Proceedings of Symposia in Applied Mathematics 1991; 233 pp; softcover Volume: 43 Reprint/Revision History: reprinted 2000 ISBN10: 0821819259 ISBN13: 9780821819258 List Price: US$51 Member Price: US$40.80 Order Code: PSAPM/43.S
 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 SpragueGrundy 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 errorcorrecting 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 gamesWelter's Game, Sylver Coinage, and DotsandBoxes. A list of three dozen open problems and a bibliography of 400 items are appended. Reviews "Constitutes a very good short course on the subject of combinatorial games ... a series of eight introductory papers, well chosen and fitting well together. The result is an informative and readable text, useful both for those who want to get acquainted with the basics and for those interested in some special attractive topics in the area."  Mathematical Reviews Table of Contents  R. K. Guy  What is a game?
 J. H. Conway  Numbers and games
 R. K. Guy  Impartial games
 J. H. Conway  More ways of combining games
 E. R. Berlekamp  Introductory overview of mathematical go endgames
 V. Pless  Games and codes
 A. S. Fraenkel  Complexity of games
 R. J. Nowakowski  ..., Welter's game, Sylver coinage, dotsandboxes, ...
 R. K. Guy  Unsolved problems in combinatorial games
 A. S. Fraenkel  Selected bibliography on combinatorial games and some related material
