Models

A model is a representation of some aspect of reality that is created for a specific purpose, and if the representation involved mathematics, it is referred to as a mathematical model. Usually, the model is a representation of a very complex real-life situation that is highly simplified to promote understanding, and there is no single "correct" model for any situation. For example, maps and plans are models, which show a representation of reality that includes only the features relevant to the purpose of the map. By including different details, maps are produced for different purposes. Models do not have to be absolutely correct; they only have to work well enough to be truly useful. For example, linear functions are often used in modelling over short ranges where linear approximation to the true state of affairs is reasonable, because they are mathematically simpler than most other functions. One description of the main stages of the process of mathematical modelling is the following: Specify the purpose (e.g. to make predictions, improve understanding) Create a model (e.g. identify relevant variables, specify assumptions, write the mathematical function) Do the mathematics Interpret the results Evaluate the model (e.g. revise assumptions and adjust the model)