Books in the Discrete Mathematics and Its Applications series

This book presents methods for the summation of infinite and finite series and the related identities and inversion relations. The summation includes the column sums and row sums of lower triangular matrices. The convergence of the summation of infinite series is considered. The author's focus is on symbolic methods and the Riordan array approach. In addition, this book contains hundreds summation formulas and identities, which can be used as a handbook for people working in computer science, applied mathematics, and computational mathematics, particularly, combinatorics, computational discrete mathematics, and computational number theory. The exercises at the end of each chapter help deepen understanding.Much of the materials in this book has never appeared before in textbook form. This book can be used as a suitable textbook for advanced courses for high lever undergraduate and lower lever graduate students. It is also an introductory self-study book for re- searchers interested in this field, while some materials of the book can be used as a portal for further research.

This book presents methods for the summation of infinite and finite series and the related identities and inversion relations. The summation includes the column sums and row sums of lower triangular matrices. The convergence of the summation of infinite series is considered.

The new edition of this award-winning, graduate textbook is upated throughout. Including mostly enumerative combinatorics,yet there are algebraic, analytic, and topological parts as well, and many applications. The author continues to reveal the usefulness of the subject for both students and researchers.

"The purpose of the book is to give a comprehensive and detailed introduction to the computational complexity of counting and sampling. The book will consist of three main topics: I. Counting problems that are solvable in polynomial running time, II. Approximation algorithms for counting and sampling, III. Holographic algorithms"--

Provides an introduction to the methods used in the combinatorics of pattern avoidance and pattern enumeration in compositions and words. This book describes the strengths and weaknesses of a wide variety of solution techniques and approaches, presents an overview of the field, and illustrates fresh methods and definitions with worked examples.

Enables readers to prove hundreds of mathematical results. This title presents the formal development of natural numbers from axioms, which leads into set theory and transfinite induction. It covers Peano's axioms, weak and strong induction, double induction, infinite descent downward induction, and variants of these inductions.

Collecting some of the most popular graph algorithms and optimization procedures, this book provides the source code for a library of Java programs that can be used to solve problems in graph theory and combinatorial optimization.

Covers a range of algebraic, analytic, combinatorial, cryptographic, and geometric aspects of number theory. This text also offers coverage of algebraic number theory, binary quadratic forms, Diophantine approximation, arithmetic functions, p-adic analysis, Dirichlet characters, density and primes.

Applied Mathematical Modeling is an outstanding collection of in-depth case studies that span the mathematical sciences.

The first thing readers will notice about this book is that it is fun to read. It is meant for browsers, for students, and for specialists wanting to know more about the subject. The footnotes give an historical background to the text, in addition to providing deeper applications of the concept that is being cited. This allows browsers to look more deeply into the history or to pursue a given sideline. Those who are only marginally interested in the area will be able to read the text, pick up information easily, and be entertained at the same time by the historical and philosophical digressions. It is rich in structure and motivation in its concentration upon quadratic orders.

Enumerative Combinatorics provides systematic coverage of the theory of enumeration. The author first lays a foundation with basic counting principles and techniques and elementary classical enumerative topics, then proceeds to more advanced topics, including the partition polynomials, Stirling numbers, and the Eulerian numbers of generalized binomials. The text is supported by remarks and discussions, numerous tables, exercises, and a wealth of examples that illustrate the concepts, theorems, and applications of the subject. Designed to serve as a text for upper-level and graduate students, this book will be useful and enlightening to anyone who uses combinatorial methods.

A comprehensive and self-contained treatment of the subject, Authentication Codes and Combinatorial Designs covers optimal authentication codes, unconditionally secure authentication schemes, and both symmetric and asymmetric authentication codes. The book addresses an important area in cryptography, namely the authentication of codes. It ties together the notion of authentication codes and combinatorial designs and demonstrates how ideas from combinatorics can be used for cryptographic applications. The author proves the information-theoretic and combinatorial bounds and the conditions for achieving these bounds in simple, clean, and comprehensive language of mathematics.

The book has two goals: (1) Provide a unified treatment of the binomial coefficients, and (2) Bring together much of the undergraduate mathematics curriculum via one theme (the binomial coefficients).

Presents methods for solving counting problems and other types of problems that involve discrete structures. This work illustrates the relationship of these structures to algebra, geometry, number theory and combinatorics. It addresses topics such as information and game theories.

Applicable to any problem that requires a finite number of solutions, finite state-based models (also called finite state machines or finite state automata) have found wide use in various areas of computer science and engineering. This handbook provides a complete collection of introductory materials on finite state theories, algorithms, and the latest domain applications. For beginners, the book is a handy reference for quickly looking up model details. For more experienced researchers, it is suitable as a source of in-depth study in this area.

This handbook examines the dichotomy between the structure of products and their subgraphs. It also features the design of efficient algorithms that recognize products and their subgraphs and explores the relationship between graph parameters of the product and factors. Extensively revised and expanded, this second edition presents full proofs of many important results as well as up-to-date research and conjectures. It illustrates applications of graph products in several areas and contains well over 300 exercises. Supplementary material is available on the book¿s website.

Edited by a pioneer in graph drawing and with contributions from leaders in the graph drawing research community, this handbook shows how graph drawing and visualization can be applied in the physical, life, and social sciences. It covers topological and geometric foundations, algorithms, software systems, and visualization applications. Whether you are a mathematics researcher, IT practitioner, or software developer, the book will help you understand graph drawing methods and graph visualization systems, use graph drawing techniques in your research, and incorporate graph drawing solutions in your products.

This book fills the gap between introductory texts in discrete mathematics and advanced graduate texts in enumerative combinatorics. The text first deals with basic counting principles, compositions and partitions, and generating functions. It then focuses on the structure of permutations, graph enumeration, and extremal combinatorics. Lastly, the book discusses supplemental topics, including error-correcting codes, properties of sequences, and magic squares. The second edition adds a new chapter on analytic combinatorics, new sections on advanced applications of generating functions, and new exercises to all chapters.

Presenting the state of the art, the Handbook of Enumerative Combinatorics brings together the work of today¿s most prominent researchers. The first two chapters provide a comprehensive overview of the most frequently used methods in combinatorial enumeration. These chapters supply an overview that is impressive both in its breadth and its depth, including algebraic, geometric, and analytic methods. Subsequent chapters illustrate applications of these methods for counting a wide array of objects.

Although sequent calculi constitute an important category of proof systems, they are not as well known as axiomatic and natural deduction systems. Addressing this deficiency, this book presents a comprehensive treatment of sequent calculi, including a wide range of variations. It focuses on sequent calculi for various non-classical logics, from intuitionistic logic to relevance logic, linear logic, and modal logic. The author presents a variety of proof systems for classical and non-classical logics and devotes chapters to proofs of cut theorems and decidability theorems.

This bestselling, classic textbook continues to provide a complete one-semester introduction to mathematical logic. The sixth edition incorporates recent work on Gödel¿s second incompleteness theorem as well as an appendix on consistency proofs for first-order arithmetic. It also offers historical perspectives and many new exercises of varying difficulty, which motivate and lead students to an in-depth, practical understanding of the material.

Developed from the author¿s popular graduate-level course, this self-contained text presents a complete treatment of number-theoretic algorithms. Avoiding advanced algebra and requiring no prior experience with number theory or sophisticated algebraic tools, the book covers many computational aspects of number theory and highlights important and interesting engineering applications. With an emphasis on implementation issues, it uses the freely available number-theory calculator GP/PARI to demonstrate complex arithmetic computations. The text includes numerous examples and exercises throughout and omits lengthy proofs, making the material accessible to students and practitioners.

Sets forth a procedure called OVMSP: Order-Verification via the Manufactured Solution Procedure that offers an opportunity to identify virtually all coding 'bugs' that prevent correct solution of the governing partial differential equations. This book provides guidance to OVMSP and demonstrates its effectiveness.

Presents working algorithms and implementations that can be used to design and create real systems. This book emphasises on the underlying concepts governing information theory and the mathematical basis for modern coding systems. It also provides the practical details of important codes like Reed-Solomon, BCH, and Turbo codes.

Features appendices that contain tabular material including class numbers of real and complex quadratic fields up to 104; class group structures; and, fundamental units of real quadratic fields.