Program Overview
The MS in Mathematical Foundations of AI is designed for students who want to understand AI at its deepest level — not just how to use tools, but why they work (and sometimes don't). The program provides rigorous preparation in the mathematical structures underlying modern machine learning: linear algebra, probability, optimization, information theory, and statistical learning theory.
Curriculum Highlights
- Core Mathematics: Real analysis, linear algebra (spectral theory, SVD), probability and measure theory
- Optimization: Convex optimization, first- and second-order methods, stochastic optimization, non-convex landscapes
- Statistical Learning: PAC learning framework, VC dimension, Rademacher complexity, generalization bounds
- Information Theory: Entropy, mutual information, channel capacity, rate-distortion; connections to compression and learning
- Deep Learning Theory: Neural tangent kernel, overparameterization, implicit regularization, double descent
Sample Courses
- MATH-401: Real Analysis for Machine Learning
- MATH-410: Advanced Linear Algebra and Matrix Theory
- MATH-420: Probability and Measure Theory
- MATH-430: Optimization for Machine Learning
- MATH-440: Statistical Learning Theory
- MATH-450: Information Theory and Learning
- MATH-490: Seminar: Deep Learning Theory