Ramsey Theory on the Integers
About this Title
Bruce M. Landman, State University of West Georgia, Carrollton, GA and Aaron Robertson, Colgate University, Hamilton, NY
Publication: The Student Mathematical Library
Publication Year 2004: Volume 24
ISBNs: 978-0-8218-3199-1 (print); 978-1-4704-1818-2 (online)
MathSciNet review: MR2020361
MSC: Primary 05D10; Secondary 11B75
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 level: a glimpse into the world of mathematical research and the opportunity to begin pondering unsolved problems themselves.
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.
Advanced undergraduates, graduate students, and research mathematicians interested in combinatorics.
Table of Contents
- Chapter 1. Preliminaries
- Chapter 2. Van der Waerden’s theorem
- Chapter 3. Supersets of $AP$
- Chapter 4. Subsets of $AP$
- Chapter 5. Other generalizations of $w(k;r)$
- Chapter 6. Arithmetic progressions (mod $m$)
- Chapter 7. Other variations on van der Waerden’s theorem
- Chapter 8. Schur’s theorem
- Chapter 9. Rado’s theorem
- Chapter 10. Other topics