https://faculty.math.illinois.edu/~r-sowers(this syllabus can be found there)
Text: R. Durrett Probability: Theory and Examples , 2nd ed., 1995, Wadsworth & Brooks/Cole.
This is the first-year graduate course in probability theory. The goal of this course is to understand the basic tools of modern probability theory, and also to point out (in some small way) some connections with other areas of mathematics and science (analysis, number theory, queuing theory, and physics). Essentially, we shall look at probability theory as consisting of several common ways of modelling randomness (i.e., Markov and martingale properties, independence, etc.) and as a collection of limit theorems which allow one to extract some simple deterministic properties from a more complicated random system (i.e., the laws of large numbers, central limit theorems, ergodic theorems, martingale convergence theorems). See also the Course Catalog Entry for Math 451 or the list of UIUC Probability Theory Classes.
In comparison with previous years, we shall put less emphasis on some technicalities of the Central Limit Theorem. This will free up some time for discussion of large deviations and tightness.
Final: 40% of grade Midterm: 30% of grade Homework (4 assignments): 30% of grade Total: 100% of gradeThe midterm and final exam might be a take-home tests. If there is a regular final exam, it will be on Wednesday, May 8, 1996, from 1:30--4:30 PM.