1. First of all, I take notes during lecture. I take notes for 2.5 reasons: (1) to keep a record of what the professor covered, (2) to imprint the data on my brain a 3rd way (aurally & visually were the 1st 2), and (2.5) to stay awake. When a problem has reached a point where I can do it, I work at the same or faster pace than the prof. This helps me catch mistakes (mine or the prof's), and gives me extra practice without spending extra time on the subject.

 
2. Some prof's advocate that you re-write your lecture notes after each lecture. This is not just an exercise in handwriting. Make sure you understand all the steps that were executed explicitly or implicitly. By re-understanding what you re-write, you are re-viewing the material in a literal sense.

 
3. I keep a list of the important new ideas and even the familiar ones, so that I can see, in a condensed form, what we have covered. I keep a list, as opposed to 3x5 cards, because I want to see the progression of ideas building on one another, a common occurrence in math. This list would be composed from lecture, text, quizzes, exams and homework.

 
4. Another suggestion (and not just to salvage your investment in 3x5 cards) is, as you complete each section of material, to write down 2 or 3 moderate-to-tough homework problems, each on its own card. Write at least 1 problem for each test (quiz, midterm, final) you will have on that material. Keep a separate stack for each exam. On the back of each card, write the correct answer and the section of the text where the problem came from (in case you have difficulty arriving at the correct answer).

   The value of this idea lies in how you use the cards: when you study for a test, pull out a stack of cards and shuffle them; you have just created a sample exam. It is important to shuffle them because even students who are successful in mastering the material section by section can get confused when presented with similar problems out of context.


 
5. When studying for a test, starting a few days in advance, I will take out whatever source material I have (lecture notes, text, quizzes, exams, homework problems, summary list) and write a new summary list. But this time I only write down the things that I don't remember instantly. In other words, I create a review sheet. Simultaneously, I generate a list of questions to ask my study partner(s), my TA, or my professor (in that order).

 
6. The next day, I go over my review sheet, and again write everything that I don't instantly remember. Ideally, this process gets repeated 3 or more times, so that by the day of the exam, the list is blank, or very short. If it is not blank, the night before the exam I resort to brute-force memorization of the last few items.

 
7. Speed drills: do homework (and quiz and exam) problems AS FAST AS I CAN. And especially the sample exam (created in (4) above).

 
8. Last, and most important, get a good night's sleep the night before an exam. If your brain is fried, it won't function well, no matter how well you have mastered the material. For this reason, among others, CRAMMING is a BAD study "technique".

Continuing on the brain-pampering notion, have a good, light, meal an hour or so before the exam. The best brain food is lean "white" meat, preferably FISH, but not deep fried or slathered with some other form of fat. Consuming fatty food, or large quantities of food, makes you groggy, because your system is concentrating on your stomach. Sugar is also BAD, since it stimulates insulin production, which will soon lower the sugar available to your brain. If you need something sweet, choose FRUIT; it metabolizes more slowly, so you don't get that insulin "crash".

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