Advice on solving problems

Physics should be approached differently than other disciplines. There is much more emphasis on problem solving than what you might be used to. As a result many students often do not learn the material as well as they could due to ineffective study habits. Here are some suggestions on problem solving, and studying.

Physics has little memorization. Examples should not be memorized but they should be understood. Understanding is much more difficult. You cannot solve a problem by taking formulas from other examples and applying them hoping that somehow things will work out. This will almost never work. You have to use logical reasoning to solve a new problem. Just studying the solutions to examples is of little use. You've got to cover up the solutions and try it yourself. The same with homework problems. Asking friends and TA's is useful, but the wrong use can be extremely detrimental to your own learning abilities. Remember that your goal is to learn how to figure out an entire problem without anybody's assistance. This is not meant to discourage you from seeking help to reach this goal! You are strongly advised to regularly attend discussion sections and office hours, but you should approach it with the correct attitude. It's just like learning to ride a bicycle. You can watch other people riding, and think that you are learning a lot by doing so. Then you can put on training wheels so that you feel like you are actually balancing. But it is not the same as when you take off the training wheels. That is the crucial moment where you have to learn to balance. The same with physics. At some point you'll have to think through an entire problem by yourself without having someone giving you some crucial hint. Otherwise you will never learn.

You should attend discussion section to get a better handle on how to solve problems. You should not attend just to get solutions. If you do this, you are going to end up doing less well than if you spent the same time just trying to figure out a problem by yourself.

To solve physics problems it is often very useful to draw diagrams of the actual physical situation, and to identify the various variables you are going to use. NEVER plug in numbers at the beginning. You will do MUCH better in this course if you learn to work with symbols instead of just numbers. Try to organize your thoughts as clearly as you can. Resist the temptation to jump two steps ahead. If you are systematic and identify what equations to use, and what is known and unknown, it should make things a lot easier.

So to really learn efficiently, you should find some quiet place, like a library, and concentrate hard by yourself without being distracted. Pick an example from the book that you have not already memorized. Before you look at the solution to an example, you should try to see how far you can work the example by yourself. Don't give up immediately but think hard about the problem for at least half an hour. You can reread the book, or look at other examples. Anything but look at the solution. Then if you are still stuck, see how much of the solution you need to uncover to proceed further. Try to figure out what it was that prevented you from getting it by yourself. What principle did you not understand? Find the relevant section of the book and reread it several times to try and understand it better. Continue this way until you've gone through the whole example. Continue doing this with many examples.

So remember, the most important purpose of an example is to give you experience on how to go about solving a problem, that is to help you learn a procedure.