Irina Sitnikova

The article examines the existing in academic literature approaches to the definition of "geometric vector" concept. The authors offer, reasonable from the viewpoint of physical-technical disciplines, definition of "vector value". they investigate specifics of the operations on vectors defined in physical space. The differentiation of vector values adopted in physical and technical applications is discussed.

The article explores the possibilities of continuity principle implementing in the framework of "school - university" in the construction of mathematical problems system. As an example, a set of tasks is proposed for studying the concept of "polygonal function" in the topic "Operational calculus". It is shown that the application of the continuity principle helps to develop skills necessary for this concept learning.

The paper is devoted to possibilities of comparison and analogy in the study of some branches of mathematical analysis at university. The authors examine the application of scientific methods in the study of the section "Functions of several variables". It is shown how analogy can help in understanding of basic concepts and theorems of this section.

The paper is devoted to the principle of applied-ness in the study of mathematics on economic specialties in higher educational institutions. To this end, it is revealed what is meant by a focus on practical application of teaching mathematics. On the example of studying some crystals of linear algebra shows how this principle can be implemented on lectures and seminars.

The paper is devoted to teaching the application of concepts at practical lessons of mathematics at higher educational institutions. The author points out the actions, implementation of which involves the mastery of the concept. On the example of one of the themes of linear algebra and analytical geometry the author shows how you can teach students to implement specified actions when solving mathematical problems.