**Probability theory and Mathematical statistics **

**Purpose**: to introduce students with the basic concepts, theoretical positions 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, education of mathematical culture, promotion of the development of logical and analytical thinking of students.

**Content of the discipline:**

Random events. Statistical probabilities, their properties and distributions

Statistical probabilities. Axiomatic construction of probability theory

Random sizes and distribution of their probabilities. Random vectors

The law of large numbers.

Elements of mathematical statistics

**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, interpretation of the solution in the source contexts of problems.

**Intel Learning Training for the Future **

**Purpose**: to develop the skills of the effective use of information and communication technologies for students in the study of various educational subjects with the help of innovative pedagogical technologies that provide independent (individual or group) research activity of students. The results of each student's study program are to develop and protect their own Portfolio of a training project in front of their colleagues, which meets the special requirements for its content for subsequent use in the educational process of general education institutions.

**Objective**: to teach effectively to use computer technologies while studying educational subjects of general educational institutions; to form skills to plan and carry out project activity in conditions of modeling of educational environment, to improve skills of independent research activity during solving of practically directed tasks; to expand the limits of subject competence and creative activity; to improve Mathematical competence and competence in mathematics teaching methodology.

** Methodology of Teaching Mathematics**

**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.**

GENERAL METHODOLOGY.

Goals and objectives of general education and the goals of teaching Mathematics in a general education school. Problems of differentiation of training. The content and role of general mental actions and methods of mental activity. Method of formation of mathematical concepts in the school course of Mathematics. Methodology of teaching students to prove mathematical assertions. Method of solving mathematical problems. Method of extracurricular work in mathematics. Requirements for a modern Math lesson in school.

SPECIAL METHOD

Method of studying natural numbers. Method of studying ordinary fractions. Methodology for studying decimal fractions and percentages. Study of algebraic expressions and their identical transformations in the school course. Equality and inequality in primary school and the method of their study. Functions in the course of basic school algebra. The method of the first lesson planimeter. Geometric constructions on a plane. Coordinates and vectors on the plane and the method of their study. Geometric quantities and methods of their study at the school.

**Results of the discipline training.**

Knowledge and understanding of basic concepts, ideas and methods of teaching mathematics, skills: plan the work of a Mathematics teacher, compile a plan and a summary 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.

**Algebra and number theory **

**Purpose****: **the development of general algebraic and number-theoretic culture in future Mathematics teachers, which is necessary for the formation of their special professional qualities.

**Content of the discipline:**

Elements of set theory and binary relations.

Elements of Mathematical logic. Complex number.

Algebraic operations. Group. Ring. Field. Ordered field.

Homomorphisms of algebraic structures.

**Results of the discipline training****: **

Knowledge and understanding of basic concepts, ideas and methods of algebra and number theory. Skills of operating with complex numbers. Possession of algorithms for research of algebraic structures.

**Linear algebra **

**Purpose****: **formation of the system of knowledge and skills in the theory of linear spaces, methods solving systems of linear equations, theory of matrices for future math teachers.

**Content of the discipline**:

Arithmetic vector space. The basis and rank of the system of vectors.

Matrices and determinants. Ring of the matrices.

Systems of linear equations and methods their solution (Gauss method, Cramer`s formula, inverse matrix).

**Results of the discipline training****:**

Knowledge and understanding of basic concepts, ideas and methods of linear algebra. Ability to explore systems of vectors and systems of linear equations. Skills at work with matrices and determinants. Ability to solve systems of linear equations in different ways – Gauss method, Cramer`s formula, using matrices.

**Elementary Mathematics (discipline description)**

**Purpose****: **assimilation of students by the system of knowledge, namely: basic concepts, methods, theorems and their proofs, algorithms, rules of elementary math and mastering the generalized methods of action learning knowledge.

Introduction to methods of mathematical proofs, mastering the basic techniques, ways and methods of solving the problems of Elementary Mathematics.

Repvesent introduce students with elements of educational and professional activity.

Improve skills of organization own educational activity.

**Content of the discipline:**

Number sets. Mathematical expressions and their transformation. Functions and their graphs. Algebraic equations and inequalities. System of algebraic equations and their solving methods. Geometric shapes and quantities.

**Results of the discipline training****: **deep knowledge and understanding the basic concepts, methods of Elementary Math; the ability to build mathematical models in process of solving theoretical and practical problems; solve the problems of Elementary Mathematics according to known rules, algorithms, methods, find heuristic methods of solving tasks; construct algorithms; apply the terminology of Elementary Mathematics, correctly construct oral and written language; organize their own educational activities, carry out self-examination, self-control of the learning process.

**Discrete Mathematics**

** ****Purpose****: **to repvesent introduce students the basics of discrete Mathematics: disclosure of the contents of the basic concepts, proof of theorems, examining examples and problem solving.

Repvesent introduce students historical information about emergence and development of discrete Math and awareness of their sense.

Providing knowledge from the discipline, namely: learning basic concepts, theorems, algorithms, methods of solving problems of combinatorics and graph theory.

Acquiring skills of independent work in process of studying the discipline.

Content of the discipline:

Elements of combinatorial analysis: basic rules of combinatorics, combinatorial configurations; binomial theorem, properties of binomial coefficients; inclusion–exclusion principle, recurrence relations.

Elements of Graph theory: definition of graph, types of graphs, graph operations; connectivity; trees, applications of trees; planar graphs; graph colorings.

**Results of the discipline training****: **deep knowledge and understanding of basic concepts and methods of Discrete Math, the ability to solve basic tasks on their basis, find heuristic methods of solving discrete tasks, formulate and prove the theorem of Discrete Math, independently find proofs; knowledge and understanding of algorithms of Discrete Mathematics, ability to act according to given algorithms and create algorithms; ability to use the terminology of Discrete Mathematics, correctly construct oral and written language; the ability to find, select and analyze scientific sources for performing educational tasks.