Bøger i Discrete Mathematics and Its Applications serien

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.

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.

Offers an introduction to the areas of design theory as well as to more contemporary designs based on applications in a variety of fields. This work also introduces balanced designs and finite geometries. It then delves into balanced incomplete block designs, covering difference methods, residual and derived designs, and resolvability.

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.

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.

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.

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.

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

Like its bestselling predecessor, this book develops the theory of elliptic curves to provide a basis for both number theoretic and cryptographic applications. This edition now includes alternative coordinate systems and related computational issues, a more elementary treatment of the Tate???Lichtenbaum pairing, additional elliptic curve cryptosystems, and Doud??'s analytic method for computing torsion on elliptic curves over Q. It also contains new chapters on isogenies and hyperelliptic curves as well as discusses how to compute elliptic curves in some popular computer algebra systems. Basic exercises appear at the end of each chapter, with selected answers in an appendix.

Cryptography, in particular public-key cryptography, has emerged an important discipline that is not only the subject of an enormous amount of research, but provides the foundation for information security in many applications. This title provides a treatment that introduces the practical aspects of both conventional and public-key cryptography.

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.

Presents some of the techniques used for constructing combinatorial designs. This work contains material on embeddings, directed designs, universal algebraic representations of designs and intersection properties of designs. It also includes important results in combinatorial designs.

Using mathematical tools from number theory and finite fields, this text presents practical methods for solving problems in data security and data integrity. It covers many algorithms that arise in cryptography and error-control codes.

Bringing the material up to date to reflect modern applications, this second edition has been completely rewritten and reorganized to incorporate a new style, methodology, and presentation. It offers a more complete and involved treatment of Galois theory, a more comprehensive section on Pollard's cubic factoring algorithm, and more detailed explanations of proofs to provide a sound understanding of challenging material. This edition also studies binary quadratic forms and compares the ideal and form class groups. The text includes convenient cross-referencing, a comprehensive index, and numerous exercises and applications.

Covers the constructions of designs, existence results, properties of designs, and applications of designs. This book contains chapters on the history of design theory, various codes, bent functions, and numerous designs as well as tables, including BIBDs, PBDs, MOLS, and Hadamard matrices.

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 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.

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.

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.

Introduces the theory and algorithms involved in curve-based cryptography. This book provides ready-to-implement algorithms for the group operations and computation of pairings. It explores methods for point counting and constructing curves with the complex multiplication method and provides algorithms.

Covers the subject of computational group theory (CGT). This book describes the connections between the different aspects of CGT and other areas of computer algebra. It is suitable for graduate students who have some knowledge of group theory and computer algorithms.

Includes two chapters on various applications that cover topics such as electronic mail, Internet security, protocol layers and SSL, firewalls, client-server model and cookies, network security, wireless security, smart cards, and biometrics. This book provides information on cryptanalysis, primality testing, DES, and primitive roots.

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 core areas such as sequences, recursions, generating functions, evaluation of sums, and graphs. This book discusses topics like partitions and polynomials, algebraic counting, and designs.

Explores connections between major topics in graph theory and graph colorings. This book presents various fundamentals of graph theory that lie outside of graph colorings, including basic terminology and results, trees and connectivity, Eulerian and Hamiltonian graphs, matchings and factorizations, and graph embeddings.

Placing combinatorial and graph-theoretical tools at the forefront of the development of matrix theory, this book uses graphs to explain basic matrix construction, formulas, computations, ideas, and results.

An exploration of applied mathematical modelling, covering a broad range of applications. It stresses a multidisciplinary approach that illustrates the entire development of a model, from formulation to analysis to implementation. There are case studies spanning the mathematical sciences.