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Covers the theoretical foundation of machine learning using ideas from functional analysis, spectral graph theory, stochastic processes and other branches of physics. The emphasis is on modern physics-inspired mathematical, statistical and Monte Carlo methods for analyzing scientific data. Topics to be covered include review of linear algebra and Hilbert space, spectral graph theory, clustering methods, dimensional reduction techniques, Reproducing Kernel Hilbert Space, kernel embedding, Grassmannian manifolds, matrix and tensor decompositions, stochastic sampling methods, numerical optimization, cross entropy method, Markov Chain Monte Carlo, and Gaussian Process. Course Information: 4 graduate hours. No professional credit. Prerequisite: Strong background in linear algebra, analysis, statistical mechanics, classical mechanics, and quantum mechanics.