Mathematical Problem Solving (Putnam Seminar)
MIT's Putnam Seminar trains undergraduates in competition style problem solving, built around weekly practice for the William Lowell Putnam Mathematical Competition. Sessions work through problems in algebra, combinatorics, number theory, calculus, and geometry, emphasizing the tricks and proof techniques that recur on the exam, such as invariants, pigeonhole arguments, generating functions, and clever substitutions. Materials on OCW include problem sets with solutions drawn from past Putnam exams and related contests, letting students test their approach against real competition questions. There are no lecture videos, the course runs as a seminar where students present and critique solutions. It suits anyone who already has a solid grounding in undergraduate math and wants sharper tools for hard, unfamiliar problems rather than a first introduction to any topic. Registered MIT students must sit the Putnam itself, but the posted materials are free to use on your own.