VIGRE2 Vertical Intergration of Research and Education Department of Mathematics, University of Utah

MATH 4800








Fall 2008 course

Topic: Random Walk: Modeling, Theory, and Applications
Instructor: Firas Rassoul-Agha
Catalog Number: MATH 4800-1
Credits: 3
Time/Location: TTh, 10:55am - 12:10pm (time subject to change)

Registering requires obtaining the class number from the instructor.
To be considered for admission to this course, fill out the application form and have a faculty member send a letter of support to

Did you know that pollen suspended in water, stock prices, heat propagation, and E coli motion are all modeled using the same mathematical object?

A random walk is a process where a given particle moves around in a random manner. An example of a random walk is the famous Brownian motion.

Random walks have a long history: the Roman Lucretius's scientific poem "On the Nature of Things" (c. 60 BC) has a remarkable description of motion of dust particles and how this indicates the existence of atoms. In 1827, while studying pollen and dust particles, Brown discovered what is now called Brownian motion. In 1900, Louis Bachelier established the mathematical grounds and used it, for the first time in history, to evaluate stock options. Albert Einstein (1905) and Marian Smoluchowski (1906) independently explained the origins of this motion bringing Bachelier's work to the attention of the physicists.

Random walk is arguably the most studied stochastic process, with the widest range of applications in fields as diverse as the physical and social sciences, engineering, and business.

This course aims at providing students with a solid understanding of random walk and applications through a combination of computer simulations and theory. Along the way, we will develop knowledge of concepts considered to be building blocks of probability theory.

Tuition Benefit:
The NSF VIGRE program provides a small tuition benefit for US students (US citizens and permanent residents). Details will be provided once total enrollment has been determined.

Past Courses:
Fall 2006, Math Finance
Spring 2007, Fractals
Fall 2007, Metric Spaces, The Contraction Mapping Principle, Fractals & Other Applications
Spring 2008, Knot Theory