Collected Works, Volume: 25
2016; Hardcover
ISBN: 978-1-4704-1682-9
Richard Stanley's work in combinatorics revolutionized and reshaped the subject. Many of his hallmark ideas and techniques imported from other areas of mathematics have become mainstays in the framework of modern combinatorics. In addition to collecting several of Stanley's most influential papers, this volume also includes his own short reminiscences on his early years, and on his celebrated proof of The Upper Bound Theorem.
Pure and Applied Undergraduate Texts, Volume: 26
2016; 217 pp; Hardcover
Print ISBN: 978-1-4704-2899-0
This accessible textbook gives beginning undergraduate mathematics students a first exposure to introductory logic, proofs, sets, functions, number theory, relations, finite and infinite sets, and the foundations of analysis. The book provides students with a quick path to writing proofs and a practical collection of tools that they can use in later mathematics courses such as abstract algebra and analysis. The importance of the logical structure of a mathematical statement as a framework for finding a proof of that statement, and the proper use of variables, is an early and consistent theme used throughout the book.
Undergraduate students interested in advancing beyond computation-oriented mathematics courses to proof-based courses.
Graduate Studies in Mathematics, Volume: 174
2016; 295 pp; Hardcover
ISBN: 978-1-4704-2307-0
This book is an introduction to the theory of quiver representations and quiver varieties, starting with basic definitions and ending with Nakajima's work on quiver varieties and the geometric realization of Kac?Moody Lie algebras.
The first part of the book is devoted to the classical theory of quivers of finite type. Here the exposition is mostly self-contained and all important proofs are presented in detail. The second part contains the more recent topics of quiver theory that are related to quivers of infinite type: Coxeter functor, tame and wild quivers, McKay correspondence, and representations of Euclidean quivers. In the third part, topics related to geometric aspects of quiver theory are discussed, such as quiver varieties, Hilbert schemes, and the geometric realization of Kac?Moody algebras. Here some of the more technical proofs are omitted; instead only the statements and some ideas of the proofs are given, and the reader is referred to original papers for details.
The exposition in the book requires only a basic knowledge of algebraic geometry, differential geometry, and the theory of Lie groups and Lie algebras. Some sections use the language of derived categories; however, the use of this language is reduced to a minimum. The many examples make the book accessible to graduate students who want to learn about quivers, their representations, and their relations to algebraic geometry and Lie algebras.
Subject Area: Higher Education - Mathematics
ISBN-13: 9780128100158
Pub Date: 10/30/2017
Product Type: Softcover
Hirsch, Devaney, and Smale’s classic Differential Equations, Dynamical Systems, and an Introduction to Chaos has been used by professors as the primary text for undergraduate and graduate level courses covering differential equations. It provides a theoretical approach to dynamical systems and chaos written for a diverse student population among the fields of mathematics, science, and engineering. Prominent experts provide everything students need to know about dynamical systems as students seek to develop sufficient mathematical skills to analyze the types of differential equations that arise in their area of study. The authors provide rigorous exercises and examples clearly and easily by slowly introducing linear systems of differential equations. Calculus is required as specialized advanced topics not usually found in elementary differential equations courses are included, such as exploring the world of discrete dynamical systems and describing chaotic systems.
Classic text by three of the world’s most prominent mathematicians
Continues the tradition of expository excellence
Contains updated material and expanded applications for use in applied studies
Subject Area: Higher Education - Probability & Statistics
ISBN-13: 9780128102459
Pub Date: 10/30/2017
Product Type: Softcover
Miller has focussed on creating a more level presentation and develp more pertinent applications to signal processing and communications, clearly the two areas of most interest to students and instructors in this course. This text is aimed at the graduate market and includes unique chapters on narrowband random processes and simulation techniques.
Exceptional exposition and numerous worked out problems make the book extremely readable and accessible
The authors connect the applications discussed in class to the textbook
The new edition contains more real world signal processing and communications applications
Includes an entire chapter devoted to simulation techniques
Subject Area: Higher Education - Mathematical Computing
ISBN-13: 9780128047767
Pub Date: 09/01/2016
Pages: Approx 900 Pages
Size: 7 1/2 X 9 1/4 in
Product Type: Softcover
Demonstrates how to take advantage of the advanced features of Mathematica 10
Introduces the fundamental theory of ordinary and partial differential equations using Mathematica to solve typical problems of interest to students, instructors, scientists, and practitioners in many fields
Showcases practical applications and case studies drawn from biology, physics, and engineering
Preface
Introduction to Differential Equations
First-Order Ordinary Differential Equations
Applications of First-Order Ordinary Differential Equations
Higher-Order Differential Equations
Applications of Higher-Order Differential Equations
Systems of Ordinary Differential Equations
Applications of Systems of Ordinary Differential Equations
Laplace Transform Methods
Eigenvalue Problems and Fourier Series
Partial Differential Equations
Appendix: Getting Started
The Mathematica Menu
Bibliography
Index
Subject Area: Higher Education - Mathematics
ISBN-13: 9780128044087
Pub Date: 08/08/2016
Pages: Approx 426 Pages
Product Type: Handbook
Offers a comprehensive presentation of fractal functions and fractal surfaces
Includes latest developments in fractal interpolation
Connects fractal geometry with wavelet theory
Includes pertinent application examples, further discusses local IFS and new fractal interpolation or fractal data, and further develops the connections to wavelets and wavelet sets
Deepens and extends the pedagogical content
Part I. Foundations
1. Mathematical Preliminaries
2. Construction of Fractal Sets
3. Dimension Theory
4. Dynamical Systems and Dimension
Part II. Fractal Functions and Fractal Surfaces
5. Constructions of Fractal Functions
6. Fractels and Self-Referential Functions
7. Dimension of Fractal Functions
8. Fractal Functions and Wavelets
9. Fractal Surfaces
10. Fractal Surfaces and Wavelets in Rn