Programming Two Person Impartial Games in Mathematica
Introduction
We wish to provide anyone with a little knowledge of Mathematica the basic elements necessary to program 2-person impartial games. We intend this site to become a resource of examples of games that can rendered, in a pleasing way, and then investigated. Thus it can serve the needs of students, teachers, researchers, hobbyists, etc. Hopefully the list of examples will grow and the tools will be expanded and improved.
An elementary exposition of these games, along with details on how to program them can be found in our paper, Playing Games with Mathematica, which appeared in Mathematica in Education and Research in 1998 and can be downloaded on the left.The standard reference for these games is the 2-volume set, Winning Ways, by Berlekamp,Conway and Guy, Academic Press, 1982. A very nice introduction to these games can be found in the text, Introduction to Discrete Math, by McEliece, Ash and Ash, Random House, 1989. Also there is a chapter on playing and programming games with Mathematica in the book, Discovering Mathematics with Mathematica, by Cowen and Kennedy, Erudition Books, 2001. Finally, there is the extensive games bibliography, compiled by Aviezri Fraenkel, which can be accessed through his home page: http://www.wisdom.weizmann.ac.il/~fraenkel/.
The common basis of the programs can be found in the Games Engine, which should usually be loaded first. The other notebooks contain individual games that can be downloaded.
We strongly encourage contributions to this project and feedback,
so that it can grow into something truly useful.
Send to: robert.cowen@gmail.com
Robert Cowen
Robert Dickau