Ramsey Theory on the Integers: (Student Mathematical Library)

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 a glimpse into the world of mathematical research and the opportunity for them to begin pondering unsolved problems. For this new edition, several sections have been added and others have been significantly updated. Among the newly introduced topics are: rainbow Ramsey theory, an “inequality” version of Schur's theorem, monochromatic solutions of recurrence relations, Ramsey results involving both sums and products, monochromatic sets avoiding certain differences, Ramsey properties for polynomial progressions, generalizations of the Erdos-Ginzberg-Ziv theorem, and the number of arithmetic progressions under arbitrary colorings. Many new results and proofs have been added, most of which were not known when the first edition was published. Furthermore, the book's tables, exercises, lists of open research problems, and bibliography have all been significantly updated. 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 subject. This breakthrough book will engage students, teachers, and researchers alike.

Table of Contents:
Preliminaries Van der Waerden's theorem Supersets of AP Subsets of AP Other generalizations of w(k;r) Arithmetic progressions (mod m) Other variations on van der Waerden's theorem Schur's theorem Rado's theorem Other topics Notation Bibliography Index

About the Author :
Bruce M. Landman, State University of West Georgia, Carrollton, GA, USA. Aaron Robertson, Colgate University, Hamilton, NY, USA.

Review :
This is an excellent undergraduate text which provides students with an introduction to research; it is also a source for all those who are interested in combinatorial or number theoretic problems... The textbook is carefully written. I recommend it to students interested in combinatorics and to their teachers as well." - Monatshafte für Mathematik