Probabilistic Systems Analysis and Applied Probability
MIT OpenCourseWare offers this core probability course, taught as both 6.041 for undergraduates and 6.431 for graduates, covering the modeling and analysis of uncertainty. Topics include sample space formulations, random variables, transform techniques, simple random processes, Markov processes, limit theorems, and elements of statistical inference. Materials include full lecture notes, problem sets with solutions, exams, and video lectures recorded from an actual MIT classroom. The course builds from basic probability axioms toward more advanced stochastic processes, giving a full semester's worth of structured material for anyone wanting a rigorous foundation in probability theory. As with other MIT OCW offerings, all materials are free to access under a Creative Commons license, with no certificate offered but complete self-study content provided.