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If a politician, executive, or medical team were to use the results of your model for some critical decision, how well would you sleep at night? As computation plays an increasingly important role in our society, understanding the limitations of its predictive capabilities becomes of the utmost importance. Uncertainty quantification (UQ) considers the intersection of probability, statistics, numerics, and disciplinary sciences to provide a computational framework for measuring and reducing uncertainties. This graduate course focuses in depth on topics that are less typically covered in a traditional introduction to UQ, with particular attention given to polynomial chaos methods, Galerkin schemes, linear transport with uncertainty, and active subspaces. Research applications will be emphasized through assignments, case studies, and student-defined projects. Prerequisite: probability and statistics at the level of CME 106 or equivalent, linear algebra at the level of CME 200 or equivalent, or consent of the instructor.