Böcker i Discrete Mathematics and Its Applications-serien

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.

With 34 new contributors, this best-selling handbook provides comprehensive coverage of the main topics in pure and applied graph theory. This second edition incorporates 14 new sections. Each chapter includes lists of essential definitions and facts, accompanied by examples, tables, remarks, and, in some cases, conjectures and open problems.

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 a comprehensive survey of the field of graph drawing, from its combinatorial and geometric foundations to its applications in various areas of the physical, life, and social sciences. This book covers combinatorial, geometric, and algorithmic foundations. It also presents various graph drawing algorithms as well as graph drawing systems.

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.

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.

The importance of discrete and combinatorial mathematics continues to increase as the range of applications to computer science, electrical engineering, and the biological sciences grows dramatically. This book presents additional material on Google's matrix, random graphs, geometric graphs, computational topology, and other key topics.

This book presents results established over the past 40 years on Laplacian matrices of graphs developed using combinatorial matrix theory. The author focuses on the spectrum of Laplacian matrices, the algebraic connectivity of graphs, associated eigenvectors of the Laplacian matrix, and submatrices of the Laplacian matrix. All of these topics illustrate how the properties of a matrix can provide information about the associated graph and vice versa. The text also covers relevant parts of graph theory, Laplacian matrices, and combinatorial matrix theory and includes sources for each theorem.

Combinatory logic is a versatile field that is connected to philosophical, mathematical, and computational logic. This comprehensive reference on combinatory logic covers results in the field from the last four decades along with classical information on the topic. The author makes combinatory logic simple to understand while providing working knowledge that is rigorous, current, and readable. Reader-friendly without compromising the precision of exposition, the book includes many new research results not found in the available literature. It also contains pointers to new directions in the field that can be pursued further by researchers.

Covers the theory of enumeration. This book features basic counting principles and techniques and elementary classical enumerative topics. It also includes advanced topics including the partition polynomials, Stirling numbers, and the Eulerian numbers of generalized binomials.

This guide provides an accessible introduction to the world of mathematics. It offers tips on how to study and write mathematics as well as how to use various mathematical tools, from LaTeX and Beamer to Mathematica® and Maple¿ to MATLAB® and R. The text also includes exercises and challenges to stimulate creativity and improve problem solving abilities. The first section of the book covers issues pertaining to studying mathematics. The second section focuses on the use of mathematical tools for mathematical typesetting, generating data, finding patterns, and much more.

Presenting both mathematical and security perspectives, this text reviews basic theory and discusses cryptographic protocols and systems. With an emphasis on experimentation and exploration, the text offers a wealth of practical examples and numerous exercises using the open source software Sage. An accompanying CD-ROM includes the necessary codes. The author covers private and public key cryptosystems, knapsack cryptosystems, digital signatures, random number generators, elliptic curves, block ciphers, hash functions, the DES and AES, finite fields, and message authentication codes.

Poised to become the leading reference in the field, this definitive handbook is exclusively devoted to the theory and applications of finite fields. Edited by two renowned researchers and with more than 80 international contributors compiling state-of-the-art research, the book uses a uniform style and format throughout and each chapter is self contained and peer reviewed. The handbook provides a comprehensive index and easy access to over 3,000 references, enabling readers to quickly locate up-to-date facts and results regarding finite fields.

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.

An introduction that provides a focused tour of the central concepts of cryptography. It delineates cryptographic concepts in chronological order, developing the mathematics as needed. It includes many examples and exercises, along with computer implementation sections that guide readers through the process of writing their own programs.

Linear algebra forms the basis for much of modern mathematics - theoretical, applied, and computational. Thsi book provides a foundation for the study of advanced mathematics and discusses applications of linear algebra to such diverse areas as combinatorics, differential equations, optimization, and approximation.

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.

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.

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.

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.

Combinatorial Algorithms: Generation, Enumeration, and Search thoroughly outlines and analyzes combinatorial algorithms for generation, enumeration, and search applications.