Hyperreal numbers: infinities and infinitesimals - "In 1976, Jerome Keisler, a student of the famous logician Tarski, published this elementary textbook that teaches calculus using hyperreal numbers. Now it's free, with a Creative Commons copyright!" (pdf—25mb :) [more inside]
Building a Computer 1: Numerals - recently my kids have been asking me about how computers work. I like to give in-depth answers to such questions, so we set out on a quest to understand how they work... Follow-up parts 2 3 4 5 6 7 8 9 10 11 12 13 14 15.
"Once you've constructed your Hexapawn opponent, it's time to start playing against it... If you play this game repeatedly ... you'll quickly notice that your matchbox opponent plays better and better until it is unbeatable!" Martin Gardner created a game called Hexapawn, and also devised an artificially intelligent opponent you can build yourself out of matchboxes and colored beads. Bonus link: An interview with Martin Gardner.
Project Euler is a running contest of programming challenges to hone your algorithm skills. "Each problem is designed according to a 'one-minute rule', which means that although it may take several hours to design a successful algorithm with more difficult problems, an efficient implementation will allow a solution to be obtained on a modestly powered computer in less than one minute."
Prof. George W. Hart, of the Computer Science Department at SUNY Stony Brook, has an enviable web presence. His Encyclopedia of Polyhedra alone is worth the visit, his geometric sculptures make the nerd in me weep at their beauty, and his trilobite recipe looks mighty yummy.