snowboardinstyle:
You mentioned not wanting to memorize sine-values, but rather understand the underlying principle? It's not that hard, you know. Perhaps you were just mentioning an example, but I will post a link that explains the theory behind trigonometric terms, like sine:
http://www.humboldt.edu/~dlj1/PreCalcul ... ircle.html
We HAD to learn the unit circle in our trigonometry class. Not understanding the unit circle when doing trigonometry is like not understanding why the calculator says that 2+3 equals 5. You don't think, but rather just accept it.
Again, perhaps you know all this, and there's some even deeper understanding you feel lacking. If you get your hands on that type of knowledge, let me know
On topic:
I sort of like math. I have finished most of the math classes available in Sweden, from derivative and integration, complex numbers, trigonometry, logarithms, differential equations, calculus, geometry ... The only thing I never managed to finish was the vectors and matrices bits. Like snowboardinstyle, I understood the calculations, but not the theory, the principle or the applicational use for it.
I got the wrong approach from the start, and it's hard to start over fresh.
I often play with numbers. There are always some series of numbers in your immediate area, so if you have five minutes you can always excersize you brain a little. The number to my local pizza place is 016-124307, which can be transformed into 0+(1+6)x(1x2)=4+3+0+7. My grannie's number is 016-130933, turns into (0x1)+6=(1^3)x(0+(9/3)+3) ...
A waste of time, sure. But then again, what isn't?