I'd just like to know what kind of math people find themselves using in AI, whether academic or applied. All I've run into so far is very simple discrete math, but I haven't done anything extremely advanced yet. How about you?

Well, there's a lot of predicate logic in many knowledge representation problems. You can generalise to set theory there too. Then there's quite a lot of probability and statistics in certain learning systems. Vector mathematics is important when it comes to spatial representation and action, such as steering behaviours or producing paths from one place to another. None of that is particularly advanced stuff either, I admit.

I'm an AI newbie with no formal background in it.

For games, I think simple integer math is the way to go. Anytime I try to do pathfinding over spheres using exact floating point, I run into mathematical problems that are very expensive to compute on today's hardware. I think discrete integer quantization of the game map you're working on is essential for tractability. That's a fancy way of saying you need either squares, hexes, or freeform territories for your game map. If you've got those, you might as well just count 'em 1 by 1.

Skip the fancy math. Most game AI isn't 'AI' anyways. Several articles have been run on Gamasutra about the state of the art of AI in the game industry from time to time. Most of it ends up being case based reasoning, i.e. glorified if..then scripts.

If you're doing AI for First Person Shooters, eh, well, fake it. Just cobble your 3D math together and do some scripts on it.

The worst I can think of is with neural networks, where you do a lot of multivariable math, and to understand backprop you need to understand derivatives and the sigmoid function.

Statistics is always important. Of course, statistics is important for any science :D . I guess it becomes super-specially important if you are working with Bayesian learning.

But most of it is indeed just discrete math, so you'd probably be fine if you just took classes up to Calc, and then learned the more complicated stuff if you found you needed it.

And those above statements only apply to academic AI. Like the previous poster said, academic AI is totally different than the AI that people actually use.

We are using a bit of discrete time control systems for our neural network. It's complicated math. Good thing I have a EE buddy who specializes in control systems.

Fuzzy logic actually uses some algebra/calculus level math
as it involves area-under-the-curve mechanisms to evaluate.

Neural nets also use similar summation functions and cyclic
patterns of reducing adjustments.

Understanding of numeric math is useful in generating/simulating curve relations that are used to control behavior (usually associated with random statistics).