I don’t know who originally wrote this list. It came to me as a typed sheet sometime in the early 1990’s. Perhaps it is from Bernard Johnston?
The more lectures you hear, the better off you will be, and that’s true for every instructor. At the very least you will pick up clues as to what will be on the tests and how you might attack the homework problems. Remember, you are the one getting the grade and that makes you responsible for learning the material.
It’s all there. Pay special attention to definitions, where the authors tell you the meaning of the words and symbols that they are going to use. Read the examples before you attempt to do the problems. Even better: read ahead of the lectures. You’ll find the lecture makes a lot more sense if the initial shock is behind you.
Do more problems than you want to. Finish the entire problem before you look at a list of answers to see if you got it right. If you can work the problems without assistance, you will do well in the course. When you’re done with a problem take a minute to think about what you just did and why. This will deepen your understanding and levitate your grade.
If you don’t understand something in the text, or if you are having trouble with some assigned problem, ask about it in class. You won’t be the only one who didn’t understand it. If your instructor is reluctant to take up class time with that particular question — this happens less often than you might expect — see him or her during office hours, or after class.
They may have some insights that you missed, and vice-versa. Learning from your classmates may be the most important factor in your education. Have the better ones tutor you; or, even better, tutor those who need extern help. Best of all: organize a study group of your own where everybody helps everybody else.
Your instructors think mathematics is beautiful; they won’t take kindly to your handing in scribbling. Organize your answers — mathematics is a language for precise thought. Use words to describe what you are doing. Don’t put calculations in the margin. Erase cleanly. Don’t write “A = B” unless A is equal to B. On the other hand, if two things are equal, make sure you indicate it clearly.
Think about what you are doing, why you are doing it, and what is necessary to accomplish each step of any given problem. Go through the book and make outlines of the material. Be honest about the parts you didn’t completely understand, and spend some extra time on those parts, figuring them out. Your goal is to master the material, to make it your own, not merely to have looked at it. Be active; don’t rely entirely on the instructor or anybody else to get you through.