Modeling is a Two-Way Street

Mathematics is a powerful tool for helping us to understand the world. In the following discussion, we will investigate two methods of using mathematical models. We will see that the two methods are really the same method, but applied in different directions.

The first method we will explore is predictive. The idea is that there is some real situation we think we understand. We convert our understanding into some assumptions then use those assumptions to develop a mathematical model of the situation. We use this model to make predictions about the situation.