Nets, Puzzles and Postmen: An Exploration of Mathematical Connections

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Overview

What do road and railway systems, mingling at parties, mazes, family trees, and the internet all have in common? All are networks—either people or places or things that relate and connect to one another. In this stimulating book, Peter Higgins shows that these phenomena—and many more—all share the same deep mathematical structure.
The mathematics of networks form the basis of many fascinating puzzles and problems, from tic-tac-toe to circular sudoku. Higgins reveals that understanding networks can give us remarkable new insights into many of these puzzles as well as into a wide array of real-world phenomena. Higgins offers new perspectives on such familiar mathematical quandaries as the four-color map and the bridges of Konisberg. He poses the tantalizing question Can you walk through all the doors of the house just once? He also sheds light on the Postman Problem, a puzzle first posed by a Chinese mathematician: what is the most efficient way of delivering your letters, so you get back to your starting point without having traversed any street twice. And he explores the Harem Problem—a generalization of the Marriage Problem—in which we work out how to satisfy all members of a set of men who have expressed a wish for a harem of wives.
Only relatively recently have mathematicians begun to explore networks and connections, and their importance has taken everyone by surprise. Nets, Puzzles, and Postmen takes readers on a dazzling tour of this new field, in a book that will delight math buffs everywhere.

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Product Details

  • ISBN-13: 9780199218424
  • Publisher: Oxford University Press, USA
  • Publication date: 2/20/2008
  • Pages: 288
  • Product dimensions: 8.60 (w) x 5.40 (h) x 1.10 (d)

Meet the Author

Peter M. Higgins is Professor of Mathematics and Head of Mathematical Sciences at the University of Essex. His previous mathematics books for a popular audience include Mathematics for the Curious, Mathematics for the Imagination, and The Official Book of Circular Sudoku. He is the inventor of Circular Sudoku, which has now appeared throughout the world in magazines, books, the internet, and handheld computer games.

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Table of Contents

Nets, Trees, and Lies     1
Trees     5
Chemical isomers     9
Lying liars and the lies they tell     10
Trees and Games of Logic     17
Familiar logic games     17
Exotic squares and Sudoku     23
The Nature of Nets     35
The small world phenomenon     35
The bridges of Konigsberg     43
Hand-shaking and its consequences     48
Cycles that take you on a tour     53
Party problems     56
Colouring and Planarity     63
The four-colour map problem     63
How edges can ruin planarity     74
Rabbits out of hats     80
Guarding the gallery     81
Innocent questions of points and lines     84
Brouwer's fixed point theorem     90
How to Traverse a Network     101
The Euler-Fleury method     101
The Chinese Postman Problem     105
One-Way Systems     111
Nets that remember where you have been     114
Nets as machines     119
Automata with something to say     128
Lattices     132
Spanning Networks     137
Sorting the traffic     140
Greedy salesmen     145
Finding the quick route     147
The P versus NP controversy     150
Going with the Flow     159
Network capacities and finding suitable boys     159
Marriage and other problems     163
Harems, maximum flows, and other things     168
Novel Applications of Nets     175
Instant Insanity     175
Sharing the wine     181
Jealousy problems     184
Mazes and labyrinths     185
Trees and codes     188
Reassembling RNA chains     191
For Connoisseurs     197
References     237
Further Reading     239
Index     243
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