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Combinatorial Game Theory
Aaron N. Siegel, San Francisco, CA

Graduate Studies in Mathematics
2013; 523 pp; hardcover
Volume: 146
ISBN-10: 0-8218-5190-X
ISBN-13: 978-0-8218-5190-6
List Price: US$89
Member Price: US$71.20
Order Code: GSM/146
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See also:

Combinatorial Problems and Exercises: Second Edition - Laszlo Lovasz

An Introductory Course on Mathematical Game Theory - Julio Gonzalez-Diaz, Ignacio Garcia-Jurado and M Gloria Fiestras-Janeiro

The Game of Cops and Robbers on Graphs - Anthony Bonato and Richard J Nowakowski

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.

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Graduate students and research mathematicians interested in combinatorial game theory.


"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

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