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Ramsey Theory on the Integers
Bruce M. Landman, State University of West Georgia, Carrollton, GA, and Aaron Robertson, Colgate University, Hamilton, NY
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Student Mathematical Library
2004; 317 pp; softcover
Volume: 24
ISBN-10: 0-8218-3199-2
ISBN-13: 978-0-8218-3199-1
List Price: US$54
Institutional Members: US$43.20
All Individuals: US$43.20
Order Code: STML/24
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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 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.

Readership

Advanced undergraduates, graduate students, and research mathematicians interested in combinatorics.

Reviews

"Students will enjoy it due to the highly accessible exposition of the material provided by the authors."

-- MAA Horizons

"What a wonderful book! ... contains a very 'student friendly' approach to one of the richest areas of mathematical research ... a very good way of introducing the students to mathematical research ... an extensive bibliography ... no other book on the subject ... which is structured as a textbook for undergraduates ... The book can be used in a variety of ways, either as a textbook for a course, or as a source of research problems ... strongly recommend this book for all researchers in Ramsey theory ... very good book: interesting, accessible and beautifully written. The authors really did a great job!"

-- MAA Online

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
  • Biobliography
  • Index
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