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| 1 | The university mathematics course occupies an important place in the basic training of engineers for various fields of modern production. Mathematical training of students of technical specialties is conducted during the first four semesters. Students study such sections as linear and vector algebra, analytical geometry, mathematical analysis, differential equations, probability theory and mathematical statistics. Currently, there is a large bank of various didactic tasks for the successful formation of mathematical knowledge and skills in all sections of the university mathematics course. Federal educational standards establish a certain set of universal and general professional competencies that students need to develop over the entire period of study at the university. In the normative documentation, competencies are considered as abilities that reflect the content of the elements of professional activity. Within the framework of teaching a discipline, it is possible to form some individual competencies. The use of conventional learning tasks and exercises does not always allow you to create conditions for the development of specified competencies. The inclusion of students in active educational activities aimed at developing competencies can be ensured by the use of complex tasks. In the context of digitalization, the importance of using information technology in solving various tasks is increasing. A complex computer-mathematical task is considered by the authors as a set of educational tasks, the solution of which requires the use of mathematical modeling and computer programming. It includes two parts – analytical and mathematical and software and computing. A complex computer-mathematical task can be educational or informative. The content of the training task involves solving a standard mathematical problem by analytical methods, constructing an algorithm of operations performed, writing a calculation program, and testing it. The content of the cognitive task includes conducting a computational experiment using a computational program. Educational complex computer and mathematical tasks are used to form educational skills, and cognitive tasks are used to form research skills. The paper presents a description of the content of educational and educational complex computer and mathematical tasks in certain sections of the university mathematics course for students studying technical specialties at a transport university. Keywords: competencies, a systematic approach, conceptual connections, complex tasks, information technology | 473 | ||||