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Ramsey Theory on the Integers (Paperback, 2nd Revised edition)
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Ramsey Theory on the Integers (Paperback, 2nd Revised edition)
Series: Student Mathematical Library
Expected to ship within 12 - 19 working days
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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 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.
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