The theory of differential equations can be used to model growths and decays. For instance, you can model how a population grows, how a disease spreads, or how a radioactive element decays.  The theory of time scales generalizes calculus to model these if there's a mix of discrete and continuous processes.  For instance, if you want to model a mosquito population, mosquitoes are continuously active in the summer, but their activity is spottier in the fall and spring.  A time scales model could model this population more accurately than the types of models you would see in a differential equations course.

The tentative plan is to start this research project by learning the basics of time scales calculus at the Rocky Mountain Mathematics Consortium Conference in Laramie, Wyoming.  This program runs from June 8-19 and you can think of it as "math immersion summer camp."  At this conference, we will meet the leaders in this research field and learn time scales in an intensive and cooperative environment.  More information can be found here.

When we return to Simpson, we will use time scales to model insect populations.  We will start by considering the Southern Pine Beetle, a destructive forest insect pest in the southeastern United States.  Other species may also be considered.  This summer research experience will also provide a number of opportunities for further research for those students interested in continued study.

For more information about this project, please contact Heidi Berger in Carver 332.