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.
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. If interested, please REGISTER as soon as possible, and let me know by email that you plan to attend. Any questions, or requests for additional information, should be sent to
griffeat@math.wisc.edu.