CCS Math 10: Combinatorial Game Theory
to view the course syllabus in pdf format.
There is also a forum
for this class. I hope to be able to set up TeX on this forum,
but at the moment I have no idea how to do that.
best book on combinatorial game theory is Winning Ways for your Mathematical Plays by Elwyn Berlekamp, John
Conway, and Richard Guy. It comprises four volumes (in the second
edition). We will only be covering the first volume in this course;
however, the other volumes are worth looking at if you are interested in
the topics they cover.
- If you
are interested in a more formal view of combinatorial game theory, On Numbers and Games by John Conway
is a good place to start. I find it less “fun” than Winning Ways,
but sometimes you may wonder why everything that is done is actually
sensible. You’ll find justifications of all sorts of shady business in ONAG. There are also a number of
interesting constructions in this book. For example, there is a simple of
way of constructing the real numbers, the surreal numbers, the ordinal
numbers, and many more fascinating objects. You can probably understand
most of this book without much background in abstract algebra and real
analysis, but if you have some familiarity with those subjects, you will
be likely to understand this book on a deeper level.
a new book on combinatorial game theory, Lessons in Play by Michael Albert, Richard Nowakowski,
and David Wolfe, that just came out earlier in 2007. This book discusses
many new games not mentioned in Winning Ways
or ONAG, but the actual
mathematical content is rather similar to Winning Ways,
Volume 1. I prefer the structure of Winning Ways,
but that’s really a matter of taste. There is also a website for this book.
are two books, Games of No Chance
and More Games of No Chance,
edited by Richard Nowakowski, consisting of
papers from conferences on combinatorial game theory. There are many
topics not discussed in Winning Ways
or ONAG that appear in these
papers, including applications of combinatorial game theory to more
interesting games (e.g. chess, go, mancala,
Papers and other resources
- “An introduction
to Conway’s games and numbers” by Dierk
Schleicher and Michael Stoll is a survey paper in the same spirit as ONAG, but I think it is an easier
games bright and beautiful” by John Conway is a sort of summary of ONAG. (You need access to JSTOR for
this link to work.)
- “Misère games and misère
quotients” by Aaron
Siegel is a good place to start if you are interested in misère games. More generally, this website has lots of
information about misère games. Warning: the theory of misère games is much more complicated than that of
- Combinatorial Game Suite is a Java
program written by Aaron Siegel that helps you to find values of certain
of the papers from Games of No
Chance are available online here.
Similarly, the papers from More
Games of No Chance are available here.
Please email me
if you have any questions or suggestions.