Topics in Combinatorics: Analysis of Boolean Functions
MIT OpenCourseWare offers this advanced topics course on Fourier analysis of Boolean functions, a tool used across theoretical computer science and combinatorics. The material starts with influences, noise sensitivity, and hypercontractivity, then builds toward major results in the field such as the KKL theorem, the Fourier-analytic view of arrow's theorem style social choice results, and applications to property testing and PCPs. Lecture notes and problem sets are provided, following MIT's typical OCW format for advanced seminar courses, letting a learner work through the same material assigned to MIT graduate and advanced undergraduate students. There is no instructor video lecture series here, only written notes and assignments, so the course suits someone comfortable with independent, proof-based study of discrete mathematics and probability. All materials are free to access under MIT's open license.