Concept
Mathematical model
Overview
A mathematical model is an abstract description of a concrete system using mathematical concepts and language. The process of developing a mathematical model is termed mathematical modeling. Mathematical models are used in many fields, including applied mathematics, natural sciences, social sciences and engineering. In particular, the field of operations research studies the use of mathematical modelling and related tools to solve problems in business or military operations. A model may help to characterize a system by studying the effects of different components, which may be used to make predictions about behavior or solve specific problems.
Overview adapted from Wikipedia (CC BY-SA 4.0; see the article history for authors).
Possible passages
Found by search and not yet checked by a person; they may only mention the idea in passing.
There are nevertheless, in mathematics, some examples of so-called Induction, in which the conclusion does bear the appearance of a generalization grounded on some of the particular cases included in it. A mathematician, when he has calculated a sufficient number of the terms of an algebraical or arithmetical series to have ascertained what is called the _law_ of the series, does not hesitate to fill up any number…
John Stuart Mill, A System of Logic
States what Mathematical model is.
The nature of abstract mathematics (the general division of which will be examined in the following chapter) is clearly and exactly determined. It is composed of what is called the _Calculus_,[2] taking this word in its greatest extent, which reaches from the most simple numerical operations to the most sublime combinations of transcendental analysis. The _Calculus_ has the solution of all questions relating to…
Auguste Comte, The philosophy of mathematics
States what Mathematical model is.
When we think of mathematics, we have in our mind a science devoted to the exploration of number, quantity, geometry, and in modern times also including investigation into yet more abstract concepts of order, and into analogous types of purely logical relations. The point of mathematics is that in it we have always got rid of the particular instance, and even of any particular sorts of entities.
Alfred North Whitehead, Science and the modern world
Close in meaning to Mathematical model; the term itself is not named.
Related ideas
- Game theory
- General relativity
- Differential equation
- Integer
- Isaac Newton
- Intuition
- Function (mathematics)
- Mathematics
- Geometry
- Classical mechanics
- Mechanics
- Maxwell's equations
- Probability
- Physics
- Applied mathematics
- Parameter
- Paradigm shift
- Quantum mechanics
- Thomas Kuhn
- Set (mathematics)
- Social science
- Special relativity
- Experience
- Theory of relativity
Place in the tradition
Part of Ecological economics.