A mathematical model is a description of a system using mathematical concepts and language. The process of building a mathematical model is termed mathematical modeling. Mathematical models are used in the natural sciences (such as physics, biology, earth science, meteorology) and engineering disciplines (e.g. computer science, artificial intelligence). They are also used in the social sciences (such as economics, psychology, sociology and political science). Physicists, engineers, statisticians, operations research analysts and economists use mathematical models a lot.
Mathematical models can take many forms. The types of models include:
- dynamical systems - for systems that change,
- statistical models - for finding patterns in large groups of measurements or data,
- differential equations - to study how variables change over time, or
- game theoretic models - for studying how many independent decision makers can interact.
These and other types of models can overlap, with a given model involving a variety of abstract structures. Mathematical models can include logical models. In many cases, the quality of a scientific field depends on how well the mathematical models built on theory agree with results of repeatable experiments. When theoretical mathematical models do not match experimental measurements, scientists try to correct the model. Such corrections lead the way to better theories to explain the facts.
- Bender, E.A. [ 1978 ] ( 2000 ). An Introduction to Mathematical Modeling, New York : Dover. ISBN 0-486-41180-X
- Gershenfeld, N., The Nature of Mathematical Modeling, Cambridge University Press, (1998). ISBN 0521570956
- Yang, X.-S., Mathematical Modelling for Earth Sciences, Dudedin Academic, (2008). ISBN 1903765927
- Specific applications
- Peierls, Rudolf. Model-making in physics, Contemporary Physics, Volume 21 (1), January 1980, 3-17
- Korotayev A., Malkov A., Khaltourina D. ( 2006 ). Introduction to Social Macrodynamics: Compact Macromodels of the World System Growth. Moscow : Editorial URSS. ISBN 5-484-00414-4
- General reference material
- McLaughlin, Michael P. ( 1999 ) 'A Tutorial on Mathematical Modeling' PDF (264 KiB)
- Plus teacher and student package: Mathematical Modelling. Brings together all articles on mathematical modeling from Plus, the online mathematics magazine produced by the Millennium Mathematics Project at the University of Cambridge.
- Philosophical background
- Frigg, R. and S. Hartmann, Models in Science, in: The Stanford Encyclopedia of Philosophy, (Spring 2006 Edition)
- Griffiths, E. C. (2010) What is a model? Archived 2012-03-12 at the Wayback Machine