Syllabus

Math 561, CRN 38173, Section F1
Theory of Probability I

This is the first half of the basic graduate course in probability theory. The goal of this course is to understand the basic tools and language of modern nprobability theory (see also the Course Catalog Entry for Math 561 or the list of UIUC Probability Theory Classes). While I do not wish to sound discouraging, this will be an honest course. When you finish, you will feel comfortable with the ``plumbing'' of modern probability.

Provisional Schedule

  1. Introduction and probabilistic framework
  2. Information, Independence, and Conditioning
  3. Asymptotics: limit theorems
  4. Martingales
  5. Weak Convergence
  6. Construction of Wiener Measure
Additional References:
D. Stroock, Probability Theory: an Analytic View, Cambridge University Press, 1993
H. Royden, Real Analysis, McMillan, 1968

Grades will be determined on the basis of homework (30%), a midterm (30%) and a final (40%). I will attempt announce relevant things on my Twitter Feed.



Richard Sowers (Home Page)

Department of Mathematics
University of Illinois at Urbana-Champaign
1409 W Green St.
Urbana, IL 61801
r-sowers@illinois.uiuc.edu (217) 333-6246