DATA 690 Special Topics: Mathematical Foundations for Machine Learning

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