О НЕКОТОРЫХ БАЗОВЫХ АКЦЕНТАХ ИЗУЧЕНИЯ КУРСА «МАТЕМАТИЧЕСКИЙ АНАЛИЗ» В ВУЗАХ

Abstract

The article explores the problem of improving the quality of mathematical education at universities. Recent frequent transitions to various Federal State Educational Standards, the shift of the learning vector towards obtaining new scientific knowledge, and recently possible long-term distance learning, suggest that a modern bachelor has such qualities as the ability to work effectively and cope with a large flow of information. Unfortunately, not all students due to various reasons are ready to meet new requirements (especially freshmen, since at the present stage the thinking operations that underlie the organization of educational actions cease to develop effectively already at school: school education has other priorities). Almost all mathematical disciplines are connected by basic concepts (vector, matrix, determinant, limit, derivative, integral, continuity, etc.), therefore, the main task at the first stage of teaching mathematics at a university, in our opinion, is to “cement” basic concepts with their transformation in subsequent courses into the foundation of studying other disciplines. The motivational component of this process, as shown by many years of experience, is the initial keen interest in the subject of study, which arises when solving simple, unusual and interesting problems (examples of such problems are given in the article). While studying “Mathematical Analysis”, it is proposed to place in-depth emphasis on its basic concepts, such as the limit of sequence, integral, etc. The set of notions is justified both from the point of view of the content of sections of mathematical analysis, and from the point of view of interdisciplinary connections of mathematical disciplines studied later. These are the cornerstones of all mathematics. Without exaggeration, it can be stated that the degree of understanding by students of such mathematical phenomena depends on the result of the subsequent work of teachers, and, therefore, the totality of knowledge and scientific knowledge of future graduates, the high potential of which will allow them to successfully realize themselves in professional occupation.