Teaching

6.7720/18.619/15.070 Discrete Probability and Stochastic Processes

Spring 2025, Graduate-Level Probability

MIT’s Course Description: Provides an introduction to tools used for probabilistic reasoning in the context of discrete systems and processes. Tools such as the probabilistic method, first and second moment method, martingales, concentration and correlation inequalities, theory of random graphs, weak convergence, random walks and Brownian motion, branching processes, Markov chains, Markov random fields, correlation decay method, isoperimetry, coupling, influences and other basic tools of modern research in probability will be presented. Algorithmic aspects and connections to statistics and machine learning will be emphasized.

6.S891: Algorithmic Counting and Sampling

Fall 2023, Graduate special topics course

This course introduces the modern theory of algorithms for sampling from high-dimensional probability distributions and estimating their partition functions. These fundamental algorithmic primitives lie at the foundation of statistics, physics, and machine learning. We will study a diverse set of algorithmic paradigms for solving these problems based on Markov chains, decay of correlations, geometry of polynomials, and more. We will further study the rich set of analytic, probabilistic, and algebraic tools used to give performance guarantees to these algorithms.

6.1220: Design and Analysis of Algorithms

Spring 2024, Fall 2024, Undergraduate Algorithms

Algorithmic Design Paradigms: Greedy, Divide-and-Conquer, Dynamic Programming, Randomized/Approximation/Sublinear/Sketching/Streaming/Online Algorithms