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Encyclopedia of Mathematics and Its Applications Ser.: Combinatorial Games : Tic-Tac-Toe Theory by József Beck (2008, Hardcover)
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Combinatorial Games : Tic-tac-toe Theory, Hardcover by Beck, Jozsef, ISBN 0521461006, ISBN-13 9780521461009, Brand New, Free shipping in the US A comprehensive and unique volume by the master of combinatorial game theory.
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Product Identifiers
PublisherCambridge University Press
ISBN-100521461006
ISBN-139780521461009
eBay Product ID (ePID)1927487
Product Key Features
Number of Pages748 Pages
LanguageEnglish
Publication NameCombinatorial Games : Tic-Tac-Toe Theory
SubjectGame Theory, Probability & Statistics / General, Combinatorics, Discrete Mathematics
Publication Year2008
TypeTextbook
AuthorJózsef Beck
Subject AreaMathematics
SeriesEncyclopedia of Mathematics and Its Applications Ser.
FormatHardcover
Dimensions
Item Height1.7 in
Item Weight42.7 Oz
Item Length9.3 in
Item Width6.5 in
Additional Product Features
Intended AudienceScholarly & Professional
Dewey Edition22
Reviews'… a most thorough and useful treatment of the subject (so far insufficiently presented in the literature) with an enormous store of results, links with other theories, and interesting open problems.' A. Pultr, Mathematical Reviews, 'This seems to be the best and most useful treatment of the subject so far … The book is recommended for a broad mathematical audience. Almost all concepts from other parts of mathematics are explained so it is convenient both for the specialist seeking a detailed survey of the topic and for students hoping to learn something new about the subject. The book has a potential to become a milestone in the development of combinatorial game theory.' EMS Newsletter, "This is an excellent, extensive, and readable review of combinatorial game theory... The book, which is very hard to put down, ends with an extremely helpful dictionary and list of open problems." M. Bona, University of Florida for CHOICE, '… this book is a milestone in Game Theory, it will become a classic …' Acta Scientiarum Mathematicarum, 'This seems to be the best and most useful treatment of the subject so far. ... The book is recommended for a broad mathematical audience. Almost all concepts from other parts of mathematics are explained so it is convenient both for the specialist seeking a detailed survey of the topic and for students hoping to learn something new about the subject. The book has a potential to become a milestone in the development of combinatorial game theory.' EMS Newsletter, "A most thorough and useful treatment of the subject (so far insufficiently presented in the literature), with an enormous store of results, links with other theories, and interesting open problems." A. Pultr, Mathematical Reviews, '... this book is a milestone in Game Theory, it will become a classic ...' Acta Scientiarum Mathematicarum, "József Beck has done a tremendous amount of work in this area. Many results appear in this book for the first time. This is a great book that brings many (all?) of the results in this field under one roof." William Gasarch for SIGACT News
Series Volume NumberSeries Number 114
IllustratedYes
Dewey Decimal519.3
Table Of ContentPreface; A summary of the book in a nutshell; Part I. Weak Win and Strong Draw: 1. Win vs. weak win; 2. The main result: exact solutions for infinite classes of games; Part II. Basic Potential Technique - Game-Theoretic First and Second Moments: 3. Simple applications; 4. Games and randomness; Part III. Advanced Weak Win - Game-Theoretic Higher Moment: 5. Self-improving potentials; 6. What is the Biased Meta-Conjecture, and why is it so difficult?; Part IV. Advanced Strong Draw - Game-Theoretic Independence: 7. BigGame-SmallGame decomposition; 8. Advanced decomposition; 9. Game-theoretic lattice-numbers; 10. Conclusion; Appendix A. Ramsey numbers; Appendix B. Hales-Jewett theorem: Shelah's proof; Appendix C. A formal treatment of positional games; Appendix D. An informal introduction to game theory; Appendix E. New results; Complete list of the open problems; What kinds of games? A dictionary; Dictionary of the phrases and concepts; References.
SynopsisTraditional game theory has been successful at developing strategy in games of incomplete information: when one player knows something that the other does not. But it has little to say about games of complete information, for example, tic-tac-toe, solitaire and hex. The main challenge of combinatorial game theory is to handle combinatorial chaos, where brute force study is impractical. In this comprehensive volume, J zsef Beck shows readers how to escape from the combinatorial chaos via the fake probabilistic method, a game-theoretic adaptation of the probabilistic method in combinatorics. Using this, the author is able to determine the exact results about infinite classes of many games, leading to the discovery of some striking new duality principles. Available for the first time in paperback, it includes a new appendix to address the results that have appeared since the book's original publication., In this comprehensive volume, József Beck shows readers how to escape from the combinatorial chaos arising in the analysis of many games by using the fake probabilistic method, a game-theoretic adaptation of the probabilistic method in combinatorics. Striking results are obtained and new duality principles discovered., Traditional game theory has been successful at developing strategy in games of incomplete information: when one player knows something that the other does not. But it has little to say about games of complete information, for example, tic-tac-toe, solitaire and hex. The main challenge of combinatorial game theory is to handle combinatorial chaos, where brute force study is impractical. In this comprehensive volume, József Beck shows readers how to escape from the combinatorial chaos via the fake probabilistic method, a game-theoretic adaptation of the probabilistic method in combinatorics. Using this, the author is able to determine the exact results about infinite classes of many games, leading to the discovery of some striking new duality principles. Available for the first time in paperback, it includes a new appendix to address the results that have appeared since the book's original publication.
LC Classification NumberQA269 .B335 2008
