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Modern data often consists of feature vectors with a large number of features. High-dimensional geometry and Linear Algebra (Singular Value Decomposition) are two of the crucial areas which form the mathematical foundations of Data Science. This mini-course covers these areas, providing intuition and rigorous proofs. Connections between Geometry and Probability will be brought out. Text Book: Foundations of Data Science.nnSee more on this video at www.microsoft.com/en-us/research/video/foundations-of-data-science-lecture-1/