This course is a fast-paced, rigorous introduction to the mathematical theory of probability, and statistical inference. It is ideal for students who want a crash-course in probability and mathematical statistics. A good working knowledge of calculus and basic linear algebra is required. Topics include sample spaces, probability, conditional probability, generating functions, sampling distributions, law of large numbers, the central limit theorem, maximum likelihood, the bootstrap, hypothesis testing, Bayesian inference, decision theory. Students studying Computer Science, or considering graduate work in Statistics or Operations Research, should carefully consider taking this course instead of 36-225 after consultation with their advisor. Not open to students who have received credit for 36-217 or 36-225.