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.About the Author:
Bruce M. Landman , State University of West Georgia, Carrollton, GA, USA. Aaron Robertson , Colgate University, Hamilton, NY, USA.
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Descripción American Mathematical Society, 2014. Paperback. Estado de conservación: New. book. Nº de ref. de la librería 0821898671
Descripción Amer Mathematical Society, 2014. Paperback. Estado de conservación: Brand New. 2nd edition. 384 pages. 8.50x5.50x1.00 inches. In Stock. Nº de ref. de la librería 0821898671
Descripción American Mathematical Society, 2014. Estado de conservación: New. Brand New, Unread Copy in Perfect Condition. A+ Customer Service!. Nº de ref. de la librería ABE_book_new_0821898671
Descripción American Mathematical Society, 2014. Paperback. Estado de conservación: New. Nº de ref. de la librería P110821898671