This book, suitable for graduate students and professional mathematicians alike, didactically introduces methodologies due to Furstenberg and others for attacking problems in chromatic and density Ramsey theory via recurrence in topological dynamics and ergodic theory, respectively. Many standard results are proved, including the classical theorems of van der Waerden, Hindman, and Szemerédi. More importantly, the presentation strives to reflect the extent to which the field has been streamlined since breaking onto the scene around twenty years ago. Potential readers who were previously intrigued by the subject matter but found it daunting may want to give a second look.

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Bibliographic Information

Book Title: Elemental Methods in Ergodic Ramsey Theory
Authors: Randall McCutcheon
Series Title: Lecture Notes in Mathematics
DOI: https://doi.org/10.1007/BFb0093959
Publisher: Springer Berlin, Heidelberg
eBook Packages: Springer Book Archive
Copyright Information: Springer-Verlag Berlin Heidelberg 1999
Softcover ISBN: 978-3-540-66809-1Published: 15 December 1999
eBook ISBN: 978-3-540-46699-4Published: 14 November 2006
Series ISSN: 0075-8434
Series E-ISSN: 1617-9692
Edition Number: 1
Number of Pages: VI, 166
Topics: Combinatorics, Global Analysis and Analysis on Manifolds, Real Functions

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Table of contents (6 chapters)

Front Matter

Introduction

Ramsey theory and topological dynamics

Infinitary Ramsey theory

Density Ramsey theory

Three ergodic roth theorems

Two Szemerédi theorems

Back Matter

About this book