Math 6710: Probability Theory I
- Instructor: Nate Eldredge
- Office hours: Tuesdays at 11:25 (right after class), Wednesdays 10:00-11:00, or by appointment (send email)
- Office: 593 Malott Hall
- Teaching Assistant: Mark Cerenzia
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 random walk,
martingales, and possibly Markov chains, all in discrete time.
Textbook R. Durrett, Probability: Theory and Examples, 4th
edition. Here is an unofficial errata
list. Let me know if you find other errors and I will add them to
this list (and pass them along to Rick.)
Also, several other texts are on reserve at the Mathematics Library
(Malott Hall, 4th floor). You can check them out for 24 hours at a
time. See here
for the list.
Some other potentially useful references:
Caution! These lecture notes are very rough. They are mainly
intended for my own use during lecture. They almost surely contain
errors and typos. In many cases details, precise statements, and
proofs are left to Durrett's text, homework or presentations. But
perhaps these notes will be useful as
a reminder of what was done in lecture. If I do something that is
substantially different from Durrett I will put it in here.
Anyway here they are. 6710-lecture-notes.pdf
- (Due Thu, Aug 30) hw01.pdf (Correction posted August 26)
- (Due Thu, Sep 6) hw02.pdf
- (Due Thu, Sep 13) hw03.pdf
- (Due Thu, Sep 20) hw04.pdf (Updated September 17 with minor typo fixes)
- (Due Thu, Sep 27) hw05.pdf (Updated September 26 to remove problem 1)
- (Due Thu, Oct 4) hw06.pdf
- There is no HW 7. Enjoy fall break!
- (Due Thu, Oct 18) hw08.pdf
- (Due Thu, Oct 25) hw09.pdf
- (Due Thu, Nov 1) hw10.pdf
- (Due Thu, Nov 8) hw11.pdf
- (Due Thu, Nov 15) hw12.pdf
- There is no HW 13. Enjoy Thanksgiving break!
- (Due Thu, Nov 29) hw14.pdf
Written homework will be due in class on Thursdays.
Late homework policy: You will have 3 automatic extensions
which you can use any time during the semester to turn in an
assignment on the Tuesday after it is due. You can use these for any
reason you like; if you have an emergency, travel, or just want more
time to work on the assignment. You don't have to tell me in advance;
just hand in the assignment on Tuesday and write "extension" on it.
You cannot use multiple extensions on the same assignment. Note that
homework turned in with an extension may not be graded until the
following week. Other than this, no late homework will be accepted
without a compelling reason.
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.
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. A few times 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 will generally 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.