On the modern problems of teaching mathematical disciplines in an engineering university

The obvious need to transform the pedagogical technologies of university mathematics is in agreement with the introduction of STEM concept in engineering education. All the increasingly complex global processes, including production, require, on the one hand, strengthening the fundamental nature of the graduate training in engineering and economic areas, and, on the other hand, to ensure the practical orientation of this training. The solution to this fundamental problem can only lie in the plane of introducing innovative technologies for mathematical training, reforming both its content and teaching methods themselves, including the development of methodological materials using the capabilities of the electronic educational environment. The author analyzes these and other problems using a large number of domestic and foreign sources, including materials from specialized conferences "Modern Education: Content, Technology and Quality". In the context of the coronavirus pandemic, it was possible to develop, test and implement mass distance learning technologies, as well as evaluate both the effectiveness of new educational mechanisms and their impact on students' health. An important task of the entire higher school is to preserve and improve the quality of mathematical training drawing on new electronic educational resources. The positive side of innovative technologies is the possibility of excluding routine mathematical procedures, presenting vivid visualization examples giving students a deeper understanding of the processes and phenomena of the world. The reverse side of e-learning is the growing possibility of academic dishonesty, increased lack of independence in completing test papers and examination tasks. Examples of mechanisms to compensate for the negative consequences of the distance technology introduction, both organizational and didactic, are also provided.