Ramsey Theory (eBook)

Yesterday, Today, and Tomorrow

Alexander Soifer (Herausgeber)

eBook Download: PDF

2010 | 2011
XIV, 190 Seiten
Birkhäuser Boston (Verlag)
978-0-8176-8092-3 (ISBN)

Infos

This book 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.

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.

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Ramsey theory is a relatively "e;new,"e; 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.

Inhalt

Ramsey Theory 2
What This Book Is About and How It Came into Being 7
Contents 10
Ramsey Theory Before Ramsey, Prehistory and Early History: An Essay in 13 Parts 14
EightyYearsof RamseyR(3,k)andCounting! 40
Ramsey Numbers Involving Cycles 53
On the Function of Erdos and Rogers 75
Large Monochromatic Components in Edge Colorings of Graphs: A Survey 89
Szlam's Lemma: Mutant Offspring of a Euclidean Ramsey Problem from 1973, with Numerous Applications 109
Open Problems in Euclidean Ramsey Theory 126
Chromatic Number of the Plane Its Relatives, History, Problems and Results: An Essay in 11 Parts 132
Euclidean Distance Graphs on the Rational Points 173
Open Problems Session 187

Produkt-Details

• Erscheint lt. Verlag: 29.10.2010
• Reihe/Serie: Progress in Mathematics
• Reihe/Serie: Progress in Mathematics
• Zusatzinfo: XIV, 190 p. 28 illus.
• Verlagsort: Boston
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik ► Graphentheorie
• Themenwelt: Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik
• Themenwelt: Technik
• Schlagworte: combinatorics • discrete math • Extremal graph theory • graph theory • Ramsey Number
• ISBN-10: 0-8176-8092-6 / 0817680926
• ISBN-13: 978-0-8176-8092-3 / 9780817680923