Across the Board - John J. Watkins

Across the Board

The Mathematics of Chessboard Problems

(Autor)

Buch | Softcover
272 Seiten
2007
Princeton University Press (Verlag)
978-0-691-13062-0 (ISBN)
26,15 inkl. MwSt
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A work on chessboard problems. From Knight's Tour Problem and Queens Domination to their many variations, it surveys various problems in this area of recreational mathematics.
"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".

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

Erscheint lt. Verlag 6.5.2007
Reihe/Serie Princeton Puzzlers
Zusatzinfo 204 line illus.
Verlagsort New Jersey
Sprache englisch
Maße 152 x 229 mm
Gewicht 340 g
Themenwelt Sachbuch/Ratgeber Freizeit / Hobby Spielen / Raten
Sachbuch/Ratgeber Natur / Technik
Mathematik / Informatik Mathematik Allgemeines / Lexika
Mathematik / Informatik Mathematik Graphentheorie
ISBN-10 0-691-13062-0 / 0691130620
ISBN-13 978-0-691-13062-0 / 9780691130620
Zustand Neuware
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