Nets, Puzzles and Postmen: An Exploration of Mathematical Connections

by Peter M. Higgins

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
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.

Genres: Nonfiction, Mathematics, Science

256 pages, Hardcover

First published February 20, 2007

Reviews

[Brandon Minster · Rating 4 out of 5]

I had a question about this book, so I e-mailed the author, and he replied the same day. His reply was very nice, considering how lame my question turned out to be.

[Maurizio Codogno · Rating 4 out of 5]

La teoria dei grafi è un campo abbastanza negletto nella cosiddetta "matematica per il grande pubblico". A parte i ponti di Königsberg e il problema "acqua luce e gas", non se ne parla molto, un po' per la complessità della materia - basti pensare che il teorema dei quattro colori è stato risolto solo con il computer - non si trova molto materiale in giro. Ecco dunque l'utilità di questo libro, che permette ai lettori che non si lasciano spaventare dal trovarsi un po' di conti (soprattutto nell'ultimo capitolo, che è una specie di appendice) una panoramica dei temi e metodi in questo campo, e i legami con altri campi apparentemente diversi. Lo stile è chiaro, e i più avventurosi possono provare a cimentarsi con i problemi sparsi nel testo e risolti nelle ultime pagine. Ma anche senza mettersi così in gioco è davvero bello scoprire come da un lato ci sono risultati a prima vista ostici che si possono dimostrare facendo poco più di qualche conto banale, e dall'altra che risultati apparentemente banali sono ancora al di fuori delle nostre capacità.

[Chris Herdt · Rating 4 out of 5]

Flipped through this at the bookstore. An exploration of graph theory and its applications--it looked interesting.

Although it's a very casual approach to this branch of mathematics, it is a book filled with puzzles and explorations that should be accompanied by a scratch pad and a pencil: you will frequently want to pause and explore some of the puzzles on your own.

I thought the book would have been improved by additional figures throughout the text. Occasionally the author's text explanations took a little too much effort to figure out.

A quote from the further reading section, referring to 2 of the author's sources: "Both of these books are weighty tomes in the modern American style." I am grateful to have discovered this slim volume in what is presumably the English style.

(I am the only person to have checked this book out from the Penn library in its 5 years on their shelves. Poor neglected book!)

[Brian Palmer · Rating 5 out of 5]

I loved it. A good sense of humor and convivial carrying along through proofs -- this felt like real math, not simply a popular description of math, but I won't hesitate to recommend this to most people. I think it got a little bit weaker in the final chapters, as the examples are more involved and the diagrams a bit further away, but in fairness it had been so readable that I had read a huge swathe straight through.

[Joc · Rating 5 out of 5]

This book is an excellent introduction to the mathematical concept of a graph (an object made up of just vertices and edges), a gentle read even for people with no mathematical background. More surprisingly, it even contains tasty extra bits for advanced readers, so this book is likely to have something interesting for everyone.

[Russell · Rating 4 out of 5]

Accessible to non-mathematicians with only a small number (3 or 4) lapses into uninteresting academic/pure/abstract maths proofs, the book covers all sorts of combinatorial, path finding, and optimisation problems. 4.5/5

[Seth]

This book has an audience problem. Billed as a primer on mathematical networks and why they're so important, it quickly devolves into discussing specialized applications that aren't compelling for a reader who just learned what a network is 25 pages ago.

[Dipesh Sharma]

Very interesting....