Natalya Byshmeleva

The urgency of the presented research is conditioned by the need to ensure the fundamental character of education in a university and to eliminate contradictions in the system of professional training of specialists in applied mathematics, fundamental computer science and programming. The main idea here is full use of interdisciplinary integration potential, implemented with the introduction of modern information technologies into learning process. It is shown, that in the solution of the formulated problem, a significant role is played by training courses, their subject of study are mathematical models based on interdisciplinary integration. An example of such integrated disciplines is a course devoted to the fractal sets elements theory. At the same time, an optimal combination in the content of teaching theory, abstraction and realization is proposed. Thus, the aim of the study is to construct a methodological system for teaching the fractal sets elements theory as a component of future specialists in the field of applied mathematics, fundamental computer science and programming fundamental training system. As a result of the experimental research having been carried out since 2010 and the experimental teaching of the course " Fractal sets elements theory ", various methodological approaches to the study of the proposed course contents by students of various specialties have been formed. All developed approaches contribute to the development of students’ research competencies through an appropriately constructed system of tasks that helps students to acquire a system of thinking, the ability to structure and analyze information, draw conclusions, reason, and think creatively. In the process of teaching fractal geometry, the motivational, cognitive, developing, controlling, control-evaluation and other functions of the learning process are performed, interdisciplinary skills are established and developed. Students master mathematical methods of research, comprehend methodology of mathematical models, understand the interrelationships of scientific methods, approaches and techniques developed in different fields of knowledge, and that contributes to the development of their scientific world outlook.

The paper presents the model of analytical competence of university students while teaching special mathematical disciplines with the use of information and communication environment based on the integration of mathematical, information and pedagogical knowledge. The authors describe the conditions of efficient formation of students’ analytical competence, providing them the opportunity to work and continue professional education.

The article is devoted to the educational process of association with the research and innovation activities in higher education. It offered some general ideas and solutions of the problem, the result of the implementation of which will be the rapid adaptation of the existing system of training in high school, a well-developed, but conservative to modern requirements and increase the efficiency of the educational process as a whole.

The article focuses on the integration of disciplines in the practice of university teaching. Its aim is to demonstrate the possibilities of the use of various information technologies in the study of the classical discipline