Applied Mathematics Colloquium

Achievement and Avoidance Games on geometries, graphs, grids, groups and numbers

 

Abstract

Thus far, the games which I have been discovering deal with geometries, graphs , groups, games played on grids [where they generalize tic-tac-toe in many directions], numbers, and chess pieces. There are unsolved problems galore, both for `pure' mathematicians and for computer scientists. Some of the graph games have catchy names like: Kingmaker, Blockbuster, Pathfinder, Trailblazer. The number games can be useful in teaching children arithmetic in a rather enjoyable way.  I will be delighted when these games are programmed for a person to play against a computer. A beginning of the realization of this ambition was made by the mathematician/computer scientist Wolfgang Slany of Vienna and the computer program which learns from experience almost always wins! Several of these games will be played. These games have relevance to pedagogy as children of all ages enjoy playing them and thus enjoy while learning the mathematical operations needed to play them. They represent research challenges to both mathematicians and computer scientists as only a few of their strategies have been developed.