>|>Memorize? I can't remember ever memorizing anything. Better just to >|>practice until you understand. Discuss, ask questions, apply. That way >|>you memorize, of course, but that's just a side-effect. >| >|No, for proof classes, which linear algebra is in many places, >|it is crucial to *memorize* the definitions.
I'm afraid not. It really is crucial to know the definitions once you get past the lower level undergraduate courses in math.
>|This holds for >|all the proof classes at higher levels also. There is simply no >|way of giving rigorous proofs if you don't know the actual >|definitions.
>it tends to be crucial to know the actual definitions at the moment >that you're giving a rigorous proof. since at least a few thousand >years ago this can be accomplished simply by having some technical >device (book, computer, crib sheet, or the like) do the memorization >for you. it's hardly necessary to do anything as totally insane as >wasting human effort on rote memorization.
Um. All math classes after the elementary level are *proof* classes. The students better know those definitons inside and out so they can do the needed proofs on exams, qualifiers, etc.