Across the Board:
The Mathematics of Chessboard Problems
John J. Watkins

Paper | 2007 | $23.95 / £16.95
Cloth | 2004 | $46.00 / £31.95
272 pp. | 6 x 9 | 204 line illus.

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Chapter 1 [HTML] or [PDF]

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Across the Board is the definitive work on chessboard problems. It is not simply about chess but the chessboard itself--that simple grid of squares so common to games around the world. And, more importantly, the fascinating mathematics behind it. From the Knight's Tour Problem and Queens Domination to their many variations, John Watkins surveys all the well-known problems in this surprisingly fertile area of recreational mathematics. Can a knight follow a path that covers every square once, ending on the starting square? How many queens are needed so that every square is targeted or occupied by one of the queens?

Each main topic is treated in depth from its historical conception through to its status today. Many beautiful solutions have emerged for basic chessboard problems since mathematicians first began working on them in earnest over three centuries ago, but such problems, including those involving polyominoes, have now been extended to three-dimensional chessboards and even chessboards on unusual surfaces such as toruses (the equivalent of playing chess on a doughnut) and cylinders. Using the highly visual language of graph theory, Watkins gently guides the reader to the forefront of current research in mathematics. By solving some of the many exercises sprinkled throughout, the reader can share fully in the excitement of discovery.

Showing that chess puzzles are the starting point for important mathematical ideas that have resonated for centuries, Across the Board will captivate students and instructors, mathematicians, chess enthusiasts, and puzzle devotees.

John J. Watkins is Professor of Mathematics at Colorado College where, in 2005, he was given the Boettcher Award for Faculty Excellence in the sciences. He is the coauthor of Graph Theory: An Introductory Approach.

Reviews:

"This book is extremely well written and is, no doubt, the best exposition of the connection between the chessboard problems and recreational mathematics. The author surveys all the well-known problems about chess and the chessboard. . . . The problems are treated in depth from their beginnings through to their status today."--Mohammed Aassila, MAA Review

"Torus-shaped boards, three-dimensional boards, a shape called the Klein bottle--the simple checkerboard pattern proves to be creatively malleable when Watkins puts his mind to his hobbylike subject. Watkins' invitational tone ensures attention from the finite but enthusiastic audience for mathematical recreation."--Booklist

"Watkins offers an excellent invitation to serious mathematics."--Choice

"I would be happy to recommend this book to you. . . . The book is an easy and entertaining read that shows numerous paths into various branches of discrete mathematics and graph theory."--Paul J. Campbell, Mathematics Magazine

Endorsements:

"This beautiful book is absolutely the best treatment of the connection between chess and recreational mathematics I have ever seen. What makes it stand apart (and far above) other chess puzzle books is the underlying mathematical theory, presented in an entertaining, fascinating, and educational manner."--Paul J. Nahin, author of When Least Is Best

"Watkins has a friendly writing style, and the reader is brought along nicely from simple concepts to slightly more complicated ones."--Ron Graham, 2003 Steele Prize for Lifetime Achievement, American Mathematical Society, and President, Mathematical Association of America

Table of Contents:

Preface ix
Chapter One
Introduction 1
Chapter Two
Knight's Tours 25
Chapter Three
The Knight's Tour Problem 39
Chapter Four
Magic Squares 53
Chapter Five
The Torus and the Cylinder 65
Chapter Six
The Klein Bottle and Other Variations 79
Chapter Seven
Domination 95
Chapter Eight
Queens Domination 113
Chapter Nine
Domination on Other Surfaces 139
Chapter Ten
Independence 163
Chapter Eleven
Other Surfaces, Other Variations 191
Chapter Twelve
Eulerian Squares 213
Chapter Thirteen
Polyominoes 223
References 247
Index 251

This book has been translated into:

• Dutch

Another Princeton book by John J. Watkins:

• Topics in Commutative Ring Theory.

Subject Area:

• Mathematics

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Paper: $23.95 ISBN13: 978-0-691-13062-0
Cloth: $46.00 ISBN13: 978-0-691-11503-0

For customers in Europe, Africa, the Middle East, and India
Paper: £16.95 ISBN13: 978-0-691-13062-0
Cloth: £31.95 ISBN13: 978-0-691-11503-0

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File created: 10/18/2009

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