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Across the Board: The Mathematics of Chessboard Problems (Princeton Puzzlers)by John J Watkins
Synopses & ReviewsPublisher Comments:Across the Board is the definitive work on chessboard problems. It is not simply about chess but the chessboard itselfthat 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 wellknown 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 threedimensional 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. Synopsis:"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 Synopsis:Across the Board is the definitive work on chessboard problems. It is not simply about chess but the chessboard itselfthat 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 wellknown 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 threedimensional 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. About the AuthorJohn J. Watkins is professor emeritus of mathematics at Colorado College. An awardwinning teacher, he is the author of Topics in Commutative Ring Theory (Princeton) and coauthor of Graphs: An Introductory Approach.
Table of ContentsPreface 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 What Our Readers Are SayingBe the first to add a comment for a chance to win!Product Details
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