A mathematical model is a representation of some system (maybe biology, chemistry, physics, engineering, economics, ...) in mathematical terms. Mathematical operations are used to define the quantitative relationships between various items or groups of items in the system (maybe time in minutes, maybe dollars,...). These items or groups of items are the independent and dependent variables, and the numbers that relate them are parameters.

It is important to understand the purpose of models. In particular, in these modules, models are not intended to be a complete, accurate representation of the system. (It was once said that having a complete, accurate model would be like having a map of a city that was as big as the city. It would be accurate, but not very useful.) Simplifications have been carefully chosen to de-emphasize parts of the system that are not being examined, and to emphasize parts of the system that we would like to know more about. Models are often used in this way, and so different models of the same system will look different, depending upon their purpose. Since the purpose of these models is educational, the simplifications are chosen to produce mathematically intuitive models that may no longer retain a great deal of their detailed predictive nature.