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.
Author(s): Peter M Higgins
Year: 2008
Language: English
Pages: 288
Contents......Page 8
1. Nets, Trees, and Lies......Page 10
Trees......Page 14
Chemical isomers......Page 18
Lying liars and the lies they tell......Page 19
Familiar logic games......Page 26
Exotic squares and Sudoku......Page 32
The small world phenomenon......Page 44
The bridges of Königsberg......Page 52
Hand-shaking and its consequences......Page 57
Cycles that take you on a tour......Page 62
Party problems......Page 65
The four-colour map problem......Page 72
How edges can ruin planarity......Page 83
Rabbits out of hats......Page 89
1. Guarding the gallery......Page 90
2. Innocent questions of points and lines......Page 93
3. Brouwer’s fixed point theorem......Page 99
The Euler–Fleury method......Page 110
The Chinese Postman Problem......Page 114
6. One-Way Systems......Page 120
Nets that remember where you have been......Page 123
Nets as machines......Page 128
Automata with something to say......Page 137
Lattices......Page 141
7. Spanning Networks......Page 146
Sorting the traffic......Page 149
Greedy salesmen......Page 154
Finding the quick route......Page 156
The P versus NP controversy......Page 159
Network capacities and finding suitable boys......Page 168
Marriage and other problems......Page 172
Harems, maximum flows, and other things......Page 177
Instant Insanity......Page 184
Sharing the wine......Page 190
Jealousy problems......Page 193
Mazes and labyrinths......Page 194
Trees and codes......Page 197
Reassembling RNA chains......Page 200
10. For Connoisseurs......Page 206
References......Page 246
Further Reading......Page 248
C......Page 252
K......Page 253
N......Page 254
U......Page 255
W......Page 256
