Math is a delightfully introspective subject. I know more about my innermost thoughts and the deeper workings of my mind through hours staring at a whiteboard than a psychologist could gather in a hundred years.
From this, I know that I cannot take notes. Ever. If I have any form of paper in front of me during a lecture, then I have a blank slate for my thoughts and math, usually unrelated to whatever topic I'm trying to learn, will soon have pervaded the paper. Instead, I have to prepare extensively before class and simply listen to lectures I attend.
I include this as a helpful guide toward developing your study/lecture/learning habits. You, and only you, can figure out what works best. My suggestion is to experiment. Once you find a method that works well for you, stick with it.
There are, however, five rules that should point you in the right direction:
- Thou shalt not rote-memorize proofs.
- Thou shalt not rote-memorize theorems.
- Rote memorization is bad.
- Rote memorization is bad.
- Rote memorization is bad.
Probably contrary to most of your academic experiences thus far, you cannot rote memorize math past this point and expect to do well. We cannot "just know things." For a related, anecdotal reference on the habit of just learning machinery, see this post.
As far as I know, there are only two ways to be successful in math:
You will only understand the theorems if you use them enough to know them by heart. Play with them! If you intend to become a mathematician, these will be your toys for the rest of your life. If you do not wholeheartedly want to work/play with these for the rest of your life, then you might want to consider changing your major.
Of course, if you don't want to go into mathematics, none of this applies and you should, by all means, rote-memorize everything.