For the sake of time, is it bad to just accept some fast paced class's theorem's (such as MIT's algebra class) as true even if you don't completely understand the proof or can't remember the proof off top of your head (after a while has passed?). I often find myself wasting too much time trying to memorize proofs when that's not the point of the class (and I can actually wait to memorize the proof later). Sometimes, I get caught up in one detail of the proof for hours and end up not having time to learn how to actually use the theorem and do the homework. Also, is it bad to gain a complete and working understanding of something after you take the class. I am not mentally capable of fully absorbing both what the class want's us to get and thinking about it enough to have a complete and sufficiently deep understanding of the subject all in one semester. However, I feel bad if I wait to think deeply about the class material until after the course is done, but I simply don't have enough time to fully understand some things during the semester. I always hear this advice on making sure you understand everything when you are studying to practice/do mathematics, but that seems not practical if you are taking four or more classes and struggling to make sure you understand what you need to for your other classes have other obligations to attend to.(and also if English is not your first language). I feel like a lot of the advice I hear is for native English speakers (I came to the U.S. when I was four, so I'm practically a native English speaker, but not when it comes to understanding things well the first time through in math, or at least making the understand be thorough by a native English speaker's standards.)
The reason I ask this is because I can't say I fully understand something in English unless I can explain the proof verbally/descriptively to someone.