Formation and development of differential geometry as an academic subject in Russia

Differential geometry as a scientific discipline is a branch of mathematics in which the properties of curves, surfaces and other geometric manifolds are studied by mathematical analysis methods. From the perspective of an academic discipline, it can be interpreted as a pedagogically adapted system of knowledge, skills, competencies and work experience, expressing the main content of the relevant section of mathematics, which has interdisciplinary content, in which mathematical analysis, geometry and algebra are integrated. A multidimensional study of the process of formation and development of differential geometry as an academic subject in Russian higher education allowed us to identify the main trends of this process and determined its division into five periods:
- The first period (the 30s - the end of the 70s of the XVIII century) is the stage preceding the formation of the course of differential geometry in Russian universities.
- The second period (the 80s of the XVIII century – the first third of the XIX century) – the stage of penetration of individual differential geometric information into higher mathematics courses.
- The third period (the 30s – the end of the 40s of the XIX century) is a stage of stabilization of the content of information on differential geometry reported in the course of mathematical analysis.
- The fourth period (the second half of the XIX century) is the stage of the allocation of differential geometry as an independent educational course.
- The fifth period (the end of the XIX century – XX century) is the stage of introducing the course of differential geometry into all curricula of physics and mathematics faculties and its improvement taking into account the achievements of science, as well as the profile of the relevant university.
The talk will describe in detail each of these periods, as well as the activities of those mathematicians who played a key role in the formation and development of differential geometry as an educational subject in Russia.
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