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Ramsey Theory for Product Spaces
 
Pandelis Dodos University of Athens, Athens, Greece
Vassilis Kanellopoulos National Technical University of Athens, Athens, Greece
Ramsey Theory for Product Spaces
Hardcover ISBN:  978-1-4704-2808-2
Product Code:  SURV/212
List Price: $129.00
MAA Member Price: $116.10
AMS Member Price: $103.20
eBook ISBN:  978-1-4704-3017-7
Product Code:  SURV/212.E
List Price: $125.00
MAA Member Price: $112.50
AMS Member Price: $100.00
Hardcover ISBN:  978-1-4704-2808-2
eBook: ISBN:  978-1-4704-3017-7
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
Ramsey Theory for Product Spaces
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Ramsey Theory for Product Spaces
Pandelis Dodos University of Athens, Athens, Greece
Vassilis Kanellopoulos National Technical University of Athens, Athens, Greece
Hardcover ISBN:  978-1-4704-2808-2
Product Code:  SURV/212
List Price: $129.00
MAA Member Price: $116.10
AMS Member Price: $103.20
eBook ISBN:  978-1-4704-3017-7
Product Code:  SURV/212.E
List Price: $125.00
MAA Member Price: $112.50
AMS Member Price: $100.00
Hardcover ISBN:  978-1-4704-2808-2
eBook ISBN:  978-1-4704-3017-7
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 Details
     
     
    Mathematical Surveys and Monographs
    Volume: 2122016; 245 pp
    MSC: 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 infinite-dimensional 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 first-rate! It is timely, well written, and has a great selection of topics.

    Ron Graham, University of California, San Diego

    Readership

    Graduate 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
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Volume: 2122016; 245 pp
MSC: 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 infinite-dimensional 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 first-rate! It is timely, well written, and has a great selection of topics.

Ron Graham, University of California, San Diego

Readership

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
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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