Uncertainty Quantification
Variational inference, diffusion, Monte Carlo, Kalman methods, Langevin and Hamiltonian dynamics, rare events, and simulation based inference.
Course materials
04 · Teaching
Mathematics that moves between theory and computation.
My courses connect rigorous mathematical foundations with modern computational practice, emphasizing how assumptions, algorithms, and empirical behavior fit together.
Selected courses
Recent teaching
Course pages preserve lecture notes, assignments, and reference material from the original offerings.
Statistical Learning for Data Analysis
Regression, uncertainty, resampling, model interpretation, and the statistical workflow from assumptions to diagnosis.
Course materialsStatistical Learning
Optimization, generalization, kernels, neural networks, generative models, and the mathematical foundations of modern learning.
Course materialsLinear Algebra
Linear systems, geometry, eigenvalues, singular values, least squares, and computational interpretations.
Course materialsMathematical Foundations of Generative AI
Probability, stochastic processes, optimal transport, diffusion, sequential inference, and inference time computation.
Scientific Machine Learning
Approximation, PDE learning, operator learning, physics informed models, uncertainty quantification, and scaling laws.
Start from a mathematical question
Students should understand what a method estimates, what information it uses, and what can fundamentally go wrong before they memorize an algorithm.
Connect proof to computation
Derivations are paired with experiments that reveal scaling, stability, and approximation behavior. The computation is part of the argument.
Make research ownership visible
Open ended projects ask students to formulate a precise question, defend their evaluation, and explain what evidence would change their conclusion.