Math 350 - Fall 2012

Section Information

Section Time Location Instructor Office Hours (Cupples I, Room 17)
1 Mon Wed Fri 1:00PM - 2:00PM Cupples I, 199 Renato Feres Tue Thu 12:00PM - 2:00PM

Please include Math 350 in the subject line of any email message that pertains to this course. It will help avoid accidental deletion of your still unread message. My e-mail address is


Real phenomena are often described mathematically by probabilistic models such as Markov chains, diffusion processes, and other related stochastic processes. This course is an introduction to techniques for the analysis of probabilistic models by use of numerical simulation. Course work will involve both theoretical and computer assignments. Prerequisite: Math 233 and Math 309. Familiarity with basic concepts in probability and statistics at the level of Math 2200 is strongly recommended.



Explorations in Monte Carlo Methods by Ronald W. Shonkwiler and Franklin Mendivil, Springer (2009).

Homework and Grading Information

Our plan is to have 11 homework assignments, of which the worst score will be dropped. In addition, there will be one mid-semester term paper, due October 17, and a final project, due no later than December 19. The term paper will consist of a "research proposal" for a topic you will develop in the final project, involving an application of the stochastic methods studied in the course. We will have much more to say about the project in class.

Let H, M, and F be the scores, out of 100 points, of the homework assignments, mid-semester paper and final project, respectively. Then the total score is

S = 0.70*H + 0.10*M + 0.20*F.

The value of S will be translated into a letter grade of A, B, C, D, F (with plus and minus shadings to be decided later) in a way that is not stricter than the following table:

Numerical Range Letter Grade
[90,100] A-, A, A+
[75,90) B-, B, B+
[60-75) C-, C, C+
[50-60) D
[0,50) NCR (F)

Course plan

Week Chapter/Section Assignments and reading
Aug 29 - Aug 31

Chapter 1
Do Assignment 00 on getting started with Matlab.
(It won't be collected and is not for grade.)
Read pages 1 to 9 of the textbook.
Try to understand and execute the simple programs on pages 4, 6, and 9.
Sept 03 - Sept 07

9/3 (Labor Day)
Chapter 1
This write-up has a list of useful Matlab functions related
to random numbers and histograms: Random Numbers in Matlab.

Homework 1 due 9/07
Solutions (9/14)
Sept 10 - Sept 14

Chapter 1/2

Homework 2 due 9/14
Solutions (9/21)
Sept 19 - Sept 23

Chapter 2

Lecture notes on random variables.

Homework 3 due 9/21
Solutions (9/28)
Sept 24 - Sept 28

Homework: 9/28
Chapter 2

Homework 4 due 9/28
Solutions (10/05)
Oct 01 - Oct 05

Homework: 10/05
Chapter 2/3

Homework 5 due 10/05
Solutions (10/17)
Oct 8 - Oct 12

Homework: 10/12
Chapter 3
Homework 6 due 10/12
Solutions (10/17)
Oct 15 - Oct 19

10/19 (Fall break)
Chapter 3
Oct 22 - Oct 26

Homework: 10/26
Chapter 3
Homework 7 due 10/31
Solutions (11/05)
Oct 29 - Nov 02

11/02 (no class today)
Chapter 3
Homework 8 due 11/12
Solutions (11/12)
Nov 05 - Nov 9

Homework: 11/9
Chapter 4
Homework 9 due 11/19
Solutions (11/19)
Nov 12 - Nov 16

Homework: 11/19
Chapter 4
Nov 19 - Nov 23

11/21 (Thanksgiving)
11/23 (Thanksgiving)
Chapter 5
Homework 10 due 11/19
Solutions (11/30) Ising model animation, courtesy of Will Gooding.
Nov 26 - Nov 30

Homework: 11/30
Chapter 5
Homework 11 due 12/07
Solutions (12/07)
Dec 03 - Dec 07

Homework: 12/07
Chapter 5
December 19


End of the semester paper and research project

Here is a selection of papers on MCMC from which we may take for class discussion. I found them through a random search on-line. If you do your own search you will find a large number of tutorials, lecture notes, as well as videos of lectures on the topic. There is also a large number of texts on MCMC that you can find at the Olin library (they are typically at a more advanced level than our textbook, but you don't need to understand everything in order to find useful information even in the most advanced texts.)

Take a look at some of the below links and other sources as you think about your research project. If any of the links is not accessible to you, do an on-line search with the titles and authors, and you will likely find alternative working links. Wikipedia is also a very good source of information.

It is completely open to you what kind of project to undertake, both in theme and form. Here are some possibilities:

Students' projects

Below are some of the final projects developed by the students in the Fall of 2012 (posted with their permissions).

Mathematics software

Homework assignments will often contain questions requiring the use of mathematical software. The textbook uses Matlab and this is the sofware I am most familiar with. Other programs such as Mathematica, Maple, R, etc., would also work fine, but I may not be able to provide assistance in using them. GNU Octave works essentially identically to Matlab and is free to download. R is also free, and it would be in some respects ideal for the course, so you are encouraged to try it.

Matlab is installed in most PCs in the computer lab at Eads, and I believe in the engineering computers. (Presently, I do not know if it is available at the business school computers.) I do not assume that you are already familiar with it.

Here are some links to information about the free software mentioned above:

Renato Feres
Cupples I, Room 17
(314) 935 - 6752 (office phone)

Department of Mathematics
Washington University
Campus Box 1146
Saint Louis
Missouri, 63130 USA.

Last Updated: August 10, 2012