1. Study the material before your professor lectures on it. While you won’t understand everything you’re reading, you will ultimately understand much more if you read before the lecture.
2. Do your homework well in advance. This gives you the time needed to process difficult questions and then to visit your professor if you are still unable to understand them.
3. Do all of your homework. In math, homework is the best way to study. If you notice that you still don’t really get it after completing the assigned homework, do some more. Keep working problems until you truly know the concepts.
4. Review your homework, tests, and quizzes. If you get questions wrong, make sure you understand both why they are wrong, and what you should have done.
5. Visit your professor with good questions. That means you don’t just walk in and say, “I don’t understand this,” while pointing at a problem or an entire section of your book. Figure out exactly what it is that you do not understand and ask specific questions.
6. Pay attention to notation. If you’re not sure about notation, pay attention to how your professor writes things in class. You can’t go wrong if you follow that notation.
7. Be careful to justify the steps in your proofs. A proof is an argument, not just a calculation. Make sure you write out the details.
8. Be familiar with the theorems. Know them well, and know how to apply them.
9. Study groups are only helpful if you are with a group of students that are dedicated to learning. If they are just trying to finish the problems and get out, they will likely miss important details and hurt your understanding.
10. Above all else, know your definitions like you know your own name. Math is meaningless without a proper understanding of the definitions. Make sure you learn them as they are taught so you do not have to look them up. You will be much more prepared for the test if you learn them as you go.
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