Nets, Puzzles, and Postmen. An Exploration of Mathematical Connections
In this lovely and fascinating book, the author describes the world and the main functions of networks, which are all around us (from age-old examples, such as family trees, to the modern phenomena of the Internet and the World Wide Web). Beginning with structures of chemical isomers, family trees, simple mathematical puzzles (for example tic-tac-toe, familiar logic games, exotic squares, Sudoku) and famous mathematical problems (the bridges of Königsberg, the hand-shaking problem, the Hamilton cycle, the party problem), the author explains how networks are represented, how they work, and how they can be described, deciphered and understood. After some puzzles and games, the author introduces examples and applications of networks from natural sciences, social sciences, technology, economics, transportation sciences and genetics. Various topics are discussed (the four-colour map problem, guarding the museum, the Brouwer fixed point theorem, the Chinese postman problem, nets as machines, automata, planning routes, maximizing profits, the quick route, spanning networks, secret codes, RNA reconstructions, labyrinths and mazes and so on).
Understanding the book does not require a deep mathematical knowledge. For the reader wanting to study these topics from a mathematical point of view, the final chapter “For Connoisseurs” can be recommended. The book will open the eyes of the reader to hidden networks, hence it can be recommended to people wanting to discover a remarkable new view of our world.