OF FUNCTIONS OF A SINGLE REAL VARIABLE.
1. The Real Numbers.
2. Sequences of Real Numbers.
3. Continuous Functions.
4. Differentiable Functions.
5. The Riemann Integral I.
6. Series of Real Numbers I.
7. Some Set Theory.
8. The Riemann Integral II.
9. The Lebesgue Integral.
10.Series of Real Numbers II.
11.Sequences of Functions.
12.Transcendental Functions.
13.Numerical Methods
PART II. ANALYSIS IN ABSTRACT SPACES.
14.Integration on Measure Spaces.
15.The Abstract Venues for Analysis.
16.The Topology of Metric Spaces.
17.Differentiation in Normed Spaces.
18.Measure, Topology and Differentiation.
19.Introduction to Differential Geometry
20.Hilbert Spaces.
PART III. APPLIED ANALYSIS.
21.Physics Background.
22.Ordinary Differential Equations.
23.The Finite Element Method.
Conclusion and Outlook.
APPENDICES.
A.Logic.
A.1 Statements.
A.2 Negations.
B.Set Theory.
B.1 The ZermeloFraenkel Axioms.
B.2 Relations and Functions.
C.Natural Numbers, Integers and Rational Numbers.
C.1 The Natural Numbers.
C.2 The Integers.
C.3 The Rational Numbers.
Bibliography.
Index.
Bernd S.W. Schroder, PhD, is Edmondson/Crump Professor in the Program of Mathematics and Statistics at Louisiana Tech University. Dr. Schröder is the author of over thirty refereed journal articles on subjects such as ordered sets, probability theory, graph theory, harmonic analysis, computer science, and education. He earned his PhD in mathematics from Kansas State University in 1992.




Operations Research (Revised and Updated Edition)  J.P. Singh 
Author 
J.P. Singh N.P. Singh


Cover Price : Rs 550.00

Imprint : Ane Books Pvt. Ltd. ISBN : 9789380618128 YOP : 2017

Binding : Paperback Size : 6.25 Total Pages : 562 CD : No


About the Book
This book is written for courses like MBA, PGDM, M. Corn., MCA, BCA, B. Tech. BBA, BBA (CAM) and B. Sc. (Computers) for courses taught under titles as Management Science, Quantitative Methods, Introduction to Operations Research, Quantitative Techniques for Management, Quantitative Aids to Decision Making in GGSIPU, UPTU, MDU and other Indian Universities and BSchools.
Contents
1. Introduction, 2. Linear Programming: Formulation, 3. Linear Programming; The Graphical Method, 4. Linear Programming: The Simplex Method, 5. Duality and Sensitivity Analysis, 6. Transportation Problem, 7. Assignment Problem, 8. Decision Theory, 9. Game Theory, 10. Project Management: CPM and PERT, 11. Queuing Theory, 12. Replacement Models, 13. Sequencing Problem
About the Authors
JP Singh is a Professor in the Department of Mathematics at Jagan Institute of Management Studies (Affiliated to GGSIP University), Delhi. He has over 15 years of teaching experience in Operations Research, Discrete Mathematics, Numerical Methods, Mathematical Statistics and Calculus. He has taught at various affiliated institutes of GGSIPU. He has undergone rigorous training from IIT Delhi in Financial Mathematics. He is a certified Six Sigma Green belt from Indian Statistical Institute, Delhi. He is a lifetime member of the Indian Mathematical Society and Ramanujan Mathematical Society. His areas of interest include Operations Research, Mathematical Statistics, Stochastic Process, Numerical Methods, Number Theory, Discrete Mathematics and Theory of Computation.
NP Singh is a faculty in the Department of Management at Guru Nanak Institute of Management (GNIM), Delhi. He was awarded Gold Medal for securing top position in PGDM (Finance). He earned his M. Phil. (Finance) from University of Delhi. He has over 11 years of teaching experience in Operations Research, Business Statistics, Financial Management, Security Analysis and Portfolio management, International Financial Management and Derivatives and Risk Management. Teaching and research has been his core interests. He is also heading Centre for Research in Finance (CRIF) at GNIM. His research areas include Commodity and Financial Derivatives, Financial Modeling, Security Analysis and applications of Optimization Techniques in Finance. Some of his research papers have been published in journals of national repute. He has participated in research projects/CEP/workshops on topics like optimization methods, quantitative finance, financial modeling and risk management at institutes like IIM Calcutta, IIT Delhi and IIT Kharagpur.




Introduction to Matrix Theory  Arindama Singh 

Cover Price : Rs 995.00

Imprint : Ane Books Pvt. Ltd. ISBN : 9789386761200 YOP : 2018

Binding : Hardback Size : 6.25" X 9.50" Total Pages : 212 CD : No


About the Book
Keeping the modest goal as a text book on matrix theory the approach here is straight forward and quite elementary. Using elementary row operations and GramSchmidt orthogonalization as basic tools the text develops characterization of equivalence and similarity, and various factorizations such as rank factorization, ORfactorization, Schur triangularization, Diagonalization of normal matrices, Jordan decomposition, singular value decomposition and polar decomposition. Along with GaussJordan elimination for linear systems, it also discusses best approximations and least squares solutions_ It includes norms on matrices as a means to deal with iterative solutions of linear systems and exponential of a matrix. The topics are dealt with in a lively manner. Each section of the book has exercises to reinforce the concepts; and problems have been added at the end of each chapter. Most of these problems are theoretical in nature and they do not fit into the running text linearly. Exercises and problems form an integral part of the book.
Contents
1. Matrix Operations 2. Systems of Linear Equations 3. Subspace and Dimension 4. Orthogonality 5. Eigenvalues and Eigenvectors 6. Canonical Forms 7. Norms of Matrices, Short Bibliography, Index.
About the Author
Dr. Arindama Singh is currently Professor at the Department of Mathematics, IIT Madras. He has 27 years of teaching and research experience out of which last 22 years is at IIT Madras. He has guided 5 Ph.D, 4 M.Phil and 18 M.Sc. students so far. He has published 3 books, 36 articles in refereed Journals and 10 papers in refereed conference proceedings. His areas of interest and research are Logic, Theory of Computation and LinearAlgebra.




Mathematics for Chemistry  Quddus Khan 

Cover Price : Rs 1,995.00

Imprint : Ane Books Pvt. Ltd. ISBN : 9789386761712 YOP : 2018

Binding : Hardback Size : 6.25" X 9.50" Total Pages : 468 CD : No


About the Book
This textbook, Mathematics for Chemistry is written in accordance with the UGC model syllabus for the postgraduate students of chemistry of all Indian universities. It will also be useful for competitive examinations like IAS, PCS etc. The text starts with a chapter on preliminaries detailing the basic concepts and the results thereof that will be referred throughout the book. This is followed by an indepth study of matrix algebra, vector algebra, calculus (differential and integral), differential equations, permutation and combination, and theory of probability.
Some of the key features are: • Basics concepts presented in an easytounderstand style. • Includes a large number of solved examples • Notes and remarks given at appropriate places. • Clean and clear illustrations/figures for better understanding • Exercise questions at the end of each Chapter
Contents
1. Preliminaries 2. Matrix Algebra 3. Vector Algebra 4. Differential Calculus 5. Integral Calculus 6. Elementary Differential Equations 7. Permutation and Combination 8. Theory of Probability, Bibliography, Index
About the Author
Dr. Quddus Khan is Associate Professor in the Department of Applied Science and Humanities, Faculty of Engineering and Technology, Jamia Millia Islamia, New Delhi. He has been teaching UG & PG classes for the last eighteen years. He had also taught in Shibli National R G. College, Azamgarh (U.P.). He had also worked as a Young Scientist (PDF) in the Department of Mathematics, Faculty of Natural Science, Jamia Millia Islamia, New Delhi. Dr. Khan has to his credit 20 research papers on differentiable manifolds published in various national and international journals, five books on D.G. of manifolds, D.G. and its Application, Tensor analysis and its Application, Fundamental Concepts of recurrent manifold and Sasakian manifold and fundamental concept of symmetric manifold and Sasakian manifold and has also supervised two PhDs.




Essentials of Business Statistics  B.M.Aggarwal 

Cover Price : Rs 495.00

Imprint : Ane Books Pvt. Ltd. ISBN : 9789381162736 YOP : 2014

Binding : Paperback Total Pages : 800 CD : No


About the Book
The book has been designed specifically to meet the requirements of all the students pursuing undergraduate studies in commerce. The book will serve equally well for the undergraduate management courses like BBA, BBE, etc.
Salient features:
1. The treatment of the subject is conceptual and easily graspable even by average students.
2. A large variety of questions as solved examples have been selected from the question papers of equivalent examinations of different universities to apprise the students about the varying trends.
3. A large number of unsolved questions have been given at the end of each chapter for practice.
4. Numerous MCQs have been given at the end of each chapter for better conceptual understanding of the subject.
5. Keeping in view the wide applications, special emphasis has been given in detailed explanation of
concepts and in normal distribution with separate tables.
6. Some unique features and their details have been added in rank correlation.
Contents
1. Statistical Averages (Measures of Central Tendency)
2. Measures of Variation
3. Moments, Skewness
and Kurtosis
4. Probability and Mathematical Expectation
5. Probability Distribution (Theoretical
Distribution)
6. Decision Theory
7. Correlation and Regression Analysis Correlation
8. Index Numbers
9. Time Series
About the Author
B.M. Aggarwal, B.Sc. (Hons.) from Punjab University, later graduated from the Institute of Electronics and Telecommunication Engineers, New Delhi. He did his M.Sc (Mathematics) from Merrut University. In addition, he passed certificate courses in Microwave and Satellite Engineering from ALT Centre,Ghaziabad.
The author is a visiting professor in quantitative techniques, operations research and research methods in various premier Institutes like IMT Ghaziabad, ICFAI Gurgaon, Asia Pacific Institutes of Management, Delhi besides several other Institutes. He has been in the field of books, from 1986 onwards, and has many books to his credit.




Calculus of Variations, Applications and Computations  C. Bandle (EX) 
Author 
C Bandle J Bemelmans M Chipot J Paulin


Cover Price : Rs 4,995.00

Imprint : CRC / Lewis ISBN : 9780582239623 YOP : 2014

Binding : Hardback Total Pages : 294 CD : No


ABOUT THIS VOLUME
This Research Note presents some recent advances in various important domains of partial differential equations and applied mathematics including calculus of variations, control theory, modelling, numerical analysis and various applications in physics, mechanics and engineering.
These topics are now part of various areas of science and have experienced tremendous development during the last decades.
Readership: This book should interest not only experts in partial differential equations but also graduate students, applied mathematics and computer users.
PITMAN RESEARCH NOTES IN MATHEMATICS SERIES
The aim of this series is to disseminate important new material of a specialist nature in economic form. It ranges over the whole spectrum of mathematics and also reflects the changing momentum of dialogue between hitherto distinct areas of pure and applied parts of the discipline.
The editorial board has been chosen accordingly and will from time to time be recomposed to represent the full diversity of mathematics as covered by Mathematical Review.
This is a rapid means of publication for current material whose style of exposition is that of a developing subject. Work that is in most respects final and definitive, but not yet refined into a formal monograph. Will also be considered for a place in the series. Normally homograph, material is required, even if written by more than one author, thus multiauthor works will be included provided that there is a strong linking theme or editorial pattern.
Contents
Preface
Isoperimetric Inequalities for a Generalized Multidimensional Muskat Problem
Solution of a Free Boundary Problem of the HeleShaw Type, in the Ovsjannikov Scales
Continuous Polarization and Symmetry of Solutions of Variational Problems with Potentials
An Optimal Control Problem for a Nonlinear Elliptic Equation Arising from Population Dynamics
Global existence of Functional Solutions for the VlasovPoissonFokkerPlanck System in 3 D with Bounded Measures as Initial Data
Numerical Methods for a Forward Backward Heat Equation
On a Dirichlet Problem Related to the Invertibility of Mappings Arising in 2D Grid Generation
On Rank One Convex Functions Which are Homogeneous of Degree One
On the Approximation of the Curve Shortening Flow
Flows Through Saturated Mass Exchanging Porous Media Under High Pressure Gradients
Existence of Nontrivial Solutions to the MarguerreVon Karman Equations,
Quasiconvex Envelopes of Stored Energy Densities that are Convex with Respect to the Strain Tensor
Application of Quasi Steady Solutions of Soil Freezing for Geotechnical Engineering
Curvature Driven Interface Motion
Discretization of Second Order Elliptic Differential Equations on Sparse Grids
Hydrodynamic stability and a Posterior Error Control in the Solution of the NavierStokes Equations
Partial Regularity for Incompressible Materials with Approximation Methods
A Note About Relaxation of Vectorial Variational Problems
Numerical Simulation of Boundary Layer Problem with Separation
Maximal Inequalities and Applications to Regularity Problems in the Calculus of Variations
Critical Points for Pairs of Functionals and Semilinear Elliptic Equations
Front Propagation in Diffusion Problems on Trees
A Gamma Limit Approach for Viscosity Stationary Solutions of a Model Convection Equation 



Nonlinear Partial Differential Equations and Their Application  D.Cioranescu (EX) 
Author 
D Cioranescu J.L. Lions


Cover Price : Rs 4,995.00

Imprint : CRC / Lewis ISBN : 9780582369269 YOP : 2014

Binding : Hardback Total Pages : 352 CD : No


ABOUT THIS VOLUME
This book contains the texts of selected lectures delivered by leading international experts at the wellestablished weekly seminar held at the College de France. The main theme of the Seminar is recent work in the field of nonlinear partial differential equations – a field of growing importance, both in pure and applied mathematics. The emphasis is laid on applications to numerous areas, including control theory, theoretical physics, fluid and continuum mechanics, free boundary problems, dynamical systems, scientific computing, numerical analysis and engineering. Volume XIII of the College de France Seminar proceedings will be of particular interest to postgraduate students and specialists in these areas.
PITMAN RESEARCH NOTES IN MATHEMATICS SERIES
The aim of this series is to disseminate important new material of a specialist nature in economic form. It ranges over the whole spectrum of mathematics and also reflects the changing momentum of dialogue between hitherto distinct areas of pure and applied parts of the discipline.
The editorial board has been chosen accordingly and will from time to time be recomposed to represent the full diversity of mathematics as covered by Mathematical Review.
This is a rapid means of publication for current material whose style of exposition is that of a developing subject. Work that is in most respects final and definitive, but not yet refined into a formal monograph. Will also be considered for a place in the series. Normally homograph, material is required, even if written by more than one author, thus multiauthor works will be included provided that there is a strong linking theme or editorial pattern.
Contents
Preface
A Nonlinear LaxMilgram Lemma Arising in the Modeling of Elastomers.
Regularity for Solutions to the Equation of Surfaces of Prescribed Mean Curvature Using the Coarea Formula.
HConvergence for Perforated Domains.
Some Mathematical Problems in Marine Modelling.
A Modelling of the Stability of Aluminium Electrolysis Cells.
Dense Oscillations for the Compressible 2d Euler Equations.
The Hysteretic Event in the Computation of Magnetism and Magnetostriction.
From ThreeDimensional Elasticity to the Nonlinear Membrane Model.
Turbulence et structures cohérentes dans les fluides.
Construction d'une base spéciale pour la résolution de quelques problèmes non linéaires d'Oceanographie physique en dimension deux.
Homogenization of LatticeLike Domains: LConvergence.
Time Decays: An Analogy between Kinetic Transport, Schrödinger and Gas Dynamics Equations.
Théorème d'unicité et contrôle pour les équations hyperboliques.
Shock Waves in General Relativity  A Generalization of the OppenheimerSnyder Model for Gravitational Collapse.
Nonlinear Wave Equations.
Mathematical Models of Hysteresis  A Survey.




Ordinary and Partial Differential Equations, Indian Reprint 2014  B.D.Sleeman (EX) 
Author 
B.D. Sleeman R.J. Jarvis


Cover Price : Rs 4,995.00

Imprint : CRC / Lewis ISBN : 9780582091375 YOP : 2014

Binding : Hardback Total Pages : 304 CD : No


ABOUT THIS VOLUME
This volume arises from the twelfth Dundee Conference on Ordinary and Partial differential Equations held at the University of Dundee in June 1992. It contains papers by a number of experts. Special emphasis is given to recent developments in the asymptotic behaviour of solutions to differential equations, scattering theory and neural system. Of particular note is a comprehensive survey of major contributions to the study of counting function asymptotics for fractal domains.
Topics covered include direct and inverse scattering problems, asymptotic expansions and Stokes phenomenon, the Wey IBerry conjecture, pattern generation in neural systems, reactive transport and dispersal of waste, and integral inequalities.
Readership: Graduate students and research workers in the theory of ordinary and partial differential equations, nonlinear analysis, applied mathematics and mathematical biology.
PITMAN RESEARCH NOTES IN MATHEMATICS SERIES
The aim of this series is to disseminate important new material of a specialist nature in economic form. It ranges over the whole spectrum of mathematics and also reflects the changing momentum of dialogue between hitherto distinct areas of pure and applied parts of the discipline.
The editorial board has been chosen accordingly and will from time to time be recomposed to represent the full diversity of mathematics as covered by Mathematical Review.
This is a rapid means of publication for current material whose style of exposition is that of a developing subject. Work that is in most respects final and definitive, but not yet refined into a formal monograph. Will also be considered for a place in the series. Normally homogeneous, material is required, even if written by more than one author, thus multiauthor works will be included provided that there is a strong linking theme or editorial pattern.
Contents
Preface
The effect of nonlinearity on the scattering of sound by lightly loaded thin elastic structures, I D Abrahams
Analytic and numerical aspects of the HELP integral inequality, W N Everitt
Some reactive transport, dispersal and flow problems associated with geological disposal of radioactive waste, P Grindrod
Central pattern generators in neural systems, oscillations, bifurcations and coupled nonlinear oscillators, A V Holden and Julie Hyde
Numerical algorithms in inverse scattering theory, A Kirsch
Asymptotic series and remainders, D S Jones
Vibrations of fractal drums, the Riemann hypothesis, waves in fractal media and the WeylBerry conjecture, M L Lapidus
Fourier Asymptotics, J Lighthill
Inverse Fourier asymptotics, J Lighthill
Exponentiallyimproved asymptotic solutions of ordinary differential equations, F W J Olver
Scattering from unbounded surfaces, G F Roach




Introduction to Mathematical Population Dynamics  Mimmo Iannelli 
Author 
Mimmo Iannelli Andrea Pugliese


Cover Price : Euro 59.99

Imprint : Springer ISBN : 9783319030258 YOP : 2014

Binding : Paperback Total Pages : 356 CD : No


This book is an introduction to mathematical biology for students with no experience in biology, but who have some mathematical background. The work is focused on population dynamics and ecology, following a tradition that goes back to Lotka and Volterra, and includes a part devoted to the spread of infectious diseases, a field where mathematical modeling is extremely popular. These themes are used as the area where to understand different types of mathematical modeling and the possible meaning of qualitative agreement of modeling with data. The book also includes a collections of problems designed to approach more advanced questions. This material has been used in the courses at the University of Trento, directed at students in their fourth year of studies in Mathematics. It can also be used as a reference as it provides uptodate developments in several areas.
CONTENTS
Part I The growth of a single population
1 Malthus, Verhulst and all that
2 Population models with delays
3 Models of discretetime population growth
4 Stochastic modeling of population growth
5 Spatial spread of a population
Part II Multispecies Models
6 Predatorprey models
7 Competition among species
8 Mathematical modeling of epidemics
9 Models with several species and trophic levels
Appendix A. Basic theory of Ordinary Differential Equations
Appendix B. Delay Equations
Appendix C. Discrete dynamics
Appendix D. Continuoustime Markov chains
References 



Primer of Algebraic Geometry, Indian Reprint  Huishi Li (EX) 
Author 
Huishi Li Freddy Van Oystaeyen


Cover Price : Rs 4,995.00

Imprint : CRC Press ISBN : 9780824703747 YOP : 2015

Binding : Hardback Total Pages : 384 CD : No


About the Book
Written for senior undergraduate and firstyear graduate students, as well as a refresher for seasoned mathematicians, A Primer of Algebraic Geometry presents a systematic treatment of elementary algebraic geometry, offering algebraic structure theory in an "effective" way  covering dimension theory for varieties that agree with the use of the Zariski topology.
Emphasizing the new Groebner basis method that relies on the ordered ideal structure theory in polynomial rings and the Weierstrass theory of elliptic curves, topics in A Primer of Algebraic Geometry range from polynomials and affine space to radical ideals and the Nullstellensatz, from the Zariski topology and irreducible algebraic sets to rational functions and local rings. From projective space to multiprojective space and Segre product, from monomial orderings to Hilbert basis theorem and Groebner basis, from the algebraic set of a monomial ideal to the topological dimension of an affine algebraic set, from regular functions on varieties to nonsingular points in algebraic sets from nonsingular curves to the RiemannRoch theorem, from the standard form of a cubic nonsingular curve to elliptic functions and Weierstrass theory, and more.
"A selfcontained resource complete with exercises in each section, a Primer of Algebraic Geometry is a reference for pure and applied mathematicians, algebraists, number theorists, algebraic geometers, and computer scientists, and an out standing text for upperlevel undergraduate and graduate students with an interest in computer algebra, robotics and computational geometry, theoretical computer science, and mathematical methods of technology.
Contents
Ch. I. Affine Algebraic Sets and the Nullstellensatz
Ch. II. Polynomial and Rational Functions
Ch. III. Projective Algebraic Sets
Ch. IV. Groebner Basis
Ch. V. Dimension of Algebraic Sets
Ch. VI. Introduction to Local Theory
Ch. VII. Curves
Ch. VIII. Elliptic Curves
App. I. Finiteness Conditions and Field Extensions
App. II. Localization, Discrete Valuation Rings and Dedekind Domains.
References
Index
About the Authors
Huishi Li is Assistant Professor of Mathematics at Bilkent University, Turkey. Previously he was Professor of Mathematics at the Shaanxi Normal University, People’s Republic of China. The author or coauthor of several articles, he is coauthor with Professor Van Oystaeyen of Zariskian Filtrations. Dr. Li received the Ph.D degree (1990) in mathematics from the University of Antwerp /UIA, Belgium.
Freddy Van Oystaeyen is a Professor of Mathematics at the University of Antwerp/UIA in Belgium. The author, coauthor, editor, or coeditor of over 200 articles, proceedings. Book chapters, and books, including Brauer Groups and the Cohomology of Graded Rings and Commutative Algebra and Algebraic Geometry (both titles, Marcel Dekker, Inc.), he is a board member of the Belgium Mathematical Society. Professor Van Oystaeyen received the Ph.D.degree (1972) in mathematics from the free University of Amsterdam, The Netherlands, and the Habilitation degree (1975) from the University of Antwerp/UIA, Belgium.




Topological Vector Spaces,2nd ed, Indian Reprint  Lawrence Narici (EX) 
Author 
Lawrence Narici Edward Beckenstein


Cover Price : Rs 4,995.00

Imprint : CRC Press ISBN : 9781584888666 YOP : 2015

Binding : Hardback Total Pages : 628 CD : No


With many new concrete examples and historical notes, Topological Vector Spaces, Second Edition provides one of the most thorough and uptodate treatments of the Hahn–Banach theorem. This edition explores the theorem’s connection with the axiom of choice, discusses the uniqueness of Hahn–Banach extensions, and includes an entirely new chapter on vectorvalued Hahn–Banach theorems. It also considers different approaches to the Banach–Stone theorem as well as variations of the theorem.
The book covers locally convex spaces; barreled, bornological, and webbed spaces; and reflexivity. It traces the development of various theorems from their earliest beginnings to present day, providing historical notes to place the results in context. The authors also chronicle the lives of key mathematicians, including Stefan Banach and Eduard Helly.
Features
 Provides extensive coverage of the HahnBanach and BanachStone theorems
 Discusses the evolution of the HahnBanach theorem and Eduard Helly’s considerable contribution to it.
 Presents historical notes on the development of many important theorems and the people who discovered and proved them, including The Scottish Café group
 Includes numerous endofchapter exercises, a broad spectrum of examples, and detailed proofs
Suitable for both beginners and experienced researchers, this book contains an abundance of examples, exercises of varying levels of difficulty with many hints, and an extensive bibliography and index.
Contents
Background
Commutative Topological Groups
Completeness
Topological Vector Spaces
Locally Convex Spaces and Seminorms
Bounded Sets
Hahn–Banach Theorems
Duality
Krein–Milman and Banach–Stone Theorems
VectorValued Hahn–Banach Theorems
Barreled Spaces
Inductive Limits
Bornological Spaces
Closed Graph Theorems
Reflexivity
Norm Convexities and Approximation
Bibliography
Index




Number Theory, Indian Reprint, Don Redmond (EX) 

Cover Price : Rs 4,995.00

Imprint : CRC Press ISBN : 9780824796969 YOP : 2015

Binding : Hardback Total Pages : 764 CD : No


About the Book…
This reference/text provides a detailed introduction to number theory and demonstrates how other areas of mathematics enter into the study of the properties of natural numbers.
Offering helpful problem sets within each section and at the end of each chapter to reinforce essential concepts, Number Theory contains uptodate information on divisibility properties…. polynomial congruence, the sums of squares and trigonometric sum… Diophantine approximation …the behavior of prime numbers….algebraic number fields…and more.
Furnishing a useful bibliography, allowing reader to further investigate the results presented, Number Theory is an ideal reference for research mathematicians in terested in algebra and number theory, and a valuable text for upperlevel undergraduate and graduate students in these disciplines.
Contents
Preface
A Historical Introduction
Primes and Divisibility
Congruences
Quadratic Residues
Approximation of Real Numbers
Diophantine Equations I
Diophantine Equations II
Arithmetic Functions
The Average Order of Arithmetic Functions
Prime Number Theory
An Introduction to Algebraic Number Theory.
Tables
Bibliography
Index
About the Author
Don Redmond is an Associate Professor in the Mathematics Department at Southern Illinois university at Carbondale. Dr. Redmond is a member of the American Mathematical Society, the Mathematical Association of America, the National Council of Teachers of Mathematics, and Sigma Xi. He received the Ph.D degree (1976) in mathematics from the University of Illinois at Urbana Champaign. 



Introduction to Fourier Series, Indian Reprint  Rupert Lasser (EX) 

Cover Price : Rs 4,995.00

Imprint : CRC Press ISBN : 9780824796105 YOP : 2015

Binding : Hardback Total Pages : 294 CD : No


This concise, selfcontained reference/text addresses all of the major topics in Fourier series  emphasizing the concept of approximate identities; presenting applications, particularly in time series analysis; stressing throughout the idea of homogeneous Banach spaces; and providing new results.
Utilizing techniques from functional analysis and measure theory, Introduction to Fourier Series furnishes representation theorems such as Herglotz's theorem and Wiener's theorem...compares the performance of approximate identities with elements of best approximation...develops results on spectral synthesis applying Banach algebra techniques...derives characterizations of absolute convergence of Fourier series...studies Fourier and Plancherel transformations on the real axis establishing the relation to Fourier series using the Poisson summation formula...and more.
Written by an internationally recognized expert, Introduction to Fourier Series is an incomparable reference for pure and applied mathematicians and signal processing engineers and the text of choice for all upperlevel undergraduate and graduate students taking courses in Fourier analysis, harmonic analysis, or approximation theory with a basic knowledge of real and abstract analysis.
Contents
Fourier Coefficients
Approximate Identities
Approximate Identities and Pointwise Convergence
Square Integrable Functions
Convergence of Fourier Series in Norm
Local Convergence
Characterization of Fourier Coefficients
Hilbert Transform
Characterizations Of Approximate Identities.
Triangular Schemes
Elements of Best Approximation
Poisson Integrals and Hardy Spaces
Conjugation of Approximate Identities
SzegoKolmogorivTheorem
Absolute convergence of Fourier series
Fourier Transform on R
Plancherel Transform on R
Poisson Summation Formula
Appendices
Appendix A: Measure Theory
Appendix B: Banach Spaces
Appendix C: Banach Algebras
Referemces
Index




Differential Forms on Singular Varieties, Indian Reprint  Vincenzo Ancona (EX) 
Author 
Vincenzo Ancona Bernard Gaveau


Cover Price : Rs 4,995.00

Imprint : CRC Press ISBN : 9780849337390 YOP : 2015

Binding : Hardback Total Pages : 332 CD : No


The cohomology of a singular complex space cannot carry a pure hodge structure
it must be a mixed Hodge structure, wherein the weight filtration of Deligne and Grothendieck induces a graduation on the cohomology, and each quotient space of the graduation carrier a pure Hodge structure. While it is relatively easy to explain the mixed Hodge structure on the cohomology of an algebraic manifold it is not so straightforward for a singular space. The weight filtration constructured by Deligne using the “descente cohomologique” make it difficult to see how the mixed Hodge structure is made.
Differential Forms on Singular Varieties: De Rham and Hodge Theory Simplified uses complexes of differential forms to give a complete treatment of the Deligne theory of mixed Hodge structures on the cohomology of singular spaces. This book features an approach that employs recursive arguments on dimension and does not introduce spaces of higher dimension than the initial space. It simplifies the theory through easily identifiable and welldefined weight filtration, and to maintain accessibility,It also avoids discussion of cohomological descent theory. The treatment is selfcontained and brings together information that allows readers to follow and understand this difficult but important subject without jumping from one reference to another.
Features
 Provides a clear, selfcontained treatment of classical Hodge theory on manifolds, including complex manifolds, Khaeler manifolds, and De Rham theory
 Offers a particularly elegant explanation to the singular analogue of De Rham theory on manifolds
 Summarizes topics such as sheaf theory, cohomology, and complex spaces, important in many branches of mathematics
 Features an approach to mixed Hodge structures that employs recursive arguments on dimension
Contents
Classical Hodge Theory.
Spectral Sequences and Mixed Hodge Structures.
Complex Manifolds, Vector Bundles, Differential Forms.
Sheaves and Cohomology.
Harmonic Forms on Hermitian Manifolds.
Hodge Theory on Compact Kählerian Manifolds.
The Theory of Residues on a Smooth Divisor.
Complex Spaces.
Differential Forms on Complex Spaces.
The Basic Example.
Differential Forms in Complex Spaces.
Mixed Hodge Structures on Compact Spaces.
Mixed Hodge Structures on Noncompact Spaces.
Residues and Hodge Mixed Structures: Leray Theory.
Residues and Mixed Hodge Structures on Noncompact Manifolds.
Mixed Hodge Structures in Noncompact Spaces: The Basic Example.
Mixed Hodge Structures on Noncompact Singular Spaces.
References
Vincenzo Ancona is a professor in the Department of Mathematics, University of Firenze, Italy.
Bernard Gaveau is a professor in the Department of Mathematics, University Pierre et Marie Curie, Paris, France.




Elements of Real Analysis, Indian Reprint  M.A.AlGwaiz (EX) 

Cover Price : Rs 4,995.00

Imprint : CRC Press ISBN : 9781584886617 YOP : 2015

Binding : Hardback Total Pages : 450 CD : No


Focusing on one of the main pillars of mathematics, Elements of Real Analysis provides a comprehensive introduction to analysis on the real line, The book prepares you for conducing analysis in higher dimensions and more abstract spaces by building up the analytical skills and structures needed for handling the basic notions of limits and continuity in a simple concrete setting.
Largely selfcontained, the book begins with the fundamental axioms of the real number system and gradually develops the core of real analysis. The first few chapters present the essentials needed for analysis, including the concepts of sets, relations, and functions. The following chapters cover the theory of calculus on the real line, addressing theorems like mean value, inverse function, Taylor’s, and weierstrass approximation. The final chapters focus on the more advanced theory of Lebesgue measure and integration.
Requiring only basic knowledge of elementary calculus, this book presents the necessary material for students and professionals in various mathematics related fields, such as engineering, statistics, computer science, to explore real analysis.
Features
 Presents a foundation in real analysis, starting with the basics and gently progressing to more computer topics
 Covers the real number system, sequences, and infinite series
 Explores functions, limits, continuity, differentiability, and integration, including Riemann integrals
 Includes sequences and series of functions and their modes of convergence, naturally building on the properties of numerical sequences and series
 Provides an introduction to advanced probability and stochastic theory by including two chapters on Lebesgue and integration
Contents
Preface
preliminaries
Real Numbers
Sequences
Infinite Series
Limit of a Function
Continuity
Differentiation
The Riemann Integral
Sequences and Series of Functions
Lebesgue Measure
Lebesgue Integration
References
notation
Index
M.A.AlGwaiz and S.A.Elsanousi are mathematics professors at King Saud University, Riyadh, Saudi Arabia.




Algorithmic Lie Theory for Solving Ordinary Differential Equations , Indian Reprint  Fritz Schwarz (EX) 

Cover Price : Rs 4,995.00

Imprint : CRC Press ISBN : 9781584888895 YOP : 2015

Binding : Hardback Total Pages : 444 CD : No


Despite the fact that Sophus Lie's theory was virtually the only systematic method for solving nonlinear ordinary differential equations (ODEs), it was rarely used for practical problems because of the massive amount of calculations involved. But with the advent of computer algebra programs, it became possible to apply Lie theory to concrete problems. Taking this approach, Algorithmic Lie Theory for Solving Ordinary Differential Equations serves as a valuable introduction for solving differential equations using Lie's theory and related results.
After an introductory chapter, the book provides the mathematical foundation of linear differential equations, covering Loewy's theory and Janet bases. The following chapters present results from the theory of continuous groups of a 2D manifold and discuss the close relation between Lie's symmetry analysis and the equivalence problem. The core chapters of the book identify the symmetry classes to which quasilinear equations of order two or three belong and transform these equations to canonical form. The final chapters solve the canonical equations and produce the general solutions whenever possible as well as provide concluding remarks. The appendices contain solutions to selected exercises, useful formulae, properties of ideals of monomials, Loewy decompositions, symmetries for equations from Kamke's collection, and a brief description of the software system ALLTYPES for solving concrete algebraic problems.
Features
 Explores two fundamental additions to Lie theory: Loewy’s theory of linear ODEs and Janet’s theory of linear PDEs
 Discusses the close connection between Lie symmetries and closed form solutions
 Includes numerous worked examples and problems, along with detailed solutions in an appendix
 Provides a website that contains the software for performing lengthy algebraic calculations
Contents
INTRODUCTION
LINEAR DIFFERENTIAL EQUATIONS
Linear Ordinary Differential Equations
Janet's Algorithm
Properties of Janet Bases
Solving Partial Differential Equations
LIE TRANSFORMATION GROUPS
Lie Groups and Transformation Groups
Algebraic Properties of Vector Fields
Group Actions in the Plane
Classification of Lie Algebras and Lie Groups
Lie Systems
EQUIVALENCE AND INVARIANTS OF DIFFERENTIAL EQUATIONS
Linear Equations
Nonlinear FirstOrder Equations
Nonlinear Equations of Second and Higher Order
SYMMETRIES OF DIFFERENTIAL EQUATIONS
Transformation of Differential Equations
Symmetries of FirstOrder Equations
Symmetries of SecondOrder Equations
Symmetries of Nonlinear ThirdOrder Equations
Symmetries of Linearizable Equations
TRANSFORMATION TO CANONICAL FORM
FirstOrder Equations
SecondOrder Equations
Nonlinear ThirdOrder Equations
Linearizable ThirdOrder Equations
SOLUTION ALGORITHMS
FirstOrder Equations
SecondOrder Equations
Nonlinear Equations of Third Order
Linearizable ThirdOrder Equations
CONCLUDING REMARKS
A: Solutions to Selected Problems
B: Collection of Useful Formulas
C: Algebra of Monomials
D: Loewy Decompositions of Kamke's Collection
E: Symmetries of Kamke's Collection
F: ALLTYPES Userinterface
REFERENCES
INDEX




Weakly Connected Nonlinear Systems, Indian Reprint  Anatoly Martynyuk (EX) 

Cover Price : Rs 3,995.00

Imprint : CRC Press ISBN : 9781466570863 YOP : 2015

Binding : Hardback Total Pages : 228 CD : No


Weakly Connected Nonlinear Systems: Boundedness and Stability of Motion provides a systematic study on the boundedness and stability of weakly connected nonlinear systems, covering theory and applications previously unavailable in book form. It contains many essential results needed for carrying out research on nonlinear systems of weakly connected equations.
After supplying the necessary mathematical foundation, the book illustrates recent approaches to studying the boundedness of motion of weakly connected nonlinear systems. The authors consider conditions for asymptotic and uniform stability using the auxiliary vector Lyapunov functions and explore the polystability of the motion of a nonlinear system with a small parameter. Using the generalization of the direct Lyapunov method with the asymptotic method of nonlinear mechanics, they then study the stability of solutions for nonlinear systems with small perturbing forces. They also present fundamental results on the boundedness and stability of systems in Banach spaces with weakly connected subsystems through the generalization of the direct Lyapunov method, using both vector and matrixvalued auxiliary functions.
Designed for researchers and graduate students working on systems with a small parameter, this book will help readers get up to date on the knowledge required to start research in this area.
Contents
Preface
Acknowledgments
Preliminaries
Introductory Remarks
Fundamental Inequalities
Stability in the Sense of Lyapunov
Comparison Principle
Stability of Systems with a Small Parameter
Comments and References
Analysis of the Boundedness of Motion
Introductory Remarks
Statement of the Problem
μBoundedness with Respect to Two Measures
Boundedness and the Comparison Technique
Boundedness with Respect to a Part of Variables
Algebraic Conditions of μBoundedness
Applications
Comments and References
Analysis of the Stability of Motion
Introductory Remarks
Statement of the Problem
Stability with Respect to Two Measures
Equistability via Scalar Comparison Equations
Dynamic Behavior of an Individual Subsystem
Asymptotic Behavior
Polystability of Motion
Applications
Comments and References
Stability of Weakly Perturbed Systems
Introductory Remarks
Averaging and Stability
Stability on a Finite Time Interval
Methods of Application of Auxiliary Systems
Systems with Nonasymptotically Stable Subsystems
Stability with Respect to a Part of Variables
Applications
Comments and References
Stability of Systems in Banach Spaces
Introductory Remarks
Preliminary Results
Statement of the Problem
Generalized Direct Lyapunov Method
μStability of Motion of Weakly Connected Systems
Stability Analysis of a TwoComponent System
Comments and References
Bibliography
Index




Measure Theory and Integration, Indian Reprint  M.M.Rao (EX) 

Cover Price : Rs 4,995.00

Imprint : CRC Press ISBN : 9780824754013 YOP : 2015

Binding : Hardback Total Pages : 782 CD : No


About the Book…
Significantly revised and expanded, this authoritative reference/text comprehensively describes concepts in measure theory, classical integration, and generalized Riemann integration of both scalar and vector typesproviding a complete and detailed review of every aspect of measure and integration theory using offering valuable examples, exercises, and applications.
Examines the HenstockKurzweil integral with approaches not found in any other text.
With more than 170 references for further investigation of the subject, this Second Edition provides more than 60 pages of new information, including a new chapter on nonabsolute integrals…contains extended discussions on the four basic results of Banach spaces… presents an indepth analysis of the classical integrals with many applications, including integration of nonmeasurable functions, Lebesgue spaces, and their properties… details the basic properties and extensions of the LebesgueCaratheaodory measure theory, as well as the structure and convergence of real measurable functions…and covers the Stone isomorphism theorem, the lifting theorem, the Daniell method of integration, and capacity theory
Contents
Preface to the Second Edition
Preface to the First Edition
Introduction and Preliminaries
Measurability and Measures
Measurable Functions
Classical Integration
Differentiation and Duality
Product Measures and Integrals
Nonabsolute Integration
Capacity Theory and Integration
The Lifting Theorem
Topological Measures
Some Complements and Applications
Appendix
References
Index of Symbols and Notation
Author Index
Subject Index
About the Autor…
M.M.Rao is Professor of Mathematics, University of California, Riverside, The author, coauthor, editor, or coeditor of numerous professional papers, monographs, and books, including Applications of Orlicz Spaces, Theory of Orlicz Spaces, and Conditional Measures and Applications (all titles, Marcel Dekker, Inc.), he is a Fellow of the Institute of Mathematical Statistics and the American Association for the Advancement of Science and a member of the American Mathematical Society and the International Statistical Institute. He received the B.A.degree (1949) from Andhra University, India, the M.A.(1952) and M.Sc. (1955) degrees from the University of Madras, India, and the Ph.D.degree (1959) from the University of Minnesots, Minneaplis.




C*Algebras and Numerical Analysis, Indian Reprin  Ronald Hagen (EX) 
Author 
Roland Hagen Steffen Roch Bernd Silbermann


Cover Price : Rs 4,995.00

Imprint : CRC Press ISBN : 9780824704605 YOP : 2015

Binding : Hardback Total Pages : 384 CD : No


This book examines the relationship between C*algebras and numerical analysis; discusses fractalitycovering asymptotic properties of approximation operators, such as stability, regularizability behavior of condition numbers, eigenvalues, pseudoeigen values, singular values, and Rayleigh quotients; and describes fredholmness focusing on algebras that arise from concrete approximation methods.
Featuring more than 1000 mathematical expressions, C* Algebras and Numerical Analysis presents Arveson’s results culminating in a generalization of the Szego limit theorem… introduces kernel and cokernel dimension for approximation sequences… outlines the lifting theorem and the structure of fractal lifting homomorphisms studies piecewise continuous and quasicontinuous coefficients … details polynomial collocation and finite sections of band dominated … considers spectra, pseudospectra, numerical ranges and their limiting sets… spotlights MoorePenrose inverses and regularization of matrices and operators… surveys finite sections to Toeplitz operators… and more.
Contents
Preface
Introduction
 The algebraic language of numerical analysis
 Regularization of approximation methods
 Approximation of spectra
 Stability analysis for concrete approximation methods
 Representation theory
 Fredholm sequences
 Selfadjoint approximation sequences
Bibliography
Index
About the Author
Ronald Hagen Is Teacher of Mathematics at Freies Gymnasium Penig, Penig, Germany, The author or coauthor of over 20 professional publications. Dr. Hagen received the Diploma in mathematics and the Teacher’s Diploma (1976 ) from the State University, Odessa, Russia, and the Ph.D. degree from the Teachnische Hochschule, KarlMarxStadt, Germay.
Steffen Roch is a Lectures at the Technical University of Darmastadt, Germany, The author or coauthor of over 50 peerreviewed articles, Dr. Roch received the Diploma in mathematics (1982) and the Ph.D. degree (1988) from the Technische Hochschule, KarlMarxStadt, Germany, and the Habilitation (1992) from the Technical University, Chemnitz, Germany.
Bernd Silbermann is Professor of Mathematics, Technical University, Cheminitz, Germany. The coauthor of six monographs in operator theory and numerical analysis, Dr. Silbermann received the Diploma in mathematics (1967) from Lomonossov University, Moscow, Russia, and the Ph.D. degree (1970) and Habilitation (1974) from the Technische Hochschule,KarlMarxStadt, Germany. 



Matrix Theory, Indian Reprint  Robert Piziak (EX) 
Author 
Robert Piziak P.L. Odell


Cover Price : Rs 4,995.00

Imprint : CRC Press ISBN : 9781584886259 YOP : 2015

Binding : Hardback Total Pages : 568 CD : No


Highlighting the generalized inverse of a matrix and the method of full rank factorization, Matrix Theory: From Generalized Inverses to Jordan Form probes introductory as well as more sophisticated linear algebra concepts. This presentation helps connect linear algebra to more advanced abstract algebra and matrix theory.
The book first focuses on the central problem of linear algebra: solving systems of linear equations. It then discusses LU factorization, derives Sylvester's rank formula, introduces fullrank factorization, and describes generalized inverses, including the MoorePenrose inverse. After discussions on norms, QR factorization, and orthogonality, the authors prove the important spectral theorem. They also highlight the primary decomposition theorem, Schur's triangularization theorem, singular value decomposition, and the Jordan canonical form theorem. The book concludes with a chapter on multilinear algebra.
Always mathematically constructive, this book helps readers delve into elementary linear algebra ideas at a deeper level and prepare for further study in matrix theory and abstract algebra.
Features
Focuses on the development of the MoorePenrose inverse, offering excellent preparation for work on advanced treatises
Uses concrete examples to make arguments more clear
Presents MATLAB examples and exercises throughout since it is often used when dealing with matrices
Includes appendices that review basics linear algebra and related prerequisites
Provides numerous homework Problem and suggestions for further reading
Contents
THE IDEA OF INVERSE
Solving Systems of Linear Equations
The Special Case of "Square" Systems
GENERATING INVERTIBLE MATRICES
A Brief Review of Gauss Elimination with Back Substitution
Elementary Matrices
The LU and LDU Factorization
The Adjugate of a Matrix
The Frame Algorithm and the CayleyHamilton Theorem
SUBSPACES ASSOCIATED TO MATRICES
Fundamental Subspaces
A Deeper Look at Rank
Direct Sums and Idempotents
The Index of a Square Matrix
Left and Right Inverses
THE MOOREPENROSE INVERSE
Row Reduced Echelon Form and Matrix Equivalence
The Hermite Echelon Form
Full Rank Factorization
The MoorePenrose Inverse
Solving Systems of Linear Equations
Schur Complements Again
GENERALIZED INVERSES
The {1}Inverse
{1,2}Inverses
Constructing Other Generalized Inverses
{2}Inverses
The Drazin Inverse
The Group Inverse
NORMS
The Normed Linear Space Cn
Matrix Norms
INNER PRODUCTS
The Inner Product Space Cn
Orthogonal Sets of Vectors in Cn
QR Factorization
A Fundamental Theorem of Linear Algebra
Minimum Norm Solutions
Least Squares
PROJECTIONS
Orthogonal Projections
The Geometry of Subspaces and the Algebra of Projections
The Fundamental Projections of a Matrix
Full Rank Factorizations of Projections
Affine Projections
Quotient Spaces
SPECTRAL THEORY
Eigenstuff
The Spectral Theorem
The Square Root and Polar Decomposition Theorems
MATRIX DIAGONALIZATION
Diagonalization with Respect to Equivalence
Diagonalization with Respect to Similarity
Diagonalization with Respect to a Unitary
The Singular Value Decomposition
JORDAN CANONICAL FORM
Jordan Form and Generalized Eigenvectors
The Smith Normal Form
MULTILINEAR MATTERS
Bilinear Forms
Matrices Associated to Bilinear Forms
Orthogonality
Symmetric Bilinear Forms
Congruence and Symmetric Matrices
SkewSymmetric Bilinear Forms
Tensor Products of Matrices
APPENDIX A: COMPLEX NUMBERS
What is a Scalar?
The System of Complex Numbers
The Rules of Arithmetic in C
Complex Conjugation, Modulus, and Distance
The Polar Form of Complex Numbers
Polynomials over C
Postscript
APPENDIX B: BASIC MATRIX OPERATIONS
Introduction
Matrix Addition
Scalar Multiplication
Matrix Multiplication
Transpose
Submatrices
APPENDIX C: DETERMINANTS
Motivation
Defining Determinants
Some Theorems about Determinants
The Trace of a Square Matrix
APPENDIX D: A REVIEW OF BASICS
Spanning
Linear Independence
Basis and Dimension
Change of Basis
INDEX




Linear Algebra Over Commutative Rings, Indian Reprint  Bernard R.McDonald (EX) 
Author 
Bernard R. McDonald


Cover Price : Rs 4,995.00

Imprint : CRC Press ISBN : 9780824771225 YOP : 2015

Binding : Hardback Total Pages : 554 CD : No


About the Book
Linear Algebra Over Commutative Rings provides an ideal, comprehensive introduction to and an uptodate survey of matrix theory, linear algebra, and projective modules and their endomorphisms over commutative rings.
Utilizing a commutative scalar ring for the matrices discusses, this volume fully describes: matrix theory over commutative rings… the theory of solutions of systems of linear equations… the structure of the general linear group…free modules and projective modules… the Morita duality and the Baer correspondences of endomorphism rings… the automorphism theory of endomorphism ring… localization and the structure of projective modules including a proof of Serre’s Theorem… the theory of single endomorphism with an analysis of similarity, trace, determinant, characteristic polynomial, equivalence, and determinanttrace polynomials… and basic results in the Ktheory of projective modules and the Ktheory of their endomorphism rings.
Contents
PREFACE
1. MATRIX THEORY OVER COMMUTATIVE RINGS
2. FREE MODULES
3. THE ENDOMORPHIS RING OF A PROJECTIVE MODULE
4. PROJECTIVE MODULES
5. THEORY OF A SINGLE ENDOMORPHISM
BIBLIOGRAPHY
INDEX
About the Author
BERNARD R.MCDONALD is Program Director for Algebra and Number theory for the Division of Mathematical Sciences of the National Science Foundation, Washington, D.C.Prior to this position, Dr.McDonald was professor and chairman of the Dept of Mathematics at the University of Oklahoma, Norman . Dr. McDonald’s research interests include the study of commutative algebra, linear and geometric algebra, quadratic form and combinatorics. He is the author of Geometric Algebra Over Local Rings and Finite Rings with Identity, editor of Ring Theory and Algebra III: Proceedings of the Third Oklahoma Conference, coeditor (with Robert A.Morris) of Ring Theory II: Proceedings of the Social Oklahoma Conference and (With Andy R. Magid and Kirby C. Smith) of Ring Theory: Proceedings of the Oklahoma Conference (all titles, Marcel Dekker,Inc.) and has published articles in various mathematical journals. Dr.McDonald is a member of the American Mathematical Society and the Mathematical Association of America. He received the Ph.D.degree (1968) from Michigan State University. 



General Topology  John L.Kelley 

Cover Price : Rs 695.00

Imprint : Springer ISBN : 9781493975167 YOP : 2017

Binding : Paperback Total Pages : 312 CD : No


John L.Kelley received his Ph.D.from The University of Virginia in 1940. He taught at Notre Dame University and the University of Chicago prior to coming to the University of California at Berkeley. Since coming to Berkeley he has held visiting appointments at Tulane University, the University of Kansas, Cambridge University (as Fullbright Research Professor), and the Indian Institute of Technology at Kanpur. Professor Kelley is the author of several books and research articles on topology and functional analysis.
CONTENTS
Preliminaries
1. Topological Spaces
2. MooreSmith Convergence
3. Product and Quotient Spaces
4. Embedding and Metrization
5. Compact Spaces
6. Uniform Spaces
7. Function Spaces
Appendix: Elementary Set Theory 



Graph Theory  J.A.Bondy 
Author 
J.A. Bondy U.S.R Murty


Cover Price : Rs 995.00

Imprint : Springer ISBN : 9781447173601 YOP : 2017

Binding : Paperback Total Pages : 668 CD : No


Graph theory is a flourishing discipline containing a body of beautiful and powerful theorems of wide applicability. Its explosive growth in recent years is mainly due to its role as an essential structure underpinning modern applied mathematics  computer science, combinatorial optimization, and operations research in particular but also to its increasing application in the more applied sciences. The versatility of graphs makes them indispensable tools in the design and analysis of communication networks, for instance.
The primary aim of this book is to present a coherent introduction to the subject, suitable as a textbook for advanced undergraduate and beginning graduate students in mathematics and computer science. It provides a systematic treatment of the theory of graphs without sacrificing its intuitive and aesthetic appeal. Commonly used proof techniques are described and illustrated, and a wealth of exercises  of varying levels of difficulty  are provided to help the reader master the techniques and reinforce their grasp of the material.
A second objective is to serve as an introduction to research in graph theory. To this end, sections on more advanced topics are included, and a number of interesting and challenging open problems are highlighted and discussed in some detail. Despite this more advanced material, the book has been organized in such a way that an introductory course on graph theory can be based on the first few sections of selected chapters.
Contents
1 Graphs
2 Subgraphs
3 Connected Graphs
4 Trees
5 Nonseparable Graphs
6 TreeSearch Algorithms
7 Flows in Networks
8 Complexity of Algorithms
9 Connectivity
10 Planar Graphs
11 The FourColour Problem
12 Stable Sets and Cliques
13 The Probabilistic Method
14 Vertex Colourings
15 Colourings of Maps
16 Matchings
17 Edge Colourings
XII Contents
18 Hamilton Cycles
19 Coverings and Packings in Directed Graphs
20 Electrical Networks
21 Integer Flows and Coverings
Unsolved Problems
References
General Mathematical Notation
Graph Parameters
Operations and Relations
Families of Graphs
Structures
Other Notation
Index




Frontiers in Interpolation and Approximation  N.K.Govil 
Author 
N.K. Govil H.N. Mhaskar Ram N. Mohapatra Zuhair Nashed


Cover Price : Rs 4,995.00

Imprint : CRC Press ISBN : 9781584886365 YOP : 2015

Binding : Hardback Total Pages : 497 CD : No


Dedicated to the memory of the wellrespected research mathematician Ambikeshwar Sharma, Frontiers in Interpolation and Approximation is a collection of papers by mathematicians with international reputations in several areas of approximation theory, interpolation theory, and classical analysis.
Some of the topics covered are the theory of multivariate polynomial, approximation inequalities for multivariate polynomials, exponential sums, the linear combination of Gaussians, orthogonal polynomials and their zeroes, uncertainty principles in wavelet analysis, approximation on the sphere, interpolation in the complex domain, weighted approximation on an infinite interval, and abstract approximation theory.
Features
 Present complex interpolation by algebraic and trigonometric polynomials and transcendental entire functions
 Investigates the optimality of uncertainty products
 Proposes alternatives to interpolation including hyperinterpolation and quasiinterpolation on the sphere and Euclidean spaces
 Provides fast algorithms for approximation on the sphere
Containing both original research and comprehensive surveys, this book will be valuable to researchers and graduate students by offering many important results of interpolation and approximation.
Contents
Foreword
Preface
Editors
Contributors
Ambikeshwar Sharma
MarkovType Inequalities for Homogeneous Polynomials on Nonsymmetric StarLike Domains
Local Inequalities for Multivariate Polynomials and Plurisubharmonic Functions
The Norm of an Interpolation Operator on H8(D)
Sharma and Interpolation, 19932003: The Dutch Connection
Freeness of Spline Modules from a Divided to a Subdivided Domain
Measures of Smoothness on the Sphere
Quadrature Formulae of Maximal Trigonometric Degree of Precision
Inequalities for Exponential Sums via Interpolation and TuránType Reverse Markov Inequalities
Asymptotic Optimality in TimeFrequency Localization of Scaling
Functions and Wavelets
Interpolation by Polynomials and Transcendental Entire Functions
Hyperinterpolation on the Sphere
Lagrange Interpolation at Lacunary Roots of Unity
A Fast Algorithm for Spherical Basis Approximation
Direct and Converse Polynomial Approximation Theorems on the Real Line with Weights having Zeros
Fourier Sums and Lagrange Interpolation on (0,+8) and (8,+8)
On Bounded Interpolatory and QuasiInterpolatory Polynomial Operators
Hausdorff Strong Uniqueness in Simultaneous Approximation
Zeros of Polynomials Given as an Orthogonal Expansion
Uniqueness of Tchebycheff Spaces and their Ideal Relatives
Index




Moving Shape Analysis and Control 
Author 
Marwan Moubachir JeanPaul Zolesio


Cover Price : Rs 4,995.00

Imprint : Ane Books Pvt. Ltd. ISBN : 9781584886112 YOP : 2015

Binding : Hardback Total Pages : 312 CD : No


Problems involving the evolution of two and threedimensional domains arise in many areas of science and engineering. These range from free surface flows, phase changes, and fracture and contact problems to applications in civil engineering construction, biomechanical systems, and computer vision. Emphasizing an Eulerian approach, Moving Shape Analysis and Control: Applications to Fluid Structure Interactions presents valuable tools for the mathematical analysis of evolving domains.
The book illustrates the efficiency of the tools presented through different examples connected to the analysis of noncylindrical partial differential equations , such as Navier–Stokes equations for incompressible fluids in moving domains. The authors begin by providing all of the details of existence and uniqueness of the flow in both strong and weak cases. After establishing several important principles and methods, they devote several chapters to demonstrating Eulerian evolution and derivation tools for the control of systems involving fluids and solids. The book concludes with boundary control of fluid–structure interaction systems, followed by helpful appendices that review some of the advanced mathematics used throughout the text.
Offering new, robust approaches to evolving domains, this book…
 Provides various tool to handle moving domains on the level of intrinsic definition, computation, optimization, and control
 Addresses realworld engineering problems with applications
 Emphasizes the Eulerian approach using evolution and derivation tools for controlling fluids and systems
 Includes two chapters devoted to fluid control described using NavierStokes equations
 Features new approaches to deal with boundary control fluidstructure interaction systems
Contents
Introduction
Classical and Moving Shape Analysis
Fluid–Structure Interaction Problems
Plan of the Book
Detailed Overview of the Book
An Introductory Example: The Inverse Stefan Problem
The Mechanical and Mathematical Settings
The Inverse Problem Setting
The Eulerian Derivative and the Transverse Field
The Eulerian Material Derivative of the State
The Eulerian Partial Derivative of the State
The Adjoint State and the Adjoint Transverse Field
Weak Evolution of Sets and Tube Derivatives
Introduction
Weak Convection of Characteristic Functions
Tube Evolution in the Context of Optimization Problems
Tube Derivative Concepts
A First Example: Optimal Trajectory Problem
Shape Differential Equation and Level Set Formulation
Introduction
Classical Shape Differential Equation Setting
The Shape Control Problem
The Asymptotic Behavior
Shape Differential Equation for the Laplace Equation
Shape Differential Equation in Rd+1
The Level Set Formulation
Dynamical Shape Control of the Navier–Stokes Equations
Introduction
Problem Statement
Elements of Noncylindrical Shape Calculus
Elements of Tangential Calculus
State Derivative Strategy
MinMax and Function Space Parameterization
MinMax and Function Space Embedding
Conclusion
Tube Derivative in a Lagrangian Setting
Introduction
Evolution Maps
Navier–Stokes Equations in Moving Domain
Sensitivity Analysis for a Simple Fluid–Solid Interaction System
Introduction
Mathematical Settings
WellPosedness of the Coupled System
Inverse Problem Settings
KKT Optimality Conditions
Conclusion
Sensitivity Analysis for a General Fluid–Structure Interaction System
Introduction
Mechanical Problem and Main Result
KKT Optimality Conditions
Appendix A: Functional Spaces and Regularity of Domains
Appendix B: Distribution Spaces
Appendix C: The Fourier Transform
Appendix D: Sobolev Spaces
References
Index




Linear Systems and Control  Martin J.Corless 
Author 
Martin J. Corless Arthur E. Frazho


Cover Price : Rs 4,995.00

Imprint : CRC Press ISBN : 9780824707293 YOP : 2015

Binding : Hardback Total Pages : 352 CD : No


Based largely on state space models, this text/reference utilizes fundamental linear algebra and operator techniques to develop classical and modern results in linear systems analysis and control design.
Linear Systems and Control presents stability and performance results for linear systems… provides a geometric perspective on controllability and observability….develops state space realizations of transfer functions…. studies stabilizability and detectability…. constructs state feedback controllers and asymptotic state estimators…. covers the linear quadratic regulator problem in detail….offers an introduction to Hinfinity control…. and presents results on Hamiltonian matrices and Riccati equations.
CONTENTS
Preface
Systems and Contol
Stability
Lyapunov Theory
Observability
Controllability
Controllable and Observable Realizations
More Realization Theory
State Feedback and Stabilizability
State Estimators and Detectability
Output Feedback Controllers
Zeros of Transfer Functions
Linear Quadratic Regulators
The Hamilitonian Matrix and Riccati Equations
H∞ Analysis
H∞ Control
Appendix: Least Squares
Bibliography
Index
About the Authors….
Martin J.Corless is a Professor in the Department of Aeronautics and Astronautics, purdue University, West Lafayette, Indiana. He Received the B.E.degree (1977) in mechanical engineering from university the B.E.degree (1977) in mechanical engineering from University College, Dublin, Ireland, and the Ph.D. degree (1984) in mechanical engineering from the University of California, Berkeley.
Arthure E. Frazho is a Professor in the Department of Aeronautics and Astronautics, Purdue University, West Lafayette, Indiana. He received the B.S.E. degree(1973) and the M.S.E. (1974) and the Ph.D.(1977) degrees in computer information and control engineering from the University of Michigan, Ann Arbor.




Discrete Geometry  Andras Bezdek 

Cover Price : Rs 4,995.00

Imprint : CRC Press ISBN : 9780824709686 YOP : 2015

Binding : Hardback Total Pages : 480 CD : No


Celebrating the work of Professor W. Kuperberg, this reference explores packing and covering theory, tilings, combinatorial and computational geometry, and convexity featuring an extensive collection of problems compiled at the Discrete Geometry Special Session of the American Mathematical Society in New Orleans, Louisiana.
Discrete Geometry analyzes packings and coverings with congruent convex bodies…., arrangements on the sphere…. line transversals…. Euclidean and spherical tilings… geometric graphs…. polygons and polyhedral… and fixing systems for convex figures.
Offering research and contributions from more than 50 esteemed international authorities Discrete Geometry is a fascinating collection for pure and applied mathematicians, geometers, topologists, combinatorialists, and upperlevel undergraduate and graduate students in these disciplines.
Contents
Preface
Contributors
Biographical notes and work of W.Kuperberg
Andras Bezdek and Gabor Fejes Toth
 Transversal lines to lines and intervals, Jorge L. Arocha, Javier Bracho, and Luis Montejano
 On a shortest path problem of G. Fejes, Toth Donald R. Baggett and Andras Bezdek
 A short survey of (r,q)structures, Vojtech Balint
 Lattice points on the boundary of the integer hull, Imre Barany and Karoly Boroczky, Jr
 The ErdosSzekeres problem for planar points in arbitrary position, Tibor Bisztriczky and Gabor Fejes Toth
 Separation in totallysewn 4polytopes, Tibor Bisztriczky and Deborah Oliveros
 On a class of equifacetted polytopes, Gerd Blind and Roswitha Blind
 Chessboard Ramsey numbers, JensP. Bode, Heiko Harborth, and Stefan Krause
 Maximal primitive fixing systems for convex figures, Vladimir Boltyanski and Hernan GonzalezAguilar
 The NewtonGregory problem revisited, Karoly Boroczky
 Arrangements of 13 points on a sphere Karoly Boroczky and Laszlo Szabo
 On point sets without k collinear points, Peter Brass
 The BeckmanQuarles theorem for rational dspaces, d even and d> 6, Robert Connelly and Joseph Zaks
 Eedgeantipodal convex polytopes  a proof of Talata's conjecture, Balazs Csikos
 Singlesplit tilings of the sphere with right triangles, Robert J. MacG. Dawson
 Vertexunfoldings of simplicial manifolds, Erik D. Demaine, David Eppstein, Jeff Erickson, George W. Hart, and Joseph O'Rourke
 Viewobstruction through trajectories of codimension three Vishwa C. Dumir and Rajinder J. HansGill
 Fat 4polytopes and fatter 3spheres, David Eppstein, Greg Kuperberg, and Gunter M. Ziegler
 Arbitrarily large neighbourly families of congruent symmetric convex 3polytopes, Jeff Erickson and Scott Kim
On the nonsolidity of some packings and coverings with circles, August Florian and Aladar Heppes
On the mth Petty numbers of normed spaces Karoly Bezdek, Marton Naszodi and Balazs Visy
 Cubic polyhedra, Chaim GoodmanStrauss and John M. Sullivan
New uniform polyhedra, Branko Grunbaum
 On the existence of a convex polygon with a specified number of interior points, Kiyoshi Hosono, Gyula Karolyi and Masatsugu Urabe
 Online 2adic covering of the unit square by boxes, Janusz Januszewski and Marek Lassak
 An example of a stable, even order quadrangle which is determined by its angle function, Janos Kincses
Sets with a unique extension to a set of constant width, Marton Naszodi and Balazs Visy
 The number of simplices embracing the origin, Janos Pach and Mario Szegedy
 Hellytype theorems on definite supporting lines for kdisjoint families of convex bodies in the plane, Sorin Revenko and Valeriu Soltan
Combinatorial aperiodicity of polyhedral prototiles, Egon Schulte
 Sequences of smoothed polygons, G.C. Shephard
 On a packing inequality, Graham, Witsenhausen and Zassenhaus, Jorg M. Wills
 Covering a triangle with homothetic copies, Zoltan Furedi
 Open problems, Andras Bezdek.
Index
About the Editor is Professor of Mathematics, Auburn University, Alabama, and Senior Research Fellow at the Alfred Renyi Institute of Mathematics, Hungarian Academy of Sciences, Budapest, Hungary. Previously, he held visiting position at Cornell University, Ithaca, New York, and the University of Calgary, Alberta, Canada. He received the Ph.D degree (1986) from Ohio State University, Columbus, and the Habilitation degree (1999) from Eotvos University, Budapest, Hungary.




Stochastic Versus Determininistic Systems of Differential Equations  G.S.Ladde 
Author 
G.S. Ladde M. Sambandham


Cover Price : Rs 4,995.00

Imprint : CRC Press ISBN : 9780824746971 YOP : 2015

Binding : Hardback Total Pages : 336 CD : No


This peerless reference/text unfurls a unified and systematic study of the two types of mathematical models of dynamic processesstochastic and deterministicas placed in the context of systems of stochastic differential equations. Using the tools of variational comparison, generalized variation of constants, and probability distribution as its methodological backbone, Stochastic Versus Deterministic Systems of Differential Equations addresses questions relating to the need for a stochastic mathematical model and the betweenmodel contrast that arises in the absence of random disturbances/fluctuations and parameter uncertainties both deterministic and stochastic.
With numerical examples and figures embedded throughout the text, Stochastic Versus Deterministic Systems of Differential Equations scrutinizes random algebraic polynomials…explores the initial value problems (IVP) for ordinary differential systems with random parameters… investigates stochastic boundary value problems (SBVP) with random parameters… independently studies IVP and SBVP for itotype stochastic differential systems…. Provides an integrated approach to stability, relative stability, and error estimate analysis…. explicitly illustrates the role of randomness and rate functions…. and interweaves presentation of methods with presentation of applications in population dynamics, hydrodynamics, and physics.
Contents
Preface
Notation and Abbreviations
Chapter 1: Random Polynomials
Chapter 2: Ordinary Differential Systems with Random Parameters
Chapter 3: Boundary Value Problems with Random Parameters
Chapter 4: ItoType Stochastic Differential Systems
Chapter 5: Boundary Value Problems of ItoType
Appendix
References
Index
About the Aurthor
G.S.Ladde is Professor of Mathematics at The University of Texas at Arlington. The coauthor or coeditor of over nine books, including four monographs, Dr. Ladde has published more than 125 refereed research articles. He is the founder and coeditor of the journals Stochastic Analysis and Applications (Marcel Dekker, Inc.), and serves on several journal editorial boards. A Life Member of the American Mathematical Society, Sigma Xi, the Indian Mathematical Society, and the Marathwada Mathematical Society and a Senior Member of the Institute of Electrical and Electronics Engineers, Dr Ladde received the B.Sc degree (1963) from People’s College, Nanded , India the M.Sc.degree (1965) from Marathwada University, Aurangabad, India, and the Ph.D.degree (1972) from the University of Rhode Island, Kingston.
M.Sambandham is Professor of Mathematics at Morehouse College, Atlanta, Georgia. In addition to coauthoring two monographs and publishing 75 refereed research articles, Dr. Sambandham serves as an editor for six international journals. His many professional membership include the American Mathematical Society and the Institute of Electrical and Electronics Engineers. Dr. Sambandham received the B.S.degree (1969) from the University of Madras, Chennai, India, and the M.Sc. (1971) and Ph.D. (1976) degrees from Annamalai University, Annamalai Nagar, India.




Advanced Mapping of Environmental Data  Mikhail Kanevski 

Cover Price : Rs 4,995.00

Imprint : Wiley ISBN : 9788126552023 YOP : 2015

Binding : Hardback Total Pages : 328 CD : No


Contents
Preface
Chapter 1. Advanced Mapping of Environmental Data: Introduction
M. KANEVSKI
1.1. Introduction
1.2. Environmental data analysis: problems and methodology
1.2.1. Spatial data analysis: typical problems
1.2.2. Spatial data analysis: methodology
1.2.3. Model assessment and model selection
1.3. Resources
1.3.1. Books, tutorials
1.3.2. Software
1.4. Conclusion
1.5. References
Chapter 2. Environmental Monitoring Network Characterization and Clustering
D. TUIA and M. KANEVSKI
2.1. Introduction
2.2. Spatial clustering and its consequences
2.2.1. Global parameters
2.2.2. Spatial predictions
2.3. Monitoring network quantification
2.3.1. Topological quantification
2.3.2. Global measures of clustering
2.3.2.1. Topological indices
2.3.2.2. Statistical indices
2.3.3. Dimensional resolution: fractal measures of clustering
2.3.3.1. Sandbox method
2.3.3.2. Boxcounting method
2.3.3.3. Lacunarity
2.4. Validity domains
2.5. Indoor radon in Switzerland: an example of a real monitoring network
2.5.1. Validity domains
2.5.2. Topological index
2.5.3. Statistical indices
2.5.3.1. Morisita index
2.5.3.2. Kfunction
2.5.4. Fractal dimension
2.5.4.1. Sandbox and boxcounting fractal dimension
2.5.4.2. Lacunarity
2.6. Conclusion
2.7. References
Chapter 3. Geostatistics: Spatial Predictions and Simulations
E. SAVELIEVA, V. DEMYANOV and M. MAIGNAN
3.1. Assumptions of geostatistics
3.2. Family of kriging models
3.2.1. Simple kriging
3.2.2. Ordinary kriging
3.2.3. Basic features of kriging estimation
3.2.4. Universal kriging (kriging with trend)
3.2.5. Lognormal kriging
3.3. Family of cokriging models
3.3.1. Kriging with linear regression
3.3.2. Kriging with external drift
3.3.3. Cokriging
3.3.4. Collocated cokriging
3.3.5. Cokriging application example
3.4. Probability mapping with indicator kriging
3.4.1. Indicator coding
3.4.2. Indicator kriging
3.4.3. Indicator kriging applications
3.4.3.1. Indicator kriging for 241Am analysis
3.4.3.2. Indicator kriging for aquifer layer zonation
3.4.3.3. Indicator kriging for localization of crab crowds
3.5. Description of spatial uncertainty with conditional stochastic simulations
3.5.1. Simulation vs. estimation
3.5.2. Stochastic simulation algorithms
3.5.3. Sequential Gaussian simulation
3.5.4. Sequential indicator simulations
3.5.5. Cosimulations of correlated variables
3.6. References
Chapter 4. Spatial Data Analysis and Mapping Using Machine Learning Algorithms
F. RATLE, A. POZDNOUKHOV, V. DEMYANOV, V. TIMONIN and E. SAVELIEVA
4.1. Introduction
4.2. Machine learning: an overview
4.2.1. The three learning problems
4.2.2. Approaches to learning from data
4.2.3. Feature selection
4.2.4. Model selection
4.2.5. Dealing with uncertainties
4.3. Nearest neighbor methods
4.4. Artificial neural network algorithms
4.4.1. Multilayer perceptron neural network
4.4.2. General Regression Neural Networks
4.4.3. Probabilistic Neural Networks
4.4.4. Selforganizing (Kohonen) maps
4.5. Statistical learning theory for spatial data: concepts and examples
4.5.1. VC dimension and structural risk minimization
4.5.2. Kernels
4.5.3. Support vector machines
4.5.4. Support vector regression
4.5.5. Unsupervised techniques
4.5.5.1. Clustering
4.5.5.2. Nonlinear dimensionality reduction
4.6. Conclusion
4.7. References
Chapter 5. Advanced Mapping of Environmental Spatial Data: Case Studies
L. FORESTI, A. POZDNOUKHOV, M. KANEVSKI, V. TIMONIN, E. SAVELIEVA, C. KAISER, R. TAPIA and R. PURVES
5.1. Introduction
5.2. Air temperature modeling with machine learning algorithms and geostatistics
5.2.1. Mean monthly temperature
5.2.1.1. Data description
5.2.1.2. Variography
5.2.1.3. Stepbystep modeling using a neural network
5.2.1.4. Overfitting and undertraining
5.2.1.5. Mean monthly air temperature prediction mapping
5.2.2. Instant temperatures with regionalized linear dependencies
5.2.2.1. The Föhn phenomenon
5.2.2.2. Modeling of instant air temperature influenced by Föhn
5.2.3. Instant temperatures with nonlinear dependencies
5.2.3.1. Temperature inversion phenomenon
5.2.3.2. Terrain feature extraction using Support Vector Machines
5.2.3.3. Temperature inversion modeling with MLP
5.3. Modeling of precipitation with machine learning and geostatistics
5.3.1. Mean monthly precipitation
5.3.1.1. Data description
5.3.1.2. Precipitation modeling with MLP
5.3.2. Modeling daily precipitation with MLP
5.3.2.1. Data description
5.3.2.2. Practical issues of MLP modeling
5.3.2.3. The use of elevation and analysis of the results
5.3.3. Hybrid models: NNRK and NNRS
5.3.3.1. Neural network residual kriging
5.3.3.2. Neural network residual simulations
5.3.4. Conclusions
5.4. Automatic mapping and classification of spatial data using machine learning
5.4.1. knearest neighbor algorithm
5.4.1.1. Number of neighbors with crossvalidation
5.4.2. Automatic mapping of spatial data
5.4.2.1. KNN modeling
5.4.2.2. GRNN modeling
5.4.3. Automatic classification of spatial data
5.4.3.1. KNN classification
5.4.3.2. PNN classification
5.4.3.3. Indicator kriging classification
5.4.4. Automatic mapping – conclusions
5.5. Selforganizing maps for spatial data – case studies
5.5.1. SOM analysis of sediment contamination
5.5.2. Mapping of socioeconomic data with SOM
5.6. Indicator kriging and sequential Gaussian simulations for probability mapping. Indoor radon case study
5.6.1. Indoor radon measurements
5.6.2. Probability mapping
5.6.3. Exploratory data analysis
5.6.4. Radon data variography
5.6.4.1. Variogram for indicators
5.6.4.2. Variogram for Nscores
5.6.5. Neighborhood parameters
5.6.6. Prediction and probability maps
5.6.6.1. Probability maps with IK
5.6.6.2. Probability maps with SGS
5.6.7. Analysis and validation of results
5.6.7.1. Influence of the simulation net and the number of neighbors
5.6.7.2. Decision maps and validation of results
5.6.8. Conclusions
5.7. Natural hazards forecasting with support vector machines – case study: snow avalanches
5.7.1. Decision support systems for natural hazards
5.7.2. Reminder on support vector machines
5.7.2.1. Probabilistic interpretation of SVM
5.7.3. Implementing an SVM for avalanche forecasting
5.7.4. Temporal forecasts
5.7.4.1. Feature selection
5.7.4.2. Training the SVM classifier
5.7.4.3. Adapting SVM forecasts for decision support
5.7.5. Extending the SVM to spatial avalanche predictions
5.7.5.1. Data preparation
5.7.5.2. Spatial avalanche forecasting
5.7.6. Conclusions
5.8. Conclusion
5.9. References
Chapter 6. Bayesian Maximum Entropy – BME
G. CHRISTAKOS
6.1. Conceptual framework
6.2. Technical review of BME
6.2.1. The spatiotemporal continuum
6.2.2. Separable metric structures
6.2.3. Composite metric structures
6.2.4. Fractal metric structures
6.3. Spatiotemporal random field theory
6.3.1. Pragmatic S/TRF tools
6.3.2. Spacetime lag dependence: ordinary S/TRF
6.3.3. Fractal S/TRF
6.3.4. Spacetime heterogenous dependence: generalized S/TRF
6.4. About BME
6.4.1. The fundamental equations
6.4.2. A methodological outline
6.4.3. Implementation of BME: the SEKSGUI
6.5. A brief review of applications
6.5.1. Earth and atmospheric sciences
6.5.2. Health, human exposure and epidemiology
6.6. References
List of Authors
Index




Calculus in Vector Spaces, 2nd Ed  Lawrence J.Corwin 
Author 
Lawrence J. Corwin Robert H. Szczarba


Cover Price : Rs 4,995.00

Imprint : CRC Press ISBN : 9780824792794 YOP : 2015

Binding : Hardback Total Pages : 604 CD : No


About the first edition….
“…a unique book based on the year course taught at Yale University…a mathematically beautiful development of the material.”
About the second edition…
Addressing linear algebra from the basics to the spectral theorem and examining a host of topics in multivariable calculus, including differentiation, integration, maxima and minima, the inverse and implicit function theorems, and differential forms, this thoroughly revised Second Edition of an invaluable reference/text—widely successful through five printings—continues to provide unified, integrated coverage of the two fields.
Demonstrating that mathematics is a noncompartmentalized discipline of interrelated subjects, Calculus in Vector Spaces, Second Edition Introduces the derivative as a linear transformation…presents linear algebra in a concrete context based on complementary ideas in calculus…explains differential forms on Euclidean space permitting Green’s theorem, Gauss’s theorem, and Stokes’s theorem to be understood in a natural setting…gives a new clarification of compactness as defined in terms of coverings and in terms of sequences…supplies a novel treatment of eigenvalues and eigenvectors…and more.
Contexts
Some Preliminaries.
Vector Spaces.
The Derivative.
The Structure of Vector Spaces.
Compact and Connected Sets.
The Chain Rule, Higher Derivatives, and Taylor's Theorem.
Linear Transformations and Matrices.
Maxima and Minima.
The Inverse and Implicit Function Theorems.
The Spectral Theorem.
Integration.
Iterated Integrals and the Fubini Theorem.
Line Integrals.
 Surface Integrals.
Differential Forms.
Integration of Differential Forms.
Appendix 1: The existence of determinants,
Appendix 2.: Jordan canonical form, solutions of selected exercises.
Solution of Selected Excercises
INdex
About the Authors
Lawrence J. Corwin was Professor of Mathematics at Rutgers University, New Brunswick, New Jersey, until his death in 1992. Previously he was an Assistant Professor at Yale University, New Haven, Connecticut. The coauthor, with Robert H. Szczarba, of the book Multivariable Calculus (Marcel Dekker, Inc.), he was twice a member of the Institute for Advanced Study, Princeton, New Jersey, held a Sloan Foundation Fellowship, and was a member of the American Mathematical Society, the Mathematical Association of America, and the Society for industrial and Applied Mathematics. Dr. Corwin’s research interests focused on harmonic analysis and representation theory for topological groups. He received the M.A. (1965) and Ph.D. (1968) degrees in mathematics from Harvard University, Cambridge, Massachusetts.
Robert H. Szczarba is Deputy Provost for Physical Sciences and Engineering and Professor of Mathematics at Yale University, New Haven, Connecticut. A member of the American Mathematical Society and a twotime member of the Institute for Advanced Study, Princeton, New Jersey, he is the coauthor, with Lawrence J. Corwin, of the book Multivariable Calculus (Marcel Dekker, Inc.) and the author of many papers that reflect his research interests in differential and algebraic topology. Dr. Szczarba received the M.S. (1957) and Ph.D. (1960) degrees in mathematics from the University of Chicago, Illinois.




Tensors and the Clifford Algebra  Alphonse Charlier 
Author 
Alphonse Charlier Alain Berard MarieFrance Charlier Daniele Fristot


Cover Price : Rs 4,995.00

Imprint : CRC Press ISBN : 9780824786663 YOP : 2015

Binding : Hardback Total Pages : 334 CD : No


About the Book…
This practical reference/text presents the applications of tensors, Lie groups and algebra to Maxwell, KleinGordon and Dirac equations, making elementary theoretical physics comprehensible and highlevel theoretical physics accessible.;
Providing the fundamental mathematics necessary to understand the applications, Tensors and the Clifford Algebra offers lucid discussions of covariant tensor calculus; examines subjects from a variety of perspectives; supplies highly detailed developments of all calculations; employs the language of physics in its explanations; and illustrates the use of Clifford algebra and tensor calculus in studying bosons and fermions.; and much more!
With over 2800 display equations and 14 appendixes, Tensors and the Clifford Algebra is a valuable reference for mathematical physicists and applied mathematicians, and an important text for upperlevel undergraduate and graduate students in quantum mechanics, relativity, electromagnetism, theoretical physics, elasticity, and field theory courses.
Contents
Tensor analysis; Minkowski space; covariant formulation of electromagnetism; the CayleyKlein parameters; vector algebra; application of Clifford algebra to bosons  KleinGordon equation; fermions  Dirac equation. Bibliography, Index
About the Authors
Alphonse Charlier is Professor of Theoretical Physics and Head of the Solid Physics Laboratory, University of Metz, France. He received the Ph.D.degree (1965) in physics from Louis Pasteur University, Strasbourg, France.
Alain Berard is Conference Chair in Theoretical Physics in the Department of Physics, University of Metz, France. He received the These de IIICycle degree (1976) in elementary particle physics from the University of Paris XI, France.
MarieFrance Charlier is Conference Chair in Mechanics and Quantum Mechanics in the Department of Physics, University of Metz, France. She received the Doctorat de Specialite degree (1970) in solid state physics from Louis Pasteur University, Strasbourg, France.
Deniele Fristot is Research Associate in SolidState Physics at the Solid Physics Laboratory, University of Metz, France. She received the D.E.A. Genie Physique et Mechanique degree (1989) from the University of Metz.




Noncommutative Geometry and Cayleysmooth Orders  Lieven Le Bruyn 

Cover Price : Rs 4,995.00

Imprint : CRC Press ISBN : 9781420064223 YOP : 2015

Binding : Hardback Total Pages : 588 CD : No


Noncommutative Geometry and Cayleysmooth Orders explains the theory of Cayleysmooth orders in central simple algebras over function fields of varieties. In particular, the book describes the étale local structure of such orders as well as their central singularities and finite dimensional representations.
After an introduction to partial desingularizations of commutative singularities from noncommutative algebras, the book presents the invariant theoretic description of orders and their centers. It proceeds to introduce étale topology and its use in noncommutative algebra as well as to collect the necessary material on representations of quivers. The subsequent chapters explain the étale local structure of a Cayleysmooth order in a semisimple representation, classify the associated central singularity to smooth equivalence, describe the nullcone of these marked quiver representations, and relate them to the study of all isomorphism classes of ndimensional representations of a Cayleysmooth order. The final chapters study Quillensmooth algebras via their finite dimensional representations.
Noncommutative Geometry and Cayleysmooth Orders provides a gentle introduction to one of mathematics' and physics' hottest topics.
Features
• Presents background information on a variety of topics, including invariant theory, algebraic geometry, and central simple algebras
• Discusses the use of étale topology in noncommutative algebra, such as Azumaya algebras and algebras via Luna slices
• Explores the indecomposable roots of quivers, the determination of dimension vectors of simple representations, and the results on general quiver representations
• Contains the main results on Cayleysmooth orders, including semisimple and nilpotent representations
• Provides an introduction to the fast developing theory of Quillensmooth algebras
Contents
Preface
Introduction
Noncommutative algebra
Noncommutative geometry
Noncommutative desingularizations
CayleyHamilton Algebras
Conjugacy classes of matrices
Simultaneous conjugacy classes
Matrix invariants and necklaces
The trace algebra
The symmetric group
Necklace relations
Trace relations
CayleyHamilton algebras
Reconstructing Algebras
Representation schemes
Some algebraic geometry
The Hilbert criterium
Semisimple modules
Some invariant theory
Geometric reconstruction
The GerstenhaberHesselink theorem
The real moment map
Étale Technology
Étale topology
Central simple algebras
Spectral sequences
Tsen and Tate fields
Coniveau spectral sequence
The ArtinMumford exact sequence
Normal spaces
KnopLuna slices
Quiver Technology
Smoothness
Local structure
Quiver orders
Simple roots
Indecomposable roots
Canonical decomposition
General subrepresentations
Semistable representations
Semisimple Representations
Representation types
Cayleysmooth locus
Reduction steps
Curves and surfaces
Complex moment map
Preprojective algebras
Central smooth locus
Central singularities
Nilpotent Representations
Cornering matrices
Optimal corners
Hesselink stratification
Cornering quiver representations
Simultaneous conjugacy classes
Representation fibers
BrauerSeveri varieties
BrauerSeveri fibers
Noncommutative Manifolds
Formal structure
Semiinvariants
Universal localization
Compact manifolds
Differential forms
deRham cohomology
Symplectic structure
Necklace Lie algebras
Moduli Spaces
Moment maps
Dynamical systems
Deformed preprojective algebras
Hilbert schemes
Hyper Kähler structure
Calogero particles
Coadjoint orbits
Adelic Grassmannian
References
Index
Lieven le Bruyn is Professor of Algebra and Geometry at the University of Antwerp, Belgium. Previously, he served as Research Director of the Belgian Science Foundation. Dr. Le Bruyn is a Iaureate of the Belgian Academy of Sciences and winner of the Louis Empain Prize for Mathematics.




Norm Estimations for Operator Valued Functions and Applications  Michael I.Gil 

Cover Price : Rs 4,995.00

Imprint : CRC Press ISBN : 9780824796099 YOP : 2015

Binding : Hardback Total Pages : 366 CD : No


Providing valuable new tools for specialists in functional analysis and stability theory, this stateofart reference presents a systematic exposition of estimations for norms of operatorvalued function and applies the estimates to spectrum perturbations of linear operators and stability theory.
Demonstrating a novel approach to spectrum perturbations, Norm Estimations for OperatorValued Functions and Applications considers a common procedure for the stability analysis of various classes of equations…extends the wellknown spectrum perturbation result for selfadjoint operators to quasiHermitian operators…examines spectrum perturbations of operators on a tensor product of Hilbert spaces…covers systems of ordinary differential equations…deals with retarded systems…studies the absolute stability of systems of Volterra equations…emphasizes semilinear evolution equations…
Norm Estimations for OperatorValued Functions and Applications is an ideal resource for mathematicians specializing in functional analysis, stability theory, and control systems theory; mathematical biologists; circuit design engineers; and graduate students in these disciplines.
Contents
MATRIXVALUED FUNCTIONS
FUNCTIONS OF COMPACT OPERATORS
FUNCTIONS OF NONSELFADJOINT OPERATORS
PERTERBATIONS OF FINITE DIMENSIONAL AND COMPACT OPERATORS
PERTERBATIONS OF NONCOMPACT OPERATORS
PERTERBATIONS OF OPERATORS ON A TENSOR PRODUCT OF HILBERT SPACES
STABILITY AND BOUNDEDNESS OF ORDINARY DIFFERENTIAL SYSTEMS
STABILITY OF RETARDED SYSTEMS
ABSOLUTE STABILITY OF SOLUTIONS OF VOLETTA INTEGRAL EQUATIONS
STABILITY OF SEMILINEAR PARABOLIC SYSTEMS
STABILITY OF VOLTERRA INTEGRODIFFERENTIAL SYSTEMS AND APPLICATIONS TO VISCOELASTICITY
SEMILINEAR BOUNDARY VALUE PROBLEMS
LIST OF MAIN SYMBOLS.
About the Author
Michael I. Gil’ is a Professor at the Institute for Industrial Mathematics, Beersheva, Israel. The author of several professional publications, Dr. Gil’ is a member of the International Federation of Nonlinear Analysis. He received the Ph.D. degreed (1973) in mathematics from Voronezh State University, Russia, and the Doctor of Physical and Mathematical Sciences (fourth) degree (1990) from the Moscow Institute of System research of the former Soviet Union’s Academy of Science (now the Russian Academy of Science), Russia.




Quadratic Irrationals: An Introduction to Classical Number Theory  Franz HalterKoch 

Cover Price : Rs 4,995.00

Imprint : CRC Press ISBN : 9781466591837 YOP : 2015

Binding : Hardback Total Pages : 432 CD : No


Quadratic Irrationals: An Introduction to Classical Number Theory gives a unified treatment of the classical theory of quadratic irrationals. Presenting the material in a modern and elementary algebraic setting, the author focuses on equivalence, continued fractions, quadratic characters, quadratic orders, binary quadratic forms, and class groups.
The book highlights the connection between Gauss’s theory of binary forms and the arithmetic of quadratic orders. It collects essential results of the theory that have previously been difficult to access and scattered in the literature, including binary quadratic Diophantine equations and explicit continued fractions, biquadratic class group characters, the divisibility of class numbers by 16, F. Mertens’ proof of Gauss’s duplication theorem, and a theory of binary quadratic forms that departs from the restriction to fundamental discriminants. The book also proves Dirichlet’s theorem on primes in arithmetic progressions, covers Dirichlet’s class number formula, and shows that every primitive binary quadratic form represents infinitely many primes. The necessary fundamentals on algebra and elementary number theory are given in an appendix.
Research on number theory has produced a wealth of interesting and beautiful results yet topics are strewn throughout the literature, the notation is far from being standardized, and a unifying approach to the different aspects is lacking. Covering both classical and recent results, this book unifies the theory of continued fractions, quadratic orders, binary quadratic forms, and class groups based on the concept of a quadratic irrational.
Contents
Foreword
Introduction and preface to the reader
Notations
Quadratic Irrationals
Quadratic irrationals, quadratic number fields and discriminants
The modular group
Reduced quadratic irrationals
Two short tables of class numbers
Continued Fractions
General theory of continued fractions
Continued fractions of quadratic irrationals I: General theory
Continued fractions of quadratic irrationals II: Special types
Quadratic Residues and Gauss Sums
Elementary theory of power residues
Gauss and Jacobi sums
The quadratic reciprocity law
Sums of two squares
Kronecker and quadratic symbols
LSeries and Dirichlet’s Prime Number Theorem
Preliminaries and some elementary cases
Multiplicative functions
Dirichlet Lfunctions and proof of Dirichlet’s theorem
Summation of Lseries
Quadratic Orders
Lattices and orders in quadratic number fields
Units in quadratic orders
Lattices and (invertible) fractional ideals in quadratic orders
Structure of ideals in quadratic orders
Class groups and class semigroups
Ambiguous ideals and ideal classes
An application: Some binary Diophantine equations
Prime ideals and multiplicative ideal theory
Class groups of quadratic orders
Binary Quadratic Forms
Elementary definitions and equivalence relations
Representation of integers
Reduction
Composition
Theory of genera
Ternary quadratic forms
Sums of squares
Cubic and Biquadratic Residues
The cubic Jacobi symbol
The cubic reciprocity law
The biquadratic Jacobi symbol
The biquadratic reciprocity law
Rational biquadratic reciprocity laws
A biquadratic class group character and applications
Class Groups
The analytic class number formula
Lfunctions of quadratic orders
Ambiguous classes and classes of order divisibility by 4
Discriminants with cyclic 2class group: Divisibility by 8 and 16
Appendix A: Review of Elementary Algebra and Number Theory
Appendix B: Some Results from Analysis
Bibliography
List of Symbols
Subject Index




Representation Theory and Higher Algebraic KTheory  Aderemi Kuku 

Cover Price : Rs 4,995.00

Imprint : CRC Press ISBN : 9781584886037 YOP : 2015

Binding : Hardback Total Pages : 460 CD : No


Representation Theory and Higher Algebraic KTheory is the first book to present higher algebraic Ktheory of orders and group rings as well as characterize higher algebraic Ktheory as Mackey functors that lead to equivariant higher algebraic Ktheory and their relative generalizations. Thus, this book makes computations of higher Ktheory of group rings more accessible and provides novel techniques for the computations of higher Ktheory of finite and some infinite groups.
Authored by a premier authority in the field, the book begins with a careful review of classical Ktheory, including clear definitions, examples, and important classical results. Emphasizing the practical value of the usually abstract topological constructions, the author systematically discusses higher algebraic Ktheory of exact, symmetric monoidal, and Waldhausen categories with applications to orders and group rings and proves numerous results. He also defines profinite higher K and Gtheory of exact categories, orders, and group rings. Providing new insights into classical results and opening avenues for further applications, the book then uses representationtheoretic techniquesespecially induction theoryto examine equivariant higher algebraic Ktheory, their relative generalizations, and equivariant homology theories for discrete group actions. The final chapter unifies Farrell and BaumConnes isomorphism conjectures through DavisLück assembly maps.
Features
• Explores connections between CG and higher algebraic Ktheory of C for suitable categories, such as exact, symmetric monoidal, and Waldhausen
• Collects computational methods of higher Ktheory of noncommutative rings, such as orders and group rings
• Describes all higher algebraic Ktheory as Mackey functors that lead to equivariant higher algebraic Ktheory and their relative generalizations for finite, profinite, and compact Lie group actions
• Obtains results on higher Ktheory of orders ?, and hence group rings, for all n = 0
• Uses certain computations of higher Ktheory of orders to produce results on higher Ktheory of some infinite groups
Contents
Introduction
REVIEW OF CLASSICAL ALGEBRAIC KTHEORY AND REPRESENTAION THEORY
Notes on Notations
Category of Representations and Constructions of Grothendieck Groups and Rings
Category of representations and Gequivariant categories
Grothendieck group associated with a semigroup
K0 of symmetric monoidal categories
K0 of exact categories  definitions and examples
Exercises
Some Fundamental Results on K0 of Exact and Abelian Categories with Applications to Orders and Group Rings
Some fundamental results on K0 of exact and Abelian categories
Some finiteness results on K0 and G0 of orders and groupings
Class groups of Dedekind domains, orders, and group rings plus some applications
Decomposition of G0 (RG) (G Abelian group) and extensions to some nonAbelian groups
Exercises
K1, K2 of Orders and Group Rings
Definitions and basic properties
K1, SK1 of orders and grouprings; Whitehead torsion
The functor K2
Exercises
Some Exact Sequences; Negative KTheory
MayerVietoris sequences
Localization sequences
Exact sequence associated to an ideal of a ring
Negative Ktheory Kn, n positive integer
Lower Ktheory of group rings of virtually infinite cyclic groups
HIGHER ALGEBRAIC KTHEORY AND INTEGRAL REPRESENTATIONS
Higher Algebraic KTheoryDefinitions, Constructions, and
Relevant Examples
The plus construction and higher Ktheory of rings
Classifying spaces and higher Ktheory of exact categoriesconstructions and examples
Higher Ktheory of symmetric monoidal categoriesdefinitions and examples
Higher Ktheory of Waldhausen categoriesdefinitions and examples
Exercises
Some Fundamental Results and Exact Sequences in Higher KTheory
Some fundamental theorems
Localization
Fundamental theorem of higher Ktheory
Some exact sequences in the Ktheory of Waldhausen categories
Exact sequence associated to an ideal, excision, and MayerVietoris sequences
Exercises
Some Results on Higher KTheory of Orders, Group Rings and
Modules over "EI" Categories
Some finiteness results on Kn, Gn, SKn, SGn of orders and groupings
Ranks of Kn(?), Gn(?) of orders and group rings plus some consequences
Decomposition of Gn(RG) n = 0, G finite Abelian group;
Extensions to some nonAbelian groups, e.g., quaternion and dihedral groups
Higher dimensional class groups of orders and group rings
Higher Ktheory of group rings of virtually infinite cyclic groups
Higher Ktheory of modules over "EI" categories
Higher Ktheory of P(A)G, A maximal orders in division algebras, G finite group
Exercises
Modm and Profinite Higher KTheory of Exact Categories, Orders, and Groupings
Modm Ktheory of exact categories, rings and orders
Profinite Ktheory of exact categories, rings and orders
Profinite Ktheory of padic orders and semisimple algebras
Continuous Ktheory of padic orders
MACKEY FUNCTORS, EQUIVARIANT HIGHER ALGEBRAIC KTHEORY, AND EQUIVARIANT HOMOLOGY THEORIES
Exercises
Mackey, Green, and Burnside Functors
Mackey functors
Cohomology of Mackey functors
Green functors, modules, algebras, and induction theorems
Based category and the Burnside functor
Induction theorems for Mackey and Green functors
Defect basis of Mackey and Green functors
Defect basis for KG0 functors
Exercises
Equivariant Higher Algebraic KTheory Together with Relative
Generalizations for Finite Group Actions
Equivariant higher algebraic Ktheory
Relative equivariant higher algebraic Ktheory
Interpretation in terms of group rings
Some applications
Exercises
Equivariant Higher KTheory for Profinite Group Actions
Equivariant higher Ktheory (absolute and relative)
Cohomology of Mackey functors (for profinite groups)
Exercises
Equivariant Higher KTheory for Compact Lie Group Actions
Mackey and Green functors on the category A(G) of homogeneous spaces
An equivariant higher Ktheory for Gactions
Induction theory for equivariant higher Kfunctors
Exercise
Equivariant Higher KTheory for Waldhausen Categories
Equivariant Waldhausen categories
Equivariant higher Ktheory constructions for Waldhausen categories
Applications to complicial biWaldhausen categories
Applications to higher Ktheory of group rings
Exercise
Equivariant Homology Theories and Higher KTheory of Group Rings
Classifying space for families and equivariant homology theory
Assembly maps and isomorphism conjectures
FarrellJones conjecture for algebraic Ktheory
BaumConnes conjecture
DavisLück assembly map for BC conjecture and its identification with analytic assembly map
Exercise
Appendices
A: Some computations
B: Some open problems
References
Index




Ordinary Differential Equations  Jane Cronin 

Cover Price : Rs 4,995.00

Imprint : CRC Press ISBN : 9780824723378 YOP : 2015

Binding : Hardback Total Pages : 402 CD : No


Requiring only a background in advanced calculus and linear algebra, Ordinary Differential Equations: Introduction and Qualitative Theory, Third Edition includes basic material such as the existence and properties of solutions, linear equations, autonomous equations, and stability as well as more advanced topics in periodic solutions of nonlinear equations.
This third edition of a highly acclaimed textbook provides a detailed account of the Bendixson theory of solutions of twodimensional nonlinear autonomous equations, which is a classical subject that has become more prominent in recent biological applications. By using the Poincaré method, it gives a unified treatment of the periodic solutions of perturbed equations. This includes the existence and stability of periodic solutions of perturbed nonautonomous and autonomous equations (bifurcation theory). The text shows how topological degree can be applied to extend the results. It also explains that using the averaging method to seek such periodic solutions is a special case of the use of the Poincaré method.
Features
Illustrates existence theorems with various examples, such as Volterra equations for predatorprey systems, Hodgkin–Huxley equations for nerve conduction, the Field–Noyes model for the Belousov–Zhabotinsky reaction, and Goodwin equations for a chemical reaction system
Provides a detailed account of the Bendixson theory of solutions of twodimensional autonomous systems
Presents a unified treatment of the perturbation problem for periodic solutions, covering the Poincaré method, autonomous systems, and bifurcation problems
Shows how topological degree is used to obtain significant extensions of perturbation theory
Describes how the averaging method is used to study periodic solutions
Contents
Prefaces
Introduction
Existence Theorems
What This Chapter Is About
Existence Theorem by Successive Approximations
Differentiability Theorem
Existence Theorem for Equation with a Parameter
Existence Theorem Proved by Using a Contraction Mapping
Existence Theorem without Uniqueness
Extension Theorems
Examples
Linear Systems
Existence Theorems for Linear Systems
Homogeneous Linear Equations: General Theory
Homogeneous Linear Equations with Constant Coefficients
Homogeneous Linear Equations with Periodic Coefficients: Floquet Theory
Inhomogeneous Linear Equations
Periodic Solutions of Linear Systems with Periodic Coefficients
Sturm–Liouville Theory
Autonomous Systems
Introduction
General Properties of Solutions of Autonomous Systems
Orbits near an Equilibrium Point: The TwoDimensional Case
Stability of an Equilibrium Point
Orbits near an Equilibrium Point of a Nonlinear System
The Poincaré–Bendixson Theorem
Application of the Poincaré–Bendixson Theorem
Stability
Introduction
Definition of Stability
Examples
Stability of Solutions of Linear Systems
Stability of Solutions of Nonlinear Systems
Some Stability Theory for Autonomous Nonlinear Systems
Some Further Remarks Concerning Stability
The Lyapunov Second Method
Definition of Lyapunov Function
Theorems of the Lyapunov Second Method
Applications of the Second Method
Periodic Solutions
Periodic Solutions for Autonomous Systems
Stability of the Periodic Solutions
Sell’s Theorem
Periodic Solutions for Nonautonomous Systems
Perturbation Theory: The Poincaré Method
Introduction
The Case in which the Unperturbed Equation Is Nonautonomous and Has an Isolated Periodic Solution
The Case in which the Unperturbed Equation Has a Family of Periodic Solutions: The Malkin–Roseau Theory
The Case in which the Unperturbed Equation Is Autonomous
Perturbation Theory: Autonomous Systems and Bifurcation Problems
Introduction
Using the Averaging Method: An Introduction
Introduction
Periodic Solutions
Almost Periodic Solutions
Appendix
Ascoli’s Theorem
Principle of Contraction Mappings
The Weierstrass Preparation Theorem
Topological Degree
References
Index




Differential Equations with Maxima  Drumi D.Bainov 
Author 
Drumi D. Bainov Snezhana G. Hristova


Cover Price : Rs 4,995.00

Imprint : CRC Press ISBN : 9781439867570 YOP : 2015

Binding : Hardback Total Pages : 312 CD : No


Differential equations with "maxima"—differential equations that contain the maximum of the unknown function over a previous interval—adequately model realworld processes whose present state significantly depends on the maximum value of the state on a past time interval. More and more, these equations model and regulate the behavior of various technical systems on which our everadvancing, hightech world depends. Understanding and manipulating the theoretical results and investigations of differential equations with maxima opens the door to enormous possibilities for applications to realworld processes and phenomena.
Presenting the qualitative theory and approximate methods, Differential Equations with Maxima begins with an introduction to the mathematical apparatus of integral inequalities involving maxima of unknown functions. The authors solve various types of linear and nonlinear integral inequalities, study both cases of single and double integral inequalities, and illustrate several direct applications of solved inequalities. They also present general properties of solutions as well as existence results for initial value and boundary value problems.
Later chapters offer stability results with definitions of different types of stability with sufficient conditions and include investigations based on appropriate modifications of the Razumikhin technique by applying Lyapunov functions. The text covers the main concepts of oscillation theory and methods applied to initial and boundary value problems, combining the method of lower and upper solutions with appropriate monotone methods and introducing algorithms for constructing sequences of successive approximations. The book concludes with a systematic development of the averaging method for differential equations with maxima as applied to firstorder and neutral equations. It also explores different schemes for averaging, partial averaging, partially additive averaging, and partially multiplicative averaging.
A solid overview of the field, this book guides theoretical and applied researchers in mathematics toward further investigations and applications of these equations for a more accurate study of realworld problems.
Contents
Introduction
Integral Inequalities with Maxima
Linear Integral Inequalities with Maxima for Scalar Functions of One Variable
Nonlinear Integral Inequalities with Maxima for Scalar Functions of One Variable
Integral Inequalities with Maxima for Scalar Functions of Two Variables
Applications of the Integral Inequalities with Maxima
General Theory
Existence Theory for Initial Value Problems
Existence Theory for Boundary Value Problems
Differential Equations with "Maxima" via Weakly Picard Operator Theory
Stability Theory and Lyapunov Functions
Stability and Uniform Stability
Integral Stability in Terms of Two Measures
Stability and Cone Valued Lyapunov Functions
Practical Stability on a Cone
Oscillation Theory
Differential Equations with "Maxima" versus Differential Equations with Delay
Oscillations of Delay Differential Equations with "Maxima"
Oscillations of Forced nth Order Differential Equations with "Maxima"
Oscillations and Almost Oscillations of nth Order Differential Equations with "Maxima"
Oscillations of Differential Inequalities with "Maxima"
Asymptotic Methods
MonotoneIterative Technique for Initial Value Problems
MonotoneIterative Technique for a Periodic Boundary Value Problem
MonotoneIterative Technique for Second Order Differential Equations with "Maxima"
Method of Quasilinearization for an Initial Value Problem
Method of Quasilinearization for a Periodic Boundary Value Problem
Averaging Method
Averaging Method for an Initial Value Problem
Averaging Method for Multipoint Boundary Value Problem
Partial Averaging Method
Partially Additive and Partially Multiplicative Averaging Method
Notes and Comments
Bibliography




Semigroups  P.A.Grillet 

Cover Price : Rs 4,995.00

Imprint : CRC Press ISBN : 9780824796624 YOP : 2015

Binding : Hardback Total Pages : 410 CD : No


This invaluable, singlesource reference/text offers concise coverage of the structure theory of semigroupsthoroughly examining constructions and descriptions of semigroups and emphasizing finite, commutative, regular, and inverse semigroups.
Providing a core of classical results, Semigroups introduces, for the first time in a selfcontained volume, a host of structure theorems on regular and commutative semigroups...examines associativity and products, homomorphisms, congruences, and free semigroups...discusses Green's relations and the ReesSushkevich theorem...describes ideal extensions, semilattice decompositions, subdirect products, and group coextensions ... presents the most important theorems for each area of commutative, finite, regular, and inverse semigroups...furnishes uptodate analyses of current results in semigroup theory...and much more.
Containing key bibliographic citations to facilitate more indepth study of special topics, Semigroups is a useful reference for pure and applied mathematicians, particularly semigroup theorists and algebraists, as well as computer scientists, and an indispensable text for graduatelevel students taking courses in semigroup theory.
Contents
Semigroups; Green's relations; constructions; commutative semigroups; finite semigroups; regular semigroups; inverse semigroups; fundamental regular semigroups; four classes of regular semigroups.
About the Author
P. A. GRILLET is a Professor of Mathematics at Tulane University, New Orleans, Louisiana. A member of the American Mathematical Society, he is the author of two monographs and over 60 professional papers that reflect his interest in semigroups and other subjects. Dr. Grillet received the Ph.D. degree (1965) in mathematics from the Universite de Paris (Sorbonne), France.




Theory of Distributions  M.A. AlGwaiz 

Cover Price : Rs 4,995.00

Imprint : CRC Press ISBN : 9780824786724 YOP : 2015

Binding : Hardback Total Pages : 270 CD : No


This concise reference/text presents a rigorous, motivated introduction to the theory of distributions based on the duality of certain topological vector spaces. Theory of Distributions explicates mathematical structures, including the spaces of distributions and their properties, as well as the Hilbert space aspect of the theory and its applications to typical boundary value problems for secondorder linear partial differential equations.
Covering all points of the subject, Theory of Distributions discusses locally convex spaces ...distributions of finite order .. . the Fourier transformation .. . and the trace operator in Sobolev space. Aiding classroom work or selfstudy, this highly readable volume offers over 100 workedout examples; endofchapter problems; over 1500 figures and display equations; a clear, informal presentation; an emphasis on applications; and more!
Theory of Distributions is a useful reference for pure and applied mathematicians as well as theoretical physicists, and an excellent textbook for graduatelevel students in the theory of distributions and related mathematics and physics courses.
Contents
Preface,
1. LOCALLY CONVEX SPACES
2. TEST FUNCTIONS AND DISTRIBUTIONS
3. DISTRIBUTIONS WITH COMPACT SUPPORT AND CONVOLUTIONS
4. FOURIER TRANSFORMS AND TEMPERED DISTRIBUTIONS
5. DISTRIBUTIONS IN HILBERT SPACE
6. APPLICATIONS TO BOUNDARY VALUE PROBLEMS
NOTATION
REFERENCES
INDEX
About the Author
M. A. ALGWAIZ is an Associate Professor of Mathematics at King Saud University, Riyadh, Saudi Arabia. He is the author of a textbook on complex analysis and of a number of papers which reflect his research interests in boundary value problems for partial di~rential equations, differential geometry, and mathematical physics. Dr. AlGwaiz is a member of the American Mathematical Society and the National Society for Mathematics (Saudi Arabia). He received the M .S. degree (1967) in mathematics from the Courant Institute of Mathematical Sciences, New York University, and the Ph.D. degree (1972) in mathematics from the University of Wisconsin  Madison.




Divergence Theorem and Sets of Finite Perimeter  Washek F.Pfeffer 

Cover Price : Rs 4,995.00

Imprint : CRC Press ISBN : 9781466507197 YOP : 2015

Binding : Hardback Total Pages : 260 CD : No


This book is devoted to a detailed development of the divergence theorem. The framework is that of Lebesgue integration — no generalized Riemann integrals of Henstock–Kurzweil variety are involved.
In Part I the divergence theorem is established by a combinatorial argument involving dyadic cubes. Only elementary properties of the Lebesgue integral and Hausdorff measures are used. The resulting integration by parts is sufficiently general for many applications. As an example, it is applied to removable singularities of Cauchy–Riemann, Laplace, and minimal surface equations.
The sets of finite perimeter are introduced in Part II. Both the geometric and analytic points of view are presented. The equivalence of these viewpoints is obtained via the functions of bounded variation. These functions are studied in a selfcontained manner with no references to Sobolev’s spaces. The coarea theorem provides a link between the sets of finite perimeter and functions of bounded variation.
The general divergence theorem for bounded vector fields is proved in Part III. The proof consists of adapting the combinatorial argument of Part I to sets of finite perimeter. The unbounded vector fields and mean divergence are also discussed. The final chapter contains a characterization of the distributions that are equal to the flux of a continuous vector field.
Contents
DYADIC FIGURES
Preliminaries
The setting
Topology
Measures
Hausdorff measures
Differentiable and Lipschitz maps
Divergence Theorem for Dyadic Figures
Differentiable vector fields
Dyadic partitions
Admissible maps
Convergence of dyadic figures
Removable Singularities
Distributions
Differential equations
Holomorphic functions
Harmonic functions
The minimal surface equation
Injective limits
SETS OF FINITE PERIMETER
Perimeter
Measuretheoretic concepts
Essential boundary
Vitali’s covering theorem
Density
Definition of perimeter
Line sections
BV Functions
Variation
Mollification
Vector valued measures
Weak convergence
Properties of BV functions
Approximation theorem
Coarea theorem
Bounded convex domains
Inequalities
Locally BV Sets
Dimension one
Besicovitch’s covering theorem
The reduced boundary
Blowup
Perimeter and variation
Properties of BV sets
Approximating by figures
THE DIVERGENCE THEOREM
Bounded Vector Fields
Approximating from inside
Relative derivatives
The critical interior
The divergence theorem
Lipschitz domains
Unbounded Vector Fields
Minkowski contents
Controlled vector fields
Integration by parts
Mean Divergence
The derivative
The critical variation
Charges
Continuous vector fields
Localized topology
Locally convex spaces
Duality
The space BVc(Ω)
Streams
The Divergence Equation
Background
Solutions in Lp(Ω; Rn)
Continuous solutions
Bibliography
List of Symbols
Index




Unilateral Contact Problems  Christof Eck 
Author 
Christof Eck Jiri Jarusek Miroslav Krbec


Cover Price : Rs 4,995.00

Imprint : CRC Press ISBN : 9781574446296 YOP : 2015

Binding : Hardback Total Pages : 416 CD : No


The mathematical analysis of contact problems, with or without friction, is an area where progress depends heavily on the integration of pure and applied mathematics. This book presents the state of the art in the mathematical analysis of unilateral contact problems with friction, along with a major part of the analysis of dynamic contact problems without friction.
Much of this monograph emerged from the authors' research activities over the past 10 years and deals with an approach proven fruitful in many situations. Starting from thin estimates of possible solutions, this approach is based on an approximation of the problem and the proof of a moderate partial regularity of the solution to the approximate problem. This in turn makes use of the shift (or translation) technique  an important yet often overlooked tool for contact problems and other nonlinear problems with limited regularity. The authors pay careful attention to quantification and precise results to get optimal bounds in sufficient conditions for existence theorems.
Unilateral Contact Problems: Variational Methods and Existence Theorems a valuable resource for scientists involved in the analysis of contact problems and for engineers working on the numerical approximation of contact problems. Selfcontained and thoroughly up to date, it presents a complete collection of the available results and techniques for the analysis of unilateral contact problems and builds the background required for further research on more complex problems in this area.
Contents
PREFACE
INTRODUCTION
Notations
Linear Elasticity
Formulation of Contact Problems
Variational Principles in Mechanics
The Static Contact Problem
Geometry of Domains
The Method of Tangential Translations
BACKGROUND
Fixed Point Theorems
Some General Remarks
Crash Course in Interpolation
Besov and LizorkinTriebel Spaces
The Potential Spaces
VectorValued Sobolev and Besov Spaces
Extensions and Traces
Spaces on Domains
STATIC AND QUASISTATIC CONTACT PROBLEMS
Coercive Static Case
Semicoercive Contact Problem
Contact Problems for Two Bodies
Quasistatic Contact Problem
DYNAMIC CONTACT PROBLEMS
A Short Survey About Results for Elastic Materials
Results for Materials With Singular Memory
Viscoelastic Membranes
Problems With Given Friction
DYNAMIC CONTACT PROBLEMS WITH COULOMB FRICTION
Solvability of Frictional Contact Problems
Anisotropic Material
Isotropic Material
ThermoViscoelastic Problems
BIBLIOGRAPHY
LIST OF NOTATION
SUBJECT INDEX
About the Author
Christof Eck is a Lecturer in the Institute of Applied Mathematics, University Erlangen, Germany.
Jiri Jarusek and Miroslay Krbec are with the Institute of Mathematics, Academy of Sciences of the Czech Republic, Prague.




Invariant Descriptive Set Theory  Su Gao 

Cover Price : Rs 4,995.00

Imprint : CRC Press ISBN : 9781584887935 YOP : 2015

Binding : Hardback Total Pages : 398 CD : No


Exploring an active area of mathematics that studies the complexity of equivalence relations and classification problems, Invariant Descriptive Set Theory presents an introduction to the basic concepts, methods, and results of this theory. It brings together techniques from various areas of mathematics, such as algebra, topology, and logic, which have diverse applications to other fields.
After reviewing classical and effective descriptive set theory, the text studies Polish groups and their actions. It then covers Borel reducibility results on Borel, orbit, and general definable equivalence relations. The author also provides proofs for numerous fundamental results, such as the Glimm–Effros dichotomy, the Burgess trichotomy theorem, and the Hjorth turbulence theorem. The next part describes connections with the countable model theory of infinitary logic, along with Scott analysis and the isomorphism relation on natural classes of countable models, such as graphs, trees, and groups. The book concludes with applications to classification problems and many benchmark equivalence relations.
By illustrating the relevance of invariant descriptive set theory to other fields of mathematics, this selfcontained book encourages readers to further explore this very active area of research.
Features
• Reviews classical descriptive set theory
• Covers all aspects of Polish group actions and equivalence relations
• Explores diverse applications in mathematics, including applications to classification problems
• Includes a large number of exercises at the end of most sections
• Contains an appendix with proofs of useful results about the Gandy–Harrington topology
Contents
Preface
Polish Group Actions
Preliminaries
Polish spaces
The universal Urysohn space
Borel sets and Borel functions
Standard Borel spaces
The effective hierarchy
Analytic sets and Σ 1/1 sets
Coanalytic sets and π 1/1 sets
The Gandy–Harrington topology
Polish Groups
Metrics on topological groups
Polish groups
Continuity of homomorphisms
The permutation group S∞
Universal Polish groups
The Graev metric groups
Polish Group Actions
Polish Gspaces
The Vaught transforms
Borel Gspaces
Orbit equivalence relations
Extensions of Polish group actions
The logic actions
Finer Polish Topologies
Strong Choquet spaces
Change of topology
Finer topologies on Polish Gspaces
Topological realization of Borel Gspaces
Theory of Equivalence Relations
Borel Reducibility
Borel reductions
Faithful Borel reductions
Perfect set theorems for equivalence relations
Smooth equivalence relations
The Glimm–Effros Dichotomy
The equivalence relation E0
Orbit equivalence relations embedding E0
The Harrington–Kechris–Louveau theorem
Consequences of the Glimm–Effros dichotomy
Actions of cli Polish groups
Countable Borel Equivalence Relations
Generalities of countable Borel equivalence relations
Hyperfinite equivalence relations
Universal countable Borel equivalence relations
Amenable groups and amenable equivalence relations
Actions of locally compact Polish groups
Borel Equivalence Relations
Hypersmooth equivalence relations
Borel orbit equivalence relations
A jump operator for Borel equivalence relations
Examples of Fσ equivalence relations
Examples of π 0/3 equivalence relations
Analytic Equivalence Relations
The Burgess trichotomy theorem
Definable reductions among analytic equivalence relations
Actions of standard Borel groups
Wild Polish groups
The topological Vaught conjecture
Turbulent Actions of Polish Groups
Homomorphisms and generic ergodicity
Local orbits of Polish group actions
Turbulent and generically turbulent actions
The Hjorth turbulence theorem
Examples of turbulence
Orbit equivalence relations and E1
Countable Model Theory
Polish Topologies of Infinitary Logic
A review of firstorder logic
Model theory of infinitary logic
Invariant Borel classes of countable models
Polish topologies generated by countable fragments
Atomic models and Gδorbits
The Scott Analysis
Elements of the Scott analysis
Borel approximations of isomorphism relations
The Scott rank and computable ordinals
A topological variation of the Scott analysis
Sharp analysis of S∞orbits
Natural Classes of Countable Models
Countable graphs
Countable trees
Countable linear orderings
Countable groups
Applications to Classification Problems
Classification by Example: Polish Metric Spaces
Standard Borel structures on hyperspaces
Classification versus nonclassification
Measurement of complexity
Classification notions
Summary of Benchmark Equivalence Relations
Classification problems up to essential countability
A roadmap of Borel equivalence relations
Orbit equivalence relations
General Σ 1/1 equivalence relations
Beyond analyticity
Appendix: Proofs about the Gandy–Harrington Topology
The Gandy basis theorem
The Gandy–Harrington topology on Xlow
References
Index




Degenerate Differential Equations in Banach Spaces 
Author 
Angelo Favini Atsushi Yagi


Cover Price : Rs 4,995.00

Imprint : CRC Press ISBN : 9780824716776 YOP : 2015

Binding : Hardback Total Pages : 326 CD : No


This innovative reference contains a detailed study of linear abstract degenerate differential equations and the regularity of their relations, using the semigroups generated by multivalued (linear) operators and extensions of the operational method of Da Prato and Grisvard.
Degenerate Differential Equations in Banach Spaces establishes the analyticity of the semigroup generated by degenerate parabolic operators in spaces of continuous functions ... studies the maximal regularity in time of solutions to degenerate equations of parabolic type in Banach spaces ... guarantees the existence of "regular" solutions in contrast to the generalized (distributional) solutions appearing in the literature ... introduces the semigroups of weak type generated by multivalued linear operators for the first time ... includes classical results pertaining to linear operators, evolution equations, and interpolation theory ... examines existence theory for the multivalued linear Cauchy problem in the hyperbolic and parabolic cases ... presents recent results on the regularity of semigroups generated by second order degenerate parabolic operators in various function spaces ... and more.
With over 1500 references and equations, Degenerate Differential Equations in Banach Spaces is suitable for mathematical analysts, differential geometers, topologists, pure and applied mathematicians, physicists, engineers, and graduate students in these disciplines.
Contents
PREFACE
INTRODUCTION
PRELIMINARIES AND NOTATIONS; MULTIVALUED LINEAR OPERATORS; DEGENERATE EQUATIONS OF HYPERBOLIC TYPE; DEGENERATE EQUATIONS OF PARABOLIC TYPE I; DEGENERATE EQUATIONS OF PARABOLIC TYPE II; DEGENERATE EQUATIONS  THE GENERAL CASE; DEGENERATE DIFFERENTIAL EQUATIONS OF THE SECOND ORDER; DEGENERATE PARABOLIC EQUATIONS; BIBLIOGRAPHICAL REMARKS. BIBLIOGRAPHY. LIST OF SYMBOLS. INDEX
About the Author
ANGELO FAVINI is a Professor in the Department of Mathematics at the University of Bologna, Italy. The author, coauthor, or editor of over 70 research articles and conference proceedings, he is a member of the Gruppo Nazionale per l'Analisi Funzionale e le sue Applicazioni of the Consiglio Nazionale delle Ricerche (Italy). Dr. Favini received the laurea in mathematics (1969) from the University of Bologna, Italy.
ARSUSM YAGI is a Professor of Mathematics in the Department of Applied Physics, Osaka University, Japan. A member of the Mathematical Society of Japan, Dr. Yagi received the B.S. degree (1973) in mathematics from Niigata University, Niigata City, Japan, and the M.S. (1975) and Ph.D. (1982) degrees from Osaka University, Japan.




Oscillation Theory for Functional Differential Equations  L.H. Erbe 

Cover Price : Rs 4,995.00

Imprint : CRC Press ISBN : 9780824795986 YOP : 2015

Binding : Hardback Total Pages : 496 CD : No


This valuable reference examines the latest developments in the oscillatory and nonoscillatory properties of solutions for functional differential equations, clearly presenting basic oscillation theory as well as uptotheminute; resultsmany previously unpublished.
Showing how to extend the techniques for boundary value problems of ordinary differential equations to those of functional differential equations, Oscillalion Theory for Functional Differential Equations explores in detail important topics such as the existence of oscillatory solutions…estimates of the distance between zeros...asymptotic classification of nonoscillatory solutions and criteria for certain types of nonoscillatory solutions...the oscillation of equations with nonlinear neutral terms and the oscillation of systems of equations ... boundary value problems for both singular and nonsingular functional differential equations of second order and equations of nth order ... and more
With key bibliographic citations, Oscillalion Theory for Functional Differential Equations is an indispensable resource for pure and applied mathematicians, mathematical analysts, engineers working with differential equations and oscillation theory, and upperlevel undergraduate and graduate students in these disciplines.
Contents
PRELIMINARIES; OSCILLATIONS OF FIRST ORDER DELAY DIFFERENTIAL EQUATIONS; OSCILLATION OF FIRST ORDER NEUTRAL DIFFERENTIAL EQUATIONS; OSCILLATION AND NONOSCILLATION OF SECOND ORDER DIFFERENTIAL EQUATIONS WITH DEVIATING ARGUMENTS; OSCILLATION OF HIGHER ORDER NEUTRAL DIFFERENTIAL EQUATIONS; OSCILLATION OF SYSTEMS OF NEUTRAL DIFFERENTIAL EQUATIONS; BOUNDARY VALUE PROBLEMS FOR SECOND ORDER FUNCTIONAL DIFFERENTIAL EQUATIONS.REFERENCES, INDEX
L. H. ERBE is Professor in the Mathematics Department at the University of Alberta, Edmonton, Canada. He is the author or coauthor of more than JOO professional papers and book chapters focusing mainly on differential equations and boundary value problems. Dr. Erbe received the Ph.D. degree (1968) in mathematics from the University of Nebraska at Lincoln.
QINGKAI KONG is Assistant Professor in the Department of Mathematical Sciences at Northern Illinois University, De Kalb. An invited lecturer at many conferences on the applications of differential equations, he is the author of numerous professional papers in this area. Dr Kong received the Ph.D. degree (1992) in mathematics from the University of Alberta, Edmonton, Canada.
B. G. ZHANG is a Professor in the Department of Mathematics at the Ocean University of Qingdao, Shandong, People's Republic of China. The coauthor of four books, including, with G. S. Ladde and V. Lakshmikantham, Oscillation Theory of Differential Equations with Deviating Arguments (Marcel Dekker, Inc.) and over l 00 professional papers focusing mainly on oscillation theory, he is a member of the American Mathematical Society and the Society of Mathematics of China. Dr. Zhang graduated from Shandong University, Jinan, People's Republic of China, in 1957




Real Function Algebras  S.H. Kulkarni 

Cover Price : Rs 3,995.00

Imprint : CRC Press ISBN : 9780824786533 YOP : 2015

Binding : Hardback Total Pages : 194 CD : No


This selfcontained reference/text presents a thorough account of the theory of real function algebras. Employing the intrinsic approach, avoiding the complexification technique, and generalizing the theory of complex function algebras, this singlesource volume includes: an introduction to real Banach algebras; various generalizations of the StoneWeierstrass theorem; Gleason parts; Choquet and Shilov boundaries; isometries of real function algebras; extensive references; and a detailed bibliography…and more!
Real Function Algebras offers results of independent interest such as: topological conditions for the commutativity of a real or complex Banach algebra; Ransford's short elementary proof of the BishopStoneWeierstrass theorem; the implication of the analyticity or antianalyticity of f from the harmonicity of Re f, Re f(2), Re f(3), and Re f(4); and the positivity of the real part of a linear functional on a subspace of C(X).
With over 600 display equations, this reference is for mathematical analysts; pure, applied, and industrial mathematicians; and theoretical physicists; and a text for courses in Banach algebras and function algebras.
Contents
Gleason parts of a real function algebra; boundaries for a real function algebra; isometries of real function algebras; symbols.
S. H. KULKARNI is an Assistant Professor in the Department of Mathematics at the Indian
Institute of Technology, Madras. The author of more than 25 professional papers, his research
interests include functional analysis and numerical analysis, specifically Banach algebras
and Fourier transforms. Dr. Kulkarni received the B.Sc. degree (1974) in mathematics from
the University of Poona, Pune, India, and the M.Sc. (1976) and Ph.D. (1980) degrees in
mathematics from the Indian Institute of Technology, Bombay.
B. V. LIMAYE is a Professor in the Department of Mathematics at the Indian Institute of
Technology, Bombay. He is the author or editor of five books, and the author of more than
40 professional papers and presentations. His research interests include algebraic analysis
and numerical functional analysis, specifically real Banach algebras and the iterative computation of approximate eigenvalues and eigenvectors of differential and integral operators
Dr. Limaye received the B.A. degree (1964) in mathematics from the University of Poona,
Pune, India, and the A.M. (1966) and Ph.D. (1969) degrees in mathematics from the University
of Rochester, New York.




Abstract Algebra: A Comprehensive Treatment  Claudia Menini 
Author 
Claudia Menini Freddy Van Oystaeyen


Cover Price : Rs 4,995.00

Imprint : CRC Press ISBN : 9780824709853 YOP : 2015

Binding : Hardback Total Pages : 764 CD : No


An ambitious, comprehensive book covering subject matter typically taught over the course of two or three years, Abstract Algebra offers a selfcontained presentation, detailed definitions, and excellent chaptermatched exercises to automatically smooth the trajectory of learning algebra from zero to one.
Fieldtested through advance use in the ERASMUS educational project in Europe.
Including an original treatment of representation of finite groups that avoids the use of semisimple ring theory, Abstract Algebra explains sets, maps, posets, lattices, and other essentials of the algebraic language…Peano’s axioms and cardinality…groupoids, semigroups, monoids, groups… cyclic groups and the symmetric group…Sylow’s theorems…rings, ideals, homomorphisms, and quotient rings…unique factorization and principal ideal and Euclidean domains…quotient fields and the factoriality of rings of polynomials…modules and vector spaces…Galois theory…linear codes…and ordered rings.
Contents
Preface
General Mathematical Concepts
Sets
Maps
Cartesian Product and Binary Relations
Posets, Lattices, Zorn's Lemma
Peano's Axions
Cardinality
Quotient Sets
Algebraic Structures
Groupoids, Semigroups, Monoids
Groups
The Integers
Congruences
Normal Subgroups
Isomorphism Theorems for Groups
Cyclic Groups
Direct Product of Groups
The Symmetric Group
Further Results on Groups
Rings, Ideals, and Homomorphisms
Quotient Rings
Direct Product of Rings
Domains, Prime and Maximal Ideals
Polynomials
UFD, PID and Euclidean Domains
The Quotient Field of a Domains
Factoriality of Rings of Polynomials
Modules and Vector Spaces
Field Extensions
Galois Extension
Finite Fields
The Galois Theory of Equations
Ruler and compass Constructions
Secrets in Finite Fields: Codes
Ordered Rings. The Real Numbers
Representation of Finite Groups
Some Historical Remarks
Suggestions for Further Reading
Index
CLAUDIA MENINI is Professor of Mathematics at the University of Ferrara, Ferrara, Italy. The author or coauthor of over 50 articles and the coeditor of one book, she has more then 15 years’ experience as a full professor. A member of the Unione Matematica Italiana and the American Mathematical Society, Professor Menini received the Doctor in Mathematics degree (1976) from the University of Ferrara, Ferrara, Italy.
FREDDY VAN OYSTAEYEN is Professor of Mathematics at the University of Antwerp, UIA, Belgium. The author, coauthor, editor, or coeditor of over 200 articles, proceedings, book chapters, and books, including Algebraic Geometry for Associative Algebras, Brauer Groups and the Cohomology of Graded Rings, Commutative Algebra and Algebraic Geometry, Hopf Algebras and Quantum Groups, Interactions Between Ring Theory and Representations of Algebras, and A Primer of Algebraic Geometry (all titles, Marcel Dekker, Inc.), he is a board member of the Belgium Mathematical Society and a member of the Liaisons Committee of the European Mathematical Society. Professor Van Oystaeyen received the Ph.D. degree (1972) in mathematics from the University of Amsterdam, The Netherlands, and the habilitation (1975) from the University of Antwerp, UIA, Belgium.




Functional Analytic Methods for Partial Differential Equations Hiroki Tanabe 

Cover Price : Rs 4,995.00

Imprint : CRC Press ISBN : 9780824797744 YOP : 2015

Binding : Hardback Total Pages : 424 CD : No


Combining both classical and current methods of analysis, this valuable resource presents clear, detailed discussions on the application of functional analytic methods in partial differential equations.
Examining evolution equations in Banach spaces, Functional Analytic Methods for Partial Differential Equations furnishes a slightly simplified, selfcontained proof of AgmonDouglis Nirenberg's LP estimates for boundary value problems...addresses the theory of function spaces, including interpolation inequalities, the GalgliardoNirenberg inequality, and Sobolev's imbedding theorems...describes adjoint boundary value problems...offers recent results on parabolic and hyperbolic equations...illustrates the solvability of retarded functional differential equations in Hilbert spaces...gives results on control problems...and much more.
Written by a recognized international expert in the field, Functional Analytic Methods for Partial Differential Equations is an important reference for mathematical analysts, geometers, pure and applied mathematicians, physicists, engineers. and graduatelevel students in these disciplines.
Contents
PRELIMINARIES; SINGULAR INTEGRALS; SOBOLEV SPACES; ELLIPTIC BOUNDARY VALUE PROBLEMS; ELLIPTIC BOUNDARY VALUE PROBLEMS (CONTINUED); PARABOLIC EVOLUTION EQUATIONS; HYPERBOLIC EVOLUTION EQUATIONS; RETARDED FUNCTIONAL DIFFERENTIAL EQUATIONS;
BIBLIOGRAPHICAL REMARKS
BIBLIOGRAPHY
LIST OF SYMBOLS
INDEX
HIROKI TAN ABE is a Professor in the Department of Economics at Otemon Gakuin University, Osaka, Japan. The author of three books on functional analysis and evolution equations, he is a member of the Mathematical Society of Japan and the American Mathematical Society Dr. Tanabe received the Ph.D. degree (1960) in mathematics from Osaka University, Japan.




Inequalities for Finite Difference Equations  B.G. Pachpatte 

Cover Price : Rs 4,995.00

Imprint : CRC Press ISBN : 9780824706579 YOP : 2015

Binding : Hardback Total Pages : 524 CD : No


This reference/text is a treatise on finite difference inequalities that have important applications to theories of various classes of finite difference and sumdifference equations, including several linear and nonlinear finite difference inequalities appearing for the first time in book formproviding a survey of results on fundamental linear and nonlinear finite difference inequalities and applications.
Featuring more than 3500 mathematical expressions and over 200 references, Inequalities for Finite Difference Equations introduces a variety of new finite difference inequalities...discusses perturbations...describes applications to various types of finite difference and sumdifference equations...focuses on stability of finite difference systems...considers inequalities involving iterated sums...examines basic multidimensional finite difference inequalities…identifies bounds on the solutions of difference equations...and more.
Contents
LINEAR FINITE DIFFERENCE INEQUALITIES; NONLINEAR FINITE DIFFERENCE INEQUALITIES I; NONLINEAR FINITE DIFFERENCE INEQUALITIES II; LINEAR MULTIDIMENSIONAL FINITE DIFFERENCE INEQUALITIES; NONLINEAR MULTIDIMENSIONAL FINITE DIFFERENCE INEQUALITIES.
REFERENCES
AUTHOR INDEX
SUBJECT INDEX
B. G. PACHPATTE is Professor of Mathematics, Marathwada University, Aurangabad, India. Formerly he was a visiting professor of mathematics under IndoAmerican Fellowship at the University of Texas at Arlington. A researcher of differential, integral, and difference equations and inequalities, Dr. Pachpatte is the author or coauthor of numerous professional papers and one book, and an associate editor of six international journals. Dr. Pachpatte received the Ph.D. degree (1972) from Marathwada University, Aurangabad, India.




Introduction to Functions of a Complex Variable  J. H. Curtiss 

Cover Price : Rs 4,995.00

Imprint : CRC Press ISBN : 9780824765019 YOP : 2015

Binding : Hardback Total Pages : 412 CD : No


Introduction to Functions of a Complex Variable provides an introduction to complex analysis at the advanced undergraduate and graduate levels The textbook features a rigorous treatment that should be accessible to those with some knowledge of the structure of the real number system and elementary calculus
The book begins at a basic level, and gradually increases in complexity. For example, the Cauchy Integral Theoremthe central contour integration theorem of the subjectis first dealt with in an elementary manner, and then discussed m more detail as the reader' depth of understanding is increased. In early chapters of the book the Cauchy Integral Theorem is proved only for a starlike region. Despite this restricted validation, a large number of the core results of complex function theory can be correctly derived The generalizations of the Cauchy theory to arbitrary closed curves are then taken up; the methods used employ Runge's Theorem on approximation by rational function
The emphasis on approximations by rational functions and polynomialsencompassing an early introduction to power series and a later discussion of deep applications of conformal mapping to polynomial approximations is an important secondary theme not usually found m texts of this kind The several hundred exercises that are also provided make this an outstanding textbook for students of mathematics on the undergraduate and graduate level.
Contents
FOREWORD
PREFACE
1. THE REAL AND COMPLEX NUMBER FIELDS
2. SEQUENCES AND SERIES
3. SEQUENCES AND SERIES OF COMPLEXVALUE FUNCTIONS
4. INTRODUCTION TO POWER SERIES
5. SOME ELEMENTARY TOPOLOGICAL CONCEPTS
6. COMPLEX DIFFERENTIAL CALCULUS
7. THE EXPONENTIAL AND RELATED FUNCTIONS
8. COMPLEX LINE INTEGRALS
9. INTRODUCTION TO THE CAUCHY THEORY
10. ZEROS AND ISOLATED SINGULARITIES OF ANALYTIC FUNCTIONS
11. RESIDUES AND RATIONAL FUNCTIONS
12. APPROXIMATION OF ANALYTIC FUNCTIONS BY RATIONAL FUNCTIONS, AND GENERALIZATIONS OF THE CAUCHY THEORY
13. CONFORMAL MAPPING
SOME NOTATION LISTED BY CHAPTER AND SECTION WHERE THEY FIRST APPEAR
REFERENCES
INDEX
J. H. CURTISS (d. 1977) was Professor Emeritus of Mathematics at the University of Miami, Coral Gables, Florida. He received his Ph D from Harvard University (1935), and taught at Cornell University (19361943) and the University of Miami (19591975) Dr. Curtiss' research interests included functional approximation on the complex domain, approximations by harmonic polynomials, problems in mathematical statistics, and the theory of numerical analysis. He published more than forty research papers, expository papers, and reviews in the professional literature. He was a fellow of the American Association for the Advancement of Science, a member of the American Mathematical Society, and a fellow of the Institute of Mathematical Statistics. He was Executive Director of the AMS from 1953 to 1959.




Vector and Tensor Analysis, Second Edition  Eutiquio C. Young 

Cover Price : Rs 4,995.00

Imprint : CRC Press ISBN : 9780824787899 YOP : 2015

Binding : Hardback Total Pages : 510 CD : No


about the first edition…
“…the presentation is very much oriented towards classical elementary physics. The treatment of tensors at this earthy level is unusual but may be just what some students need" – The American Mathematical Monthlv
about the second edition...
Revised and updated throughout, the Second Edition of Vector and Tensor Analysis presents the fundamental concepts of vector and tensor analysis with their corresponding physical and geometric applications  emphasizing the development of computational skills and basic procedures and exploring highly complex and technical topics in simplified settings.
Maintaining the features that made the first edition so popular, this informative reference/ text incorporates transformation of rectangular cartesian coordinate systems and the invariance of the gradient, divergence, and the curl into the discussion of tensors...combines the test for independence of path and the path independence sections...offers new examples and figures that demonstrate computational methods as well as clarify concepts...introduces subtitles in each section to highlight the appearance of new topics. Provides definitions and theorems in boldface type for easy identification...and more.
Contents
VECTOR ALGEBRA; DIFFERENTIAL CALCULUS OF VECTOR FUNCTIONS OF ONE VARIABLE; DIFFERENTIAL CALCULUS OF SCALAR AND VECTOR FIELDS; INTEGRAL CALCULUS OF SCALAR AND VECTOR FIELDS; TENSORS IN RECTANGULAR CARTESIAN COORDINATE SYSTEMS; TENSOR IN GENERAL COORDINATES; SOLUTIONS TO SELECTED PROBLEMS.
INDEX.
EUTIQUIO C. YOUNG is Professor of Mathematics, Florida State University, Tallahassee The author or coauthor of several journal acticles, he is a member of the Mathematical Association of America, Phi Mu Epsilon, and Phi Kappa Phi. Dr. Young received the B.S. degree (1954) in electrical engineering from the Far Eastern University, Manila, Republic of the Philippines, and the M.A. (1960) and Ph.D. (1962) degrees in mathematics from the University of Maryland at College Park.




Plane Algebraic Curves  G. Orzech 
Author 
G. Orzech M. Orzech


Cover Price : Rs 4,995.00

Imprint : CRC Press ISBN : 9780824711597 YOP : 2015

Binding : Hardback Total Pages : 234 CD : No


Plane Algebraic Curves is a classroomtested textbook for advanced undergraduate and beginning graduate students in mathematics. The book introduces the contemporary notions of algebraic varieties, morphisms of varieties, and adeles to the classical subject of plane curves over algebraically closed fields. By restricting the rigorous development of these notions to a traditional context the book makes its subject accessible without extensive algebraic prerequisites Once the reader's intuition for plane curves has evolved, there is a discussion of how these objects can be generalized to higher dimensional settings. These features, as well as a proof of the RiemannRoch Theorem based on a combination of geometric and algebraic considerations, make the book a good foundation for more specialized study in algebraic geometry, commutative algebra, and algebraic function fields
Plane Algebraic Curves is suitable for readers with a variety of backgrounds and interests The book begins with a chapter outlining prerequisites, and contains informal discussions giving an overview of its material and relating it to nonalgebraic topics which would be familiar to the general reader. There is an explanation of why the algebraic genus of a hyperelliptic curve agrees with its geometric genus as a compact Riemann surface, as well as a thorough description of how the classically important elliptic curves can be described in various normal forms. The book concludes with a bibliography which students can incorporate into their further studies.
Contents
PREFACE
CHAPTER 0: PREREQUISITES
CHAPTER 1: SOME FACTS ABOUT POLYNOMIALS
CHAPTER 2: AFFINE PLANE CURVES
CHAPTER 3: TANGENT SPACES
CHAPTER 4: THE LOCAL RING AT A POINT
CHAPTER 5: PROJECTIVE PLANE CURVES
CHAPTER 6: RATIONAL MAPPINGS, BIRATIONAL CORRESPONDENCES AND ISOMORPHISMS OF CURVES
CHAPTER 7: EXAMPLES OF RATIONAL CURVES
CHAPTER 8: THE CORRESPONDENCE BETWEEN VALUATIONS AND POINTS
CHAPTER 9: AN OVERVIEW AND SIDEWAYS GLANCE
CHAPTER 10: DIVISORS
CHAPTER 11: THE DIVISOR OF A FUNCTION HAS DEGREE 0
CHAPTER 12: RIEMANN’S THEOREM
CHAPTER 13: THE GENUS OF A NONSINGULAR PLANE CURVE
CHAPTER 14: CURVES OF GENUS 0 AND 1
CHAPTER 15: A CLASSIFICATION OF ISOMORPHISM CLASSES OF CURVES OF GENUS 1
CHAPTER 16: THE GENUS OF A SINGULAR CURVE
CHAPTER 17: INFLECTION POINTS ON PLANE CURVES
CHAPTER 18: BEZOUT’S THEOREM
CHAPTER 19: ADDITION ON A NONSINGULAR CUBIC
CHAPTER 20: DERIVATIONS, DIFFERENTIALS AND THE CANONICAL CLASS
CHAPTER 21: ADELES AND THE RIEMANNROCH THEOREM
BIBLIOGRAPHY
NOTATION
INDEX
GRACF ORZECH is Assistant Professor of Mathematics at Queen's University m Kingston. Canada She received her M.A. degree (1965) from Cornell University and her Ph.D. degree (1970) from the University of Illinois at ChampaignUrbana Dr. Orzech is managing editor for the series Queen's Papers in Pure and Applied Mathematics, and she has published two articles on triple cohomology. She is a member of the Mathematical Association of America and the Association for Women in Mathematics.
MORRIS ORZECH is Associate Professor of Mathematics at Queen's University in Kingston, Canada He received his Ph.D. degree ( 1967) from Cornell University and was a member of the Institute for Advanced Study at Princeton University (19741975). Dr. Orzech's publications include articles about Galois extensions of rings, Brauer groups, and the Hopfian property for rings and modules He is coauthor with Charles Small of The Brauer Groups of Commutative Rings (Marcel Dekker, Inc.). Dr. Orzech is a member of the American Mathematical Society.




Coding Theory and Cryptography: The Essentials, Second Edition  D.C. Hankerson 
Author 
D.C. Hankerson Gary Hoffman D.A. Leonard Charles C Lindner


Cover Price : Rs 3,995.00

Imprint : CRC Press ISBN : 9780824704650 YOP : 2015

Binding : Hardback Total Pages : 360 CD : No


about the first edition...
"...provides an excellent introduction to the subject at a level that allows all of the important concepts to be developed.” – Zentralblatt fur Mathematik urd ihre Grenzgebiete
about the second edition…
This highly successful textbook, proven by the authors in a popular twoquarter course, presents coding theory, construction, encoding, and decoding of specific code families in an easytouse manner appropriate for students with only a basic background in mathematicsoffering revised and updated material on the BerlekampMassey decoding algorithm and convolutional codes. The revised edition includes an extensive new section on cryptography, designed for an introductory course on the subject.
Contents
Preface
Part I: Coding Theory
1. Introduction to Coding Theory
2. Linear Codes
3. Perfect and Related Codes
4. Cyclic Linear Codes
5. BCH Codes
6. ReedSolomon Codes
7. Burst ErrorCorrecting Codes
8. Convolutional Codes
9. ReedMuller and Preparata Codes
Part II: Cryptography
10. Classical Cryptography
11. Topics in Algebra and Number Theory
12. Publickey Cryptography
A The Euclidean Algorithm
B Factorization of 1 + xn
C Examples of Compact Disk Encoding
D Solutions to Selected Exercises
Bibliography
Index
D. R. HANKERSON is Professor of Mathematics at Auburn University, Alabama. He received the Ph.D. degree (1986) in mathematics from the University of Nebraska at Lincoln.
D. G. HOFFMAN is Professor of Mathematics at Auburn University, Alabama. The author or coauthor of over 20 journal articles, he received the Ph.D. degree (1976) in mathematics from the University of Waterloo, Ontario, Canada.
D. A. LEONARD is Professor of Mathematics at Auburn University, Alabama. A member of the
American Mathematical Society and Institute of Combinatorics and Its Applications, he received
the Ph.D. degree (1980) in mathematics from Ohio State University, Columbus.
C. C LINDNER is Professor of Mathematics at Auburn University, Alabama. A member of the
American Mathematical Society, the Mathematical Association of America, the Combinatorial Mathematics Society of Australasia, and the Canadian Mathematical Society, he received the Ph.D. degree (1969) in mathematics from Emory University, Atlanta, Georgia.
K. T. PHELPS is Professor of Mathematics at Auburn University, Alabama. A member of the Society for Industrial and Applied Mathematics, he received the Ph.D. degree (1976) in mathematics from Auburn University, Alabama.
C. A. RODGER is Professor of Mathematics at Auburn University, Alabama. The author or coauthor of over 110 journal articles and book chapters, he is a Fellow of the Australian Mathematics Society, a Foundation Fellow of the Institute of Combinatorics and Its Applications, and a member of the Combinatorial Mathematics Society of Australasia. Professor Rodger received the Ph.D. degree (1982) in mathematics from the University of Reading, Berkshire, England.




Foundations of Translation Planes  Mauro Biliotti 
Author 
Mauro Biliotti Vikram Jha Norman Johnson


Cover Price : Rs 4,995.00

Imprint : CRC Press ISBN : 9780824706098 YOP : 2015

Binding : Hardback Total Pages : 558 CD : No


This uptotheminute reference/text provides comprehensive coverage of the construction and analysis of translation planes with regard to spreads, partial spreads, coordinate structures, automorphisms, autotopisms, and collineation groupsemphasizing the manipulation of incidence structures by various coordinate systems, including quasifields , spreads , and matrix spreadsets .
Containing geometric, algebraic, and grouptheoretic approaches to translation planes. as well as numerous problem/solution exercises ,Foundations of Translation Planes discusses the theory of coordinatization...tangentially transitive translation planes...the theorems of Ostrom, Hering, Foulser, and Andre...fundamental analysis of matrix spread sets...and more.
CONTENTS
PREFACE; AN OVERVIEW;ANDRE'S THEORY OF SPREADS; SPREADS IN PG(3,K); PARTIAL SPREADS AND TRANSL ATION NETS; SPREADSHEETS AND PARTIAL SPREADSETS; GEOMETRY OF SPREADSETS; COORDINATIZATION BY SPREADSETS  GENERAL CASES; PARTIAL QUASIFIELDS; COORDINATIZATION BY (PARTIAL) QUASIFIELDS; RATIONAL DESARGUESIAN NETS; QUASIGROUPS, LOOPS AND NUCLEI; (PRE)QUASIFIELDS ALGEBRAIC AXIOMS AND AUTOPISMS; THE KERNEL OF SPREADSETS AND QUASIFIELDS; QUADRATICS OF TWO DIMENSIONAL QUASIFIELDS  HALL SYSTEMS; SPREADS IN PROJECTIVE SPACES; KERNEL SUBPLANES ACROSS DESARGUESIAN NETS; DERIVATION OF FINITE SPREADS; FOULSER'S COVERING THEOREM; STRUCTURE OF BAER GROUPS; FROBENIUS COMPLEMENTS, PPRIMITIVE COLLINEATIONS, AND KLEIN4 GROUPS; LARGE PLANAR GROUPS; FINITE GENERALIZED ANDRE SYSTEMS AND NEARFIELDS; ELATION NET THEORY; BAERELATION THEORY; SIMPLE TEXTENSIONS OF DERIVABLE NETS; CYCLIC SEMIFIELDS; BAER GROUPS ON PARABOLIC SPREADS; LIFTING AND QUASIFIBRATIONS; MIXED TANGENTIALLY TRANSITIVE PLANES; MAXIMAL PARTIAL SPREADS; FOULSERJOHNSON SL (2,Q)THEOREM; APPENDICES; BIBLIOGRAPHY;INDEX
MAURO BILIOTTI is Professore Ordinario di Geometria Superiore at the University of Lecce, Italy. The author or coauthor of numerous publications, he serves on the Editorial Board of Note di Matematica. A contributing author to Mostly Finite Geometries, edited by Norman L. Johnson (Marcel Dekker, Inc.), he received the Professore Straordinario di Geometria Superiore (1981) and the Professore Ordinario di Geometria Superiore (1984) at the University of Lecce,Italy.
VIKRAM JHA is a Reader in the Mathematics Department of Glasgow Caledonian University, Scotland. The author or coauthor of over 60 research articles on translation planes and related areas of finite geometries and nonassociative algebras, he is a member of the Institute of Combinatorics and Its Applications. A contributing author to Mostly Finite Geometries, edited by Norman L. Johnson (Marcel Dekker, Inc.), he received the PhD. degree (1972) from Queen Mary and Westfield College, University of London, England.
NORMAN L. JOHNSON is a Professor of Mathematics at the University of Iowa, Iowa City. The author or coauthor of over 200 books and research articles and an Editor of Note di Matematica, he is the author, coauthor, or coeditor of Finite Geometries, Mostly Finite Geometries, and Subplane Covered Nets (all titles, Marcel Dekker, Inc.) and a referee for numerous journals, the National Science Foundation, the National Security Association, and the Research Councils of Canada and CONICET. He received the BA. degree (1964) from Portland State University, Oregon, and the MA. (1966) and PhD. (1968) degrees from Washington State University, Pullman.




Compatibility, Stability, and Sheaves  J.L. Bueso 
Author 
J.L. Bueso P. Jara A. Verschoren


Cover Price : Rs 4,995.00

Imprint : CRC Press ISBN : 9780824795894 YOP : 2015

Binding : Hardback Total Pages : 280 CD : No


This unique. selfcontained referencethe first indepth examination of compatibility of its kindintegrates fundamental techniques from algebraic geometry, localization theory, and ring theory and demonstrates how each of these topics is enhanced by interaction with the others, providing new results within a common framework
Connecting classical theory and novel methods, Compatibility, Stability, and Sheaves furnishes clear presentations of technical conclusions illustrated with concrete examples…supplies all necessary background information on abstract localization theory…highlights the second layer condition...describes basic sheaf constructions over arbitrary rings…studies in detail different types of ring extensions, concentrating on features related to the behavior of prime ideals and localization...investigates the ArtinRees property and its variants in the noncommutative case and shows how they are related…discusses structure sheaves, including the compatibility results needed to understand their construction and functorial behavior…and more.
Written by three of the world's acknowledged experts in the field, Compatibility, Stability, and Sheaves 1s an excellent resource for algebraists, number, ring, category, and Ktheorists, pure and applied mathematicians; geometers and algebraic geometers; topologists; mathematical analysts working with sheaves or localization; and graduatelevel students in these disciplines.
CONTENTS
LOCALIZATION; EXTENSIONS; STABILITY; COMPATIBILITY AND SHEAVES; BIBLIOGRAPHY; INDEX
J L BUESO is a Professor m the Department of Algebra at the University of Granada, Spam. The author or editor of four books and some 30 professional papers, he is the organizer of several meetings in ring theory and its applications Dr Bueso received the Ph.D degree (1980) in mathematics from the University of Granada, Spain.
P JARA 1s a Professor in the Department of Algebra at the University of Granada, Spain. A member of the American Mathematical Society and the Real Sociedad Matematica Espanola, he is the author or editor of three books and the author of over 25 professional papers Dr. Jara received the Ph. D degree (1983) in mathematics from the Umversuy of Granada, Spain.
A VERSCHOREN is a Professor of Geometry at the University of Antwerp, Belgium. He is the author, coauthor, or coeditor of 11 books. including Reflectors and Localization Application to Sheaf Theory, Relative Invariants of Rings• The Commutative Theory. Relative Invariants of Rings: The Noncommutative Theory, all with F. Van Oystaeyen, and Relative Invariants of Sheaves (all titles, Marcel Dekker, Inc ) In addition, he is the author or coauthor of over 100 professional papers and a member of the American Mathematical Society, the Belgian Mathematical Society, and the European Mathematical Society. A Laureate of the Belgian Academy of Sciences, Professor Verschoren received the Ph. D degree (1979) in algebraic geometry from the University of Antwerp. Belgium.




Linear and Integer Programming: Theory and Practice, Second Edition  Gerard Sierksma 

Cover Price : Rs 4,995.00

Imprint : CRC Press ISBN : 9780824706739 YOP : 2015

Binding : Hardback Total Pages : 650 CD : No


about the first edition...
" ... this book is wellsuited to accompany courses in operations research .... mathematical theory is well motivated by interesting and plausible examples." Mathematical Reviews
about the second edition...
This authoritative reference/text combines the theoretical and practical aspects of linear and integer programmingproviding practical case studies and techniques, including roundingoff, columngeneration, game theory, multiobjective optimization, and goal programming as well as realworld solutions to the transportation and transshipment problem, project scheduling, decentralization, and machine scheduling problems.
Thoroughly reorganized throughout to provide enhanced logical and clear presentation of the topics discussed, linear and Integer Programming, Second Edition decouples theory and solutions for indepth analyses ... covers duality, degeneracy, and multiplicity from a geometrical viewpoint...considers branchandbound, simplex, revised simplex, and network simplex techniques...examines sensitivity analysis ... details the GilmoreGomory and Bender decomposition methods...highlights the interior path version of Karmarkar's method ... examines mixedinteger programming and the theory of logical variables ... demonstrates the theory of totally unimodular and network matrices ... outlines linear algebra, convexity, and graph theory...displays flow diagrams for composing courses .. contains software for the interior path method...and more.
CONTENTS
LINEAR OPTIMISATION; BASIC CONCEPTS; DANTZIG'S SIMPLEX METHOD; DUALITY AND OPTIMALITY; SENSITIVITY ANALYSIS; KARMARKAR'S INTERIOR PATH METHOD; INTEGER LINEAR PROGRAMMING; LINEAR NETWORK MODELS; COMPUTATIONAL COMPLEXITY ISSUES; MODEL BUILDING, CASE STUDIES, AND ADVANCED TECHNIQUES; SOLUTIONS TO SELECTED EXERCISES. APPENDICES: LINEAR ALGEBRA; CONVEXITY; GRAPH THEORY; COMPUTER PACKAGE INTPM. BIBLIOGRAPHY; LIST OF SYMBOLS;INDEX
GERARD SIERKSMA is a Professor of Logistical Management and Operations Research at the
University of Groningen, The Netherlands. The author or coauthor of numerous professional publications, ranging from pure mathematics and philosophy to logistics and sports, Dr. Sierksma 1s a Fellow of the Canadian Institute of Combinatorics and Its Applications and a member of the American Institute for Operations Research and Management Sciences, the Netherlands Society for Statistics and Operations Research, and the Dutch Mathematical Society. He received the M.Sc. degree (1970) in mathematics and physics and the Ph.D. degree (1976) in mathematics from the University of Groningen, The Netherlands.




Differential Geometry and Relativity Theory  Richard L. Faber 

Cover Price : Rs 4,995.00

Imprint : CRC Press ISBN : 9780824717490 YOP : 2015

Binding : Hardback Total Pages : 266 CD : No


Differential Geometry and Relativity Theory: An Introduction approaches relativity as a geometric theory of space and time in which gravity is a manifestation of spacetime curvature, rather than a force. Uniting differential geometry and both special and general relativity in a single source, this easytounderstand text opens the general theory of relativity to mathematics majors having a background only in multivariable calculus and linear algebra.
The book offers a broad overview of the physical foundations and mathematical details of relativity, and presents concrete physical interpretations of numerous abstract concepts in Riemannian geometry. The work is profusely illustrated with diagrams aiding in the understanding of proofs and explanations. Appendices feature important material on vector analysis and hyperbolic functions.
Differential Geometry and Relativity Theory: An Introduction serves as the ideal text for highlevel undergraduate courses in mathematics and physics, and includes a solutions manual augmenting classroom study. It is an invaluable reference for mathematicians interested in differential and Riemannian geometry, or the special and general theories of relativity.
Contents
PREFACE
ACKNOWLEDGMENTS
I SURFACES AND THE CONCEPT OF CURVATURE
 Curves
 Gauss Curvature (Informal Treatment)
 Surfaces in E3
 The First Fundamentals Form
 The Second Fundamental Form
 The Gauss Curvature in Detail
 Geodesics
 The Curvature Tensor and the Theorema Egregium
 Manifolds
II SPECIAL RELATIVITY (THE GEOMETRY OF FLAT SPACETIME)
 Inertial Frames of Reference
 The MichelsonMorley Experiment
 The Postulates of Relativity
 Relativity of Simultaneity
 Coordinates
 Invariance of the Interval
 The Lorentz Transformation
 Spacetime Diagrams
 Lorentz Geometry
 The Twin Paradox
 Temporal Order and Causality
III GENERAL RELATIVITY (THE GEOMETRY OF CURVED SPACETIME)
 The Principles of Equivalence
 Gravity as Spacetime Curvature
 The Consequence’s of Einstein’s Theory
 The Universal Law of Gravitation
 Orbit’s in Newton’s Theory
 Geodesics
 The Field Equations
 The Schwarzschild Solution
 Orbits in General Relativity
 The Bending of Light
APPENDIX A  Vector Geometry and Analysis
APPENDIX B – Hyperbolic Functions
BIBLIOGRAPHY
INDEX
RICHARD L. FABER is Associate Professor of Mathematics at Boston College, Chestnut Hill, Massachusetts–a position he has held since 1971. He received the B.S. degree (1960) from Massachusetts Institute of Technology, and the M.A. and Ph.D degrees (1962, 1965 respectively) from Brandeis University, Waltham, Massachusetts. Dr. Faber's research interests include computer science, nonEuclidean geometry, differential geometry, history of geometry, and general relativity, and he has published a number of papers in these areas. He is the author of Foundations of Euclidean and NonEuclidean Geometry (Marcel Dekker, Inc.).




Advanced Calculus  William L.Voxman 
Author 
William L. Voxman Roy H. Goetschel


Cover Price : Rs 4,995.00

Imprint : CRC Press ISBN : 9780824769499 YOP : 2015

Binding : Hardback Total Pages : 690 CD : No


Advanced Calculus An Introduction to Modem Analysis, an advanced undergraduate textbook, provides mathematics majors, as well as students who need mathematics In their field of study, with an introduction to the theory and applications of elementary analysis. The text presents, in an accessible form, a carefully maintained balance between abstract concepts and applied results of significance that serves to bridge the gap between the two or threesemester calculus sequence and senior/graduate level courses in the theory and applications of ordinary and partial differential equations, complex variables, numerical methods, and measure and integration theory.
The book focuses on topological concepts, such u compactness, connectedness, and metric spaces, and topics from analysis including Fourier series, numerical analysis, complex integration, generalized functions, and Fourier and Laplace transforms. Applications from genetics, spring systems, enzyme transfer, and a thorough introduction to the classical vibrating string, heat transfer, and brachistochrone problems illustrate this book's usefulness to the nonmathematics major. Extensive problem sets found throughout the book test the student's understanding of the topics and help develop the student's ability to handle more abstract mathematical ideas.
Advanced Calculus: An Introduction to Modem Analysis is intended for junior• and seniorlevel undergraduate students in mathematics, biology, engineering, physics, and other related disciplines An excellent textbook for a oneyear course In advanced calculus, the methods employed in this text will increase students' mathematical maturity and prepare them solidly for senior/graduate level topics. The wealth of materials in the text allows the instructor to select topics that are of special interest to the student A two or threesemester calculus sequence is required for successful use of this book.
Contents
Preface
Chapter 1: Preliminaries
Chapter 2: Introduction to Linear Algebra and Ordinary Differential Equations
Chapter 3: Limits and Metric Spaces
Chapter 4: Continuity, Compactness, and Connectedness
Chapter 5: The Derivation: Theory and Elementary Applications
Chapter 6: A first Look at Integration
Chapter 7: Differentiation of Functions of Several Variables
Chapter 8: Sequences and Series
Chapter 9: Elementary Applications of Infinite Series
Chapter 10: An Introduction to Fourier Analysis
Chapter 11: An Introduction to Modern Integration Theory
Chapter 12: An Introduction to Complex Integration
Chapter 13: The Fourier and Laplace Transforms
Chapter 14: A Sampling of Numerical Analysis
Answers to Selected Problems
Appendix: Table of Laplace Transforms
Symbols Used in the Text
Index
WILLIAM L. VOXMAN is Professor of Mathematics at the University of Idaho, Moscow. Dr. Voxman received his B.A. (1960), M.S. (1963) and PhD. degrees (1968) from the University of Iowa. He has taught in Chile and Ecuador on Latin American Teaching Fellowships and Fullbright Travel Grants, and coauthored a book with Charles O. Christenson, Aspects of Topology (Marcel Dekker, Inc.). A member of Sigma Xi and the American Mathematical Society, Dr. Voxman's research interests are general topology, mathematical applications to biology, and fuzzy sets and systems.
ROY H. GOETSCHEL, JR. is Associate Professor of Mathematics at the University of Idaho, Moscow. Dr. Goetschel received his PhD. degree (1966) from the University of Wisconsin, and he taught at Sonoma State College from 1966 to 1969 before joining the University of Idaho faculty in 1969. Dr. Goetachel's research interests include asymptotic methods, turning point problems in differential equations, and fuzzy set theory.




Classes of Modules  John Dauns 
Author 
John Dauns Yiqiang Zhou


Cover Price : Rs 4,995.00

Imprint : CRC Press ISBN : 9781584886600 YOP : 2015

Binding : Hardback Total Pages : 228 CD : No


By working with natural classes and type submodules (TS), Classes of Modules demonstrates the importance of the next generation of ring and module theory. It shows how to achieve positive results by placing restrictive hypotheses on only a small subset of the complement submodules, i.e., the TS. Furthermore, it explains why direct sum decompositions of various kinds exist.
Carefully developing the foundations of the subject, the authors begin by providing background on the terminology and introducing the different module classes. The modules classes consist of torsion, torsionfree, s[M], natural, and prenatural. They expand the discussion by exploring advanced theorems and new classes, such as new chain conditions, TSmodule theory, and the lattice of prenatural classes of right Rmodules. The book finishes with a study of the lattice of prenatural classes and its Boolean sublattice of natural classes.
Through the novel concepts presented, Classes of Modules provides a new, unexplored direction to take in ring and module theory.
Features
• Explores the themes of natural classes and TS, and how they structure much of ring and module theory
• Gives tools, new methods, and new concepts to advance ring and module research
• Compiles previously scattered material with improved and expanded results as well as simplified proofs
• Offers new proofs and explanations that cannot be found in other literature
• Provides selfcontained, accessible material for those with some knowledge of basic ring theory
Contents
Preface
Note to the Reader
List of Symbols
PRELIMINARY BACKGROUND
Notation and Terminology
Lattices
IMPORTANT MODULE CLASSES AND CONSTRUCTIONS
Torsion Theory
The Module Class s[M]
Natural Classes
MNatural Classes
PreNatural Classes
FINITENESS CONDITIONS
Ascending Chain Conditions
Descending Chain Conditions
Covers and Ascending Chain Conditions
TYPE THEORY OF MODULES: DIMENSION
Type Submodules and Type Dimensions
Several Type Dimension Formulas
Some NonClassical Finiteness Conditions
TYPE THEORY OF MODULES: DECOMPOSITIONS
Type Direct Sum Decompositions
Decomposability of Modules
Unique Type Closure Modules
TSModules
LATTICES OF MODULE CLASSES
The Lattice of PreNatural Classes
More Sublattice Structures
Lattice Properties of Npr (R)
More Lattice Properties of Npr (R)
The Lattice Nr(R) and Its Applications
The Boolean Ideal Lattice
REFERENCES
INDEX
John Dauns is a member of the American Mathematical Society and a professor of mathematics at Tulane University, New Orleans, Louisiana, USA.
Yiqiang Zhou is a member of the Canadian Mathematical Society and an associate professor of mathematics at Memorial University of Newfoundland, St. John’s, Canada.




Direct Sum Decompositions of Torsion Free Finite Rank Groups  Theodore G.Faticoni 
Author 
Theodore G. Faticoni


Cover Price : Rs 4,995.00

Imprint : CRC Press ISBN : 9781584887263 YOP : 2015

Binding : Hardback Total Pages : 338 CD : No


With plenty of new material not found in other books, Direct Sum Decompositions of TorsionFree Finite Rank Groups explores advanced topics in direct sum decompositions of abelian groups and their consequences. The book illustrates a new way of studying these groups while still honoring the rich history of unique direct sum decompositions of groups.
Offering a unified approach to theoretic concepts, this reference covers isomorphism, endomorphism, refinement, the Baer splitting property, Gabriel filters, and endomorphism modules. It shows how to effectively study a group G by considering finitely generated projective right End(G)modules, the left End(G)module G, and the ring E(G) = End(G)/N(End(G)). For instance, one of the naturally occurring properties considered is when E(G) is a commutative ring. Modern algebraic number theory provides results concerning the isomorphism of locally isomorphic rtffr groups, finitely faithful Sgroups that are Jgroups, and each rtffr Lgroup that is a Jgroup.
Features
• Uses modern algebraic number theory to answer various questions regarding groups
• Discusses direct sum decompositions of rtffr groups using A(.)
• Employs the localization theory in S to study E(G)
• Examines commutative endomorphism rings of rtffr groups–rings that have often been overlooked in the literature
• Characterizes rtffr groups G that satisfy the Baer splitting property
• Investigates possible homological dimensions of the left End(G)module G
• Contains useful appendices, motivational examples, and numerous exercises to reinforce the concepts
Contents
PREFACE
NOTATION AND PRELIMINARY RESULTS
Abelian Groups
Associative Rings
Finite Dimensional QAlgebras
Localization in Commutative Rings
LocalGlobal Remainder
Integrally Closed Rings
SemiPerfect Rings
Exercise
MOTIVATION BY EXAMPLE
Some Well Behaved Direct Sums
Some Badly Behaved Direct Sums
Corner's Theorem
ArnoldLadyMurley Theorem
Local Isomorphism
Exercises
Questions for Future Research
LOCAL ISOMORPHISM IS ISOMORPHISM
Integrally Closed Rings
Conductor of an Rtffr Ring
Local Correspondence
Canonical Decomposition
Arnold's Theorem
Exercises
Questions for Future Research
COMMUTING ENGOMORPHISMS
Nilpotent Sets
Commutative Rtffr Rings
EProperties
SquareFree Ranks
Refinement and SquareFree Rank
Hereditary Endomorphism Rings
Exercises
Questions for Future Research
REFINEMENT REVISITED
Counting Isomorphism Classes
Integrally Closed Groups
Exercises
Questions for Future Research
BAER SPLITTING PROPERTY
Baer's Lemma
Splitting of Exact Sequences
GCompressed Projectives
Some Examples
Exercises
Questions for Future Research
JGROUPS, L GROUPS, AND S GROUPS
Background on Ext
Finite Projective Properties
Finitely Projective Groups
Finitely Faithful SGroups
Isomorphism versus Local Isomorphism
Analytic Number Theory
Eichler LGroups Are JGroups
Exercises
Questions for Future Research
GABRIEL FILTERS
Filters of Divisibility
Idempotent Ideals
Gabriel Filters on Rtffr Rings
Gabriel Filters on QEnd(G)
Exercises
Questions for Future Research
ENDOMORPHISM MODULES
Additive Structures of Rings
EProperties
Homological Dimensions
SelfInjective Rings
Exercises
Questions for Future Research
APPENDIX A: Pathological Direct Sums
Nonunique Direct Sums
APPENDIX B: ACD Groups
Example by Corner
APPENDIX C: Power Cancellation
Failure of Power Cancellation
APPENDIX D: Cancellation
Failure of Cancellation
APPENDIX E: Corner Rings and Modules
Topological Preliminaries
The Construction of G
Endomorphisms of G
APPENDIX F: Corner's Theorem
Countable Endomorphism Rings
APPENDIX G: Torsion TorsionFree Groups
ETorsion Groups
SelfSmall Corner Modules
APPENDIX H: EFlat Groups
Ubiquity
Unfaithful Groups
APPENDIX I: Zassenhaus and Butler
Statement
Proof
APPENDIX J: Countable ERings
Countable TorsionFree ERings
APPENDIX K: Dedekind ERings
Number Theoretic Preliminaries
Integrally Closed Rings
BIBLIOGRAPHY
INDEX
Theodore G. Faticoni is a professor in the department of mathematics at Fordham University, Bronx, New York, USA.




Analysis and Approximation of Contact Problems with Adhesion Or Damage  Mircea Sofonea 
Author 
Mircea Sofonea , Weimin Han Meir Shillor


Cover Price : Rs 3,995.00

Imprint : CRC Press ISBN : 9781584885856 YOP : 2015

Binding : Hardback Total Pages : 238 CD : No


Research into contact problems continues to produce a rapidly growing body of knowledge. Recognizing the need for a single, concise source of information on models and analysis of contact problems, accomplished experts Sofonea, Han, and Shillor have carefully selected and thoroughly examined several models in Analysis and Approximation of Contact Problems with Adhesion or Damage. The book describes the most recent models of contact processes with adhesion or damage along with their mathematical formulations, variational analysis, and numerical analysis.
Following an introduction to modeling, functional and numerical analysis, the book devotes individual chapters to models involving adhesion and material damage, respectively, with each chapter exploring a particular model. For each model, For each model, the authors provide a variational formulation and establish the existence and uniqueness of a weak solution. They study a fully discrete approximation scheme that uses the finite element method to discretize the spatial domain and finite differences for the time derivatives. The final chapter summarizes the results, presents bibliographic comments, and considers future directions in the field.
• Provides a unified presentation of new dynamic and quasistatic models for contact with adhesion or material damage
• Presents a systematic development of optimal order error estimates for numerical solutions of the contact problems
• Demonstrates convergence of the problems with normal compliance to those with the Signorini condition
• Offers a selfcontained presentation of the results
Employing recent results on elliptic and evolutionary variational inequalities, convex analysis, nonlinear equations with monotone operators, and fixed points of operators, Analysis and Approximation of Contact Problems with Adhesion or Damage places these important tools and results at your fingertips in a unified, accessible reference.
Contents
Preface
List of Symbols
Modeling and Mathematical Background
Basic Equations and Boundary Conditions
Physical Setting and Evolution Equations
Boundary Conditions
Contact Processes with Adhesion
Constitutive Equations with Damage
Preliminaries on Functional Analysis
Function Spaces and Their Properties
Elements of Nonlinear Analysis
Standard Results on Variational Inequalities and Evolution Equations
Elementary Inequalities
Preliminaries on Numerical Analysis
Finite Difference and Finite Element Discretizations
Approximation of Displacements and Velocities
Estimates on the Discretization of Adhesion Evolution
Estimates on the Discretization of Damage Evolution
Estimates on the Discretization of Viscoelastic Constitutive Law
Estimates on the Discretization of Viscoplastic Constitutive Law
Frictionless Contact Problems with Adhesion
Quasistatic Viscoelastic Contact with Adhesion
Problem Statement
Existence and uniqueness
Continuous Dependence on the Data
Spatially Semidiscrete Numerical Approximation
Fully Discrete Numerical Approximation
Dynamic Viscoelastic Contact with Adhesion
Problem Statement
Existence and Uniqueness
Fully Discrete Numerical Approximation
Quasistatic Viscoplastic Contact with Adhesion
Problem Statement
Existence and Uniqueness for the Signorini Problem
Numerical Approximation for the Signorini Problem
Existence and Uniqueness for the Problem with Normal Compliance
Numerical Approximation of the Problem with Normal Compliance
Relation between the Signorini and Normal Compliance Problems
Contact Problems with Damage
Quasistatic Viscoelastic Contact with Damage
Problem Statement
Existence and Uniqueness
Fully Discrete Numerical Approximation
Dynamic Viscoelastic Contact with Damage
Problem Statement
Existence and Uniqueness
Fully Discrete Numerical Approximation
Quasistatic Viscoplastic Contact with Damage
Problem Statement
Existence and Uniqueness for the Signorini Problem
Numerical Approximation for the Signorini Problem
Existence and Uniqueness for the Problem with Normal Compliance
Numerical Approximation of the Problem with Normal Compliance
Relation between the Signorini and Normal Compliance Problems
Notes, Comments, and Conclusions
Bibliographical Notes, Problems for Future Research, and Conclusions
Bibliographical Notes
Problems for Future Research
Conclusions
References
Index
Mircea Sofonea is Professor of Mathematics at the Universite de Perpignan, Perpignan, France.
Weimin Han is Professor of Mathematics at the University of lowa, lowa City, USA.
Meir Shillor is Professor of Mathematical Sciences at Oakland University, Rochester, Michigan, USA.




Linear Models  Brenton R.Clarke 

Cover Price : Rs 4,495.00

Imprint : Wiley ISBN : 9788126552900 YOP : 2015

Binding : Hardback Total Pages : 270 CD : No


Contents
Preface.
Acknowledgments.
Notation.
1. Introduction.
1.1Â The Linear Model and Examples.
1.2 What Are the Objectives?.
1.3 Problems.
2. Projection Matrices and Vector Space Theory.
2.1 Basis of a Vector Space.
2.2 Range and Kernel.
2.3 Projections.
2.3.1 Linear Model Application.
2.4 Sums and Differences of Orthogonal Projections.
2.5 Problems.
3. Least Squares Theory.
3.1 The Normal Equations.
3.2 The GaussMarkov Theorem.
3.3 The Distribution of SÎ©.
3.4 Some Simple Significance Tests.
3.5 Prediction Intervals.
3.6 Problems.
4. Distribution Theory.
4.1 Motivation.
4.2 NonCentral X2 and F Distributions.
4.2.1 NonCentral FDistribution.
4.2.2 Applications to Linear Models.
4.2.3 Some Simple Extensions.
4.3 Problems.
5. Helmert Matrices and Orthogonal Relationships.
5.1 Transformations to Independent Normally Distributed Random Variables.
5.2 The Kronecker Product.
5.3 Orthogonal Components in TwoWay ANOVA: One Observation per Cell.
5.4 Orthogonal Components in TwoWay ANOVA with Replications.
5.5 The GaussMarkov Theorem Revisited.
5.6 Orthogonal Components for Interaction.
5.6.1 Testing for Interaction: One Observation per Cell.
5.6.2 Example Calculation of Tukey'sÂ One's Degree of Freedom Statistic.
5.7 Problems.
6. Further Discussion of ANOVA.
6.1 The Different Representations of Orthogonal Components.
6.2 On the Lack of Orthogonality.
6.3 The Relationship Algebra.
6.4 The Triple Classification.
6.5 Latin Squares.
6.6 2k Factorial Designs.
6.6.1 Yates' Algorithm.
6.7 The Function of Randomization.
6.8Â Brief View of Multiple Comparison Techniques.
6.9 Problems.
7. Residual Analysis: Diagnostics and Robustness.
7.1 Design Diagnostics.
7.1.1 Standardized and Studentized Residuals.
7.1.2 Combining Design and Residual Effects on Fit  DFITS.
7.1.3 The CookDStatistic.
7.2 Robust Approaches.
7.2.1 Adaptive Trimmed Likelihood Algorithm.
7.3 Problems.
8. Models ThatÂ Include Variance Components.
8.1 The OneWay Random Effects Model.
8.2 The Mixed TwoWay Model.
8.3 A Split Plot Design.
8.3.1 A Traditional Model.
8.4 Problems.
9. Likelihood Approaches.
9.1 Maximum Likelihood Estimation.
9.2 REML.
9.3 Discussion of Hierarchical Statistical Models.
9.3.1 Hierarchy for the Mixed Model (Assuming Normality).
9.4 Problems.
10. Uncorrelated Residuals Formed from the Linear Model.
10.1 Best Linear Unbiased Error Estimates.
10.2 The Best Linear Unbiased ScalarCovarianceMatrix Approach.
10.3Â Explicit Solution.
10.4Â Recursive Residuals.
10.4.1Â Recursive Residuals and their Properties.
10.5 Uncorrelated Residuals.
10.5.1 The Main Results.
10.5.2 Final Remarks.
10.6 Problems.
11. Further inferential questions relating to ANOVA.
References.
Index.




Cogalois Theory  Toma Albu 

Cover Price : Rs 4,995.00

Imprint : CRC Press ISBN : 9780824709495 YOP : 2015

Binding : Hardback Total Pages : 356 CD : No


This volume offers a systematic, comprehensive investigation of field extensions, finite or not, that possess a Cogalois correspondence. The subject is somewhat dual to the very classical Galois Theory dealing with field extensions possessing a Galois correspondence. Solidly backed by over 250 exercises and an extensive bibliography, this book presents a compact and complete review of basic field theory, considers the VahlenCapelli Criterion, investigates the radical, Kneser, strongly Kneser, Cogalois, and GCogalois extensions, discusses field extensions that are simultaneously Galois and GCogalois, and presents nice applications to elementary field arithmetic. Finite Cogalois theory: preliminaries; Kneser extensions; Cogalois extensions; strong Kneser extensions; Galois GCogalois extensions; radical extensions and crossed homomorphisms; examples of GCogalois extensions; GCogalois extensions andprimitive elements; applications to algebraic number fields; connections with graded algebras and Hopf algebras. Infinite Cogalois Theory: infinite Kneser extensions; infinite GCogalois extensions; infinite Kummer theory; infinite Galois theory andPontryagin duality; infinite Galois GCogalois extensions.
Contents
Finite Cogalois theory: preliminaries; Kneser extensions; Cogalois extensions; strong Kneser extensions; Galois GCogalois extensions; radical extensions and crossed homomorphisms; examples of GCogalois extensions; GCogalois extensions andprimitive elements; applications to algebraic number fields; connections with graded algebras and Hopf algebras. Infinite Cogalois Theory: infinite Kneser extensions; infinite GCogalois extensions; infinite Kummer theory; infinite Galois theory andPontryagin duality; infinite Galois GCogalois extensions.
Toma Albu is Professor of Mathematics at Atilim University, Ankara, Turkey, and Bucharest University, Romania. His research interests involve ring theory, module theory, field theory, and algebraic number theory. Dr. Albu has authored or coauthored several books and more than 75 articles appearing in various international journals. He received the M.Sc.(1966) and Ph.D (1971) degrees from Bucharest University, Romania. He was a Humboldt Research Fellow at the Universities of Munich and Dusseldorf. Dr. Albu has also held visiting Professor positions in Osaka, Padua, Milwaukee, Columbus, and Santa Barbara.




Difference Equations with Applications to Queues  David L.Jagerman 

Cover Price : Rs 4,995.00

Imprint : CRC Press ISBN : 9780824703882 YOP : 2015

Binding : Hardback Total Pages : 260 CD : No


"This monograph presents a theory of difference and functional equations with continuous argument based on a generalization of the Riemann integral introduced by N.E. Norlund, allowing differentation with respect to the independent variable and permitting greater flexibility in constructing solutions and approximations solving the nonlinear first order equation by a variety of methods, including an adaptation of the lie grobner theory.
With over 1700 featured mathematical expressions. Difference Equations with Applications to Queues shows that the homogeneous sum admits exponential eigenfunctions with explicitly defined eigenvalues… illustrates the value of representations for practical computations… studies the linear difference equation with polynomial coefficients..obtains a singular perturbation solution for the processor sharing queue….EulerMaclaurin representation for the Norlund sum to the complex plane…gives a theory of the differential difference equation pioneered by C.Truesdell… covers the Erlang loss model of telephone traffic theory, the Engset model, the M/M/1 queue, and the lastinfirst out M/M/1 queue with reneging ….proves Heyman’s theorem and explains Casorati’s determinant… discusses linear transformations that state conditions for convergence of Newton series and Norlund sums…and more.
Contents
OPERATOR FUNCTIONS; GENERALITIES ON DIFFERENCE EQUATIONS; NORLUND SUM, PART 1; NORLAND SUM, PART II; THE FIRST ORDER DIFFERENCE EQUATION; THE LINEAR EQUATION WITH CONSTANT COEFFICIENTS; LINEAR DIFFERENCE EQUATIONS WITH POLYNOMIAL COEFFICIENTS. REFERENCES, INDEX
David L.Jagerman is a Mathematical Consultant at RUTCOR Rutgers Center for Operations Research, Rutgers University, Piscataway, New Jersey. The author or coauthor of over 50 technical papers, Dr. Jagerman is a senior member of the Institute of Electrical and Electronics Engineers. He received the B.E.E. degree from the Cooper Union for the Advancement of Science and Art, New York, New York, and the M.S. and Ph.D. degrees in mathematics from New York University, New York. He was a distinguished member of the technical staff at Bell Laboratories; professor of mathematics at Fairleigh Dickinson University, Teaneck, New Jersey; and professor of mathematics and later computer science at Stevens Institute of Technology, Hoboken, New Jersey.




Classical Sequences in Banach Spaces  Sylvie GuerreDelabriere 
Author 
Sylvie GuerreDelabriere


Cover Price : Rs 4,995.00

Imprint : CRC Press ISBN : 9780824787233 YOP : 2015

Binding : Hardback Total Pages : 224 CD : No


This unique reference/text offers in depth coverage of Branch spaces that contain co or lp subspaces, and explains the use of such tools and techniques as Schauder bases, ultrapowers, spreading models, and stable banach spaces.
Providing a broad view of the subject and completely proving both well known and the most recent results, Classical Sequences in Banach Spaces furnishes detailed discussions of the questions: does every banach space have a basis?... does every Banach space contain a subspace isomorphic to co or lp for some p e [1, +∞[?... if a Banach space contain co or lp for some p, does it contain it almost isometrically?... does any Banach space X contain a subspace isomorphic to co,l1, or a reflexive space?... is it possible to give a characterization of the set of p’s such that lp embeds in a given Banach space X?... is lp (1≤p<+∞) or co always finitely representable in Banach spaces?...does every Banach space contain an unconditional basic sequences?.... and more!
Classical Sequences in Banach Spaces is an excellent reference for pure and applied mathematicians, and an invaluable text for graduatelevel students in the geometry of Banach spaces and functional analysis courses.
Contents
Foreword, Preface, Notation and Conventions, 1. Classical Theorems 2. Ultrapowers and Spreading Models 3. Stable Banach Spaces 4. Subspaces of LpSpaces, 1 ≤ p < + ∞, References, Index
Sylvie GuerreDelabriere is Lecturer in Mathematics, University of Paris VI, France, A member of the Mathematical Society of France, she is the author of numerous professional papers on the theory of Banach spaces. Dr. GuerreDelabriere received the Ph.D. degree (1978) in mathematics from the University of Paris VII, and a higher doctorate, the Doctorates Science (1987) in mathematics from the University of Paris VI.




Binary Polynomial Transporms and Nonlinear Digital Filters  S. Agaian 
Author 
S. Agaian J. Astola K. Egiazarian


Cover Price : Rs 4,995.00

Imprint : CRC Press ISBN : 9780824796426 YOP : 2015

Binding : Hardback Total Pages : 322 CD : No


This unique reference offers a unified presentation of the theory of binary polynomial transforms and details their numerous applications in nonlinear signal processing.
Binary Polynomial Transforms and Nonlinear Digital Filters introduces the Rademacher logical functions...considers fast algorithms for computing Rademacher and polynomial logical functions...focuses attention on general auto and crosscorrelation functions...analyzes Boolean functions via binary polynomial transforms...studies standard median and order statistic filters...explores the statistical properties of stack filters...and much more.
CONTENTS
PART 1 BINARY POLYNOMIAL TRANSFORMS: BINARY POLYNOMIAL ARITHMETICAL AND LOGICAL FUNCTIONS AND MATRICES; FAST ALGORITHMS AND COMPLEXITY OF BINARY POLYNOMIAL TRANSFORMS; LOGICAL CORRELATIONS AND BINARY POLYNOMIAL TRANSFORMS. PART 2 BINARY POLYNOMIAL TRANSFORMS AND DIGITAL LOGIC: SPECTRAL METHODS IN ANALYSIS OF BOOLEAN FUNCTIONS; SPECTRAL METHODS IN MINIMIZATION OF BOOLEAN FUNCTIONS. PART 3 APPLICATIONS IN NONLINEAR DIGITAL FILTERING: MEDIAN AND ORDER STATISTIC FILTERS; WEIGHTED ORDER STATISTIC AND STACK FILTERS; STATISTICAL PROPERTIES OF STACK FILTERS INDEX
S. Agaian is a Visiting Professor in the Department of Electrical Engineering and Computer Science at Tufts University, Medford, Massachusetts, and Head of the Department of Digital Signal Processing of the Institute of Problems of Informatics and Automation, Armenian Academy of Science, Yerevan, Armenia. Dr.Agaian received the M.sc.degree (1968) in mathematics from Yerevan State University, Armenia, and the Ph.D.degree (1973) in physics and mathematics from the V.A.Steklov Institute of Mathematics, Moscow, Russia. He became a full Professor of the Academy of Sciences of the former Soviet Union the 1986.
J.Astola is a Professor of signal Processing and the Head of the Signal Processing Laboratory, Tampere University of Technology, Finland. Dr. Astola received the M.Sc.(1973), the Licentiate (1975), and the Ph.D.(1978) degrees in mathematics from the University of Turku, Finland.
K.Egiazarian is a Assistant Professor of Signal Processing at the Signal Processing Laboratory, Tempere University of Technology, Finland. Dr. Egiazarian received the M.Sc.degree (1981) in mathematics from Yerevan State University, Armenia the Ph.D. degree (1986) in physics and mathematics from Moscow M.V. Lomonosov State University, Russia, and the Doctor of Technology degree (1994) in signal processing from Tampere University of Technology, Finland. 



Hopf Algebras: An Introduction  Sorin Dascalescu 
Author 
Sorin Dascalescu Constantin Nastasescu Serban Raianu


Cover Price : Rs 4,995.00

Imprint : CRC Press ISBN : 9780824704810 YOP : 2015

Binding : Hardback Total Pages : 412 CD : No


Addressing a wide array of algebraic properties related to Hopf algebras, this exemplary introductory reference/text eloquently works through and summarizes key topics, theories, and relevant features in the fieldutilizing the easy to understand language of category theory and providing exercises, solutions, and bibliographic summaries at the end of each chapter.
Covering an extensive range of material with clarity and precision, Hopf Algebras features in depth discussions of basic concepts, classes, and theories for algebras, coalgebras, and comodules… the categories, integrals, actions, and coactions of Hopf algebras… special classes of coalgebras such as semiperfect, cofrobenius, cosemisimple, and pointed coalgebras… different sets of behavior for dual notions of coalgebras and comodule….the NicholsZoeller, TaftWilson, and KacZhu theorems…and more.
Contents
ALGEBRAS AND COALGEBRAS; COMODULES; SPECIAL CLASSES OF COALGEBRAS; BIALGEBRAS AND HOPF ALGREBRAS; INTEGRALS; ACTIONS AND COACTIONS; FINITE DIMENSIONAL HOPF ALGEBRAS; THE CATEGORY THEORY LANGUAGE; CGROUPS AND CCOGROUPS BIBLIOGRAPHY INDEX.
Sorin Dascalescu is an Associate Professor at the University of Bucharest, Romania. The author or coauthor of over 40 papers and a member of the American Mathematical Society, he received the Ph.D. degree in mathematics (1992) from the University of Bucharest, Romania.
Constantin Nastasescu is a Professor of Mathematics at the University of Buchares, Romana. The author or coauthor of over 100 papers and monographs and a member of the American Mathematical Society, he received the Ph.D. degree in mathematics (1970) from the University of Bucharest, Romania.
Serban Raianu is an Associate Professor of Mathematics at the University of Bucharest, Romania. The author or coauthor of numerous papers and a member of the American Mathematical Society, he received the Ph.D.degree in mathematics (1991) from the University of Bucharest, Romania.




Elementary Boundary Value Problems  T.A.Bick 

Cover Price : Rs 4,995.00

Imprint : CRC Press ISBN : 9780824788995 YOP : 2015

Binding : Hardback Total Pages : 258 CD : No


This practical textbook elucidates the role of BVPs as models of scientific phenomena, describes traditional methods of solution and summarizes the ideas that come from the solution techniques – revolving around the concept of orthonormal sets of functions as generalizations of the trigonometric functions.
Emphasizing the unifying nature of the material, Elementary Boundary Value Problems constructs physical models for both bounded and unbounded domains using rectangular and other coordinate systems….develops methods of characteristics, eigenfunction expansions, and transform procedures using the traditional fourier series, D'Alembert's method , and fourier integral transforms; makes explicit connections with linear algebra, analysis, complex variables, set theory, and topology in response to the need to solve BVP's presents illustrative examples in science and engineering….and more.
Providing fundamental definitions for students with no prior experience in this topic other than differential equations, Elementary Boundary Value Problems is an informative resource for upperlevel undergraduate mathematics, physics and engineering, and students in courses on boundary value problems.
Contents
BOUNDARY VALUE PROBLEMS AS MODELS; THE METHOD OF CHARACTERISTICS; FOURIER SERIES; LINEAR ALGEBRA AND STURMLIOUVILLE SYSTEMS; FOURIER TRANSFORMS; APPENDICES  A FOURIER SERIES THEORUM, A FOURIER INTEGRAL THEORUM, PROOFS OF THEORUMS 3.5.2 AND 3.5.3, UNIQUENESS THEORUM FOR SECONDORDER KINEAR ODE, ON THE SEROES OF THE BESSEL FUNCTIONS, BIBLIOGRAPHY,INDEX.
T.A.Bick is Professor of Mathematics at Union College, Schenectady, New York. The author of one book as well as various publications in the areas of ergodic theory and measure theory, he is a member of the Mathematical Association of America. Professor Bick received the B.S.degree (1958) in mathematics from Union College and the M.S. (1960) and Ph.D. (1964) degrees in mathematics from the University of Rochester.




Radical Theory of Rings  B.J.Gardner 
Author 
J.W. Gardner R. Wiegandt


Cover Price : Rs 4,495.00

Imprint : CRC Press ISBN : 9780824750336 YOP : 2015

Binding : Hardback Total Pages : 400 CD : No


Assimilating radical theory’s evolution in the decades since that last major work on rings and radicals was published, radical theory of rings distills the most noteworthy present day theoretical topics, gives a unified account of the classical structure theorems for rings, and deepens understanding of key aspects of ring theory via ring and radical constructions.
Deals with distinctive features of the radical theory of nonassociative rings, associative rings with involution, and near – rings.
Written in clear algebraic terms by globally acknowledged authorities, Radical Theory of Rings provides a systematic treatment of the theory of kurosh – Amitsur radicals as well as of concrete radicals of associative rings… delves into hereditary, supernilpotent, special, supplementing, normal, subidempotent, and Aradicals…gradually introduces concrete radicals as examples of the general theory arrives at the study of nil radicals and Jacobson, BrownMccoy, Behrens, antisimple, strongly prime, and generalized nil radicals…discusses in detail the Density Theorem, WedderburnArtin Theorem…and examines the radicals of matrix and polynomial rings and their connection with Koethe’s Problem.
Contents
Preface, Interdependence Chart, 1. General Fundamentals 2. The General Theory of Radicals 3. Radical Theory for Associative Rings 4. Concrete Radicals and Structure Theorems 5. Special Features of the General Radical Theory, Refereneces, List of Symbols, List of Standard Conditions, Author Index, Subject Index
B.J.GARDNER is a Reader in Mathematics at the University of Tasmania, Hobart, Australia. He has authored one book, edited two volumes of conference proceedings, and written some 90 mathematical papers, mostly on algebraic topics. His research areas include radical theory, ring theory, and other branches of algebra. Dr.Gardner received the B.Sc. (1967) and Ph.D. (1971) degrees from the University of Tasmania, Hobart, Australia.
R.WIEGANDT is a Scientific Advisor at the A.Renyi Institute of Mathematics, Hungarian Academy of Science, Budapest. An international expert on rings, radials, and other algebraic topics, he is the author or coauthor of some 150 mathematical publications and has served on the editorial boards of nine international mathematical journals. Dr. Wiegandt received the Candidate of Math. Sci. (1967) and Doctor of Math. Sci. (1975) degrees from the Hungarian Academy of Sciences, Budapest.




Complex Analysis and Geometry  V. Ancona 
Author 
V Ancona E Ballico R.M. MiroRoig A Silva


Cover Price : Rs 3,995.00

Imprint : CRC Press ISBN : 9780582292765 YOP : 2015

Binding : Hardback Total Pages : 200 CD : No


Based on two conferences held recently in Trento, Italy, sponsored by the Centro Internazionale per la Ricerca Matematica (CIRM), this book contains 13 research papers and 2 survey papers on complex analysis and complex algebraic geometry, The main topics are: Mori theory, polynomial hull vector bundles, qconvexity Lie groups and actions on complex space, hypercomplex structures, pseudoconvex domains, and projective varieties, The papers cover the latest advances in these topics and include several open problems.
Readership: Graduate students and researchers in complex analysis and algebraic geometry.
Contents
Preface
Contributors
On the Limits of Manifolds with nef Canonical Bundles, M. Andreatta and T. Peternell
On the Stability of the Restriction of TPn to Projective Curves, E. Ballico and B. Russo
Théorie des (a,b)Modules II. Extensions, D. Barlet
Moduli of Reflexive K3 Surfaces, C. Bartocci, U. Bruzzo, and D. Hernández Ruipérez
New Examples of Domains with NonInjective Proper Holomorphic SelfMaps, F. Berteloot and J. J. Loeb
QConvexivity. A Survey, M. Coltoiu
Commuting maps and Families of Hyperbolic Automorphisms, C. de Fabritiis
An Alternative Proof of a Theorem of BoasStraubeYu, K. Diederich and G. Herbort
Large Polynomial Hulls with No Analytic Structure, J. Duval and N. Levenberg
Canonical Connections for AlmostHypercomplex Structures, P. Gauduchon
The Tangent Bundle of P2 Restricted to Plane Curves, G. Hein
Quotients with Respects to Holomorphic Actions of Reductive Groups, P. Heinzner and L. Migliorini
Adjunction Theory on Terminal Varieties, M. Mella
Runge Theorem in Higher Dimensions, V. Vajaitu
Only Countably Many SimplyConnected Lie Groups Admit Lattices, J. Winkelmann
PITMAN RESEARCH NOTES IN MATHEMATICS SERIES
The aim of this series is to disseminate important new material of a specialist nature in economic form It ranges over the whole spectrum of mathematics and also reflects the changing momentum of dialogue between hitherto distinct areas of pure and applied parts of the discipline.
The editorial board has been chosen accordingly and will from time to time be recomposed to represent the full diversity of mathematics as covered by mathematical Reviews.
This is a rapid means of publication for current material whose style of exposition is that of a developing subject. Work that is in most respects final and definitive, but not yet refined into a formal monograph, will also be considered for a place in the series. Normally homogeneous material is required, even if written by more than one author, thus multiauthor works will be included provided that there is a strong linking theme or editorial pattern.




Approximation Theory  N.K.Govil 
Author 
N.K. Govil R.N. Mohapatra Z. Nashed A. Sharma


Cover Price : Rs 4,995.00

Imprint : CRC Press ISBN : 9780824701857 YOP : 2015

Binding : Hardback Total Pages : 542 CD : No


This truly outstanding work honors A.K. Varma’s indelible contributions to the field of approximation theory with a collection of over 30 carefully selected papers by 45 internationally distinguished mathematicians, reflecting his lifelong passion for investigating subjects such as interpolation by polynomials and splines, quadrature formulae, order of pointwise and uniform approximation of finitely differentiable functions by polynomials, and Bernstein and Markov type inequalities in Lp and uniform metrics.
Presenting uptodate research in a single volume, Approximation Theory covers and astonishing breadth of topics, including Lidstone spline interpolation and its error bounds…linear approximation operators….a new proof of the Markov inequality….reliability theory….frames and Schauder, Riesz, and unconditional bases….Birkhoff interpolation…nonlinear subdivision schemes….convex univalent functions….totally positive bases and subdivision matrices….multivariate splines…..a generalization of inequalities of Chebyshev and Turan….the Marcinkiewiez Zygmund inequality….weighted Lagrange interpolation….generalized extended Chebyshev systems and their linear spans….and more.
Contents
Foreword
E.W. Cheney
Preface
Contributors
Arum Kumar Varma: Some Reminiscences
1. Error Bounds for the Derivatives of
Lidstone Interpolation and Application Ravi P. Agarwal
Patricia J.Y. Wong
2. Higher Order Univariate Wavelet Type Approximation
George A. Anastassiou
3. Modified Weighted (0,2) Interpolation J. Balazs
4. New Approach to Markov Inequality in L(p) Norms
Mirostaw Baran
5. A Question in Reliability Theory Franck Beaucoup
Laurent Carraro
6. Notes on Miscellaneous Approximation Problems
Borislav Bojanov
7. Muntz's Theorem on Compact Subsets of
Positive Measure Peter Borwein
Tamas Erdelyi
8. Frames and Schauder Bases
Peter G. Casazza
Ole Christensen
9. Interpolation on Spheres by Positive
Definite Functions
E.W. Cheney
Xingping Sun
10. Nonparametric Density Estimation by Polynomials and by Splines
Z. Ciesielski
11. Birkhoff Type Interpolation on Perturbed Roots of Unity
M.G. de Bruin A. Sharma
J. Szabados
12. Approximation by Entire Functions with Only Real Zeros
L.T. Dechevsky
D.P. Dryanov Q.I. Rahman
13. Nonlinear Means in Geometric Modeling
Michael S. Floater
Charles A. Micchelli
14. Nonlinear Stationary Subdivision
Michael S. Floater
Charles A. Micchelli
15. Convex Univalent Functions and Omitted
Values Richard Fournier
Jinxi Ma Stephan Ruscheweyh
16. Total Positivity and Total Variation T.N.T. Goodman
17. Inequalities for Maximum Modulus of Rational Functions with Prescribed Poles
N.K. Govil
R.N. Mohapatra
18. Recent Progress on Multivariate Splines
Don Hong
19. Hermite Interpolation on Chebyshev Nodes and Walsh Equiconvergence
A. Jakimovski
A. Sharma
20. Continuous Functions Which Change Sign
Without Properly Crossing the xAxis
Peter D. Johnson, Jr.
21. Some Remarks on Weighted Interpolation Theodore Kilgore
22. A Note on Chebyshev's Inequality
Xin
23. Smooth Maclaurin Series Coefficients in Pade and Rational Approximation
D. S. Lubinsky
24. On MarcinkiewiczZygmundType
Inequalities
H.N. Mhaskar J. Prestin
25. Extermal Problems for Restricted
Polynomial Classes in L(r) Norm
Gradimir V. Milovanovic
26. New Developments on Turan's Extremal Problems for Polynomials
Gradimir V. Milovanovic
Themistocles M. Rassias
27. Recent Progress in Multivariate Markov
Inequality W. Plesniak
28. Orthogonal Expansion and Variations of
Sign of Continuous Functions Gerhard Schmeisser
29. Convolution Properties of Two Classes of
Starlike Functions Defined by Differential
Inequalities
Vikramaditya Singh
30. Weighted Lagrange Interpolation on Generalized Jacobi Nodes
P. Vertesi
31. Relative Differentiation, Descartes' Rule of Signs, and the BudanFourier Theorem
for Markov Systems R.A. Zalik
Index
N.K.Govil is a Professor of Mathematics at Auburn University, Alabama, He received the Ph.D.degree (1968) in mathematics from the University of Montreal, Canada.
R.N.Mohapatra is a Professor of Mathematics at the University of Central Floida, Orlando. He received the Ph.D.degree (1968) in mathematics from the University of Jabalpur, India.
Z.Nashed is a Professor of Mathematics as well as Electrical Engineering at the University of Delaware, Newark. He received the Ph.D.degree (1963) in mathematics from the University of Michigan, Ann Arbor.
A.Sharma is a Professor Emeritus at the University of Alberta, Edmonton, Canada He received the Ph.D.degree (1951) in mathematics from University of Lucknow, India.
J.Szabados is Head of the Department of Analysis at the Mathematical Institute of the Hungarian Academy of Science, Budapest. He received the D.Sc.degree (1976) in mathematics from the Hungarian Academy of Sciences, Budapest.




Algebraic Geometry for Associative Algebras  Freddy Van Oystaeyen 
Author 
Freddy Van Oystaeyen


Cover Price : Rs 4,995.00

Imprint : CRC Press ISBN : 9780824704247 YOP : 2015

Binding : Hardback Total Pages : 308 CD : No


This innovative reference/text facilitates the definition of a non commutative topology that makes it possible, for the first time, to construct and underlying space where geometric properties can be phrased and studiedresulting in a scheme theory that sustains the duality between algebraic geometry and commutative algebra to the noncommutative level.
Constructing the scheme theory from the interaction between graded and filtered algebras appearing as a general deformation principles among geometries, Algebraic Geometry for Associative Algebras fully introduces noncommutative topology…deformation of structure schemes…new cohomological methods….homological algebra and regularity conditions…divisor theory using noncommutative valuations….reductions of algebras….microlocalization and quantum sections….formal completion along subvarieties….and more.
Enriched with numerous examples, Algebraic Geometry for Associative Algebras serves as an important research reference for pure and applied mathematicians, particularly algebraists, number theories, ring theorists, geometers, and topologists, as well as a stimulating text for upper level undergraduate and graduate students in these disciplines.
Contents
PREFACE
INTRODUCTION
THE NONCOMMUTATIVE SITE
STRUCTURE SHEAVES AND THEIR SECTIONS
REGULAR ALGEBRAS
VALUATIONS AND DIVISORS
COHOMOLOGY THEORIES
A FUNCTORIAL APPROACH
FORMALIZING THE TOPOLOGY
REFERENCES
INDEX
FREDDY VAN OYSTAEYEN is a Professor of Mathematics at the University of Antwerp, UIA, Belgium. The author, coauthor, editor, or coeditor of over 200 articles, proceedings, book chapters, and books, including Brauer Groups and the Cohomology of Graded Rings, Commutative Algebra and Algebraic Geometry, A Primer of Algebraic Geometry, Hopf Algebras and Quantum Groups, and Interactions Between Ring Theory and Representations of Algebras (all titles, Marcel Dekker, Inc.) he is a board member of the Belgium Mathematical Society and a member of the Liaisons Committee of the European Mathematical Society. Professor Van Oystaeyen received the Ph.D.degree (1972) in mathematics from the free University of Amsterdam, The Netherlands, and the habilitation (1975) from the University of Antwerp, UIA, Belgium.




Abstract Algebra with Applications,Vol.1  Karlheinz Spindler 
Author 
Karlheinz Spindler


Cover Price : Rs 4,995.00

Imprint : CRC Press ISBN : 9780824791445 YOP : 2015

Binding : Hardback Total Pages : 774 CD : No


This outstanding textbook offers a comprehensive self contained presentation of all major topics in abstract algebra and provides an indepth treatment of the applications of algebraic techniques and the relationship of algebra to other disciplines such as number theory, combinatorics, geometry, topology, differential equations, and Markov chains.
Emphasizing both the conceptual and computational aspects of algebra to aid structural thinking as well as operational skills, Abstract Algebra with Applications (in two volumes) includes thorough discussions of group actions; matrix groups; the correlation between ring theory, number theory, and algebraic geometry; Galois theory’ and the applicability of linear algebra….begins each chapter with an introduction that acts as a guide for the material to come….motivates and prepares students for new ideas with informal remarks, enlightening examples, and illustrations that facilitate understanding….furnishes abundant end of section problems of varying levels of difficulty to help students extend and apply their comprehension of newly learned material….allows teachers to use the text for a variety of different courses by maintaining essentially independent chapters….supplies an appendix that contains prerequisites for set theory and pointset topology and their proofs….and much more!
With over 230 drawings and numerous diagrams, tables, and display equations, Abstract Algebra with Applications (in two volumes) is the perfect text for all upperlevel undergraduate and graduate algebra and related courses, including Abstract Algebra, Linear Algebra, Galois Theory, Commutative Algebra, and Applications of Algebra.
Contents
Volume I
Vector Spaces
First Introduction: Affine Geometry
Second Introduction: Linear Equations
Vector Spaces
Linear and Affine Mappings
Abstract Affine Geometry
Representations of Linear Mappings by Matrices
Determinants
Volume Functions
Eigenvectors and Eigenvalues
Classification of Endomorphisms Up to Similarity
Tensor Products and BaseField Extension
Metric Geometry
Euclidean Spaces
Linear Mappings Between Euclidean Spaces
Bilinear Forms
Groups of Automorphisms
Application: Markov Chains
Application: Matrix Calculus and Differential Equations
Groups
Introduction: Symmetries of Geometric Figures
Groups Subgroups and Cosets
Symmetric and Alternating Groups
Group Homomorphisms
Normal Subgroups and Factor Groups
Free Groups: Generators and Relations
Group Actions
GroupTheoretical Applications of Group Actions
Nilpotent and Solvable Groups
Topological Methods in Group Theory
Analytical Methods in Group Theory
Groups in Topology
Appendix
Bibliography
Index
Volume II
Preface
Rings And Fields
 Introduction: The Art of Doing Arithmetic
Rings and Ring Homomorphisms
Integral Domains and Fields
Polynomial and Power Series Rings
Ideals and Quotient Rings
Ideals in Commutative Rings
Factorization in Integral Domains
Factorization in Polynomial and Power Series Rings
NumberTheoretical Applications of Unique Factorization
Modules Noetherian Rings Field Extensions
Noetherian Rings
Field Extensions
Splitting Fields and Normal Extensions
Separability of Field Extensions
Field Theory and Integral Ring Extensions
Affine Algebras
Ring Theory and Algebraic Geometry
Localization
Factorization of Ideals
Introduction to Galois Theory: Solving Polynomial Equations
The Galois Group of a Field Extension
Algebraic Galois Extensions
The Galois Group of a Polynomial
Roots of Unity and Cyclotomic Polynomials
Pure Equations and Cyclic Extensions
Solvable Equations and Radical Extensions
Epilogue: The Idea of Lie Theory as a Galois Theory for Differential Equations
Bibliography
Index
Karlheinz SPindler works in the Flight Dynamics Department of the European Space Operations Centre, Darmstadt, Germany, Previously, he was a teacher of mathematics at the Technische Hochschule Darmstadt, Germany, and a Visiting Assistant Professor of Mathematics at Louisiana State University, Baton Rouge. Dr. Spindler is the author of several professional papers related to Lie Theory. He received his doctorate (1988) in mathematics from the Technische Hochschule Darmstadt.




Topics on Continua  Sergio Macias 

Cover Price : Rs 4,995.00

Imprint : CRC Press ISBN : 9780849337383 YOP : 2015

Binding : Hardback Total Pages : 374 CD : No


Specialized as it might be, continuum theory is one of the most intriguing areas in mathematics. However, despite being popular journal fare, few books have thoroughly explored this interesting aspect of topology.
In Topics on Continua, Sergio Macías, one of the field’s leading scholars, presents four of his favorite continuum topics: inverse limits, Jones’s set function T, homogenous continua, and nfold hyperspaces, and in doing so, presents the most complete set of theorems and proofs ever contained in a single topology volume. Many of the results presented have previously appeared only in research papers, and some appear here for the first time.
After building the requisite background and exploring the inverse limits of continua, the discussions focus on Professor Jones's set function T and continua for which T is continuous. An introduction to topological groups and group actions lead to a proof of Effros's Theorem, followed by a presentation of two decomposition theorems. The author then offers an indepth study of nfold hyperspaces. This includes their general properties, conditions that allow points of nfold symmetric products to be arcwise accessible from their complement, points that arcwise disconnect the nfold hyperspaces, the nfold hyperspaces of graphs, and theorems relating nfold hyperspaces and cones. The concluding chapter presents a series of open questions on each topic discussed in the book.
With more than a decade of teaching experience, Macías is able to put forth exceptionally cogent discussions that not only give beginning mathematicians a strong grounding in continuum theory, but also form an authoritative, singlesource guide through some of topology's most captivating facets.
Contents
PRELIMINARIES
Product Topology
Continuous Decompositions
Homotopy and Fundamental Group
Geometric Complexes and Polyhedra
Complete Metric Spaces
Compacta
Continua
Hyperspaces
References
INVERSE LIMITS AND RELATED TOPICS
Inverse Limits
Inverse Limits and the Cantor Set
Inverse Limits and Other Operations
Chainable Continua
Circularly Chainable and P–like Continua
Universal and A–H Essential Maps
References
JONES’S SET FUNCTION T
The Set Function T
Continuity of T
Applications
References
A THEOREM OF E. G. EFFROS
Topological Groups
Group Actions and a Theorem of Effros
References
DECOMPOSITION THEOREMS
Jones’s Theorem
Detour to Covering Spaces
Rogers’s Theorem
Case and Minc–Rogers Continua
Covering Spaces of Some Homogeneous Continua
References
n–FOLD HYPERSPACES
General Properties
Unicoherence
Aposyndesis
Arcwise Accessibility
Points that Arcwise Disconnect
C*n–smoothness
Retractions
Graphs
Cones
References
QUESTIONS
Inverse Limits
The Set Function T
Homogeneous Continua
n–fold Hyperspaces
References
Index
Sergio Macias is a professor at the Institute de Matematicas, Universidad Nacional Autonoma de Mexico, Mexico City.




Foundation Course in Statistical and Quantitative Reasoning  B.M.Aggarwal 

Cover Price : Rs 375.00

Imprint : Ane Books Pvt. Ltd. ISBN : 9789385259722 YOP : 2015

Binding : Paperback Total Pages : 296 CD : No


About the Book
The book has been designed specifically for Foundation Course in Statistical and Quantitative Reasoning, for MBA. Keeping in view the fast that some of the students may be from Non mathematics back ground, the concepts have been explained elaborately to make the subject easily graspable by those students also, the syllabus has been covered fully. Keeping in view the time constraint of the students. The subject has been dealt to the point but omitting thing nothing which is otherwise required for the students.
I hope, that the book will serve its purpose to the either satisfaction of the teachers and students.
Contents
• Matrices and Determinants
• Preparation of Frequency Distribution
• Statistical Averages (Measures of Central Tendency)
• Measures of Variation
• Measurement for Scale (Nominal Scale, Ordinal Scale, Interval Scale, Ratio Scale)
• Basic Concept of Probability
About the Author
B.M.Aggarwal graduated with Honors in Mathematics from Punjab University followed by Masters degree in Mathematics from Meerut University and a degree in Electronics and Telecommunication Engineering from the Institute of Electronics and Telecommunications Engineering, Lodhi Road, New Delhi.
A versatile teacher and a reputed Professor of Mathematics, Statistics and Operations Research the author has served in many reputed Management Institute in Delhi and NCR. His presentation can be seen through his lucid and logical treatment of the text.




Functional Analysis and Valuation Theory  Lawrence Narici 
Author 
Lawrence Narici Edward Beckenstein George Bachman


Cover Price : Rs 3,995.00

Imprint : CRC Press ISBN : 9780824714840 YOP : 2015

Binding : Hardback Total Pages : 200 CD : No


Functional Analysis and Valuation Theory presents some of the principal results of the theory of normed spaces and algebras over arbitrary fields with valuation. Most of the material included has not previously appeared in any other book.
The reader need not have prior knowledge of valuation theory: necessary principles are discussed in the opening chapter. The book includes versions of the BanachSteinhaus theorem, the Fredholm Alternative theorem, and the HahnBanach theorem. Normed algebras over valued field are also investigated at some length. Topics discussed include topolgizing the space of maximum ideals, a StoneWeierstrass theorem, and a representation theorem analogous to that for complex B* algebras.
So that this work can be used as a text, exercises have been included wherever possible. Some are to be employed as practice exercises while others explore topics only mentioned in the main body of the book. A number of examples with various special properties are presented in the Appendix. In addition, an index of symbols and an extensive bibliography of pertinent literature in the field have also been provided.
The book can be used a first or second year graduate text for students with a back ground in the classical theory of normed spaces and algebra, and will be of interest to mathematicians concerned with functional analysis and valuation theory.
Contents
PERFACE
1. TOPOLOGICAL RESULTS
1.1 Elementary Considerations
1.2 A Metrization Theorem
1.3 The Index of a Nonarchimedean Space
1.4 Local Compactness
Exercises 1
2.COMPLETENESS
2.1 Spherical Completeness and
PseudoCompleteness
2.2 Countable Linear Compactness
2.3 Maximal Completeness and
PseudoCompleteness
2.4 The Existence of a Maximal
Completion
2.5 FConvexity and cCompactness
Exercises 2
3. NORMED LINEAR SPACES
3.1 The Residue class Space
3.2 Local Compactness
3.3 The HahnBanach Theorem
3.4 The BanachSteinhaus Theorem
3.5 Completely Continuous Operators and
the Fredholm Alternative Theorem
3.6 The Resolvent Set of a Linear
Operator
Exercises 3
4. NORMED ALGEBRAS
4.1 Normal Algebras: MazurGelfand
Theorem
4.2 The Spectrum
4.3 Maximal Ideals
4.4 The Gelfand Subalgebra
4.5 Topologizing the Maximal Ideals
4.6 Regular Algebras
4.7 Algebraic Algebras
4.8 V*Algebras
4.9 Function Algebras
4.10 The Tietze Extension Theorem and
StoneWeierstrass Theorem
4.11 Representation Theorems
Exercises 4
APPENDIX: EXAMPLES
Index of Symbols
Index
LAWRENCE NARICIteaches mathematics at St. John's University, Jamaica, New York. His particular research interest is in functional analysis and valuation theory. Dr. Narici has written or collaborated on 17 books and resarch papers. Dr. Narici received his Ph.D. at the Polytechnic Institute of Brooklyn. In the past, he served as consultant to IBM and to the Mount Sinai School of Medicine in conjunction with their biomedical engineering program. His memberships include the American Mathematical Society, the Mathematical Association of America, and the American Association of University Professors.
EDWARD BECKEN STEINcurrently teaches mathematics at the Polytechnic Institute of Brooklyn, where he received his Ph.D. He has written 13 research papers, mostly in the areas of functional analysis and valuation theory. Dr. Beckenstein was consultant to GE and to the Mount Sinai School of Medicine in connection with their biomedical engineering program. Dr. Beckenstein belongs to the American Mathematical Society, the Mathematical Association of America, and the American Association of University Professors.
GEORGE BACHMANteaches mathematics at the Polytechnic Institute of Brooklyn. Previously, he taught at Rutgers University. Many of the 23 research papers and books that he has written are on functional analysis and measure theory. Dr. Bachman received his Ph.D. in Mathematics at the Courant Institute of Mathematical Sciences, New York University. he is a member of the American Mathematical Society, the Mathematical Association of America, and the American Association of University Professors. 



Probability and Numerical Methods, 4th Edn  J.P. Singh 

Cover Price : Rs 450.00

Imprint : Ane Books Pvt. Ltd. ISBN : 9789388264471 YOP : 2018

Binding : Paperback Size : 6.25 Total Pages : 436 CD : No


About the Book
The fourth edition of Probability and Numerical Methods is the result of the enthusiastic reception given to the earlier editions received from the students and the teachers who are the end users of this book.
The book covers the complete syllabus of BCA, semester IV of GGSIP University. It introduces Probability and Numerical Methods at undergraduate level in a simplified manner.
Salient features
• Text is selfexplanatory and the language is vivid and lucid.
• Contains numerous examples that illustrate the basic as well as high level concepts of the concerned topic.
• Additional questions provided in all the chapters for practice.
• Most of the questions conform to the trend in which the questions appear in GGSIP University.
Contents
0. Elementary Concepts
1. Combinatorics: Permutation, Combination and Binomial Theorem
2. ProbabilityI
3. ProbabilityII
4. Random Variable and Mathematical Expectations
5. Discrete Probability Distributions
6. Normal Distribution
7. Finite Difference
8. Interpolation 9. Solution of Algebraic and Transcendental Equations
10. Solution of Linear Simultaneous Equations
11. Numerical Differentiation and Integration, Tables, End Term Examination
About the Author
J.P. Singh is Professor in Department of Mathematics at Jagan Institute of Management Studies (Affiliated to GGSIP University), Delhi. He has teaching experience of 19 years and has taught at various affiliated Institutes of GGSIP University. He has undergone rigorous training from IIT Delhi in Financial Mathematics. He is a Certified Six Sigma Green Belt from Indian Statistical Institute, Delhi.
His areas of interest include Mathematical Statistics, Stochastic Process, Numerical Methods, Number Theory, Discrete Mathematics and Theory of Computation.




Algorithms for Linear Quadratic Optimization  Vasile Sima 

Cover Price : Rs 4,995.00

Imprint : CRC Press ISBN : 9780824796129 YOP : 2015

Binding : Hardback Total Pages : 380 CD : No


This uptodate reference offers valuable theoretical, algorithmic and computational guidelines for solving the most frequently encountered linearquadratic optimization problems providing an overview of recent advances in control and systems theory, numerical line algebra, numerical optimization, scientific computations and software engineering.
Examining stateoftheart linear algebra algorithms and associated software, Algorithms for LinearQuadratic Optimization presents algorithms in a concise, informal language that facilitates computer implementation…discusses the mathematical description, applicability, and limitations of particular solvers…summarizes numerical comparisons of various algorithms…highlights topics of current interest, including H∞ and H₂ optimization, defect corrections, and Schur and generalized Schur vector methods...emphasizes structurepreserving techniques… contains many worked examples based on industrial models… covers fundamental issues in control and systems theory such as regulator and estimator design, state estimation, and robust control…and more.
Furnishing valuable references to key sources in the literature, Algorithms for LinearQuadratic Optimization is an incomparable reference for applied and industrial mathematicians, control engineers, computer programmers, electrical and electronics engineers, systems analysts, operations research specialists, researchers in automatic control and dynamic optimization, and graduate students in these disciplines.
Contents
PREFACE
LINEARQUADRATIC OPTIMIZATION PROBLEMS
NEWTON ALGORITHMS
SCHUR AND GENERALIZED SCHUR ALGORITHMS
STRUCTUREPRESERVING ALGORITHMS
APPENDIXES
COMPARISON OF RICCATI SOLVERS
NOTATION AND ABBREVIATIONS
INDEX OF ALGORITHMS DEFINITIONS
INDEX
About the Author
Vasile Sima is Senior Research Fellow and VicePresident of the Scientific Council of the Research Institute for Informatics, Bucharest, Romania. The author or coauthor of several books and more than 80 professional publications, Dr. Sima serves on the editorial board of Studies in Informatics and Control. He is a member of the Numerical Analysis Network and an affiliate member of the International Federation of Automatic Control. Dr. Sima received the M.S.degree (1972) in control engineering from the Polytechnic University of Bucharest, Romania, the M.S.degree (1978) in mathematics from the University of Bucharest, Romania, and the Doctor of Engineering degree (1983) in electrical engineering from the Polytechnic University of Bucharest, Romania.




Complex Analysis  Pratiksha Saxena 

Cover Price : £ 34.95

Imprint : Athena Academic ISBN : 9781910390276 YOP : 2016

Binding : Hardback Size : 6.25" X 9.50" Total Pages : 296 CD : No


About the Book
This book has been designed keeping in mind the needs of the readers for conceptual excellence and analytically evident examples that would help understand the subject better. The basic concepts are well supported with explanatory graphs, solved and unsolved examples. To develop mathematical skills and bring about clarity of theorems, a large number of carefully graded exercises are given with working rulesand the step by step methods of problem solving. We hope this book is very useful for students as well as for academicians.
Salient Features
Comprehensively explained theorem proofs
Step by step solution of examples
220 solved examples
Figures and graphs for better representation of concepts
Contents
1. Prerequisite.
2. Function, Limit and Continuity.
3. Complex Differentiation and Analytic Function.
4. Power Series.
5. Bilinear Transformation.
6. Conformal Mapping.
7. Complex Integration.
8. Zero and Singularities of A Function.
9. The Calculus of Residues.
10. Uniform Convergence of Sequence and Series.
11. Memomorphic Function.
Concept definition and explanation in easy language
About the Editor
Dr. Pratiksha Saxena, currently teaching at the Department of Applied Mathematics, Gautam Buddha university, Greater Noida, India, has to her credit three books published with international publishers besides several papers in international journals. She has developed several books for Maharshi Dayanand university and Calicut university. A Gold Medalist in her postgraduation, she was awarded the prestigious Book Pal Memorial award at university Level. She has three Copyrights/Patents for simulation tools. She has been teaching both graduate and postgraduate students for the last sixteen years. She is the editorial board member and reviewer for a number of journals. Her research interests are in the areas of application of nonlinear programming, optimization, modeling and simulation. 


