Ramsey Theory

ISBN-13: 9780471500469 / Angielski / Twarda / 1991 / 208 str.

Ronald Graham;Graham;Rothschild

Opis

Praise for the First Edition "Anyone interested in getting an introduction to Ramsey theory will find this illuminating..."
--MAA Reviews Covering all the major concepts, proofs, and theorems, the Second Edition of Ramsey Theory is the ultimate guide to understanding every aspect of Shelah's proof, as well as the original proof of van der Waerden. The book offers a historical perspective of Ramsey's fundamental paper from 1930 and Erdos' and Szekeres' article from 1935, while placing the various theorems in the context of T. S. Motzkin's thought on the subject of "Complete Disorder is Impossible." Ramsey Theory, Second Edition includes new and exciting coverage of Graph Ramsey Theory and Euclidean Ramsey Theory and also relates Ramsey Theory to other areas in discrete mathematics. In addition, the book features the unprovability results of Paris and Harrington and the methods from topological dynamics pioneered by Furstenburg. Featuring worked proofs and outside applications, Ramsey Theory, Second Edition addresses:

• Ramsey and density theorems on both broad and meticulous scales
• Extentions and implications of van der Waerden's Theorem, the Hales-Jewett Theorem, Roth's Theorem, Rado's Theorem, Szemeredi's Theorem, and the Shelah Proof
• Regular homogeneous and nonhomogeneous systems and equations
• Special cases and broader interdisciplinary applications of Ramsey Theory principles

An invaluable reference for professional mathematicians working in discrete mathematics, combinatorics, and algorithms, Ramsey Theory, Second Edition is the definitive work on the subject.

Recenzje

"Anyone interested in getting an introduction to Ramsey theory will find this illuminating " ( MAA Reviews, December 17, 2006)

Spis treści

Sets.

Progressions.

Equations.

Numbers.

Particulars.

Beyond Combinatorics.

References.

Index.

O autorze

About the authors RONALD L. GRAHAM is Adjunct Director for Research at AT&T Bell Laboratories, and University Professor of the Mathematical Sciences at Rutgers University. He is coauthor of Concrete Mathematics and of Old and New Problems in Combinatorial Number Theory, and serves on the editorial boards of more than 25 technical journals. He received his PhD in mathematics from the University of California, Berkeley. BRUCE L. ROTHSCHILD is Professor of Mathematics at the University of California, Los Angeles. He is Managing Editor of the Journal of Combinatorial Theory. He received his PhD in mathematics from Yale University. JOEL H. SPENCER is a professor of mathematics and computer science at the Courant Institute. He is the author of Ten Lectures on the Probabilistic Method and the editor of Random Structures and Algorithms. He received his PhD in mathematics from Harvard University.

Blurb

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.