Bücher der Reihe Discrete Mathematics and Its Applications

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.

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 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"--

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.

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.

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.

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.

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.

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.

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.

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 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.

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.

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.

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.