### Content (Syllabus outline)

Introduction, motivating examples.
Numbers and sets.

Combinatorics. Basic combinatorial counting.
Sequences. Convergence of sequences and subsequences, limits, calculation and applications.

Number series. Convergence, properties, applications.

Functions. Basic properties. Functions of real variables. Elementary functions, limits and continuity. Graphs.
Derivative. Definitions, rules, use of derivatives, local extrema, global extrema. Solving practical assignments.
Integral. Indefinite integral, definite integral, generalized integral, calculating areas, curve lengths, volumes...
Series of functions. Power series. Taylor series, convergence, estimations. Applications.
Differential equations. Separable equations, natural growth, ordinary first-order equations, linear equations with constant coefficients, systems of differential equations, applications.

Linear algebra, geometry in space. Matrices, determinants, systems of linear equations, eigenvalues and eigenvectors of matrices, applications.
Functions of several real variables. Partial derivatives, local extrema, extrema with constraints, least squares method.
Fundamentals of probability. Conditional probability, Bayes’ formula, distribution function, applications. Classical distibutions.

### Prerequisites

Prerequisites for course work:

Prerequisites for admittance to final exam:

Practical examination (colloquium)

· presence at practicals

· solving homeworks

Exam:

practical examination (colloquium