Nets, Puzzles, and Postmen: An exploration of mathematical connectionsWhat do road and railway systems, electrical circuits, 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. Only relatively recently have mathematicians begun to explore such networks and connections, and their importance has taken everyone by surprise. The mathematics of networks form the basis of many fascinating puzzles and problems, from tic-tac-toe and circular sudoku to the 'Chinese Postman Problem' (can he deliver all his letters without traversing the same street twice?). Peter Higgins shows how such puzzles as well as many real-world phenomena are underpinned by the same deep mathematical structure. Understanding mathematical networks can give us remarkable new insights into them all. |
Contents
Trees and Games of Logic | |
The Nature of Nets | |
Colouring and Planarity | |
How to Traverse a Network | |
OneWay Systems | |
Spanning Networks | |
Going with the Flow | |
Harems maximum flows and other things | |
Sharing the wine | |
Trees and codes | |
For Connoisseurs | |
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Nets, Puzzles, and Postmen: An exploration of mathematical connections Peter M Higgins No preview available - 2007 |
Common terms and phrases
adjacent algorithm argument arise automata automaton begin binary string bipartite network boys bridges Bruijn graph Bruijn sequence capacity chapter Chinese Postman Problem colour common connected network consists corresponding cube cutset diagonal digraph directed Erdos Euler circuit Euler path Eulerian circuit exactly example extended bases Figure follows four fragments girls given Graeco-Latin squares Graph Theory Hamilton cycle Hamiltonian Hamiltonian path induction Konigsberg labelled language Latin squares lattice least liar lower bound mathematical mathematicians maze Mealy machine node of degree number of edges number of nodes odd nodes odd number once one-way pair of nodes picture Pigeonhole Principle planar network plane player possible power law prefix code problem proof puzzle question Ramsey numbers represents semigroup shortest path simple solution solve spanning tree subset Subset Sum Problem Sudoku suppose Theorem theory tournament traversing triangle vertices words