The right way to learn math is breadth-first, not depth-first. You need to survey the space, learn the names of things, figure out what’s what. [...]
I think the best way to start learning math is to spend 15 to 30 minutes a day surfing in Wikipedia. It’s filled with articles about thousands of little branches of mathematics. You start with pretty much any article that seems interesting (e.g. String theory, say, or the Fourier transform, or Tensors, anything that strikes your fancy.) Start reading. If there’s something you don’t understand, click the link and read about it. Do this recursively until you get bored or tired.
My timing on this is interesting. Over the past few days I’ve started playing a bit of poker (Texas hold ‘em, against computer players in PokerTH), in lieu of my usual habit of compulsively playing quick games of FreeCell at random moments. For the sheer nerdy fun of it, I want to write a program to calculate the exact odds that I have a better hand than all of my opponents, given the cards that are visible at any particular time (pre-flop, flop, turn, and river).
I’m sure it’s a solvable problem, but I’m having trouble simplifying the staggering number of permutations involved. For example, assuming you’ve got your two-card hand, there are 1,225 possible hands that a single opponent could have from the remaining 50 cards. If you have six opponents, there are approximately 9×1017 possible combinations of hands that they could have. We only care about the best hand among our opponents, so I think we can simplify things by assuming that the math is the same for six opponents as it is for one, except that any given hand is six times more likely to occur.
Anyway, I’m thinking of reading up on combinatorics. I got a bit from my discrete math and probability & statistics courses in college, but I feel like I’m missing something here. I’ve always been interested in probability and permutations in games, so it seems like a good subject to pursue.