Mathematical Go Endgames

The ancient game of Go is one of the less obvious candidates for mathematical analysis. With the development of new concepts in combinatorial game theory, the authors have been able to analyze Go games and find solutions to real endgame problems that have stumped professional Go players. Go players with an interest in mathematics and mathematicians

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.

This 2003 book documents mathematical and computational advances in Amazons, Chomp, Dot-and-Boxes, Go, Chess, Hex, and more.

This classic on games and how to play them intelligently is being re-issued in a new, four volume edition. This book has laid the foundation to a mathematical approach to playing games. The wise authors wield witty words, which wangle wonderfully winning ways. In Volume 1, the authors do the Spade Work, presenting theories and techniques to "dissect" games of varied structures and formats in order to develop winning strategies.

This volume is fourth in the series "What's Happening in the Mathematical Sciences". As the 20th century draws to a close, it presents the state of modern mathematics and its world-wide significance. It includes "Beetlemania: Chaos in Ecology", on evidence for chaotic dynamics in a population.

"The subject of combinatorics is only slowly acquiring respectability and combinatorial games will clearly take longer than the rest of combinatorics. Perhaps this partly stems from the puritanical view that anything amusing can't possibly involve any worthwhile mathematics." from the Preface.Based on lectures presented at the AMS Short Course on Combinatorial Games, held at the Joint Mathematics Meetings , the ten papers in this volume will provide readers with insight into this exciting new field. (BULLET) 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, which has emerged as a special case of the theory of games. Guy describes impartialgames, 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 demostrates the close connectionbetween 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 bibliography of 400 items are appended.

This volume is dedicated to the work of three leading mathematicians in combinatoric game theory, Elwyn Berlekamp, John Conway, and Richard Guy and includes 20 contributions from colleagues reflecting on their work.