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Ramsey Theory on the Integers: Second Edition

Bruce M. Landman University of West Georgia, Carrollton, GA
Aaron Robertson Colgate University, Hamilton, NY
Available Formats:
Softcover ISBN: 978-0-8218-9867-3
Product Code: STML/73
384 pp
List Price: $61.00 Individual Price:$48.80
Electronic ISBN: 978-1-4704-2000-0
Product Code: STML/73.E
384 pp
List Price: $61.00 Individual Price:$48.80
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List Price: $91.50 Click above image for expanded view Ramsey Theory on the Integers: Second Edition Bruce M. Landman University of West Georgia, Carrollton, GA Aaron Robertson Colgate University, Hamilton, NY Available Formats:  Softcover ISBN: 978-0-8218-9867-3 Product Code: STML/73 384 pp  List Price:$61.00 Individual Price: $48.80  Electronic ISBN: 978-1-4704-2000-0 Product Code: STML/73.E 384 pp  List Price:$61.00 Individual Price: $48.80 Bundle Print and Electronic Formats and Save! This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version. List Price:$91.50
• Book Details

Student Mathematical Library
Volume: 732014
MSC: Primary 05;

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 Erdős-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.

Reviews of the Previous Edition:

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

Undergraduate and graduate students interested in combinatorics, number theory, and Ramsey theory.

• Chapters
• Chapter 1. Preliminaries
• Chapter 2. Van der Waerden’s theorem
• Chapter 3. Supersets of $AP$
• Chapter 4. Subsets of $AP$
• Chapter 5. Other generalizations of $w(k;r)$
• Chapter 6. Arithmetic progressions $(\mathrm {mod}\,m)$
• Chapter 7. Other variations on van der Waerden’s theorem
• Chapter 8. Schur’s theorem
• Chapter 10. Other topics

• Reviews

• 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
• Request Review Copy
• Get Permissions
Volume: 732014
MSC: Primary 05;

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 Erdős-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.

Reviews of the Previous Edition:

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

Undergraduate and graduate students interested in combinatorics, number theory, and Ramsey theory.

• Chapters
• Chapter 1. Preliminaries
• Chapter 2. Van der Waerden’s theorem
• Chapter 3. Supersets of $AP$
• Chapter 4. Subsets of $AP$
• Chapter 5. Other generalizations of $w(k;r)$
• Chapter 6. Arithmetic progressions $(\mathrm {mod}\,m)$
• Chapter 7. Other variations on van der Waerden’s theorem
• Chapter 8. Schur’s theorem