Textbook: "Probability and Random Processes" by Grimmett and Stirzaker, Third edition 2009, Oxford Univ Press, ISBN 978-019-857222-0.

Pre-requsite: Willingness to learn what is needed, having had an undergraduate probability course and the equivalent of a mathematical methods course (including the rudiments of one complex variable; and Fourier and Laplace transforms) will help a lot.

Syllabus: We will cover selected materials:

1. Basic setup of probability theory (including sample spaces, conditional probability, independence). Random variables (including the elements of measure and integration theory).
2. Discrete random variables (including random walks).
3. Continuous random variables, the basic distributions, sums of random
4. Generating functions, branching processes, basic theory of characteristic functions, central limit theorems.
5. Markov chains (embedding, birth and death processes, Poisson processes)
6. Monte Carlo simulations
7. More laws of large numbers, including the law of the iterated logarithm, Martingales.
8. Various stochastic processes, including Brownian motion, queues, and applications.
9. Martingales, including stopping times and optimal stopping.
10. If time allows, the rudiments of stochastic integration (including Ito's formula and the Black-Scholes differential equation).

Office Hours: You are welcome to stop by my office at any time. However, I may have other duties as the Associate Dean and may not always be available. You can always make an appointment with me by email (Hu.1@nd.edu).

Homework: Homework problems will be assigned during class meetings and will be collected once a week on each Wednesday. The main purpose of the homework is to help you learn the material. Experience shows that students who take their homework seriously do very well in the course because they have a better understanding of the material.

Exams: There will be a midterm exam (in class) as well as a final exam (take home). Your final grade is based on 25 percent homeworks, 35 percent midterm, and 40 percent final. The final grade will be assigned by the total points as follws: A+ &ge 97, A &ge 93, A-&ge 90, B+ &ge 87, B&ge 83, B-&ge 80, C+&ge 77, C&ge 73, C-&ge 70, D&ge 60

If you receive a total score of 92.9, the final grade will be A-. Note: A+ will not be shown in your transcript.