Math 294A: Problem-Solving Seminar

The goal of this seminar is to improve students' problem solving skills by presenting several important techniques and providing numerous examples and problems for each technique. The seminar meets informally once a week, and anyone is welcome to attend. It is also possible to register for the seminar as a one-credit pass-fail course, Math 294A. In Spring 2008, the seminar meets on Wednesdays from 4:15 to 5:30 in FCS 223.

The seminar will cover six or seven major problem-solving techniques or concepts each semester. For a taste of what to expect, the handouts from 2006-07 are linked below. We will spend two weeks on each topic: an introductory session and a presentation session. During the introductory session, the technique will be presented with examples. Several problems that make use of the technique will be distributed, and students are asked to work on those problems during the week, writing up careful solutions to those that they have solved. During the presentation session, students will present their solutions to one another.

We will also work on the mathematical writing skills of the students officially enrolled in the course. At each presentation session, each student will be asked to hand in a written solution to one problem. Solution will be returned with detailed comments, and students will re-write their solutions based on these comments, iterating until the solutions are perfect.

The techniques and problems we will consider are interesting and important in their own right, but are also designed to prepare students for the Putnam Exam, a competitive nationwide exam for mathematics undergraduates. The 69th William Lowell Putnam Mathematics Competition is expected to take place on Saturday, December 6, 2008. See below for additional resources that may be useful in preparing for this difficult exam.

Students who are officially enrolled in the course will receive an alternative grade, which may be S (Superior Pass), P (Pass), C, D, or E. The grades S and P are NOT included in the calculation of the GPA, nor do they count toward meeting the criteria for dean's list, honorable mention, or academic distinctions. A grade of Superior Pass will be assigned to students with exemplary attendance (no more than two absences, and at least five problems handed in) who present one or more problems during the seminar. Students who attend at least half of the seminar meetings and hand in at least three problems (and hopefully present at least one problem during the semester) will receive a grade of Pass. Otherwise, a regular grade of C, D, or E will be assigned at the discretion of the instructor. All students who attend the seminar, but particularly those who are enrolled in Math 294A, are strongly urged to take the Putnam Exam.