From Department of Mathematics at UTSA
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| − | ==List of Topics==
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| − | {| class="wikitable"
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| − | ! Week !! Section !! Topic !! Prerequisites !! SLOs !!
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| − | | 1 || || Notions of linear systems of equations to introduce the concepts of vector and matrices;. || || ||
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| − | | 2 || || Vector and matrix operations: Dot and cross products, matrix transpose, determinants. || || ||
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| − | | 3 || || Vector and matrix operations: Matrix addition, multiplication and inverse. || || ||
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| − | | 4 || || Cramer's rule and solutions of linear systems || || ||
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| − | | 5 || || Full rank, undetermined, and overdetermined systems. Least square solutions || || ||
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| − | | 6 || || Eigenvalues and eigenvectors. Canonical solution to linear systems of differential equations. || || ||
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| − | | 7 || || Calculus operations in vectors and matrices, i.e. how to derive a matrix with respect to a vector? || || ||
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| − | | 8 || || Optimization: Linear problems, and nonlinear problems (constrained and unconstrained) || || ||
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| − | | 9 || || Lagrange multiplier || || ||
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| − | | 10 || || Taylor series in one and multiple variables. Jacobians and Hessians, i.e. nabla and Laplace operators. || || ||
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| − | | 11 || || Principal component analysis || || ||
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| − | | 12 || || Gradient descent || || ||
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| − | | 13 || || Neural networks as nonlinear transformations || || ||
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| − | | 14 || || Implementation of a simple neural network with gradient descent || || ||
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| − | |}
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Latest revision as of 17:30, 1 April 2023
