DATA 2010: This course builds the mathematical foundations essential for understanding classical and modern machine learning methods from the ground up. The focus will be on mathematical formalism and intuition rather than applications per se, however, undergirded ML methods and algorithms will be highlighted and broadly frame the topics covered and their arc: in algorithms that learn from data, we must define a representation space (linear algebra), orient ourselves (calculus), model things (probability), then learn (statistics) about our dataset using our computational tools (numerical methods). We will survey some of the most relevant ideas from these broad areas of math, including linear transformations, eigenvalues and eigenvectors, singular value decomposition, gradients, Jacobians, Hessians, random variables, probability distributions, Bayes’ Theorem, pseudo-random numbers, autodifferentiation, and numerical error.
APMA 1690: Examination of probability theory and mathematical statistics from the perspective of computing. Topics selected from random number generation, Monte Carlo methods, limit theorems, stochastic dependence, Bayesian networks, and dimensionality reduction. Computational Probability and Statistics is better suited for students with a strong math background because it’s a more challenging course. Prerequisites: APMA 1650 or equivalent; programming experience is recommended.
Both courses are typically offered in the Fall semester.