Ramsey Theory

Yesterday, Today, and Tomorrow
1. Auflage. 2010
ISBN: 978-0-8176-8091-6
Verlag: Springer Nature Singapore

Buch, Englisch, Band 285, 190 Seiten, Format (B × H): 159 mm x 241 mm, Gewicht: 1030 g

Reihe: Progress in Mathematics

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.

Zielgruppe

Graduate

Autoren/Hrsg.

Soifer, Alexander

Fachgebiete

• Interdisziplinäres Wissenschaften Wissenschaften: Allgemeines Geschichte der Naturwissenschaften, Formalen Wissenschaften & Technik
• Mathematik | Informatik Mathematik Mathematik Allgemein Geschichte der Mathematik
• Mathematik | Informatik Mathematik Stochastik
• Mathematik | Informatik Mathematik Geometrie Euklidische Geometrie
• Mathematik | Informatik Mathematik Operations Research Graphentheorie

Inhaltsverzeichnis

How This Book Came into Being.- Table of Contents.- Ramsey Theory before Ramsey, Prehistory and Early History: An Essay in 13 Parts.- Eighty Years of Ramsey R(3, k). . . and Counting!.- Ramsey Numbers Involving Cycles.- On the function of Erdá½…s and Rogers.- Large Monochromatic Components in Edge Colorings of Graphs.- Szlam’s Lemma: Mutant Offspring of a Euclidean Ramsey Problem: From 1973, with Numerous Applications.- Open Problems in Euclidean Ramsey Theory.- Chromatic Number of the Plane and Its Relatives, History,
Problems and Results: An Essay in 11 Parts.- Euclidean Distance Graphs on the Rational Points.- Open Problems Session.

Über Autor(innen)

Alexander Soifer is a Russian born and educated American mathematician, a professor of mathematics at the University of Colorado, an author of some 200 articles on mathematics, history of mathematics, mathematics education, film reviews, etc. He is Senior Vice President of the World Federation of National Mathematics Competitions, which in 2006 awarded him The Paul Erdos Award. 26 years ago Soifer founded and has since chaired the Colorado Mathematical Olympiad, and served on both the USSR and USA Mathematical Olympiads committees. Soifer's Erdos number is 1.