The following was written by Professor Kathie E. Newman in the Summer of 2004.

Exercises and Problems

Exericises are generally easier than problems. Start by warming up with the exercises. If this gives you difficulty, then start doing all of the odd exercises.

The exercises and problems chosen are mostly those solved in previous year's classes.

Pay particular attention to the * problems. These are "classics" -- which are ones that physicists tend to gravitate to when designing an exam. Yes, it is a judgement call labeling a problem a "classic." I haven't worked all of the problems, so I'm sure that my list (which had input from last year's class) isn't complete. And, remember that I'm just one physicist, and the exam is designed by a committee.

The ** problems are ones that we judged to be particularly tough. Occasionally one of these has appeared on a qualifier.

Problem-Solving Psychology

Let's start by acknowledging, there's a ton of problems, exercises, and worked examples in the book. Any one of them can become a qualifier exam problem. You will not be able to do all possible problems. So, your task is instead to become confident that you can work a certain percentage of possible problems, allowing 15 to 30 minutes per problem. You want to maximize this percentage, but it is unrealistic to think that your percentage will be 100.

Think of this like physical exercise. You are in training to run a marathon. Your goal is to finish the marathon in decent shape. You just want to cross the finish line, it doesn't matter if you are first or not.

An unlike most marathons, you have a choice which way you run. You will choose which 8 of 10 problems you solve. Just as you should assess the steepness of a hill before you run up it, you should learn to assess the difficulty of problems.

As runners do, give yourself continual internal positive messages. Try a mantra, "I am physicist and I am strong. With time, I can solve the world!" Don't use negatives in your internal messages -- eliminate the not's, don'ts, can'ts from your thoughts (yes, those two phrases were phrased in the negative) -- instead learn to phrase in the positive and tell yourself that you can solve the problem, you can understand the physics.

Be very honest with yourself. Listen carefully. When you feel uncomfortable with something, try to find out why! There's usually a point of physics that you are missing; you need to figure out what. Perhaps you never studied some of this material previously, so allow yourself more time to learn it properly. Perhaps you did study previously, but you find you really didn't understand it. Learn to tell when you have mastery.

Here's a trick. Pick an imaginary audience -- perhaps your mother, your little sister or brother or perhaps a freshman -- and now imagine teaching this area of physics to that person. What's important? What are the primary concepts? We use a variation of this trick when working problems together in groups or at the blackboard. Remember, being able to teach requires a higher-level mastery of the physics. And, if you are a teaching assistant, you will really want to have this mastery.

Try to avoid paging back in the text in order to find answers. You can't do this in a test, so form the habit now of challenging yourself to work without crutches. Think what crutches you have -- the book, the odd answers, the knowledge that a particular problem comes from a particular chapter, and the equation sheet. You are allowed one crutch in the exam -- the equation sheet -- so, try working as much as possible using just the equation sheet.

It does not hurt to do more problems or exercises than assigned, up to a certain point. Thinking again of the long-distance race metaphor, you want to train just to the point where you can handle the race easily. You don't want to start exhausted. Your goal is to learn to identify the point where you have mastery of the material.

Finally, remember that physicists are like athletes in another way. I never was enough of an athlete to enjoy the process of training. But, as physicists, I do enjoy the training, that is, the process of thinking about how physics explains the world. Halliday, Resnick, and Krane is well written; it can be fun to go through problems. Enjoy this time and chance to be a master, to be an athlete at the top of his/her form.