Ramsey Theory 2e P

ISBN-13: 9781118799666 / Angielski / Miękka / 2014 / 212 str.

Graham, Ronald L.

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.

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.

Spis treści

Sets.

Progressions.

Equations.

Numbers.

Particulars.

Beyond Combinatorics.

References.

Index.

O autorze

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.

Blurb

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.