Randomness and Computation

This course presents the mathematical and computational tools needed to solve problems that involve randomness. For example, an understanding of random variables allows us to efficiently generate the enormous prime numbers needed for information security, and to quantify the expected performance of a machine learning algorithm beyond a small data sample. An understanding of covariance allows high quality compression of audio and video. Topics include combinatorics and counting, random experiments and probability, random variables and distributions, computational modeling of randomness, Bayes' rule, laws of large numbers, vectors and matrices, covariance and principal axes, and Markov chains.

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