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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{| class="wikitable"
! Week !! Section !! Topic !! Prerequisites !! SLOs !!
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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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| 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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| 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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| 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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| 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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| 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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| 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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| 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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| 8 ||  || Optimization: Linear problems, and nonlinear problems (constrained and unconstrained) ||  ||  
 
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| 9 ||  || Lagrange multiplier ||  ||  ||  
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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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| 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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| 11 ||  || Principal component analysis ||  ||  
 
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| 12 ||  || Gradient descent ||  ||  ||  
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| 12 ||  || Gradient descent ||  ||  
 
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| 13 ||  || Neural networks as nonlinear transformations ||  ||  ||  
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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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| 14 ||  || Implementation of a simple neural network with gradient descent
 
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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