МЕТОДИЧНІ РЕКОМЕНДАЦІЇ ДО НАВЧАННЯ МАТЕМАТИЧНОМУ МОДЕЛЮВАННЮ МАЙБУТНІХ ІНЖЕНЕРІВ ПІД ЧАС АУДИТОРНИХ ЗАНЯТЬ З ТЕОРІЇ ВИПАДКОВИХ ПРОЦЕСІВ

The importance of formation of the mathematical modeling ability during the study of the theory of probability and stochastic processes by future engineers is substantiated. The notion of mathematical modeling when teaching the students of technical universities to the mathematical disciplines is examined. The paper reveals the difficulties met by students during the construction of models to the problems. The author notes that the universal formalization algorithm of real problems does not exist; therefore the most difficult for students are the first and the second stages of simulation when solving professionally oriented tasks. In order to solve a problem the techniques of heuristic activity are proposed to take advantage in the first stage of modeling. The study displays one of the ways of teaching students to the «art of modeling», namely the implementation of its development as the ability of students to «see different in the same and the same in differences». This article contains an example of building a model to a professionally oriented task during a lecture. It is shown how a teacher in the course of constructing a model can engage students into interactive debate. For this purpose the teacher’s notation on the blackboard should be accompanied by an appropriate dialogue with students. Methodological recommendations for the direction of educational and cognitive activities of students during the construction of models reflecting Markov random process of discrete state and continuous time are suggested. It is shown why such learning activities, which are to build and study models of stochastic process, contribute to the conscious assimilation of the topic by the students, as well as to the building of their understanding of the unity of some sections of higher mathematics, stochastic processes and connection with real engineering studies. The author emphasizes that the work with a mathematical model of a real engineering process enhances motivation to learn the discipline, so that the students actively master the skills necessary for their future careers. The issue of mathematical modeling training and research of other stochastic processes may become the subject of further survey in this area.