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Hardcover ISBN:  9781470428082 
Product Code:  SURV/212 
List Price:  $129.00 
MAA Member Price:  $116.10 
AMS Member Price:  $103.20 
eBook ISBN:  9781470430177 
Product Code:  SURV/212.E 
List Price:  $125.00 
MAA Member Price:  $112.50 
AMS Member Price:  $100.00 
Hardcover ISBN:  9781470428082 
eBook ISBN:  9781470430177 
Product Code:  SURV/212.B 
List Price:  $254.00 $191.50 
MAA Member Price:  $228.60 $172.35 
AMS Member Price:  $203.20 $153.20 

Book DetailsMathematical Surveys and MonographsVolume: 212; 2016; 245 ppMSC: Primary 05;
Ramsey theory is a dynamic area of combinatorics that has various applications in analysis, ergodic theory, logic, number theory, probability theory, theoretical computer science, and topological dynamics.
This book is devoted to one of the most important areas of Ramsey theory—the Ramsey theory of product spaces. It is a culmination of a series of recent breakthroughs by the two authors and their students who were able to lift this theory to the infinitedimensional case. The book presents many major results and methods in the area, such as Szemerédi's regularity method, the hypergraph removal lemma, and the density Hales–Jewett theorem.
This book addresses researchers in combinatorics but also working mathematicians and advanced graduate students who are interested in Ramsey theory. The prerequisites for reading this book are rather minimal: it only requires familiarity, at the graduate level, with probability theory and real analysis. Some familiarity with the basics of Ramsey theory would be beneficial, though not necessary.
I think that this book has a good chance of becoming a classic on density Ramsey theory at the level of the Graham–Rothschild–Spencer book on basic Ramsey theory.
—Stevo Todorcevic, University of Toronto
The book by Dodos and Kanellopoulos is firstrate! It is timely, well written, and has a great selection of topics.
—Ron Graham, University of California, San Diego
ReadershipGraduate students and researchers interested in Ramsey theory.

Table of Contents

Chapters

Chapter 1. Basic concepts

Part 1. Coloring theory

Chapter 2. Combinatorial spaces

Chapter 3. Strong subtrees

Chapter 4. Variable words

Chapter 5. Finite sets of words

Part 2. Density theory

Chapter 6. Szemerédi’s regularity method

Chapter 7. The removal lemma

Chapter 8. The density Hales–Jewett theorem

Chapter 9. The density Carlson–Simpson theorem

Part 3. Appendices

Appendix A. Primitive recursive functions

Appendix B. Ramsey’s theorem

Appendix C. The Baire property

Appendix D. Ultrafilters

Appendix E. Probabilistic background

Appendix F. Open problems


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Ramsey theory is a dynamic area of combinatorics that has various applications in analysis, ergodic theory, logic, number theory, probability theory, theoretical computer science, and topological dynamics.
This book is devoted to one of the most important areas of Ramsey theory—the Ramsey theory of product spaces. It is a culmination of a series of recent breakthroughs by the two authors and their students who were able to lift this theory to the infinitedimensional case. The book presents many major results and methods in the area, such as Szemerédi's regularity method, the hypergraph removal lemma, and the density Hales–Jewett theorem.
This book addresses researchers in combinatorics but also working mathematicians and advanced graduate students who are interested in Ramsey theory. The prerequisites for reading this book are rather minimal: it only requires familiarity, at the graduate level, with probability theory and real analysis. Some familiarity with the basics of Ramsey theory would be beneficial, though not necessary.
I think that this book has a good chance of becoming a classic on density Ramsey theory at the level of the Graham–Rothschild–Spencer book on basic Ramsey theory.
—Stevo Todorcevic, University of Toronto
The book by Dodos and Kanellopoulos is firstrate! It is timely, well written, and has a great selection of topics.
—Ron Graham, University of California, San Diego
Graduate students and researchers interested in Ramsey theory.

Chapters

Chapter 1. Basic concepts

Part 1. Coloring theory

Chapter 2. Combinatorial spaces

Chapter 3. Strong subtrees

Chapter 4. Variable words

Chapter 5. Finite sets of words

Part 2. Density theory

Chapter 6. Szemerédi’s regularity method

Chapter 7. The removal lemma

Chapter 8. The density Hales–Jewett theorem

Chapter 9. The density Carlson–Simpson theorem

Part 3. Appendices

Appendix A. Primitive recursive functions

Appendix B. Ramsey’s theorem

Appendix C. The Baire property

Appendix D. Ultrafilters

Appendix E. Probabilistic background

Appendix F. Open problems