In the field of applied sciences, a mathematical model is a type of scientific model that employs a mathematical formulisme to express relationships, predictions, variables, parameters, entities and relationships between variables and/or entities or operations.
These models are used to analyse the behaviour of complex systems in difficult to observe in real life situations.
Concerning the actual mathematics, a mathematical model is a set on which have been defined relations unary, binary and ternary, and which allows to satisfy the proposals derived from the whole of the axioms of the theory. The model theory is the branch of mathematics that focuses on the systematic study of the properties of models.
Models of the physical sciences are a translation of physical reality to apply the tools and techniques of mathematical theories in the study of the behavior of complex systems. Conversely, it is possible to transpose the numerical results in physical reality.
Mathematical models can be either deterministic (there no doubt in relation to the form of the result and the data used are quite well known and determined) be stochastic (these are probabilistic models, given that one knows not the result expected but rather its likelihood).
For what it is the function of the origin of the information used, mathematical models can be either heuristics (based on the explanations about the causes or the natural mechanisms that are at the origin of the phenomenon being studied) or empirical (based on direct observations or the results of the experiments to the phenomenon being studied).