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Combinatorial Games: (Proceedings of Symposia in Pure Mathematics)

Combinatorial Games: (Proceedings of Symposia in Pure Mathematics)

          
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About the Book

Based on lectures presented at the AMS Short Course on Combinatorial Games, held at the Joint Mathematics Meetings in Columbus in August 1990, the ten papers in this volume will provide readers with insight into this exciting field. Because the book requires very little background, it will likely find a wide audience that includes the amateur interested in playing games, the undergraduate looking for a new area of study, instructors seeking a refreshing area in which to give new courses at both the undergraduate and graduate levels, and graduate students looking for a variety of research topics.In the opening paper, Guy contrasts combinatorial games, which have complete information and no chance moves, with those of classical game theory. Conway introduces a new theory of numbers, including infinitesimals and transfinite numbers, which has emerged as a special case of the theory of games. Guy describes impartial games, with the same options for both players, and the Sprague-Grundy theory. Conway discusses a variety of ways in which games can be played simultaneously. Berlekamp uses the theory of 'hot' games to make remarkable progress in the analysis of Go Endgames.Pless demonstrates the close connection between several impartial games and error-correcting codes. Fraenkel explains the way in which complexity theory is very well illustrated by combinatorial games, which supply a plethora of examples of harder problems than most of those which have been considered in the past. Nowakowski outlines the theory of three particular games - Welter's Game, Sylver Coinage, and Dots-and-Boxes. A list of three dozen open problems and a bibliography of 400 items are appended.

Table of Contents:
What is a game? by R. K. Guy Numbers and games by J. H. Conway Impartial games by R. K. Guy More ways of combining games by J. H. Conway Introductory overview of mathematical go endgames by E. R. Berlekamp Games and codes by V. Pless Complexity of games by A. S. Fraenkel..., Welter's game, Sylver coinage, dots-and-boxes,... by R. J. Nowakowski Unsolved problems in combinatorial games by R. K. Guy Selected bibliography on combinatorial games and some related material by A. S. Fraenkel.


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Product Details
  • ISBN-13: 9780821819258
  • Publisher: American Mathematical Society
  • Publisher Imprint: American Mathematical Society
  • Height: 251 mm
  • No of Pages: 233
  • Series Title: Proceedings of Symposia in Pure Mathematics
  • Weight: 438 gr
  • ISBN-10: 0821819259
  • Publisher Date: 30 Aug 2000
  • Binding: Paperback
  • Language: English
  • Returnable: Y
  • Spine Width: 14 mm
  • Width: 177 mm


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