MATHEMATICAL MODELING: MAIN STAGES AND CLASSIFICATION OF MODELS

Abstract

The modern world needs educated people with a high level of mathematical competence and culture. A special role in this is undoubtedly played by various models, which provide an opportunity not only to investigate and understand this or that phenomenon, but also to develop the ability to analyze, create new things, think abstractly, which is a necessary basis for the further formation and development of a person as an individual. Since models are used in different areas of human activity and for different purposes, there are several bases for classifying models.

The most important type of symbolic models are mathematical models. A mathematical model is an abstraction of real processes in mechanical engineering, in which relationships between real elements, namely those of interest to the researcher, are replaced by relationships between mathematical categories. These relations are usually presented in the form of equations or inequalities, relations of formal logic between indicators (variables) that characterize the functioning of the real system being modeled. A mathematical model is considered in the scientific space as an approximate description of an arbitrary class of phenomena of the external world, presented using mathematical symbols. Mathematical modeling acts as a method of learning about the external world, as well as forecasting and management. Analysis of mathematical models allows to penetrate into the essence of the studied phenomena. As you know, mathematics as a subject and as a science makes almost the greatest contribution to the development of abstract human thinking, and the mathematical model acts as a bridge between the theoretical, abstract language of science and the real phenomenon of the surrounding world

In his activity, a person often has to deal with modeling, and especially with mathematical modeling: compiling equations, systems of equations, inequalities, recording functions, etc. This article examines the concept of model, mathematical modeling and presents the main stages and classification of models.

Keywords: model, mathematical modeling, classification of models, mathematical competence.