(The following course description borrows heavily from the introduction to the textbook.)
Problem solving is a part of mathematics organized around methods rather than theorems. For this reason it is somewhat amorphous, and difficult to study, but the ideas are applicable to almost any part of mathematics. For those not familiar with the area, there are some obvious questions about this field. For example, don't we do problem-solving in every area of mathematics, and every course we take? The answer is no, and to understand why, one needs to know what is meant in this context by a "problem". For purposes of this class, there is a distinction between problems and exercises. An exercise is a question that tests mastery of a narrowly focused technique. For example, if you have studied the chain rule for differentiation, finding the derivative of sin(cos x) is an exercise. In a problem, by contrast, the technique to be used is not immediately apparent. Problems are sometimes open-ended, poorly-defined, or even unsolvable.
This course will be run partly in a seminar format; students will be expected to regularly present their own work to the class. Students will be required to take the Putnam exam (which is held on the first Saturday in December) to obtain credit for the course.
The course is worth 4 credits and will meet MWF 3:30-4:30.
Text: The Art and Craft of Problem-Solving, by Paul Zeitz.
Office hours: MWF 11.00-12.00, and by appointment.
HERE is additional information about the organization of the course.
Here is a link to a very interesting site with tons of information about problem solving and math competitions.
Here is a recent paper about coin-weighing problems.
Here is an account of some coin-weighing problems.
Here is a link to a short article on the problem about powers of 2.
Here is a collection of Putnam problems up to 2003 (with solutions).
Here is a discussion of Ramsey Numbers.