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Targeted overview of key mathematical techniques essential to advanced AMS courses. Basics of convergence and limits. Review of multivariable calculus, including differentiability of vector-valued functions; multiple integrals and applications; implicit and inverse function theorems; interchanges of limits; change of variables. Review of linear algebra, including matrix operations, factorizations, and spectral decompositions; determinants; special matrices. Constrained optimization. Note: multivariable calculus and linear algebra are prerequisites for this course.