Combinatorial Games (Proceedings of Symposia in Applied Mathematics)

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.

Combinatorial Games (Proceedings of Symposia in Applied Mathematics, 43)

Science & Math

Richard K. Guy

Mathematics

Amer Mathematical Society

<p>Product Description      Combinatorics, or the art and science of counting, is a vibrant and active area of pure mathematical research with many applications. The Unity of Combinatorics succeeds in showing that the many facets of combinatorics are not merely isolated instances of clever tricks but that they have numerous connections and threads weaving them together to form a beautifully patterned tapestry of ideas. Topics include combinatorial designs, combinatorial games, matroids, difference sets, Fibonacci numbers, finite geometries, Pascal's triangle, Penrose tilings, error-correcting codes, and many others. Anyone with an interest in mathematics, professional or recreational, will be sure to find this book both enlightening and enjoyable. Few mathematicians have been as active in this area as Richard Guy, now in his eighth decade of mathematical productivity. Guy is the author of over 300 papers and twelve books in geometry, number theory, graph theory, and combinatorics. In addition to being a life-long number-theorist and combinatorialist, Guy's co-author, Ezra Brown, is a multi-award-winning expository writer. Together, Guy and Brown have produced a book that, in the spirit of the founding words of the Carus book series, is accessible “not only to mathematicians but to scientific workers and others with a modest mathematical background.”      About the Author      Ezra Brown: Virginia Polytechnic Institute and State University, Blacksburg, VA, Richard K. Guy: University of Calgary, Calgary, AB, Canada</p>

The Unity of Combinatorics (Classroom Resource Materials, 36)

Ezra Brown

American Mathematical Society

Unsolved Problems in Number Theory (Problem Books in Mathematics)

Springer

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