University of California, Berkeley 4 credits Mathematics
Introduction to applied linear algebra, numerical analysis and optimization with applications in data science and statistics. Topics covered include: • 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
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