The topics to be covered and the method of instruction to be used will be announced at the beginning of each semester that such courses are offered. See departmental bulletins.

Introduction to applied linear algebra and optimization with applications in data science. We will cover Parts I,II,III,VI,VII (and a few subtopics of IV,V) of Strang’s book, as well as chapters 2 and 3 of Higham’s book and Chapter 2 of Demmel’s book, including: • Floating-point arithmetic, condition number, perturbation theory, backward stability analysis • Matrix decompositions (LU/QR/Cholesky/SVD), least squares problems, orthogonal matrices • Eigenvalues, eigenvectors, Rayleigh quotients, generalized eigenvalues • Principal components, low rank approximation, compressed sensing, matrix completion • Convexity, Newton’s method, Levenberg-Marquardt method, quasi-Newton methods • Randomized linear algebra, stochastic gradient descent • Machine learning, neural networks (deep/convolution), adjoint methods, backpropagation

Prerequisites: Math 53 and 54 or equivalent (e.g., Math 91 from Fall 2022 can replace Math 54)

Repeat Rules