What's My Math Course Got to Do with Biology?

Abstract

At United States Military Academy, a unit on biological modeling applications forms the culminating component of the first semester core mathematics course for freshmen. The course emphasizes the use of problem-solving strategies and modeling to solve complex and ill-defined problems. Topic areas include functions and their shapes, data fitting, elementary matrix and vector algebra, difference equations, and an introduction to differential calculus. The course includes many topics covered in a traditional precalculus course and in many ways resembles what other colleges often refer to as a math for liberal arts course. Each biological “application” is designed to be investigated in two class periods along with some out-of-class reading. Within each application, students have the opportunity to see the mathematics they have learned in action.

In this article we describe a module that was not only well-received by our students, but, in our opinion, helped our students make connections between science and mathematics while enhancing and reviewing the mathematical skills they had developed during the semester. This module investigates an application of Leslie matrices to address age-structured population problems. The module includes a group activity that gives students a feel for how the Leslie model might be applied in the “real” world.

Keywords:

• Leslie matrix
• modeling
• problem solving
• difference equations
• population dynamics
• biology
• precalculus