Combinatorial Game Theory
Seiten
2013
American Mathematical Society (Verlag)
978-0-8218-5190-6 (ISBN)
American Mathematical Society (Verlag)
978-0-8218-5190-6 (ISBN)
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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 misere quotients and Berlekamp's generalised 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.
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 misere quotients and Berlekamp's generalised 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.
Aaron N. Siegel, San Francisco, CA, USA.
Preface
Combinatorial games
Short games
The structure of 𝔾
Impartial games
Misère play
Loopy games
Temperature theory
Transfinite games
Open problems
Mathematical prerequisites
A finite loopfree history
Bibliography
Glossary of notation
Author index
Index of games
Index
| Reihe/Serie | Graduate Studies in Mathematics |
|---|---|
| Verlagsort | Providence |
| Sprache | englisch |
| Gewicht | 1095 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Angewandte Mathematik |
| Mathematik / Informatik ► Mathematik ► Finanz- / Wirtschaftsmathematik | |
| Mathematik / Informatik ► Mathematik ► Graphentheorie | |
| ISBN-10 | 0-8218-5190-X / 082185190X |
| ISBN-13 | 978-0-8218-5190-6 / 9780821851906 |
| Zustand | Neuware |
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