Math 491 - Topics in Undergraduate Mathematics

• Prerequisites: Math 234, or consent of instructor.
• Frequency: Irregular.
• Student Body: Math majors
• Credits: 3. (N-A)
• Recent Texts:
• Past Instructors:
• Background and Goals: Math 491 is not offered on a regular basis. This topics course is used for experimenting with new courses and for presenting special topics
• Alternatives: N/A
• Subsequent Courses: N/A

Content coverage:

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An Introduction to Cellular Automata and Interacting Systems

Instructor: David Griffeath Tu, Th 11:00-12:15, B325 Van Vleck

Math 491 will be offered in conjunction with an NSF-funded CURL (Collaborative Undergraduate Research Lab). As a case study of course themes, the lab will conduct original research on idealized and realistic models for ice crystal growth. Enrollment in the course does not imply participation in the lab, but students in the lab will be required to take the course.

Description:

Math 491 will explore theoretical and experimental approaches to the study of cellular automata (CA) and other spatially distributed complex systems. The course will be interdisciplinary in spirit, stressing the use of CA dynamics, deterministic and probabilistic, as paradigms for physical phenomena from across the spectrum of applied science. We will focus on simple models for crystal growth and traffic flow in order to explore the important contemporary concepts of phase transition and self-organization.

Where possible, we will develop techniques for the rigorous mathematical analysis of such models. Tools include path representations, convex analysis, and contour methods. But the course will also stress computer simulation and dynamic, interactive visualization. Little advanced mathematical background will be required. However a basic familiarity with aspects of probability theory, combinatorics, differential equations, and/or computer algorithms at the advanced undergraduate level will be helpful. There will be no formal textbook. Reading materials for the course will be distributed.

Prerequisites:
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