November 24, 2017 Forthcoming by Chapman and Hall/CRC
Textbook - 298 Pages - 28 B/W Illustrations
ISBN 9781498778138 - CAT# K29801
Series: Textbooks in Mathematics
Offers integration of transition topics to assist with the necessary background for analysis
Can be used for either a one- or two-semester course
Explores how ideas of analysis appear in a broader context
Demonstrates major reoganization of first edition
Offers solutions in rear of book
The Second Edition offers a major re-organization of the book, with the goal of making it much more competitive as a text for students. The revised edition will be appropriate for a one- or two-semester introductory real analysis course. Like the first edition, the primary audience is the large collection of students who will never take a graduate level analysis course. The choice of topics and level of coverage is suitable for future high school teachers, and for students who will become engineers or other professionals needing a sound working knowledge of undergraduate mathematics.
Real Numbers and Mathematical Proofs. Infinite Sequences. Infinite Series. Functions. Integrals. Variations on the Riemann Sums Theme. Taylor Series and Power Series. Appendix: Solutions to Select Problems.
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January 17, 2018 Forthcoming by Chapman and Hall/CRC
Textbook - 330 Pages - 26 B/W Illustrations
ISBN 9781498778466 - CAT# K29818
Series: Textbooks in Mathematics
Follows up author's Elementary Linear Algebra
First chapter on matrices
Unique chapter on Null space, row space and column space of a matrix
Focus on intuition and rigor
For second or more theoretical courses on linear algebra
This is the first of a two-part set of books for the undergraduate linear algebra sequence. The text is for the more computational course taught in most mathematics departments. This course is based around matrices and applications. The text begins with matrices, linear equations, vector spaces, linear transformations, eigenvalues and eigenvectors. The text offers many applications to motivate students from engineering, physics, computer science and other disiplines. It offers a historical perspective. Proofs are presented to promote the further study of advanced mathematics.
Matrices. Algebra. Vector Spaces. Linear transformations. Eigenvalues and eigenvectors. Inner Product Spaces. Linear functional, dual spaces and adjoint operators.
January 15, 2018 Forthcoming by Chapman and Hall/CRC
Textbook - 328 Pages - 50 B/W Illustrations
ISBN 9781498715164 - CAT# K25327
A new approach to understanding PDEs where concepts and fundamentals would be emphasized and motivated
proofs would be presented for better understanding
Examples will be worked out step-by-step and New exercises including some challenging problems would be
included
Practical applications of PDEs would be presented with computer generated graphs for better visualization
The notion of weak solutions to PDEs
Some exercises that make use of Matlab will also be considered and Matlab codes will be available on our
website for download
Partial Differential Equations (PDEs) often arise in mathematical formulation of many physical problems in science and engineering.This book is aimed to bring out a comprehensive exposure to the basics of partial differential equations which will be accessible to a large class of engineering and science students
432pp Nov 2017
ISBN: 978-981-3229-62-4 (hardcover)
This textbook provides an introduction to abstract algebra for advanced undergraduate students. Based on the authors' notes at the Department of Mathematics, National Chung Cheng University, it contains material sufficient for three semesters of study. It begins with a description of the algebraic structures of the ring of integers and the field of rational numbers. Abstract groups are then introduced. Technical results such as Lagrange's theorem and Sylow's theorems follow as applications of group theory. The theory of rings and ideals forms the second part of this textbook, with the ring of integers, the polynomial rings and matrix rings as basic examples. Emphasis will be on factorization in a factorial domain. The final part of the book focuses on field extensions and Galois theory to illustrate the correspondence between Galois groups and splitting fields of separable polynomials.
Three whole new chapters are added to this second edition. Group action is introduced to give a more in-depth discussion on Sylow's theorems. We also provide a formula in solving combinatorial problems as an application. We devote two chapters to module theory, which is a natural generalization of the theory of the vector spaces. Readers will see the similarity and subtle differences between the two. In particular, determinant is formally defined and its properties rigorously proved.
The textbook is more accessible and less ambitious than most existing books covering the same subject. Readers will also find the pedagogical material very useful in enhancing the teaching and learning of abstract algebra.
Preliminaries
Algebraic Structure of Numbers
Basic Notions of Groups
Cyclic Groups
Permutation Groups
Counting Theorems
Group Homomorphisms
The Quotient Group
Finite Abelian Groups
Group Actions
Sylow Theorems and Applications
Introduction to Group Presentations
Types of Rings
Ideals and Quotient Rings
Ring Homomorphisms
Polynomial Rings
Factorization
Introduction to Modules
Free Modules
Vector Spaces over Arbitrary Fields
Field Extensions
All About Roots
Galois Pairing
Applications of the Galois Pairing
450pp Feb 2018
ISBN: 978-981-3228-87-0 (hardcover)
This volume aims to highlight trends and important directions of research in orthogonal polynomials, q-series, and related topics in number theory, combinatorics, approximation theory, mathematical physics, and computational and applied harmonic analysis. This collection is based on the invited lectures by well-known contributors from the International Conference on Orthogonal Polynomials and q-Series, that was held at the University of Central Florida in Orlando, on May 10?12, 2015. The conference was dedicated to Professor Mourad Ismail on his 70th birthday.
The editors strived for a volume that would inspire young researchers and provide a wealth of information in an engaging format. Theoretical, combinatorial and computational/algorithmic aspects are considered, and each chapter contains many references on its topic, when appropriate.
Preface
My Thanks to Mourad Ismail for His Work (Richard Askey)
Binomial Andrews?Gordon?Bressoud Identities (Dennis Stanton)
Symmetric Expansions of Very Well Poised Basic Hypergeometric Series (George E Andrews)
A Sturm?Liouville Theory for Hahn Difference Operator (M H Annaby, A E Hamza and S D Makharesh)
Solvability of the Hankel Determinant Problem for Real Sequences (Andrew Bakan and Christian Berg)
Convolution and Product Theorems for the Special Affine Fourier Transform (Ayush Bhandari and Ahmed I Zayed)
A Further Look at Time-and-Band Limiting for Matrix Orthogonal Polynomials (M Castro, F A Grunbaum, I Pacharoni and I Zurrian)
The Orthogonality of Al?Salam?Carlitz Polynomials for Complex Parameters (Howard S Cohl, Roberto S Costas-Santos and Wenqing Xu)
Crouching AGM, Hidden Modularity (Shaun Cooper, Jesus Guillera, Armin Straub and Wadim Zudilin)
Asymptotics of Orthogonal Polynomials and the Painleve Transcendents (Dan Dai)
From Gaussian Circle Problem to Multivariate Shannon Sampling (W Freeden, M Z Nashed)
Weighted Partition Identities and Divisor Sums (F G Garvan)
On the Ismail?Letessier?Askey Monotonicity Conjecture for Zeros of Ultraspherical Polynomials (Walter Gautschi)
A Discrete Top-Down Markov Problem in Approximation Theory (Walter Gautschi)
Supersymmetry of the Quantum Rotor (Vincent X Genest, Luc Vinet, Guo-Fu Yu and Alexei Zhedanov)
The Method of Brackets in Experimental Mathematics (Ivan Gonzalez, Karen Kohl, Lin Jiu and Victor H Moll)
Balanced Modular Parameterizations (Tim Huber, Danny Lara and Esteban Melendez)
Some Smallest Parts Functions from Variations of Bailey's Lemma (Chris Jennings-Shaffer)
Dual Addition Formulas Associated with Dual Product Formulas (Tom H Koornwinder)
Holonomic Tools for Basic Hypergeometric Functions (Christoph Koutschan and Peter Paule)
A Direct Evaluation of an Integral of Ismail and Valent (Alexey Kuznetsov)
Algebraic Generating Functions for Gegenbauer Polynomials (Robert S Maier)
q-Analogues of Two Product Formulas of Hypergeometric Functions by Bailey (Michael J Schlosser)
Summation Formulae for Noncommutative Hypergeometric Series (Michael J Schlosser)
Asymptotics of Generalized Hypergeometric Functions (Y Lin and R Wong)
Mock Theta-Functions of the Third Order of Ramanujan in Terms of Appell?Lerch Series (Changgui Zhang)
On Certain Positive Semidefinite Matrices of Special Functions (Ruiming Zhang)
Graduate students and researchers interested in orthogonal polynomials and q-series.