Mathematical Problem Solving

Summary

Math 235: Mathematical Problem Solving, Fall 2020 Professor: Darij Grinberg Organization Course description An introduction to mathematical problem solving. We will learn techniques and tools for solving problems of the kind that appear in mathematical competitions and journals. These techniques (like induction, the Pigeonhole Principle, modular arithmetic or the Cauchy-Schwarz inequality) have uses all over mathematics; we will explore these uses through hands-on problem solving. Each week will have approx. 50 minutes of video lectures (see the "Course materials" below for the links) and 40 minutes of recitations (i.e., collaborative problem-solving sessions over Zoom). Weekly homework sets will reinforce the training. Prerequisites: Math 200. Course materials Required: Recommended: David Galvin, Math 43900 - Problem Solving in Math (Fall 2020). A course similar to ours, with an ever-growing set of notes (allow javascript and note the "Download PDF" button). Simon Foucart, Problem Solving. Math 235 notes from a few years ago. Răzvan Gelca, Titu Andreescu, Putnam and Beyond, 2nd edition. Standard text for university competition training. At 857 pages, it goes far beyond what we can do in a quarter. Dušan Djukić, Vladimir Janković, Ivan Matić, Nikola Petrović, The IMO Compendium, 2nd edition. Collection of all problems ever suggested for the International Mathematical Olympiads, often with solutions. You can also get official solutions for recent shortlist problems from imo-official.org. We aren't training for the IMO, but there is a lot of overlap between IMO and Putnam topics, and more importantly, IMO shortlists are among the best sources for high-quality problems. Evan Chen, OTIS Excerpts. Olympiad training lecture notes (with focus on high school contests, but lots of relevance to undergraduate ones too). Arthur Engel, Problem-Solving Strategies. One of the first books written explicitly for math contest training. Somewhat dated and not always well-written, but ...