How do you efficiently take notes? I've recently realized how ineffective my notetaking strategy is, especially in proof-based classes. Generally, I copy every word that professors write on the board, but this is not allowing me to process the information well. However, I'm always worried about missing some single word that clarifies a proof or a word that changes the meaning of a statement. How do you take notes? Do you copy everything? Do you sum up the proofs? What do you find to be the most important part of the notes you take on proofs, especially?
 A: Presumably there are lecture notes, a text, ... In that case, use your time to read ahead of the class, and concentrate on understanding what is going on during the class. Perhaps jot down how some knot was resolved. After class, complement your text with more detailed workout of the difficult stretches. Do work on exercises around the complicated areas.
If you have problems with proofs, remember proofs are primarily for human consumption. Perhaps gang up with classmates to criticize/proofread each other's proofs. But not face-to-face, that leads to "I'll explain what I'm trying to say here", and such explanations shouldn't be necessary.
A: My personal experience, it requires my full attention to follow the logic of the proof and taking notes is a distraction.  Better to understand the gist of the proof and ask questions as needed.  Generally, the important proofs in the book.  Having another copy of said proof in my notes serves little purpose, unless the Prof's proof is quite different.
Ideally, I would have prepped for class, and seen what theorems would be proven before class even begins.  So, the prof's explanations are what I am in class to see.  If you are very diligent, edit your notes as soon as possible after class.  And don't let to much class time pass before attempting the exercises.
