Mathematical modeling
A model car is a representation of a real car. A mathematical model of a problem is a mathematical problem that represents the original problem.
Like the original problem, the mathematical model includes a situation and a question about that situation. The situation in the mathematical model may be described by a mathematical object such as a graph, a formula, a matrix, or an equation. The question of the original problem is modeled by a question about the mathematical object. For example, a question might be
Like a toy car, a good mathematical model captures the critical features of the original—the features most important to a solution--and omits less important aspects. The mathematical question represents the critical question about the original situation, again stripping away the unessential details.
The process of mathematical modeling can be summarized by this diagram:
To set up the mathematical model, you need to make assumptions about which features are important and which can be ignored. Sometimes you need to make assumptions without knowing for sure how accurate they are. After you solve the mathematical problem and translate that solution into a solution of the original problem, you may have to adjust your assumptions to lead to a more helpful solution.
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