Mathematical model

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.
Types of mathematical models
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.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.

 More reading 
Books
 Bender, E.A. [ 1978 ] ( 2000 ). An Introduction to Mathematical Modeling, New York : Dover. 
 Gershenfeld, N., The Nature of Mathematical Modeling, Cambridge University Press, (1998). 
 Yang, X.-S., Mathematical Modelling for Earth Sciences, Dudedin Academic, (2008). 

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. 

 Other websites 
General reference material
 McLaughlin, Michael P. ( 1999 )
 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? 

 References 

Category:Mathematics