Ramsey Theory

by Graham, Ronald L.; Rothschild, Bruce L.; Spencer, Joel H.

• ISBN13: 9781118799666
• ISBN10: 1118799666
• Edition: 2nd
• Format: Paperback
• Copyright: 2015-08-17
• Publisher: Wiley

Summary

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.

Author Biography

RONALD L. GRAHAM, PhD, is Professor of Mathematics and the Irwin and Joan Jacobs Professor of Computer and Information Science at the University of California in San Diego.

BRUCE L. ROTHSCHILD, PhD, is Professor of Mathematics at the University of California in Los Angeles.

JOEL H. SPENCER, PhD, is Professor of Mathematics and Computer Science at the Courant Institute of New York University. He is coauthor of The Probabilistic Method, also published by Wiley, and cofounder of the journal Random Structures and Algorithms.

Table of Contents

Sets.

Progressions.

Equations.

Numbers.

Particulars.

Beyond Combinatorics.

References.

Index.