Nets, puzzles, and postmen / Peter M. Higgins.

Format:

Book

Author/Creator:

Higgins, Peter M., 1956-

Contributor:

Class of 1939 Fund.

Language:

English

Subjects (All):

Nets (Mathematics).

Mathematical recreations.

Mathematics--Popular works.

Mathematics.

Genre:

Popular works.

Physical Description:

viii, 247 pages : illustrations ; 23 cm

Place of Publication:

Oxford ; New York : Oxford University Press, 2007.

Summary:

In this book, the renowned mathematics writer Peter Higgins brings the world of networks to life, in an exploration that ranges from mathematical puzzles to the hidden mathematical structures that underpin many real- world phenomena. We look at Circular Suduko; at the classic 'Chinese Postman Problem' which has baffled many a mathematician (and many a postman too); at social networks; and even the structure of life itself. In this lively and accessible book, Higgins shows how, by understanding the mathematics of networks, we reveal remarkable new insights into our world.

Contents:

1 Nets, Trees, and Lies 1

Trees 5

Chemical isomers 9

Lying liars and the lies they tell 10

2 Trees and Games of Logic 17

Familiar logic games 17

Exotic squares and Sudoku 23

3 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

4 Colouring and Planarity 63

The four-colour map problem 63

How edges can ruin planarity 74

Rabbits out of hats 80

1 Guarding the gallery 81

2 Innocent questions of points and lines 84

3 Brouwer's fixed point theorem 90

5 How to Traverse a Network 101

The Euler-Fleury method 101

The Chinese Postman Problem 105

6 One-Way Systems 111

Nets that remember where you have been 114

Nets as machines 119

Automata with something to say 128

Lattices 132

7 Spanning Networks 137

Sorting the traffic 140

Greedy salesmen 145

Finding the quick route 147

The P versus NP controversy 150

8 Going with the Flow 159

Network capacities and finding suitable boys 159

Marriage and other problems 163

Harems, maximum flows, and other things 168

9 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

10 For Connoisseurs 197.

Notes:

Includes bibliographical references (pages [236]-241) and index.

Local Notes:

Acquired for the Penn Libraries with assistance from the Class of 1939 Fund.

ISBN:

0199218420

9780199218424

OCLC:

163311946