Course Meeting Times

Lectures: 2 sessions / week, 1.5 hours / session


18.440 Probability and Random Variables or 6.041SC Probabilistic Systems Analysis and Applied Probability


This course is an introduction to Markov chains, random walks, martingales, and Galton-Watsom tree. The course requires basic knowledge in probability theory and linear algebra including conditional expectation and matrix.

Recommended Textbooks

Levin, David Asher, Y. Peres, and Elizabeth L. Wilmer. Markov Chains and Mixing Times. American Mathematical Society, 2008. ISBN: 9780821847398. [Preview with Google Books]

Williams, D. Probability with Martingales. Cambridge University Press, 1991. ISBN: 9780387985091.

Brémaud, Pierre. Markov Chains: Gibbs Fields, Monte Carlo Simulation, and Queues. Springer, 2008. ISBN: 9780387985091. [Preview with Google Books]

Assignments and Exams

There are 5 homework assignments, 1 midterm exam, and final exam. The midterm and the final exams are closed book, closed notes, and no calculators.


Assignments 50% (10% each)
Midterm Exam 15%
Final Project 35%