Links and Books

Webpages

Books

  • Surreal Numbers by Knuth. It is a rather accessible mathematical exploration that both teaches what the Surreal Numbers are, and teaches something about how mathematicians work, by getting a layman reader involved.
  • Foundations of Analysis over Surreal Number Fields by Alling. It is a text requiring a formidable background in mathematics (an advanced undergrad with significant background in algebra and real analysis might be ok) but which goes through the detailed theory of the Surreals very well.
  • On Numbers and Games by Conway. An introduction to number systems and some theory of partizan games with more proofs and fewer examples than Winning Ways.
  • Winning Ways by Berlekamp, Conway, and Guy. A fairly comprehensive introduction to CGT in four volumes with tons of examples, although it’s a bit light on the proofs and doesn’t have a great selection of exercises like a textbook would.
  • Mathematical Go: Chilling Gets the Last Point by Berlekamp and Wolfe. A decent introduction to CGT as applied to the Asian game of Go. It can get a little hard to follow if you don’t already have a bit of a background in Go and CGT, but is still a good book.
  • The Dots and Boxes Game: Sophisticated Child’s Play by Berlekamp. A collection of Dots and Boxes problems with some of the theory behind it. I hear it’s a bit difficult to read, though.
  • Lessons in Play: An Introduction to Combinatorial Game Theory by Albert, Nowakowski, and Wolfe. An excellent book covering some of the basics from Winning Ways vol. 1 in the style of a textbook suitable for a course or self-study.
  • Combinatorial Game Theory by Siegel. An amazing book covering essentially everything important. It’s a graduate textbook only because it doesn’t have the wealth of examples/games that Lessons in Play does. It’s written very well, though.

Above I have listed the stated authors for these books, but in some cases there may be controversy over who was responsible for which ideas, and who had permission from whom, etc.

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s