OVERVIEW

Elementary Mathematical Models (EMM) is a hybrid between traditional college algebra or precalculus and courses which focus on liberal arts instructional goals in mathematics. The core of the EMM course is a sequence of progressively more complicated growth models: arithmetic growth, quadratic growth, geometric growth, mixed models, and logistic growth. The first three of these give rise to important families of elementary functions: linear, quadratic, exponential, and logarithmic. In studying this collection of models, students are introduced in a natural and motivated way to many of the traditional topics of college algebra or precalculus. In particular, they work with the important properties and characteristics of the (non-trigonometric) elementary functions of real analysis. At the same time, there is constant consideration of how mathematical models are built and used, and in particular, of the methods associated with discrete difference equation models. The climax of the course is a discussio of the emergence of chaos in discrete logistic growth models. While the range of quantitative and conceptual ideas is ambitious, the expectations of students are realistic and feasible. Even students with weak traditional algebraic skills are generally successful in my classes. The EMM book, published by the MAA, was developed to go with the course.