**Mathematical modeling** is the process of creation of mathematic models on practice. A mathematical model is a system of mathematical relationships, which describe the process under research or the event. Mathematical modeling is applied in such science as economics, ecology, sociology, physics, chemistry, mechanics, information technologies, biology, etc. So, it is natural that every science which uses the definite numbers and statistical methods of the research has to rely on the mathematical models which help them organize the results of the analysis wisely and logically. In order to receive the mathematical model one applies the laws of ecology, special laws of exact sciences, the results of active and passive experiments, the imitative modeling with the help of the computing machines. The models help experts with the predictions about the development of the process, calculate the function, control the process, project systems with the required characteristics.

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In order to create a mathematical model one can rely on any mathematical tool, such as probability theory, mathematical logic, abstract algebra, set theory, etc. Mathematical modeling is the most popular method of research in cybernetics. The process of modelling is very important in many sciences, because it helps experts organize the process of the research in the right way and make adequate predictions of the results which can be achieved during this process. There are complicated mathematical models which are applied in cybernetics and programming and they are characterized with the fact that one complex model consists of several smaller ones which combine their own functions and data for the single more complicated aim.

Mathematical modeling is a complicated process which provides experts which the detailed and logical models of various processes and events connected with different sciences. The student, who has decided to pay attention to the topic on mathematical modeling and prepare a project on it, should think about the selection of the most thought-provoking aspects and points of the issue in order to make the proposal informative and interesting for the professor. The young person has the chance to reveal the problem from all sides and demonstrate the list of the methods for the investigation and share the predictions concerning the research on mathematical modeling and its relevance in modern sciences.

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