Bøger i Discrete Mathematics and Its Applications serien

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.

Additive Combinatorics: A Menu of Research Problems is the first book of its kind in aims and scope: it provides readers with an opportunity to actively explore the relatively new field of additive combinatorics. The author has written it specifically for students of any background and proficiency level, from beginners to advanced researchers.

The first book devoted to the crossing number, an increasingly popular object of study with surprising connections. The field has matured into a large body of work, which includes identifiable core results and techniques. The book presents a wide variety of ideas and techniques in topological graph theory, discrete geometry, and computer science.

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 is designed to be usable as a textbook for an undergraduate course or for an advanced graduate course in coding theory as well as a reference for researchers in discrete mathematics, engineering and theoretical computer science. This second edition has three parts: an elementary introduction to coding, theory and applications of codes, and algebraic curves. The latter part presents a brief introduction to the theory of algebraic curves and its most important applications to coding theory.

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.

The book offers the most important results and methods in discrete and computational geometry to those who use them in their work, both in the academic world and the professional world. This synthesis between discrete and computational geometry lies at the heart of this Handbook.

This book focuses on symmetric groups and representation theory. The symmetric group is a central object in discrete mathematics. It can be studied from a combinatorial, algorithmic, or algebraic viewpoint, and the results can be applied in a plethora of other fields, such as physics and computer science. This book is the most up-to-date one on the topic, bringing together new research and results.