Integration of Teaching Higher Mathematics, Digital Technologies and Programming with Modeling Fractal Settings

The relevance of the presented study is due to the need to ensure the fundamental nature of education in the system of professional training of students of mathematical faculties in the field of higher mathematics, digital technologies and programming. The article discusses the features of studying the course "Geometric fractals", which is a subject that integrates knowledge in higher mathematics and digital technologies. A description of technologies for using affine and projective geometric transformations in the construction of fractals and their implementation in Maple is proposed. The laws of constructing L-systems for fractal curves on a plane using turtle graphics in Python are considered. This study is aimed at organizing the interaction of a teacher with students, where teaching aids play an important role, allowing: to increase the amount of necessary educational information; improve understanding of the studied material; to systematize knowledge in subjects; develop the research abilities of students; create individual trajectories for studying a subject; increase the use of digital technologies in teaching the discipline "Geometric fractals". To prove the effectiveness of modern approaches in the proposed methodology, a set of tasks was tested that contributes to the implementation of interdisciplinary connections and the formation of students' sustainable interest in the study of higher mathematics, digital technologies and programming.