Content (Syllabus outline)

1. part
Introduction, motivating examples.
Numbers and sets.
Basics of combinatorics and counting.
Sequences. Convergence of sequences, calculating limits, applications.
Number series. Convergence, properties, applications.
Functions. Basic properties. Functions of real variables. Elementary functions, limits and continuity.
Derivative. Definitions, rules, use of derivatives, local extrema, global extrema, application of the extremal calculus.
Integral. Indefinite integral, definite integral, generalized integral, applications.
Series of functions. Power series. Taylor series. Applications.
Differential equations. Separable equations, practical applications. Ordinary first-order equations, linear equations with constant coefficients, systems of differential equations, applications.

2. part
Elements of financial mathematics: short recapitulation of sequences, their limits (number e), and series, mathematics of finance: simple and compound interest, annuities, law of natural growth.
Functions of two real variables: partial differentiation, higher order partial derivatives, maxima and minima, least squares method with several applications.
Elementary linear algebra: determinants, multiplication of matrices, inverse of a matrix, matrix equations, rank of a matrix, system of linear equations, the use of software for solving the system linear equations in professional cases; linearly independent vectors, linear combination of vectors.
Probability and random variables: permutations and combinations, trials, events, probabilities, mutually exclusive and non-exclusive events, dependent and independent events, compound events, conditional probability, Bernoulli’s formula, discrete random variables, binomial and Poisson distribution, the concept of continuous distribution, density functions and their properties, uniform and exponential density function, expected value, variance, normal distribution.

Prerequisites

1. Condition for inclusion in the work:
- Inscription to adequate academic year.

2. Condition for performing study obligations:
- Practical examination (colloquium),
- Presence at practicals,
- Solving home works.