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Combinatorial Game Theory
 
Aaron N. Siegel San Francisco, CA
Combinatorial Game Theory
Softcover ISBN:  978-1-4704-7568-0
Product Code:  GSM/146.S
List Price: $89.00
MAA Member Price: $80.10
AMS Member Price: $71.20
eBook ISBN:  978-1-4704-0944-9
Product Code:  GSM/146.E
List Price: $85.00
MAA Member Price: $76.50
AMS Member Price: $68.00
Softcover ISBN:  978-1-4704-7568-0
eBook: ISBN:  978-1-4704-0944-9
Product Code:  GSM/146.S.B
List Price: $174.00 $131.50
MAA Member Price: $156.60 $118.35
AMS Member Price: $139.20 $105.20
Combinatorial Game Theory
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Combinatorial Game Theory
Aaron N. Siegel San Francisco, CA
Softcover ISBN:  978-1-4704-7568-0
Product Code:  GSM/146.S
List Price: $89.00
MAA Member Price: $80.10
AMS Member Price: $71.20
eBook ISBN:  978-1-4704-0944-9
Product Code:  GSM/146.E
List Price: $85.00
MAA Member Price: $76.50
AMS Member Price: $68.00
Softcover ISBN:  978-1-4704-7568-0
eBook ISBN:  978-1-4704-0944-9
Product Code:  GSM/146.S.B
List Price: $174.00 $131.50
MAA Member Price: $156.60 $118.35
AMS Member Price: $139.20 $105.20
  • Book Details
     
     
    Graduate Studies in Mathematics
    Volume: 1462013; 523 pp
    MSC: Primary 91;

    It is wonderful to see advanced combinatorial game theory made accessible. Siegel's expertise and enjoyable writing style make this book a perfect resource for anyone wanting to learn the latest developments and open problems in the field.

    Erik Demaine, MIT

    Aaron Siegel has been the major contributor to Combinatorial Game Theory over the last decade or so. Now, in this authoritative work, he has made the latest results in the theory accessible, so that the subject will achieve the place in mathematics that it deserves.

    Richard Guy, University of Calgary

    Combinatorial game theory is the study of two-player games with no hidden information and no chance elements. The theory assigns algebraic values to positions in such games and seeks to quantify the algebraic and combinatorial structure of their interactions. Its modern form was introduced thirty years ago, with the publication of the classic Winning Ways for Your Mathematical Plays by Berlekamp, Conway, and Guy, and interest has rapidly increased in recent decades.

    This book is a comprehensive and up-to-date introduction to the subject, tracing its development from first principles and examples through many of its most recent advances. Roughly half the book is devoted to a rigorous treatment of the classical theory; the remaining material is an in-depth presentation of topics that appear for the first time in textbook form, including the theory of misère quotients and Berlekamp's generalized temperature theory.

    Packed with hundreds of examples and exercises and meticulously cross-referenced, Combinatorial Game Theory will appeal equally to students, instructors, and research professionals. More than forty open problems and conjectures are mentioned in the text, highlighting the many mysteries that still remain in this young and exciting field.

    Aaron Siegel holds a Ph.D. in mathematics from the University of California, Berkeley and has held positions at the Mathematical Sciences Research Institute and the Institute for Advanced Study. He was a partner at Berkeley Quantitative, a technology-driven hedge fund, and is presently employed by Twitter, Inc.

    Readership

    Graduate students and research mathematicians interested in combinatorial game theory.

  • Table of Contents
     
     
    • Chapters
    • Chapter 1. Combinatorial games
    • Chapter 2. Short games
    • Chapter 3. The structure of $\mathbb {G}$
    • Chapter 4. Impartial games
    • Chapter 5. Misère play
    • Chapter 6. Loopy games
    • Chapter 7. Temperature theory
    • Chapter 8. Transfinite games
    • Appendix A. Open problems
    • Appendix B. Mathematical prerequisites
    • Appendix C. A finite loopfree history
  • Reviews
     
     
    • The author has kept the tone of the book light and infused it with history, anecdotes, and important observations making it an entertaining and as well an educational read.

      MAA Reviews
    • For those wishing to know about combinatorial games in depth this is the book to read. ... Aaron Siegel is currently the strongest researcher in the field and has been involved with many of the central developments. In this book, he has brought them together. Moreover, he includes asides and details that explain how and why certain directions were taken; important insights from an expert. ... [He] has kept the tone of the book light and infused it with history, anecdotes, and important observations making it an entertaining as well as an educational read.

      Richard Nowakowski, MAA Reviews
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Desk Copy – for instructors who have adopted an AMS textbook for a course
    Examination Copy – for faculty considering an AMS textbook for a course
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Volume: 1462013; 523 pp
MSC: Primary 91;

It is wonderful to see advanced combinatorial game theory made accessible. Siegel's expertise and enjoyable writing style make this book a perfect resource for anyone wanting to learn the latest developments and open problems in the field.

Erik Demaine, MIT

Aaron Siegel has been the major contributor to Combinatorial Game Theory over the last decade or so. Now, in this authoritative work, he has made the latest results in the theory accessible, so that the subject will achieve the place in mathematics that it deserves.

Richard Guy, University of Calgary

Combinatorial game theory is the study of two-player games with no hidden information and no chance elements. The theory assigns algebraic values to positions in such games and seeks to quantify the algebraic and combinatorial structure of their interactions. Its modern form was introduced thirty years ago, with the publication of the classic Winning Ways for Your Mathematical Plays by Berlekamp, Conway, and Guy, and interest has rapidly increased in recent decades.

This book is a comprehensive and up-to-date introduction to the subject, tracing its development from first principles and examples through many of its most recent advances. Roughly half the book is devoted to a rigorous treatment of the classical theory; the remaining material is an in-depth presentation of topics that appear for the first time in textbook form, including the theory of misère quotients and Berlekamp's generalized temperature theory.

Packed with hundreds of examples and exercises and meticulously cross-referenced, Combinatorial Game Theory will appeal equally to students, instructors, and research professionals. More than forty open problems and conjectures are mentioned in the text, highlighting the many mysteries that still remain in this young and exciting field.

Aaron Siegel holds a Ph.D. in mathematics from the University of California, Berkeley and has held positions at the Mathematical Sciences Research Institute and the Institute for Advanced Study. He was a partner at Berkeley Quantitative, a technology-driven hedge fund, and is presently employed by Twitter, Inc.

Readership

Graduate students and research mathematicians interested in combinatorial game theory.

  • Chapters
  • Chapter 1. Combinatorial games
  • Chapter 2. Short games
  • Chapter 3. The structure of $\mathbb {G}$
  • Chapter 4. Impartial games
  • Chapter 5. Misère play
  • Chapter 6. Loopy games
  • Chapter 7. Temperature theory
  • Chapter 8. Transfinite games
  • Appendix A. Open problems
  • Appendix B. Mathematical prerequisites
  • Appendix C. A finite loopfree history
  • The author has kept the tone of the book light and infused it with history, anecdotes, and important observations making it an entertaining and as well an educational read.

    MAA Reviews
  • For those wishing to know about combinatorial games in depth this is the book to read. ... Aaron Siegel is currently the strongest researcher in the field and has been involved with many of the central developments. In this book, he has brought them together. Moreover, he includes asides and details that explain how and why certain directions were taken; important insights from an expert. ... [He] has kept the tone of the book light and infused it with history, anecdotes, and important observations making it an entertaining as well as an educational read.

    Richard Nowakowski, MAA Reviews
Review Copy – for publishers of book reviews
Desk Copy – for instructors who have adopted an AMS textbook for a course
Examination Copy – for faculty considering an AMS textbook for a course
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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