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Course Weekly Lecture Plan

Week Topic
1 1 Matrix spaces, matrix factorizations, orthogonal matrices
2 Eigenvalues and eigenvectors, positive and positive semi-definite matrices, singular value decomposition (SVD)
3 Eckart-Young Theorem, vector and matrix norms, principal component analysis (PCA)
4 The least squares method and its analysis
5 Ax=b linear equation system and its solution methods
6 Computational methods for calculating eigenvalues and singular values
7 Exponential matrices, derivatives of matrices, derivatives of singular values and their analysis
8 SVD, LU and QR factorizations and the calculation of saddle points
9 Minmax problem and its relation with saddle points
10 Function minimization, gradient descent algorithm and its acceleration
11 Stochastic gradient descent algorithm and its analysis
12 Artificial neural networks and the back-propagation algorithm, partial derivatives
13 Convolutional neural networks and the learning function
14 Finding clusters in graphs
 
 
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