Mathematical Discovery and Problem Solving Seminar

This advanced seminar develops the art and craft of mathematical problem solving and proof writing. Students engage deeply with elegant problems drawn from number theory, combinatorics, geometry, and abstract algebra, each chosen to highlight creative strategies, fundamental structures, and the beauty of rigorous reasoning. The course emphasizes discovery, conjecture, proof, and clarity of mathematical exposition. Students explore a wide range of themes central to advanced mathematical thinking, including invariants and extremal arguments, the Pigeonhole Principle, parity recursion, generating functions, advanced combinatorial enumeration, geometric transformations and symmetry.