**Methods of Mathematical statistics in scientific research **

**Purpose:** to represent masters theoretical fundamentals and modern mathematical models of probability theory and mathematical statistics for solving certain types of tasks; statistical processing of experimental data, including in psychological and pedagogical studies, providing the necessary level of theoretical training of the future teacher-researcher, education of mathematical and research culture.

**Content of the discipline:**

Empirical and theoretical probability distributions.

Checking statistical hypotheses based on nonparametric criteria.

Checking statistical hypotheses based on parametric criteria.

Methods of dispersion analysis.

Methods of correlation and regression analysis

**Results of the discipline training:** knowledge and understanding of basic concepts, ideas and methods of probability theory and mathematical statistics. Ability to apply the ideas, methods, terminology and symbols of this section of Mathematics for the statistical processing of the results of experimental research, measurement of magnitude, psychological and pedagogical research and interpretation of the solution in the source contexts of problems.

**Methodology of teaching Mathematics in a profile school**

**Purpose**. The study of discipline is intended to provide methodological training for the teacher of Mathematics, to form the professional competence of the graduate, which combines mathematical knowledge of the future teacher, his psychological and pedagogical and methodological training, personal qualities, and forms the ability to organize the educational process at the level of modern requirements.

**Content of discipline training**

Methodology of teaching Mathematics on different educational profiles and levels of mathematical preparation of senior students. Method of study of trigonometric functions. Methodology for studying power, index, logarithmic functions. Method of study of trigonometric equations. Study of trigonometric, index, logarithmic expressions and their identical transformations in the school course of algebra and the principles of analysis. Equality and inequality in the senior profile school and the method of their study. Method of carrying out the first lessons of stereometry. Geometrical construction of cross sections of geometric shapes. Coordinates and vectors in space and the method of their study. Geometric quantities and methods of their study at the school. Methodology of studying the topics "Direct and planes in space", "Polyhedra", "Body of rotation", "Volumes of bodies", "Combinations of spatial bodies".

**Results of the discipline training.**

Knowledge and understanding of basic concepts, ideas and methods of teaching Mathematics in the senior profile school, the ability to plan the work of a Mathematics teacher, compile a plan and a plan of the lesson of mathematics; to supervise and evaluate pupils' knowledge, skills and abilities; organize and conduct extra-curricular work on the subject; to carry out logico-didactic analysis of the notions, concepts, theorems and their proofs, rules and algorithms; to get a system of tasks for the assimilation of mathematical concepts and their properties.

**History of ****M****athematics and Teaching Mathematics**

**Purpose****: **study of discipline is intended to develop the mathematical outlook of graduate students, form the professional competence of the Mathematics teacher, which combines knowledge of the Mathematics history, methodological and methodical training, form the ability to perform a comprehensive analysis of scientific-pedagogical and methodological experience in mathematical education.

**Content of the discipline: **

Formation of Mathematics as a science. Subject of the Mathematics history. The main stages of the mathematics development. Development history of mathematical analysis, algebra and geometry. Leading mathematical schools. History of domestic mathematics.

History development of the Mathematics teaching methodology. Research of domestic scientists on the methodology of teaching mathematics.

**Results of the discipline training****: **knowledge and understanding of the basic periods of mathematical development, regularities of the interaction of mathematics with other sciences. Knowledge and understanding history development of mathematics teaching methodology. Ability to analyze the main events of the mathematics history, reproduce the chronology of the main events of the mathematics history, be able to use the technology of applying elements of the mathematics history in the educational process.