Math/Stat 831 Theory of Probability
Fall 2007
In-Class Exam:
Friday, December 7. Begins at 4 PM. Do arrive on time because
once somebody has left no one can be admitted into the exam.
The room is Van Vleck B139 and we have it until 6:30.
Please bring your pencil and paper and your
3 sheets of notes. No calculators or other electronic
gadgets. The exam asks you to hand in 4 problems out of 7.
Short, basic exercises from the material up to and including
martingales: types of convergence, 0-1 laws, law of large
numbers, normal and Poisson limits, conditional expectations.
Here is the syllabus
for the course.
Homework
- Homework 1 due September 13.
- Homework 2 due October 4.
- Homework 3 due October 16.
- Homework 4 due November 8.
- Homework 5 due November 27.
Bonus Problems. Bonus problems are
for those who would like to work on problems
that require further reading, or are open-ended,
interesting or hard. If there is interest in this
I will add to the list during
the semester. There is no due date for these problems.
The
Midwest Probability Colloquium
runs from Thursday October 18 to Saturday October 20.
I recommend that those who are interested
and able to make the trip participate in this meeting
in lieu of the class on October 18. (I intend to go to the
meeting.) It is held at
Northwestern University, a 2.5 hour
drive away. Usually the organizers have
some funds to assist junior participants. The earlier you
ask the better
your chances to get some, see the website. Students and faculty
from around the region and even farther away come to this conference.
It is usually a very enjoyable occasion. The
scientific program is not very heavy and there is plenty of time
for socializing.
Check out the
Probability Seminar for talks on topics that
might interest you.
Instructions for Homework
- Homework must be handed in by the due date, either in
class or by 3 PM in the instructor's office or mailbox. Late submissions
cannot be accepted in a course this large.
- Neatness and clarity are essential. Write one problem per page
except in cases of very short problems.
- It is not trivial to learn to write solutions. You have
to write enough to show that you understand the flow of
ideas and that you are not jumping to unjustified conclusions,
but not too much to get lost in details. If you are unsure
of the appropriate level of detail to include, you can separate
some of the technical details as "Lemmas" and put them at the
end of the solution.
A good rule of thumb is
if the grader needs to pick up a pencil to check your
assertion, you should have proved it. The grader can
deduct points in such cases.
- You can use basic facts from analysis and measure theory
in your homework, and the theorems we cover in class
without reproving them. If you find
a helpful theorem or passage in another book,
do not copy the passage but use the
idea to write up your own solution. If you do use other
literature for help, cite your sources
properly. However, it is better to
attack the problems
with your own resources instead of searching the literature
or the internet.
The purpose of the
homework is to strengthen your problem solving skills, not
literature search skills.
- It is valuable
to discuss ideas for homework problems with other
students. But it is not acceptable to
write solutions together or to copy another person's
solution. In the end you have to hand in your
own personal work.