18.325 Topics in Applied Mathematics

Random Walks and Diffusion

Syllabus -- Revised Feb. 13, 2001


Time & Place: Tuesdays & Thursdays 11:00am-12:30pm, Room 2-105

Instructor: Prof. Martin Z. Bazant, bazant@math.mit.edu, 253-1713.

Office Hours: Mondays 2-3pm, Wednesdays 3-4pm, 2-363B

Three Problem Sets: Due on Tuesdays... February 27, March 20, May 1.

Lecture Summaries and Homework Solutions: Each student will write detailed summaries (ideally in latex) of one or two lectures and/or solutions for some of the homework problems.

One Final Project: Topic must be approved by Tuesday April 24. A brief presentation will be given on May 15 or May 17. A written report is due by Monday May 21. (No final exam!)

Grading: Grading will be based on the problem sets (30%), lecture summaries and/or problem solutions (20%), and the final project presentation (20%) and report (30%). The homeworks will be self-graded, as soon as the solutions become available. The instructor will do some quality control.

Required Books: None. The course will be based on original lectures by the instructor and handouts. A review of probability from Chap. 1 of Bouchaud and Potters (below) is available at MIT CopyTech.

Recommended Books: Barry Hughes, Random Walks and Random Environments, Vol. 1 (Oxford, 1996); J. Crank, Mathematics of Diffusion (Oxford, second ed., 1975); D. Stauffer and A. Aharony, Introduction to Percolation Theory (Taylor & Francis, second ed., 1992). H. Risken, The Fokker-Planck Equation (Springer, second ed., 1989).

Reserved Library Books: J.-P. Bouchaud and M. Potters, Theory of Financial Risks (Cambridge, 2000); H. C. Berg, Random Walks in Biology (Princeton, 1983); N. G. van Kampen, Stochastic Processes in Physics and Chemistry (Elsevier, 1992); Barry Hughes, Random Walks and Random Environments, Vol. 2 (Oxford, 1996).

Course Outline

  1. Random Walkers and Diffusion

  2. Random Environments

  3. Interacting Random Walkers