Ramsey Theory

Yesterday, Today, and Tomorrow

  • Alexander Soifer

Part of the Progress in Mathematics book series (PM, volume 285)

Table of contents

About this book

Introduction

Ramsey theory is a relatively “new,” approximately 100 year-old direction of fascinating mathematical thought that touches on many classic fields of mathematics such as combinatorics, number theory, geometry, ergodic theory, topology, combinatorial geometry, set theory, and measure theory. Ramsey theory possesses its own unifying ideas, and some of its results are among the most beautiful theorems of mathematics. The underlying theme of Ramsey theory can be formulated as: any finite coloring of a large enough system contains a monochromatic subsystem of higher degree of organization than the system itself, or as T.S. Motzkin famously put it, absolute disorder is impossible.

Ramsey Theory: Yesterday, Today, and Tomorrow explores the theory’s history, recent developments, and some promising future directions through invited surveys written by prominent researchers in the field. The first three surveys provide historical background on the subject; the last three address Euclidean Ramsey theory and related coloring problems. In addition, open problems posed throughout the volume and in the concluding open problem chapter will appeal to graduate students and mathematicians alike.


Contributors:
J. Burkert, A. Dudek, R.L. Graham, A. Gyárfás, P.D. Johnson, Jr., S.P. Radziszowski, V. Rödl, J.H. Spencer, A. Soifer, E. Tressler.

Keywords

Extremal graph theory Ramsey Number combinatorics discrete math graph theory

Editors and affiliations

  • Alexander Soifer
    • 1
  1. 1.at Colorado Springs, College of Letters, Arts, and SciencesUniversity of ColoradoColorado SpringsUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-0-8176-8092-3
  • Copyright Information Birkhäuser Boston 2011
  • Publisher Name Birkhäuser, Boston, MA
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-0-8176-8091-6
  • Online ISBN 978-0-8176-8092-3
  • Series Print ISSN 0743-1643
  • Series Online ISSN 2296-505X
  • About this book