Math 6710: Probability Theory I

Fall 2010

Meets

MWF 10:10-11:00, 211 Upson.

Personnel

Instructor: Nate Eldredge
- Email: neldredge@math.cornell.edu
- Office hours: W 1:30-2:30, Th 10-11, or by appointment (send email)
- Office: 593 Malott Hall
Teaching Assistant: Russ Thompson
- Email: thru@math.cornell.edu
- Office hours: Tu 3-4, Th 3-4.
- Office: 104 Malott Hall

Course overview

This will be a fairly standard introduction to measure-theoretic probability theory at the graduate level. We will begin with a brief review of abstract measure theory, with a view to its use in probability: random variables, expectation, measurability and σ-fields. We will discuss the idea of independence and prove the strong law of large numbers and some related results. Next we will attack the central limit theorem, which will require some discussion of weak convergence (aka convergence in distribution) and characteristic functions (aka Fourier transforms). Finally, to begin a transition to stochastic processes, we will talk about martingales (in discrete time), stopping times, and related convergence theorems. If time permits we may talk about some other stuff as well.

Textbook

R. Durrett, Probability: Theory and Examples, 4th edition. Electronic version: PDF. The hardcover version is now also available from the usual online sites; the Cornell bookstore may or may not have it. We will not necessarily be following Durrett too closely; please watch the lecture schedule.

Also, several other texts (list) are on reserve at the Mathematics Library (Malott Hall, 4th floor).

Some other potentially useful references:

Bruce Driver's probability notes: PDF.
Rich Bass's probability notes: PDF.

Homework

Written homework will be due in class on Fridays. Late homework will not be accepted unless approved in advance.

Group work policy: The purpose of homework in this class is to gain experience in working with the ideas studied in class; this is usually where the most learning takes place. You are encouraged to discuss the homework problems with classmates or colleagues on a high level, but you should write your solutions by yourself.

Homework assignments:

Due Sep. 3. hw01.pdf
Due Sep. 10. hw02.pdf
Due Sep. 17. hw03.pdf
Due Sep. 24. hw04.pdf (corrected Sep. 21)
Due Oct. 1. hw05.pdf (updated Sep. 29)
Due Oct. 8. hw06.pdf
Due Oct. 22. hw07.pdf
Due Oct. 29. hw08.pdf (corrected Oct. 25)
Due Nov. 5. hw09.pdf
Due Nov. 12. hw10.pdf
Due Nov. 24. hw11.pdf. Watch this space for possible updates.
Due Dec. 3. hw12.pdf.

Student presentations

Since it's important to be able to communicate your mathematical work to others, we will have brief student presentations throughout the course. ~~Two or three times~~ Once or twice during the semester, each student will be given a homework-like problem or a theorem from the text, and asked to prepare it and present it during class. These should take about 5-10 minutes.

When it is your turn, I will send you an email at least 6 days ahead of the presentation date. Dates and assigned material are negotiable if there are problems. You are always welcome to come and discuss or practice your presentation with me ahead of time.

Exams

None.

Lecture schedule

neldredge@math.cornell.edu