Ramsey Theory on the Integers (Student Mathematical Library)

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9780821898673: 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 Erd s-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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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

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

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

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Bruce M. Landman, Aaron Robertson
Editorial: American Mathematical Society, United States (2014)
ISBN 10: 0821898671 ISBN 13: 9780821898673
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Descripción American Mathematical Society, United States, 2014. Paperback. Estado de conservación: New. 2nd Revised edition. Language: English . Brand New Book. 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. Nº de ref. de la librería AAN9780821898673

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Descripción American Mathematical Society, 2014. PAP. Estado de conservación: New. New Book. Shipped from UK in 4 to 14 days. Established seller since 2000. Nº de ref. de la librería CE-9780821898673

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Descripción American Mathematical Society, United States, 2014. Paperback. Estado de conservación: New. 2nd Revised edition. Language: English . Brand New Book. 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. Nº de ref. de la librería AAN9780821898673

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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

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Descripción American Mathematical Society, 2014. Paperback. Estado de conservación: New. book. Nº de ref. de la librería M0821898671

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Descripción American Mathematical Society, 2014. Paperback. Estado de conservación: New. Never used!. Nº de ref. de la librería P110821898671

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Descripción American Mathematical Society, 2014. Estado de conservación: new. Shiny and new! Expect delivery in 20 days. Nº de ref. de la librería 9780821898673-1

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