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.

Focusing in networks and keeping his commentary lively, Higgins (mathematics, U. of Essex) explains everything from social networks to circular Suduko to the underpinnings of life itself. Along the way we meet other entities which explain networks, including chemical isomers, liars, logic games, exotic squares, the "small world" phenomenon, the bridges of Königsberg, the consequences of shaking hands, four-colored maps, edges and planarity, the Euler-Fleury methods, the famous Chinese Postman Problem, nets as machines, talking automata, lattices, traffic, greedy salesmen, finding suitable boys, marriage and other problems, harems, instant insanity, wine-sharing, jealousy, mazes, labyrinths and RNA. The result is readable, enjoyable and light-hearted, especially considering that so much is at stake, like finding suitable boys. Highly recommended for math buffs and those who would like to learn more about networks practically effortlessly. Annotation ©2008 Book News, Inc., Portland, OR (booknews.com)

"Higgins writes in an invitingly transparent style, allowing nonspecialists to share intellectual adventures previously reserved for scholars."--ooklist

What do road and railway systems, mingling at parties, mazes, family tress, 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 lively and fun look at the mathematics of networks, Peter Higgins shows that these phenomena--and many more--all share the same deep mathematical structure. Filled with puzzles and other curious mathematical conundrums, this stimulating book offers new insights into such familiar mathematical quandaries as the four-color map, the bridges of Konisberg, and the Postman Problem (what is the most efficient way of delivering your letters, so you get back to your starting point without having traversed any street twice). 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.

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.

Preface

1. Nets, trees and lies

2. Trees and games of logic

3. The nature of networks

4. Coloring and Planarity

5. How to traverse a network

6. One-way systems

7. Spanning networks

8. Going with the flow

9. Novel applications of nets

10. For Connoisseurs