Mathematical Foundations of Data Science

This graduate-level course develops the linear algebra and numerical linear algebra needed for modern data science. We treat the subject rigorously, emphasizing precise definitions, theorem-proof development, and careful reasoning about algorithms. Core mathematical themes: vector spaces and duality; inner product spaces and norms; spectral theory; matrix factorizations; perturbation theory; and multilinear (tensor) algebra. Computational themes: numerical stability and conditioning; fast algorithms for structured matrices; iterative methods for large-scale linear systems and eigenproblems; and randomized methods for scalable matrix computations.