Theory of Probability
A graduate-level probability course from MIT OpenCourseWare covering sums of independent random variables, central limit phenomena, infinitely divisible laws, Levy processes, Brownian motion, conditioning, and martingales. The course builds a rigorous measure-theoretic foundation for probability, moving from classical limit theorems toward the stochastic processes that underpin modern analysis and applied mathematics. Materials include lecture notes, problem sets, and exams drawn from MIT's mathematics curriculum, free to access through OCW under a Creative Commons license with no certificate offered. The syllabus assumes prior exposure to real analysis and basic probability, positioning it as a rigorous follow-on course rather than an introduction. Anyone wanting to understand the mathematical machinery behind Brownian motion or the structure of infinitely divisible distributions will find the full theoretical development here, not just the results.