Principles of relationship of theoretical knowledge and practical skills, received by students in technical higher education institutions in the process of studying mathematics

This article is devoted to solving the problem of interaction of theoretical knowledge obtained and solving technical problems when students receive higher education within the framework of studying the discipline of higher mathematics. Teaching higher mathematics should give students not only a theoretical foundation, but it is also important to focus on the acquisition of practical skills necessary in the future professional activity of a future specialist. We propose to consider the connection of theoretical knowledge and practical skills of future specialists not as a transition from assimilation of information to application in practice, but as integration through the categories of unity, integrity of the system. In addition, students develop at a higher level the skills to systematize knowledge, establish a link between new and previously acquired knowledge. At the same time, it is often necessary to establish more precisely the boundaries in which it is possible to apply certain mathematical methods. As experience shows, an effective method of interrelation of theory and practice was the introduction of professionally-oriented tasks into the teaching process of the discipline of mathematics. The authors of the article propose to consider professionally-directed tasks in practical classes in higher mathematics.As an example, the tasks for the specialties 23.05.03"Rolling stock of railways" and 23.05.04 "Operation of railways" are given.