Ramsey Theory on the Integers
2003
American Mathematical Society (Verlag)
978-0-8218-3199-1 (ISBN)
American Mathematical Society (Verlag)
978-0-8218-3199-1 (ISBN)
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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. This book provides the study of Ramsey theory on the integers. It contains an account of solved and unsolved problems in this subarea of Ramsey theory.
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.
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.
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.
| Erscheint lt. Verlag | 1.9.2004 |
|---|---|
| Reihe/Serie | Student Mathematical Library |
| Zusatzinfo | Illustrations |
| Verlagsort | Providence |
| Sprache | englisch |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Graphentheorie |
| ISBN-10 | 0-8218-3199-2 / 0821831992 |
| ISBN-13 | 978-0-8218-3199-1 / 9780821831991 |
| Zustand | Neuware |
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