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Ramsey Theory, 2nd Edition

ISBN: 978-0-471-50046-9
208 pages
March 1990
Ramsey Theory, 2nd Edition (0471500461) cover image

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.

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Sets.

Progressions.

Equations.

Numbers.

Particulars.

Beyond Combinatorics.

References.

Index.

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