The Polynomial Method
MIT OpenCourseWare offers this graduate-level course on the polynomial method, a technique that surged through combinatorics over the past decade after solving longstanding problems like the finite field Kakeya conjecture and the joints problem. Lectures develop the method from its roots in these combinatorics breakthroughs and trace its reach into computer science, number theory, and analysis, showing how a single algebraic idea, constructing a polynomial that vanishes on a structured set and analyzing its zero set, can crack problems that resisted purely combinatorial attacks. Course materials include lecture notes and problem sets covering topics such as incidence geometry, algebraic methods in extremal combinatorics, and applications to coding theory. As with other MIT OCW offerings, all materials are free to access online and there is no certificate. The course assumes a solid background in combinatorics and algebra and suits students already comfortable with proof-based mathematics.