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- Always strive for understanding as opposed to memorization.
- If this means you have to go back, do it! Don't postpone clarifying a point you miss because everything new will build on it.
- It may be intimidating to be faced with a 1,000 page book and having to spend a day understanding a single page. But that does not mean that you'll have to spend a thousand days understanding the whole book. In understanding that one page you'll gain experience that makes the next page easier, and that process feeds on itself.
- Read the sections covered in class before you come to class. That's one of the most useful ways in which you can spend your time, because it will dramatically increase the effectiveness of the lecture.
- Do exercises. The teacher may suggest some, put you can pick them on your own from the textbook or make up your own. Select them by the amount of interest they hold for you and the degree of curiosity they stimulate in you. Avoid getting into a mode where you do a large number of exercises that are distinguished only by the numerical values assigned to some parameters.
- Always check your answers for plausibility.
- Whenever you do a problem or follow a new mathematical thread explicitly formulate expectations. Your expectations may be met, which causes a nice warm feeling (and you should probably also look for a new and different problem). But otherwise there are two possibilities: you made a mistake from which you can recover, now that you are aware of it, or there is something genuinely new that you can figure out and which will teach you something. If you don't formulate and check expectations you may miss these opportunities.
- Find a class mate who will work with you in a team. Have one of you explain the material to the other, on a regular basis, or switch periodically. Explaining math to others is one of the best ways of learning it.
- Be open and alert to the use of new technology. (I know you are because you are reading this web page.) You can go from here directly to computing help. But don't neglect thinking about the problem and understanding it, its solution, and its ramifications. The purposes of technology are not to relieve you of the need to think but:
- To check your answers.
- To take care of routine tasks efficiently.
- To do things that can't possibly be done by hand (like the visualization of large data sets).
- Once you are done with a course Keep Your Textbook and refer back to it when you need to. You have spent so much time with that book that you know it intimately and know how to use it and where to find the information you need. The small amount of money you might get by selling it does not come close to offsetting the loss in time and energy you waste being thwarted by a lack of understanding a particular piece of mathematics that you easily refamiliarize yourself with by consulting your old friend, the textbook.
来自utah大学数学系教授peter alfred。
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