CSI 709 / STAT 789

Monte Carlo Methods in Science

Spring, 2009

Instructor: James Gentle

Lectures: Wednesday, 4:30-7:10pm, Research I, room 302

This course covers applications of Monte Carlo methods in science. The course begins with a review of relevant background material in probability and statistics, and then covers algorithms for computer generation of random numbers, first from a uniform distribution, and then from various distributions of interest. Examples of applications from the physical, biological, and social sciences will be studied. Individual class projects will focus on topics chosen by the students.


The text for the course is
Gentle, James E. (2003), Random Number Generation and Monte Carlo Methods, second edition, Springer, New York.

This will be supplemented by various handouts.


We will not cover these topics sequentially.

Background and interests of class will affect the relative weighting of these topics.


No particular software system will be required, but examples will be given in R. If you have not used the open-source, freely-distributed R system, I recommend that you look into it. It is available in precompiled binary distributions for Linux, MacOS X, and MS Windows. It can be downloaded from
From that web page, go to CRAN, select a mirror, then select the appropriate distribution. I will introduce the system in the first class.

Assignments will require the use of computer software that has facilities for generating random numbers and for general programming. Instead of R, this could be Matlab, Mathematica, Maple, C, and/or Fortran.


The mathematical and statistical background required is relatively elementary; basically mathematics through multivariate calculus, and some introduction to probability and statistics.


Performance in the class will be evaluated based on
  • an in-class midterm (25%)
  • a final exam consisting of a take-home portion and an in-class portion (35%)
  • a project (30%)
  • a number of smaller assignments (10%)

    Ethical Behavior

    Each student enrolled in this course must assume the responsibilities of an active participant in GMU's scholarly community in which everyone's academic work and behavior are held to the highest standards of honesty. The GMU policy on academic conduct will be followed in this course.

    The GMU Honor Code will be strictly observed.

    Week 1, January 21

    Notes on probability distributions

    Assignment 1
    Due January 28.

    Week 2, January 28

    Assignment 2: Page 271: Exercises 7.1, 7.2, 7.3, 7.5; Page 57: Exercises 1.4, 1.5.
    Due February 11.

    Week 3, February 4

    Week 4, February 11

    Assignment 3: Page 159: Exercises 4.1, 4.2, 4.3, 4.4, 4.6, 4.7, 4.9 (Instead of Fortran or C, you can use R or some other package.)
    Due February 25.
    Comments, solutions. Also, inverse CDF for bivariate distribution.

    Week 5, February 18

    Week 6, February 25

    Week 7, March 4

    Midterm exam (open book)

    This will cover basic material on probability distributions, Section 7.1, Chapter 1 (but not Exercise 1.4), and Sections 4.1-4.7.

    The exam questions will be similar to the (easier) homework exercises, except you will not be asked to use any computer software.

    (No class March 11)

    Week 8, March 18

    Assignment 4: Page 161: Exercises 4.10, 4.11, 4.15
    Due April 8. Notice: a lot of homework is due on that day!

    Week 9, March 25

    Assignment 5: Page 162: Exercises 4.12, 4.14, 4.17
    Due April 8. Notice: a lot of homework is due on that day!

    Week 10, April 1

    Week 11, April 8

    Assignment 6: Exercises 2.1, 2.8, and 3.6
    Due April 12.

    Week 12, April 15

    Week 13, April 22

    Week 14, April 29

    May 6

    4:30pm - 7:15pm Final Exam.

    James Gentle, jgentle at gmu dot edu