Graduates

Math Courses in General

Do the homework! Not only does it make up a large part of the grade, but keeping up with the homework and understanding the concepts within is vitally important since later material builds on earlier material, and, of course, because the homework material is on the tests. Plus, the homework represents points that you have control over. Whereas you may have a bad test day, you can get decent scores on the homework if you can just complete it. Building up a good base of homework scores truly makes the exams much less strenuous.
The homework can take vast amounts of time, so much so that it is not possible to do it last minute even if you were to try very, very hard. If possible, try to break the homework up into several sessions over several days, knocking out the easier problems first.
Working environment. The many hours I was sinking into the homework went by much smoother because I had a quiet location with a large, clear desk, on which I kept a pot of tea and a cup to sip out of. Dr. Przebinda attests to the power of tea and I have come to agree with him. I have also found that I like to do my work on clean, blank paper with a dark pen, and, although it's not terribly eco-friendly, I use absolutely as many sheets as I think I might need. Often I will use multiple sheets per problem.
I think there's some studies that show that peppermint stimulates the brain. So I sometimes take little peppermint candies with me to tests. It sure doesn't hurt anything.

-- Intro to Analysis

Knowing all the definitions is really important. I, for one, am glad the quizzes were there to keep me honest on the readings and definitions. Reciting the definitions makes up part of the exams, but it's also important to really understand the definitions as well. Knowing the meanings and purposes of all the little parts of the definitions not only helps you to remember the definitions, but also greatly assists your ability to solve problems.
Flash cards are great for learning definitions, although I'm afraid I never used them. My method was only slightly different, I would copy the definitions (as well as theorems and concepts) onto sheets of paper as the semester went along, then before tests, I would create another sheet of paper which contained only the names of the definitions I needed to know. I would paper clip that sheet of names to the front of my pages of actual definitions. I would then work down that single sheet of paper and write down the definitions listed onto scratch paper, looking them up when I had to, and I would do that until I could work the entire sheet without looking up any definitions.
As suggested by Dr. Kornelson, when doing the homework, I would do all my work on scratch paper first, then carefully write down the final proofs to turn in. I would write my final proofs in pencil on lined paper.

Memorize the definitions and work problems.
Before each class it helps me to go over notes from the previous class, and possibly further back if necessary. This is to try to avoid thinking that I understand during class only to come back later and realize I can't follow it as well on my own.
If during class I don't understand something, I mark it in the margin of my notes. Usually by the end of class I'll make the connection, but if not then I know it's something I need to go back over. If I only make a mental note, I never remember to go back and figure it out.
I also mark anything to the effect of "try this on your own" - I don't do them right away, rather I save those to work on while studying for the exam. I've done both of these things in every math class I've taken, and it's proved immensely helpful to me.
Make a concerted effort to work on each homework problem by yourself before working on them with other people. I've found that when I do this, even if I don't figure it out, I learn the material better because I've thought about it harder and tried different angles. If I only glance at a problem and decide I don't know how to do it and wait to work on it with someone else, we'll usually figure it out but in the end (come test time) I don't understand it as well.

What worked for me best was giving myself enough time to do the homework. And the definitions really are paramount.
Having a study partner to discuss the proofs helped me out. I've found that explaining the proofs to other people is a sure way to cement it in my mind.

Work in very small groups but with different people, even on the same homework. Whenever more than two people worked together it seemed like someone invariably slipped by not fully understanding what we did. But working with two or more separately, I felt like we came up with better ways to think about and word things.
I found looking back on homework right after I got it back helped reinforce the new things I'd seen in class since that homework.
After about half way through the class, I found that looking through my old calc book (at the definitions) I had a MUCH better understanding of the wording they used. I recall reading it as a freshman and my eyes glazing over, but by half way through this class I could make something of it. I highly recommend reading old textbooks' definitions of these ideas as it forces you to see the idea from a different perspective and, though it's saddening to admit, drive home the notion of the *variable*. If you always see the idea written with the same variables, its meaning can get lost in trying to match up with the wording rather than the concept.
Always rewrite homework so it looks as nice as possible and keep the scratch versions with their post graded counterparts. It's not so much for the grader as it is so you can read and understand it when you go back to study it. NEVER toss out an old homework or old notes (or get them stolen from your car). There's nothing worse knowing that you already did something, not remembering how, and not being able to find where it was you saw it.
Budget at *least* 12 hours for a homework and *never* skip one. You'll be jumping through hoops to figure out what you missed and will lose the opportunity to save time by citing your old work... In any case, it's not all that often in life such a satisfying opportunity presents itself.

I tried to understand the topics at an intuitive level before moving on to the next topic. This took a lot of reading, re-reading, and drawing on a whiteboard for myself. It was much more difficult when I tried to learn the topics while working the homework instead of before.