Course Description: This course aims to provide fundamental yet necessary mathematics for graduate students to understand machine learning methods and algorithms better. Fundamental concepts of linear algebra, analytic geometry, matrix decompositions, vector calculus, and optimization is taught with Python.
Prerequisites: Enrollment in the Data Science program. Other students may be admitted with GPD’s permission.
References: TBA
Tentative Schedule
Week 1: Introduction to MFDS. Tensors and Numpy, Scipy, and Sympy.
Week 2: Systems of Linear Equations. Gaussian Elimination, Matrix Inversion, Transpose, and Special Matrices
Week 3: LU Decomposition, Vector Spaces, and Linear Transforms
Week 4: Solving Ax = b (Application: Linear Regression)
Week 5: Orthogonality, Least Squares, and Gram-Schmidt Method
Week 6: Determinant and Cramer’s rule
Week 7: Eigenvalues and Eigenvectors
Week 8: Diagonalization, Differential Equations, and Operators
Week 9: Special Matrices and Jordan Form
Week 10: Singular Value Decomposition
Week 11: Norm, Condition Number, and Pseudoinversion
Week 12: Partial Differentiation and Gradients: Vectors and Matrices
Week 13: Backpropagation and Automatic Differentiation
Week 14: Optimization Using Gradient Descent
Week 15: Constrained Optimization and Lagrange Multipliers
Week 16: Convex Optimization and review