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The goal of this course 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 two-credit pass-fail course, AS.110.225.
The seminar will cover six or seven major problem-solving techniques or concepts each semester. 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 has the option 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. This year's William Lowell Putnam Mathematics Competition is expected to take place on Saturday, December 2, 2017. All students who attend the course are strongly encouraged to take the Putnam Exam.