Definition:Mathematical Model

Definition

A mathematical model is an equation, or a system of equations, whose purpose is to provide an approximation to the behavior of a real-world phenomenon.

Constant

Let $P$ be a stochastic process which is being modelled by means of a model $M$.

A constant of $M$ is a number which implements some aspect of $P$ which is not changed during the evolution of $P$.

Parameter

Let $P$ be a stochastic process which is being modelled by means of a model $M$.

A parameter of $M$ is a number which implements some aspect of $P$ which is designed so as to be able to be modified during the evolution of $P$ as a result of analysis of the behaviour of $P$ over time.

Also see

• Principle of Parsimony

• Results about mathematical models can be found here.

Sources

• 1965: A.M. Arthurs: Probability Theory ... (previous) ... (next): Chapter $2$: Probability and Discrete Sample Spaces: $2.1$ Introduction
• 1966: Isaac Asimov: Understanding Physics ... (previous) ... (next): $\text {I}$: Motion, Sound and Heat: Chapter $2$: Falling Bodies: Inclined Planes
• 1976: K. Weltner and W.J. Weber: Mathematics for Engineers and Scientists ... (previous) ... (next): $1$. Functions: $1.1$ The Mathematical Concept of Functions: $1.1.1$ Introduction
• 1977: Gary Chartrand: Introductory Graph Theory ... (previous) ... (next): Chapter $1$: Mathematical Models: $\S 1.2$: Mathematical Models
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): model: 3.
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): model: 3.

• 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): mathematical model
• 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): model