Synopses & Reviews
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.
Review
"Higgins writes in an invitingly transparent style, allowing nonspecialists to share intellectual adventures previously reserved for scholars."--ooklist
Review
"Higgins writes in an invitingly transparent style, allowing nonspecialists to share intellectual adventures previously reserved for scholars."--ooklist
"Recommended [for] general readers; lower- and upper-division undergraduates."--Choice
"Recommended [for] general readers; lower- and upper-division undergraduates."--Choice
"In Nets, Puzzles, and Postmen, Peter Higgins offers a popular account of the mathematics of networks. Readers willing to expose themselves to mathematical reasoning will find themselves rewarded with numerous insight into the structure of networks." -- Science
Review
"Well written and easy to follow."--Mathematical Reviews
"In Nets, Puzzles, and Postmen, Peter Higgins offers a popular account of the mathematics of networks. Readers willing to expose themselves to mathematical reasoning will find themselves rewarded with numerous insight into the structure of networks." -- Science
Synopsis
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.
About 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.
Table of Contents
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