  a mathematical model is a description of a system using mathematical concepts and language. the process of developing a mathematical model is termed mathematical modeling. mathematical models are used not only in the natural sciences (such as physics, biology, earth science, meteorology) and engineering disciplines (e.g. computer science, artificial intelligence), but also in the social sciences (such as economics, psychology, sociology and political science); physicists, engineers, statisticians, operations research analysts and economists use mathematical models most extensively. a model may help to explain a system and to study the effects of different components, and to make predictions about behaviour. mathematical models can take many forms, including but not limited to dynamical systems, statistical models, differential equations, or game theoretic models. these and other types of models can overlap, with a given model involving a variety of abstract structures. in general, mathematical models may include logical models, as far as logic is taken as a part of mathematics. in many cases, the quality of a scientific field depends on how well the mathematical models developed on the theoretical side agree with results of repeatable experiments. lack of agreement between theoretical mathematical models and experimental measurements often leads to important advances as better theories are developed. == model classifications in mathematics == mathematical models are usually composed of relationships and variables. relationships can be described by operators, such as algebraic operators, functions, differential operators, etc. variables are abstractions of system parameters of interest, that can be quantified. operators can act with or without variables.http://www.macs.hw.ac.uk/~pjbk/pathways/cpp1/node160.html models can be classified in the following ways: *linear vs. nonlinear: if all the operators in a mathematical model exhibit linearity, the resulting mathematical model is defined as linear. a model is considered to be nonlinear otherwise. the definition of linearity and nonlinearity is dependent on context, and linear models may have nonlinear expressions in them. for example, in a statistical linear model, it is assumed that a relationship is linear in the parameters, but it may be nonlinear in the predictor variables. similarly, a differential equation is said to 
Applied_mathematics Collective_intelligence Conceptual_models Knowledge_representation Mathematical_modeling Mathematical_terminology