Bruce L. Rothschild

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.

Praise for the First Edition "Anyone interested in getting an introduction to Ramsey theorywill find this illuminating..." --MAA Reviews Covering all the major concepts, proofs, and theorems, theSecond Edition of Ramsey Theory is the ultimate guideto understanding every aspect of Shelah's proof, as well asthe original proof of van der Waerden. The book offers a historicalperspective of Ramsey's fundamental paper from 1930 andErdos' and Szekeres' article from 1935, while placingthe various theorems in the context of T. S. Motzkin'sthought on the subject of "Complete Disorder isImpossible." Ramsey Theory, Second Edition includes new and excitingcoverage of Graph Ramsey Theory and Euclidean Ramsey Theory andalso relates Ramsey Theory to other areas in discrete mathematics.In addition, the book features the unprovability results of Parisand Harrington and the methods from topological dynamics pioneeredby Furstenburg. Featuring worked proofs and outside applications, RamseyTheory, Second Edition addresses: * Ramsey and density theorems on both broad and meticulousscales * Extentions and implications of van der Waerden's Theorem,the Hales-Jewett Theorem, Roth's Theorem, Rado'sTheorem, Szemeredi's Theorem, and the Shelah Proof * Regular homogeneous and nonhomogeneous systems andequations * Special cases and broader interdisciplinary applications ofRamsey Theory principles An invaluable reference for professional mathematicians workingin discrete mathematics, combinatorics, and algorithms, RamseyTheory, Second Edition is the definitive work on thesubject.

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. Recent titles in the Series include: Integer and Combinatorial Optimization George L. Nemhauser and Laurence A. Wolsey "[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 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.