Random Walks and Diffusion
A graduate-level MIT mathematics course covering discrete random walks and continuum diffusion processes. Topics include the mathematics of Brownian motion, random walks on lattices, and diffusion equations, applied to polymers, disordered media, turbulence, diffusion-limited aggregation, granular flow, and derivative securities pricing. Materials on MIT OpenCourseWare include lecture notes and problem sets covering the theoretical framework connecting probabilistic random walk models to continuum diffusion descriptions, along with the physical and financial systems these models describe. The course is free to audit through MIT OpenCourseWare, with no certificate offered. It suits students with a strong background in probability and differential equations who want to see how a single mathematical framework spans statistical physics, materials science, and finance.