Olga Vergazova

Curricular and extracurricular work in mathematics should be aimed at fostering students ' interest in the subject, which obviously improves the level of mathematical training. One of the areas for such works are the consideration of intersubject relations of mathematics and other Sciences. Typically, students demonstrate the interdisciplinary connections of mathematics and physics, mathematics and chemistry, there is shown the relationship of school science subjects. Different kinds of symmetry in the plane and in the space of a school course of geometry always arouse interest in students. The theme of "Symmetry" is one of the most grateful terms of aesthetic education of students in learning mathematics. But, apart from these traditional issues, the example of symmetry is non-mathematical and numeric palindromes can be traced interdisciplinary connections between mathematics and literature, mathematics and history, mathematics and foreign language. Interdisciplinary connections that are set in school lessons and in the process of extracurricular activities, contribute to the formation and development of the integral worldview that is the most important task of the educational process at any level. The content of the article is of interest to teachers and high school students, and anyone interested in mathematics.

In order to increase the level of mathematical preparation of future students of mathematical and technical specialties required at school geometry lessons, and in the process of preparation for the Unified State Examination in mathematics (advanced level) pay special attention to the math questions without a solid knowledge of which are essential for successful learning in higher education. In this article, on the example problems on solid geometry, proposed as a task of high level on the math exam profile level, demonstrates one of the possibilities of differentiated approach in the training of future first-year students in mathematical or technical Universities, who will develop a course of higher mathematics, particularly analytical geometry. On the example of solving of some problems of solid geometry demonstrates the advantages of using the coordinate-vector method. The content of the article is of interest to professors, teachers, high school students preparing for entrance to Universities to study technical or mathematical areas.

The problem of raising the level of mathematical preparation of students of mathematical and technical specialties should be addressed to both the course of school level algebra and analysis, and the preparation to the Unified State Examination in mathematics (profile level). The example of the application of the functional-graphical method for solving trigonometric equations and inequalities in problems of high level on the use math level profile, demonstrates one of the possibilities of differentiated approach in training future first-year student of technical or mathematical University. For example, the decision of tasks demonstrates the advantages of using functional-graphical method for solving trigonometric equations and inequalities in the formation and development of skills of analysis and graphing of elementary functions. The paper is of interest to academicians, high school teachers and students wishing to enter technical or mathematical university.

The decision of modern problems of mathematical training of future engineers, of course, involves improving the efficiency of teaching mathematics. The actual solution of such problems is the changing nature of the controlled independent work of students related to the use of electronic resources. Application in learning mathematics of Junior students of remote consultations expands educational opportunities, both teachers and students. Special quality remote consultations, complementing face-to-face counselling in the framework of the controlled independent work of students related to efficiency, cost savings (optimization) time as a student and a teacher, enhance the level of student performance and the quality of the acquired knowledge, acquired skills and abilities. The article discusses the goals, challenges, opportunities, teaching characteristics and organization of various remote consultation for mathematics of Junior students of technical and mathematical disciplines.