Nets, Puzzles and Postmen: An explanation of Mathematical connections by Peter M Higgins
I was browsing in Borders bookshop waiting for my wife when I came across this book. I got hooked after the first chapter, bought it and have been reading it over the past couple of weeks. This book is a great introduction to graph theory and its applications, introducing theorems like the handshaking lemma and algorithms like the spanning tree algorithms of Djikstra and Prim and the Ford-Fulkerson min cut max flow theorem. It then goes on to show how they can be used to solve a number of practical problems. Proofs of the harder theorems are placed in a final chapter that can be read by the interested reader. It’s an easy read, but very interesting.
A few other interesting books of this type that I have read recently are: Knots: Mathematics with a twist, Four colors suffice: How the map problem was solved and Symmetry and the monster: One of the greatest quests of mathematics.