Mathematics 171 - Spring 2011
- Time and place: MWF at 11 in MS 5117
- Instructor: Thomas M. Liggett (email@example.com)
- Office hours: MWF 1-2 in MS 7919 (Students should feel free to
send questions by email as well, though we can usually accomplish
more by speaking in person.)
- Teaching Assistant: Yao Yao. Her office hours are Tu 11-12 and Wed 2-3 in MS 6160.
- Text: "Essentials of Stochastic Processes",
by Rick Durrett. There is a review chapter at the
beginning of the text, which is a good summary of
the probability that is assumed in the course. You
should read this to make sure you are up to speed.
The main subject of the course is Markov chains,
which is one of the most important classes of stochastic
processes. An errata for the book can be found at
- A stochastic process is simply a collection
of random variables indexed by time. These come up
in many contexts: position of a particle that is
influenced by some random phenomenon, price of an
option or stock, winnings of a gambler, size of
a queue (a queue is a waiting line, such as at a
checkout counter, in the skies above LAX, or in
a buffer at a node in a communications network),
and many others.
The main issue we will discuss is the behavior of
the random system after it has evolved for a long
time -- is it close to being in equilibrium, does
it grow without bound,...?
- Prerequisites: Officially, the prerequiste
is Mathematics 170A or equivalent. Mathematics 170B
(taken earlier or concurrently) is definitely helpful.
If you are not on top of the topic of convergence of
sequences and series, you should review that before the
- Discussion sections: (Thursdays at 11 in
MS 5117) These provide an opportunity
for you to ask questions about and discuss more fully
issues that are covered in the lectures. The TA will discuss
the homework that is due that day, but all questions related
to the course are fair game. In the first discussion section
(March 31), the TA will do some reviewing of probability
theory, based on the material in "Review of Probability" at
the beginning of the text. In preparation for this session,
you should look at (and try to do) problems 1.15, 1.17,
1.21, 1.25, 1.28, 2.9, 2.17, 2.19, 3.11, 3.15, 3.17,
3.20, 3.22 of this
pre-chapter. They are not to be turned in, however.
- Homework will be assigned each Friday (and
listed on this web page), and
will be due at the beginning of the discussion section the following Thursday.
It is essentially impossible to learn mathematics without
doing a lot of problems. I urge you to do the homework
with care and on time. You should also look through and
attempt as many of the unassigned problems as you have
time for. The basic rule is: The more problems you do,
the more thoroughly you will learn the material.
Note that there are answers to many of the problems at the
end of the book, so you can check your work that way. The lowest HW
score will be dropped before grades are assigned.
- Midterms: There will be two midterms, on Monday, April 25 and Monday, May 16.
Both will be in Haines A25.
- The first midterm: It will be on Monday, April 25, and will cover up to page 81. I will
take questions about this material at the beginning of the lecture on Friday, April 22. The exam will
be in Haines A25.
- Test 1 Solutions
- The second midterm It will be on Monday, May 16, in Haines A25. It will cover
Section 1.7, Chapter 2, and Sections 3.1,3.2,3.4.
- Test 2 Solutions
- Final exam: The final exam will be Wednesday, June
8, 3-6 in MS 5117. It will cover the entire quarter -- Chapters 1-4. The
emphasis is on Chapter 4. I won't
do much on the last two sections of Chapter 4 in class -- just an example or
two. You should think of this material as being further examples of the
theory that we developed in the earlier sections, so that you will benefit
from reading the latter sections.
- Final Solutions
- Finals week OH: Monday, June 6, 2pm.
- Grades will be based on homework (20%), midterms (20% each)
and final exam (40%).
- Due April 7: Homework 1
- Due April 14: Page 89, #6,7,8,9,11,13,14,15.
- Due April 21: Homework 3
- Due April 28: Pages 95-99, #35,36,43,45,48,49,50,53.
- Due May 5: Homework 5
- Due May 12: Homework 6
- Due May 19: Homework 7
- Due May 26: Homework 8
- Due June 2: Homework 9