6.7720/18.619/15.070 Discrete Probability and Stochastic Processes

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.

Administrative Stuff

Syllabus: see this
Prereqs: see this
Lecture Times: Mondays & Wednesdays, 2:30pm—4:00pm
Lecture Location: E25–111
Office Hours: Thursdays from 2:00pm—3:00pm in 32—D632
Discussion Board: Piazza
Feedback Form: Please leave anonymous constructive feedback on the course here. Or you can email me. I would greatly appreciate it!
Misc. Linkage: psetpartners

Homeworks

On Canvas

Lecture Notes

Feb. 3: Course Intro, Percolation, Connectivity Phase Transition in Erdös—Rényi
Feb. 5: Paley—Zygmund, Branching Processes
Feb. 10: Second Moment Method (cont.), Hypothesis Testing, Broadcast Process
Feb. 12: Lovász Local Lemma
Feb. 18: Weak Law of Large Numbers, Shannon’s Noisy Coding Theorem
Feb. 19: Chernoff Bounds