Syllabus for Math 392 – Problem Solving Seminar

We solve problems everyday, from figuring out our schedules to deciding the best route to take across campus. This course will improve your problem solving skills, for both mathematical and non-mathematical problems.

Learning to solve problems (especially mathematical ones) involves two main steps:

1. Understanding how and when to apply a handful of heuristics or common strategies for attacking problems (e.g. Try easy examples, Look for patterns, Do a simpler problem,…)
2. Developing better control mechanisms for knowing which path to take, when to switch directions, when to abandon all hope.

We will be talking at length about the various heuristics. As for step 2, I will continually be asking you three questions as you solve problems, with the hope that you will begin to ask yourself these same questions:

• What are you doing?
• Why are you doing it?
• How does it help you?

Grades. You will earn an A in this course if you do the following:

1. Come to class prepared, having worked on the assigned problems, and informing me of any absences beforehand. When in class, you must actively participate in the problem solving, solution presenting, and class discussion.
2. Make a short (1-3 minute) presentation on an instance where you used the problem solving strategies discussed in class to solve a problem that came up in your life (outside of any mathematical context.)
3. Complete^a either one hard^b problem or three not-so-hard^c problems.

a. Complete means that you hand in a well-written solution in full sentences (with punctuation!) and receive the comment “perfect” from me. If you hand in a problem and receive other comments you must revise and resubmit your solution.

b. Hard problems can come from the following sources: the as-yet unsolved Putnam problems from last December, the problem section of the College Mathematics Journal, and the problem section of the American Mathematics Monthly. Copies of both of these publications are on the Math wing of Schaefer Hall. Note: if you are a junior or senior math major I hope and expect that you will choose the “hard” option.

c. Not-so-hard problems include problems that we are assigned in this class. Periodically a problem will be so easy that it does not fit into this category – I will make not of this in class.

Almost forgot … Dave Kung, 175 SH, x4433 dtkung@smcm.edu