DFT/FFT

Alright. I'm a grad student in music composition and have been learning Max/MSP over the last year. One of the professors that I've been working with has begun to take me back through the basics of digital signal processing, so that I can understand more of the nitty-gritty of what's going on beneaths my Max/MSP experiments.

As would be expected, our studies have brought us upon the DFT and FFT. I am completely stuck and am just not understanding how they work. I can explain very well what takes place when these transforms are used. I guess my issue is that I understand how they work and how they are implemented, but I don't understand the mathematics behind them. I went up through AP Trig/Precalc in high school (10 years ago), but I haven't had any math courses since. I understand a good deal of the math in the DFT/FFT, but if you don't understand it all, you sort oof don't understand any of it...know what I mean?

So, I guess I'm looking for suggestions on how to proceed. My professor "doesn't know how to teach it to me" (his words, not mine), and I am the type of person who desperately wants to understand. Do I need to go to a certain math text(s) to review? Is there a better DFT/FFT introduction out there (so far I've been using Dick Moore's and Miller Puckette's)? What to do?

Thanks for your help,
BB