While the previous suggestions about textbook reading apply across the board, mathematics textbooks present some special challenges because they usually have lots of symbols and few words. Each statement and every line in the solution of a problem needs to be considered and processed slowly. Typically, the author presents the material through definitions, theorems, and sample problems. As you read, pay special attention to definitions. Learning all the terms that relate to a new topic is the first step toward understanding.

Math texts usually include derivations of formulas and proofs of theorems. You must understand and be able to apply the formulas and theorems, but unless your course has a particularly theoretical emphasis, you are less likely to be responsible for all the proofs. So if you get lost in the proof of a theorem, go on to the next item in the section. When you come to a sample problem, it’s time to get busy. Pick up pencil and paper, and work through the problem in the book. Then cover the solution and think through the problem on your own.

Of course, the exercises in each section are the most important part of any math textbook. A large portion of the time you devote to the course will be spent completing assigned exercises. It is absolutely necessary to do this homework before the next class, whether or not your instructor collects it. Success in mathematics requires regular practice, and students who keep up with math homework, either alone or in groups, perform better than students who don’t, particularly when they include in their study groups other students who are more advanced in the study of math.

After you complete the assignment, skim through the other exercises in the problem set. Reading the unassigned problems will help you understand more about the topic. Finally, talk the material through to yourself, and be sure your focus is on understanding the problem and its solution, not on memorization. Memorizing something might help you remember how to work through one problem, but it does not help you learn the steps involved so that you can use them for solving other similar problems.