the measure of how much we understood and learned in a college course is referred to as

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Can you forget math?

Even if you do this, you can still forget the mathematics, especially if the result in question was fairly easy to prove. (Note, however, that if the result is hard to prove, and you spend, let us assume, 10 hours to prove it, then you will probably never forget it for the rest of your life .)

Is math taught in undergrad classes?

The undergrad math, in fact most math taught in standard classes, is just developing a language which some people learn faster than others and some remember more than others, but what will they do with it isn't something that is taught in those classes. I would say that mathematical talent is in fact this imagination.

Is memorizing theorems a choice?

Memorizing theorems is not your choice but rather a necessity. I always disliked regurgitation and it is regrettable that this is forced unto you. I'm glad that my school would instead give us actual problems to solve - that's much closer to research anyway. Since you have to go through this lamentable process, try to come up with a method of memorization which has other benefits as well - perhaps aim at a better understanding of "what is going on" rather than the actual steps themselves. This is an important skill.