I want to demonstrate how amazing combinatorial explosion is! Please don't stop me. An animation about numbers that get large. It has a happy ending and possibly even a moral. [more inside]
Visual Patterns. Here are the first few steps. What's the equation?
Every film Pixar has produced has landed in the top fifty highest-grossing animated films of all time. What's their secret? Mathematics. Oh, and 22 Rules of Storytelling. [more inside]
Morton and Vicary on the Categorified Heisenberg Algebra - "In quantum mechanics, position times momentum does not equal momentum times position! This sounds weird, but it's connected to a very simple fact. Suppose you have a box with some balls in it, and you have the magical ability to create and annihilate balls. Then there's one more way to create a ball and then annihilate one, than to annihilate one and then create one. Huh? Yes: if there are, say, 3 balls in the box to start with, there are 4 balls you can choose to annihilate after you've created one but only 3 before you create one..." [more inside]
A generating function is a way to keep track of a lot of related numbers all at once... The study of generating functions is an art and a science known as 'generatingfunctionology,' and its bible is free for all to download. [more inside]
Ever wondered what comes next, and why? The On-Line Encyclopedia of Integer Sequences has the answers. (Previously.)
If you could use a great big free handbook of discrete math and algorithms, Jörg Arndt's fxtbook wants to be your friend. Plain text table of contents to whet your appetite.