Difference between revisions of "MAT2243"
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(Created page with "==List of Topics== {| class="wikitable" ! Week !! Section !! Topic !! Prerequisites !! SLOs !! |- | 1 || || Notions of linear systems of equations to introduce the concepts...") |
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− | ! Week !! Section !! Topic !! Prerequisites !! SLOs | + | ! Week !! Section !! Topic !! Prerequisites !! SLOs |
|- | |- | ||
− | | 1 || || Notions of linear systems of equations to introduce the concepts of vector and matrices | + | | 1 || || Notions of linear systems of equations to introduce the concepts of vector and matrices. || || |
|- | |- | ||
− | | 2 || || Vector and matrix operations: Dot and cross products, matrix transpose, determinants. | + | | 2 || || Vector and matrix operations: Dot and cross products, matrix transpose, determinants. || || |
|- | |- | ||
− | | 3 || || Vector and matrix operations: Matrix addition, multiplication and inverse. | + | | 3 || || Vector and matrix operations: Matrix addition, multiplication and inverse. || || |
|- | |- | ||
− | | 4 || || Cramer's rule and solutions of linear systems | + | | 4 || || Cramer's rule and solutions of linear systems || || |
|- | |- | ||
− | | 5 || || Full rank, undetermined, and overdetermined systems. Least square solutions | + | | 5 || || Full rank, undetermined, and overdetermined systems. Least square solutions || || |
|- | |- | ||
− | | 6 || || Eigenvalues and eigenvectors. Canonical solution to linear systems of differential equations. | + | | 6 || || Eigenvalues and eigenvectors. Canonical solution to linear systems of differential equations. || || |
|- | |- | ||
− | | 7 || || Calculus operations in vectors and matrices, i.e. how to derive a matrix with respect to a vector? | + | | 7 || || Calculus operations in vectors and matrices, i.e. how to derive a matrix with respect to a vector? || || |
|- | |- | ||
− | | 8 || || Optimization: Linear problems, and nonlinear problems (constrained and unconstrained) | + | | 8 || || Optimization: Linear problems, and nonlinear problems (constrained and unconstrained) || || |
|- | |- | ||
− | | 9 || || Lagrange multiplier | + | | 9 || || Lagrange multiplier || || |
|- | |- | ||
− | | 10 || || Taylor series in one and multiple variables. Jacobians and Hessians, i.e. nabla and Laplace operators. | + | | 10 || || Taylor series in one and multiple variables. Jacobians and Hessians, i.e. nabla and Laplace operators. || || |
|- | |- | ||
− | | 11 || || Principal component analysis | + | | 11 || || Principal component analysis || || |
|- | |- | ||
− | | 12 || || Gradient descent | + | | 12 || || Gradient descent || || |
|- | |- | ||
− | | 13 || || Neural networks as nonlinear transformations | + | | 13 || || Neural networks as nonlinear transformations || || |
|- | |- | ||
− | | 14 || || Implementation of a simple neural network with gradient descent | + | | 14 || || Implementation of a simple neural network with gradient descent |
|} | |} |
Revision as of 00:49, 30 March 2023
List of Topics
Week | Section | Topic | Prerequisites | SLOs |
---|---|---|---|---|
1 | Notions of linear systems of equations to introduce the concepts of vector and matrices. | |||
2 | Vector and matrix operations: Dot and cross products, matrix transpose, determinants. | |||
3 | Vector and matrix operations: Matrix addition, multiplication and inverse. | |||
4 | Cramer's rule and solutions of linear systems | |||
5 | Full rank, undetermined, and overdetermined systems. Least square solutions | |||
6 | Eigenvalues and eigenvectors. Canonical solution to linear systems of differential equations. | |||
7 | Calculus operations in vectors and matrices, i.e. how to derive a matrix with respect to a vector? | |||
8 | Optimization: Linear problems, and nonlinear problems (constrained and unconstrained) | |||
9 | Lagrange multiplier | |||
10 | Taylor series in one and multiple variables. Jacobians and Hessians, i.e. nabla and Laplace operators. | |||
11 | Principal component analysis | |||
12 | Gradient descent | |||
13 | Neural networks as nonlinear transformations | |||
14 | Implementation of a simple neural network with gradient descent |