Ramsey Theory on the Integers

by Bruce M. Landman

Ramsey theory is the study of the structure of mathematical objects that is preserved under partitions. In its full generality, Ramsey theory is quite powerful, but can quickly become complicated. By limiting the focus of this book to Ramsey theory applied to the set of integers, the authors have produced a gentle, but meaningful, introduction to an important and enticing branch of modern mathematics. Ramsey Theory on the Integers offers students something quite rare for a book at this a glimpse into the world of mathematical research and the opportunity for them to begin pondering unsolved problems. In addition to being the first truly accessible book on Ramsey theory, this innovative book also provides the first cohesive study of Ramsey theory on the integers. It contains perhaps the most substantial account of solved and unsolved problems in this blossoming subarea of Ramsey theory. The result is a breakthrough book that will engage students, teachers, and researchers alike.

Genres: Mathematics

317 pages, Paperback

First published January 1, 2004

Reviews

[NumberLord · Rating 5 out of 5]

This is the Bible as far as Ramsey Theory on the Integers goes. (No graph-theoretic Ramsey Theory--just integer stuff.) It contains a great discussion of van der Waerden numbers, Schur's theorem, and Rado's work on linear systems.