Playing with Discrete Math

An introduction to Discrete Mathematics through Combinatorial Game Theory

Who is this book for?

This is a textbook that Kyle Burke and Craig Tennenhouse started writing in January 2021. Our main goal is to provide a free introductory CGT textbook appropriate for undergraduate students interested in the subject. Our bonus goal is that this can be used as a discrete math text, as there is no requirement of prior discrete math knowledge.

Can I have a copy?

Yes! Download the most recent version (PDF). If you'd like a printed copy... well... we haven't figured that out yet. (Feel free to suggest things.)

The first version of this text was released on August 23, 2021. We are not keeping an archive of older versions.

What are some of the selling points?

• The book contains over 400 exercises, approximately half of which have solutions in the appendix. These are clearly marked in each section.
• This covers impartial games before partisan games, so that that entire theory can be practiced before continuing into partisan games.
• There are Math Diversions, discussions of basic concepts in discrete math.
• There are also Computational Corners, discussions of the computational ramifications of CGT topics using code examples in Python.

What are some other CGT texts?

There are three other major combinatorial games text books that we're aware of. Each of these goes deeper into the material than in our book, so we definitely recommend them for advanced readers:

• Winning Ways for your Mathematical Plays by Elwyn Berlekamp, John H Conway, and Richard Guy.
• Lessons in Play by Michael Albert, Richard Nowakowski, and David Wolfe.
• Combinatorial Game Theory by Aaron Siegel.