# Math 350 - Spring 2010

## Section Information

 Time Location Instructor Office Hours (Cupples I, 17) MWF 10:00AM - 11:00AM Cupples I - 113 Renato Feres MW 11:00AM - 12:00PM TT 3:00PM - 4:00PM

## Text

Simulation by Sheldon M. Ross (Academic Press)

The campus bookstore has the fourth edition of the text. You may also use the third edition. (I haven't seen earlier editions, but likely they would be O.K. too.)

## Subject

Real phenomena are often described mathematically by probabilistic models such as Markov chains 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. Familiarity with basic concepts in probability and statistics at the level of Math 2200 is strongly recommended.

Topics:

• Elements of probability;
• Generation of random numbers and discrete and continuous random variables;
• Statistical analysis of simulated data;
• Introduction to Markov chain Monte Carlo methods;
• Additional topics as time permits.

Grades will be based on approximately 10 homework assignments, 1 midterm exam, and 1 final exam. Exam dates are:

 Exam Date Location Time Solutions MT Friday, 3/05 Cupples I, 113 10:00AM-11:00AM Available day after exam Final Monday, 5/10 Cupples I, 113 10:00AM-11:00AM Available day after exam

Let HW, MT, and F be the scores, out of 100 points, of the homework assignments, midterm and final exams, respectively. Then the total score is

### S = 0.60*HW + 0.20*MT + 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 [75,90) B [60-75) C [50-60) D [0,50) F

## Course plan

Information will be added to this course plan as the course progresses. Solutions to homework assignments will also be posted here after the due dates.

 Week Sections from text (tentative) Homeworks, exams Jan 20 - Jan 22 2.1 - 2.7 Homework 00 Jan 25 - Jan 29 2.8 - 2.10 Homework 01 due: 1/29; Solutions Feb 01 - Feb 05 3.1 - 4.2 Homework 02 due: 2/05; Solutions Feb 08 - Feb 12 4.3 - 5.3 Homework 03 due: 2/12; Solutions Feb 15 - Feb 19 5.4 - 6.7 Homework 04 due: 2/19; Solutions Feb 22 - Feb 26 6.8 - 7.3 Homework 05 due: 2/26; Solutions Mar 01 - Mar 05 8.1 Midterm Exam: 3/05; Solutions Mar 08 - Mar 12 Spring Break Mar 15 - Mar 19 8.2 - 8.3 Homework 06 due: 3/19; Solutions Mar 22 - Mar 26 8.4 - 8.6 Homework 07 due: 3/26; Solutions Mar 29 - Apr 02 8.6 - 8.9 Homework 08 due: 4/02; Solutions Apr 05 - Apr 09 9.1 - 9.4 Homework 09 due: 4/09; Solutions Apr 12 - Apr 16 9.4 - 10.2 Homework 10 due: 4/16; Solutions Apr 19 - Apr 23 10.3 Homework 11 due: 4/23; Solutions Apr 26 - Apr 30 10.4 - 10.5 May 03 - May 07 Reading Week May 10 Final Exam

## Homework

I plan to assign approximately 10 homeworks. Mostly, they will contain questions taken from the textbook, involving a mixture of theory questions and numerical questions requiring computer calculations. Assignments must be turned in during class on the date due. They should be written clearly and concisely. Points may be taken off for confusing or difficult to read solutions, even when the results are correct. As a rule, never submit a first draft! Polish your writing, computer script, etc., before turning it in.

## Mathematics software

Homework assignments will often involve questions requiring the use of mathematical software. I am most familar with Matlab, so this is the one that I mainly plan to use in this course. Other programs such as Mathematica, Maple, R, etc., would also work fine, but I may not be able to provide assistance in using them. So unless you are already proficient with any of these other programs, you will be better off with Matlab.

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.

An alternative software which is very similar to Matlab is Scilab. I have played with it a little and so far it seems to me mostly indistinguishable from Matlab. It is a highly developed open source program that works on most computer platforms. It can be freely downloaded from the Scilab site.

Renato Feres
feres@math.wustl.edu
Cupples I, Room 17
+1 (314) 935 - 6752 (phone)
+1 (314) 935 - 6839 (fax)

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

Last Updated: January 11 2010