**Student Mathematical Library**

Volume: 73;
2014;
384 pp;
Softcover

MSC: Primary 05;

Print ISBN: 978-0-8218-9867-3

Product Code: STML/73

List Price: $61.00

Individual Price: $48.80

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**Electronic ISBN: 978-1-4704-2000-0
Product Code: STML/73.E**

List Price: $61.00

Individual Price: $48.80

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#### Supplemental Materials

# Ramsey Theory on the Integers: Second Edition

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*Bruce M. Landman; Aaron Robertson*

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

#### Readership

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

#### Reviews & Endorsements

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

#### Table of Contents

# Table of Contents

## Ramsey Theory on the Integers: Second Edition

- Cover Cover11 free
- Title page iii4 free
- Table of contents vii8 free
- Preface to the Second Edition xiii14 free
- Acknowledgements xv16 free
- Preface to the First Edition xvii18 free
- 1. Preliminaries 122 free
- 2. Van der Waerden's Theorem 2344
- 3. Supersets of AP 6788
- 4. Subsets of AP 113134
- 5. Other Generalizations of w(k; r) 147168
- 6. Arithmetic Progressions (mod m) 183204
- 7. Other Variations on van der Waerden's Theorem 203224
- 8. Schur's Theorem 221242
- 9. Rado's Theorem 251272
- 10. Other Topics 297318
- Notation 353374
- Bibliography 357378
- Index 381402 free
- Back Cover Back Cover1409