March 24, 2016 by Chapman and Hall/CRC
Textbook - 399 Pages - 115 B/W Illustrations
ISBN 9781498720960
Series: Chapman & Hall/CRC Texts in Statistical Science
Provides readers with an up-to-date, well-stocked toolbox of statistical methodologies
Includes numerous real examples that illustrate the use of R for data analysis
Covers GLM diagnostics, generalized linear mixed models, trees, and the use of neural networks in statistics
Reviews linear models as well as the basics of using R
Offers the datasets and other material on the author’s website
Expanded coverage of binary and binomial responses, including proportion responses, quasibinomial and beta regression, and applied considerations regarding these models
New sections on Poisson models with dispersion, zero inflated count models, linear discriminant analysis, and sandwich and robust estimation for generalized linear models (GLMs)
Revised chapters on random effects and repeated measures that reflect changes in the lme4 package and show how to perform hypothesis testing for the models using other methods
New chapter on the Bayesian analysis of mixed effect models that illustrates the use of STAN and presents the approximation method of INLA
Revised chapter on generalized linear mixed models to reflect the much richer choice of fitting software now available
Updated coverage of splines and confidence bands in the chapter on nonparametric regression
New material on random forests for regression and classification
Revamped R code throughout, particularly the many plots using the ggplot2 package
Revised and expanded exercises with solutions now included
September 8, 2016 Forthcoming by Chapman and Hall/CRC
Textbook - 546 Pages - 302 B/W Illustrations
ISBN 9781482251166
Series: Discrete Mathematics and Its Applications
Provides a thorough treatment of graph theory along with data structures to show how algorithms can be programmed
Includes three chapters on linear optimization which show how linear programming is related to graph theory
Emphasizes the use of programming to solve graph theory problems
Presents all algorithms from a generic point of view, usable with any programming language
Demonstrates how to draw a graph on the plane, torus, and projective plane
This comprehensive text features clear exposition on modern algorithmic graph theory presented in a rigorous yet approachable way. It covers the major areas of graph theory, including discrete optimization and its connection to graph algorithms. The authors explore surface topology from an intuitive point of view and include detailed discussions on linear programming that emphasize graph theory problems useful in mathematics and computer science. Many algorithms are provided along with the data structure needed to program the algorithms efficiently.
Graphs and Their Complements. Paths and Walks. Some Special Classes of Graphs. Trees and Cycles. The Structure of Trees. Connectivity. Alternating Paths and Matchings. Network Flows. Hamilton Cycles. Tsp. Digraphs. Graph Colorings. Planar Graphs. Graphs and Surfaces. Linear Programming. Discrete Linear Programming. Bibliography. Index
April 15, 2017 Forthcoming by Chapman and Hall/CRC
Reference - 216 Pages - 10 B/W Illustrations
ISBN 9781138030213
This book will contain lectures given by four eminent speakers at the Recent Advances in Operator Theory and Operator Algebras conference held at the Indian Statistical Institute, Bangalore, India in 2014. The main aim of this book is to bring together various results in one place with cogent introduction and references for further study.
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252pp Apr 2016
ISBN: 978-981-3109-92-6 (hardcover)
ISBN: 978-981-31-4087-5 (softcover)
This book presents a collection of problems for nonlinear dynamics, chaos theory and fractals. Besides the solved problems, supplementary problems are also added. Each chapter contains an introduction with suitable definitions and explanations to tackle the problems.
The material is self-contained, and the topics range in difficulty from elementary to advanced. While students can learn important principles and strategies required for problem solving, lecturers will also find this text useful, either as a supplement or text, since concepts and techniques are developed in the problems.
One-Dimensional Maps:
Notations and Definitions
One-Dimensional Maps
Higher-Dimensional Maps and Complex Maps:
Introduction
Two-Dimensional Maps
Complex Maps
Higher-Dimensional Maps
Bitwise Maps
Fractals
Introduction
Solved Problems
Supplementary Problems
Readership: Graduate students who focus on chaos, fractals and nonlinear dynamics.
528pp Jul 2016
ISBN: 978-981-4749-78-7 (hardcover)
ISBN: 978-981-4759-20-5 (softcover)
This book presents, in a unitary frame and from a new perspective, the main concepts and results of one of the most fascinating branches of modern mathematics, namely differential equations, and offers the reader another point of view concerning a possible way to approach the problems of existence, uniqueness, approximation, and continuation of the solutions to a Cauchy problem. In addition, it contains simple introductions to some topics which are not usually included in classical textbooks: the exponential formula, conservation laws, generalized solutions, Caratheodory solutions, differential inclusions, variational inequalities, viability, invariance, and gradient systems.
In this new edition, some typos have been corrected and two new topics
have been added: Delay differential equations and differential equations
subjected to nonlocal initial conditions. The bibliography has also been
updated and expanded
Generalities
The Cauchy Problem
Approximation Methods
Systems of Linear Differential Equations
Elements of Stability
Prime Integrals
Extensions and Generalizations
Volterra Equations
Calculus of Variations
Nonlocal Problems
Delay Functional Differential Equations
Auxiliary Results
Readership: Graduate or undergraduate students dealing with analysis and differential equations, Volterra equations, calculus of variations and mathematical modeling.
788pp Aug 2016
ISBN: 978-981-3140-95-0 (hardcover)
ISBN: 978-981-3140-96-7 (softcover)
This is the second volume of "A Course in Analysis" and it is devoted to the study of mappings between subsets of Euclidean spaces. The metric, hence the topological structure is discussed as well as the continuity of mappings. This is followed by introducing partial derivatives of real-valued functions and the differential of mappings. Many chapters deal with applications, in particular to geometry (parametric curves and surfaces, convexity), but topics such as extreme values and Lagrange multipliers, or curvilinear coordinates are considered too. On the more abstract side results such as the Stone?Weierstrass theorem or the Arzela?Ascoli theorem are proved in detail. The first part ends with a rigorous treatment of line integrals.
The second part handles iterated and volume integrals for real-valued functions. Here we develop the Riemann (?Darboux?Jordan) theory. A whole chapter is devoted to boundaries and Jordan measurability of domains. We also handle in detail improper integrals and give some of their applications.
The final part of this volume takes up a first discussion of vector calculus. Here we present a working mathematician's version of Green's, Gauss' and Stokes' theorem. Again some emphasis is given to applications, for example to the study of partial differential equations. At the same time we prepare the student to understand why these theorems and related objects such as surface integrals demand a much more advanced theory which we will develop in later volumes.
This volume offers more than 260 problems solved in complete detail which should be of great benefit to every serious student.
Part 3: Differentiation of Functions of Several Variables:
Metric Spaces
Convergence and Continuity in Metric Spaces
More on Metric Spaces and Continuous Functions
Continuous Mappings Between Subsets of Euclidean Spaces
Partial Derivatives
The Differential of a Mapping
Curves in ?n
Surfaces in ?3. A First Encounter
Taylor Formula and Local Extreme Values
Implicit Functions and the Inverse Mapping Theorem
Further Applications of the Derivatives
Curvilinear Coordinates
Convex Sets and Convex Functions in ?n
Spaces of Continuous Functions as Banach Spaces
Line Integrals
Part 4: Integration of Functions of Several Variables:
Towards Volume Integrals in the Sense of Riemann
Parameter Dependent and Iterated Integrals
Volume Integrals on Hyper-Rectangles
Boundaries in ?n and Jordan Measurable Sets
Volume Integrals on Bounded Jordan Measurable Sets
The Transformation Theorem : Result and Applications
Improper and Parameter Dependent Integrals
Part 5: Vector Calculus:
The Scope of Vector Calculus
The Area of a Surface in ?3 and Surface Integrals
Gauss' Theorem in ?3
Stokes Theorem in ?2 and ?3
Gauss' Theorem for Domains in ?n
Appendix I : Vector Spaces and Linear Mappings
Appendix II : Two Postponed Proofs of Part 3
Solutions to Problems of Part 3
Solutions to Problems of Part 4
Solutions to Problems of Part 5
References
Mathematicians Contributing to Analysis (Continued)
Subject Index
Readership: Undergraduate students in mathematics.