(Sebastien Roch, Fall 2017:)

**Modern Discrete Probability: An Essential Toolkit**

This course will give an introduction to fundamental models and techniques in graduate-level modern discrete probability. Topics covered will be taken taken mostly from probability on graphs: percolation, random graphs, Markov random fields, random walks on graphs, etc. No attempt will be made made at covering these areas in depth. Rather the emphasis will be on illustrating common and important techniques. Aimed at graduate students in mathematics, statistics, computer science, electrical engineering, physics, economics, etc. with previous exposure to basic probability theory (ideally measure-theoretic probability theory, e.g., Math 733) and stochastic processes (e.g., Math 632).

(David Anderson, Spring 2017:) This course will cover stochastic simulation and Monte Carlo methods. Topics will include a subset of the following:

- Generation of random variables.
- Simulating stochastic differential equations.
- Monte Carlo methods.
- Variance reduction.
- Multi-level Monte Carlo.
- Derivative estimation.
- Stochastic optimization.
- Markov chain Monte Carlo.

Grades will be based upon (i) homework assignments, and (ii) possibly a project.