Solving assigned problems is the most difficult task of this class. The development of problem solving skills is a fundamental goal. Recognize that the ability to solve problems cannot be taught. However, like learning to ride a bicycle or to catch a fly ball, it does help to analyze the problem of solving problems and to watch others do it. Nevertheless, it is really up to each individual person to do what is necessary in order to acquire the skills.

The only pathway to such skills involves confronting problem after problem and immersing yourself not only in solving the problems posed but in the problem of problem solving. Watch yourself in operation. If you solve a problem, reflect briefly on the way your mind worked to get to the solution. What was good? What didn't work? If you cannot arrive at a solution, then you can ponder just what you did that did not work once you are given the proper solution.

1. Arrange your study time; diligently schedule it!

Assemble your materials (calculator, book, paper, notes, etc.).

Turn off the television and music! Quiet your neighbors!

2. Rally your intentions. Think about what you are going to do. Get up the energy and commitment to give it 100% (i.e., your best shot) for some prescribed time period (20 minutes or whatever you can really handle). Then let nothing ~ you! Afterward take a break for a few minutes. Then repeat! Expand the time period gradually as your power of concentration expands. But ... it is important to prepare yourself mentally before starling by thinking privately and quietly about your intentions for a few moments. You must mobilize your powers.

3. Work out all the assigned exercises (and any others that you can find) carefully, neatly and completely. Keep a file of these worked out solutions. Don't be sloppy. If you can solve all of these problems, you will achieve a high grade in this class. More importantly, you will be on your way to bigger and better things. This is the big time. Your future depends on your choices now!

An important first step in solving any problems is to very carefully answer three questions.

1. What is being sought? (What is the unknown?)
2. What are the data given?

If you cannot identify these items, then you probably do not understand the problem. And, as you might guess, it is hopeless if you do not understand the problem!

The next step is to look for a connection between the unknown (i.e., what is being sought) and the data given. Finding the connection is the toughest part of solving a problem. But once a connection is found, you can attempt to use the connections as a pathway to the answer. There are many tricks to try when looking for a connection.

12. Try the problem backwards.

2. What else can be calculated from the given data? Is there anything here that will connect to the unknown?
1. What do you need to know in order to obtain the answer? Is there a connection between this item and the given data (or anything you can evaluate from the given data)?
2. Introduce suitable notations (like X for the unknown) and restate the problem using your notation.

Once you have solved a problem, look back over it and analyze why and how you thought about it the way you did. What did you do that did not work? What prompted you to do what eventually worked.