A couple more quick links from the Internet, where "the Internet" in this case means "Chad Orzel's blog". (No particular reason; it just happens to be the place where I saw both of these.)
Susan Beckhardt gives a nice introduction to game theory. If you have no idea what I mean by game theory, or how you can think about games mathematically, read these. If the idea is old hat to you, go play a game or something. It's a quick link!
- The basic idea of game theory, using everyone's favorite example, Nim. (Or actually not -- it's a simpler subtraction game which she calls "G(6,3)". But you think about it the same way.)
- How to analyze a simple game. (This is what people mean when they say things like Checkers is Solved.) Now, what is Supergame?
Third part to arrive after her thesis is turned in. Hopefully she'll give a description of the Supergame paradox, which I remember fondly from old Martin Gardner logic books.
And, in the "old standards" category: Relativistic Asteroids. (Java applet.)
Try the classic version, hit "S" to start the game, and then "F" to put the display in the ship's reference frame. (That's with the ship always in the center of the screen.) Accelerate around and watch Lorenz-Fitzgerald contraction in... action.
I apologize. Couldn't find any other way to end that sentence. I'll go get into the crate now.