I took Math 380 this quarter as a just-for-fun math class, counting only as a generic elective toward my degree but counting much more than that for my personal interest in math. Titled “The Art of Problem Solving,” the class has (as far as I know) no relation to the identically-named publisher of the math books that were my bread and butter during high school, but the sentiment toward a mathematical thought process is the same.

The course is loosely tied to the Putnam competition, though students in the class aren’t required to take the Putnam, nor must Putnam participants at UW have taken the class (though they very often do). It covers a broad range of fun topics across mathematics, including combinatorics, geometry, number theory, and generating functions. The goal is to work to build up our problem-solving skills to be able to tackle Putnam-level questions. (The Putnam itself is a notoriously difficult proof-based undergraduate mathematics competition, where the median score out of 120 is usually either 0 or 1. I participated this fall and greatly enjoyed the experience.)

Math 380 is co-taught by Professors Julia Pevtsova and Ioana Dumitriu, who also coordinate the Putnam at UW. Both of them are somewhat intimidatingly good at what they do, Ioana with an expansive personality and Julia even-tempered and soft-spoken. They hold their students to a high standard but are also very supportive and helpful in their straightforward Russian way.

Besides turning in weekly written homework assignments, students are also required to present full solutions to problems in front of the class several times during the quarter. The presentation problems tend to be a bit more challenging than the written homework problems, and also often have multiple solutions; I found it very interesting to see the various ways my classmates thought about the same problem. By noting which weeks felt more natural to me and what types of solutions pathways I gravitated to, I learned more about myself and my problem-solving strengths: for instance, that geometric and spatial thinking tends to sit well with me. I also got to stretch myself in sub-topics I wasn’t as much at home in and thereby grow as a mathematical problem-solver.

Below is one of my homeworks for the class. I had fun with the extra credit problems in general, but this week’s assignment contained a particularly good one.