Elemental Methods in Ergodic Ramsey Theory

ISBN-13: 9783540668091 / Angielski / Miękka / 1999 / 166 str.

Randall McCutcheon

Opis

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 Szemeredi. 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.

Spis treści

Ramsey theory and topological dynamics.- Infinitary Ramsey theory.- Density Ramsey theory.- Three ergodic roth theorems.- Two Szemerédi theorems.