Abstract
The article investigates innovative aspects of building components of the methodological system of teaching disciplines "Linear Algebra" and "Probability Theory with elements of mathematical statistics", which are provided by the educational-professional program "Secondary Education (Mathematics)" of the first level of higher education in 014 Secondary Education (Mathematics). The article contains methodological and procedural aspects of organizing calculations of orthogonal projection and orthogonal component of a vector with respect to a subspace given by a system of linear algebraic equations, as well as the application of the least squares method for processing experimental data. Theoretical and practical information of the relevant sections of these disciplines is briefly presented. A brief review of educational, methodological and scientific literature used in teaching linear algebra and probability theory with elements of mathematical statistics is carried out; the expediency of using innovative components of the corresponding methodological training systems has been substantiated. The authors proposed the use of these innovative components in the assimilation of the content of disciplines and the development of test items of different levels of complexity in linear algebra and probability theory with elements of mathematical statistics in order to objectively assess the knowledge of students. The article provides an overview of innovative aspects of learning linear algebra and probability theory with elements of mathematical statistics, as well as an analysis of the implementation of innovative components of methodological systems in the software mathematical environment Mathcad. Methodical and practical materials presented in the article can be useful for students to organize and intensify independent scientific and pedagogical activities, teachers of secondary schools, leaders of elective and group work of students, teachers of linear algebra and probability theory with elements of mathematical statistics of pedagogical higher education institutions. Key words: innovations in education, linear algebra, probability theory, mathematical statistics, Euclidean space, orthogonal projection, orthogonal component, statistical sample.
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