Lectures
Two sessions / week
1.5 hours / session
Prerequisite
18.305 (Advanced Analytic Methods in Science and Engineering) or permission of the instructor. A basic understanding of probability, partial differential equations, transforms, complex variables, asymptotic analysis, and computer programming would be helpful, but an ambitious student could take the class to learn some of these topics. Interdisciplinary registration is encouraged.
Problem Sets
There are five problem-sets for this course. Solutions should be clearly explained. You are encouraged to work in groups and consult various references (but not solutions to problem sets from a previous term), although you must prepare each solution independently, in your own words.
Scribe Reports
Each student will write a detailed summary (ideally in LATEX) of one or two lectures and/or solutions for selected homework problems. Each such report is due within one week, in a form that can be posted at the website.
Midterm Exam
A take-home midterm exam will be handed out on Lecture 18 and will be due in two days.
Final Project
There is no final exam, only a written final-project report, due at Lecture 25. The topic must be selected and approved two months earlier.
Grading
Grading will be based on the problem sets (40%), scribe reports (5%), midterm exams (25%), and final project (30%).
Required Books
Lecture notes from the Spring 2001 version of the course will be available to registered students.
Redner, Sidney. A Guide to First Passage Process. Cambridge, 2001.
Recommended Books
Hughes, Barry. Random Walks and Random Environments. Vol. 1. Oxford, 1996.
Crank, John. The Mathematics of Diffusion. 2nd ed. Oxford, 1975.
Ben-Avraham, D., and S. Havlin. Diffusion and Reactions in Fractals and Disordered Systems. Cambridge, 2000.
Bouchaud, Jean-Philippe, and Marc Potters. Theory of Financial Risks. Cambridge, 2000.