Difference Equations Seminar
Date: August 3
Difference equations provide a very accessible route to mathematical modeling. Yet they also display some amazing interesting behavior. This led mathematical biologist Robert May to write (Nature, 1976):
“The elegant body of mathematical theory pertaining to linear systems… ill equips the student to confront the bizarre behaviour exhibited by the simplest of discrete nonlinear systems… Yet such nonlinear systems are surely the rule, not the exception, outside the physical sciences. I would therefore urge that people be introduced to [nonlinear difference equations] early in their mathematical education.”
The seminar will introduce the study of linear and nonlinear difference equations, with an eye towards both their mathematical properties and toward their applications.
The target audience for the seminar is math and science students who are interested in mathematical modeling methods. Faculty are welcome to participate (or even contribute!) as well.
Each week, Prof. Allen will post a short video, along with some notes and some exercises to work on. There will be computational aspects as well; these can be done using the LC Data Science Server. All these materials will be put on a google classroom page (contact Prof. Allen for the class code), where participants are welcome to discuss the exercises, etc. The format will change if necessary.
Students should have taken at least Calculus 1 (Math 131) or Math 123. Those students who have taken Math 235 will find the compare/contrast between difference equations and differential equations to be very interesting.