Elemental Methods in Ergodic Ramsey Theory

• Main Author: McCutcheon, Randall (Author, http://id.loc.gov/vocabulary/relators/aut)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 1999.
• Edition: 1st ed. 1999.
• Series: Lecture Notes in Mathematics, 1722
• Subjects: Combinatorics.; Global analysis (Mathematics).; Manifolds (Mathematics).; Functions of real variables.; Global Analysis and Analysis on Manifolds.; Real Functions.
• Physical Description: VI, 166 p. online resource.
• ISBN: 9783540466994
• ISSN: 0075-8434 ;
• DOI: 10.1007/BFb0093959

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.