Ramsey theory (Wiley-Interscience series in discrete mathematics) - Hardcover

Graham, Ronald L

Hardcover

ISBN 10: 0471059978 ISBN 13: 9780471059974

Publisher: Wiley, 1980

Synopsis

Ramsey Theory has become the reference book its field as it contains most of the results and techniques in classical Ramsey Theory and remains the only book to cover the broad spectrum of the subject area. It provides both full proofs (in many cases more than one proof to give different vantage points) and a leisurely discussion of the major theorems, such as Ramsey's Theorem, van der Waerden's Theorem, the Hales-Jewett Theorem, and Rado's Theorem.A new chapter on Graph Ramsey has been added in light of recent emphasis on the topic within the mathematics community, and numerous new exercises have been added to help make the book more classroom friendly. This book also includes a complete treatment of Saharon Shelah's proof, which avoids double induction, involves fast growing functions, and is elementary in nature. A historical perspective is included and discusses the fundamental papers of Ramsey in 1930, and of Erdos and Szekeres in 1935.

About this title

From the Publisher

Ramsey theory has emerged as a cohesive subdiscipline of combinatorial analysis since about 1970. The present work comprises a self-contained exposition of the central results of Ramsey theory, describes recent developments in the field, and explores the influence of outside disciplines such as applications of topological dynamics and a combinatorial approach to undecidability results. New to the Second Edition is a complete treatment of Shelah's 1987 proof as well as the original proof of Van der Waerden's theorem.

From the Back Cover

Wiley-Interscience Series in Discrete Mathematics and Optimization Advisory
Editors: Ronald L. Graham, Jan Karel Lenstra, and Robert E. Tarjan

Discrete mathematics, the study of finite structures, is one of the fastest-growing areas in mathematics. The wide applicability of its evolving techniques points to the rapidity with which the field is moving from its beginnings to its maturity, and reflects the ever-increasing interaction between discrete mathematics and computer science. This Series provides broad coverage of discrete mathematics and optimization, ranging over such fields as combinatorics, graph theory, enumeration, and the analysis of algorithms. The Wiley-Interscience Series in Discrete Mathematics and Optimization will be a substantial part of the record of the extraordinary development of this field. A complete listing of the titles in the Series appears on the inside front cover of this book.

"[Integer and Combinatorial Optimization] is a major contribution to the literature of discrete programming. This text should be required reading for anybody who intends to research this area or even just to keep abreast of developments."
—Times Higher Education Supplement, London

"An extensive but extremely well-written graduate text covering integer programming."
—American Mathematical Monthly

Recent titles in the Series include:

Integer and Combinatorial Optimization George L. Nemhauser and Laurence A. Wolsey 1988 (0 471-82819-X) 763 pp.

Introduction to the Theory of Error-Correcting Codes Second Edition Vera Pless
For mathematicians, engineers, and computer scientists, here is an introduction to the theory of error-correcting codes, focusing on linear block codes. The book considers such codes as Hamming and Golay codes, correction of double errors, use of finite fields, cyclic codes, B.C.H. codes, weight distributions, and design of codes. In a second edition of the book, Pless offers thoroughly expanded coverage of nonbinary and cyclic codes. Some proofs have been simplified, and there are many more examples and problems. 1989 (0 471-61884-5) 224 pp.

Edition details

• Publisher: Wiley
• Publication date: 1980
• Language: English
• ISBN 10: 0471059978
• ISBN 13: 9780471059974
• Binding: Hardcover
• Number of pages: 174