Obligatory courses for 2nd grade JSEM (course group defined by Faculty of Mathematics, Informatics, and Mechanics)

Summer semester 2023/24

• Classes - 30 hours
• Lab - 15 hours
• Lecture - 30 hours

In the course we present several methods of finding usually approximate solutions to basic mathematical problems when finding exact solutions is either impossible or impractical.

The course includes: elements of error analysis, polynomial and spline interpolation, elements of approximation, quadrature rules, Gauss quadratures, numerical solutions of systems of linear equations, real roots of the equations, numerical eigenproblem.

Winter semester 2023/24

• Classes - 30 hours
• Lecture - 30 hours

Winter semester 2024/25

• Classes - 30 hours
• Lecture - 30 hours

The main aim of the lecture "Finance I" is to combine theoretical knowledge of finance and economics with the practical application of instruments and methods used on financial markets, taking into account the role of the state in creation a stable financial system. As part of the course students will learn about the role of the financial system in the economy, the main money and capital markets instruments and their use for selected strategies, financial reporting of the company and general assessment of its financial and economic situation, and then the criteria for selecting investment projects undertaken by enterprises. Students will learn the main tools of fundamental analysis and technical analysis of financial assets. Selected derivatives will also be discussed.

Academic year 2023/24

• Lecture - 60 hours

Academic year 2024/25

• Lecture - 60 hours

The aim of the lecture will be to present the most important issues connected with the commercial law. At first, the basic notions and definitions of the civil, corporate and commercial law will be presented. It concerns in particular the issues which are essential for conducting business activities and for establishing of business entities. During the lecture, the subject matter will also be the terms and conditions for concluding agreements, the terms and conditions of the civil liability and the terms and conditions for undertaking business activities. The lecture will present the most important types of agreements and the most popular forms of organizing business activities. In that respect, the commercial companies will be particularly put under a detailed review. Additionally, the lecture will also outline the regulations governing the capital markets and trading in securities.

There will be a final comprehensive written exam at the end of the semester.

Winter semester 2023/24

• Classes - 30 hours
• Lecture - 30 hours

Winter semester 2024/25

• Classes - 30 hours
• Lecture - 30 hours

The course will introduce students to the models and techniques used in modern macroeconomic theory at the intermediate level. The objective of the course, besides specialized knowledge acquisition, is to develop the ability of critical thinking, using the quantitative tools in macroeconomic analysis, offering alternative solutions to complex problems, defend positions in discussions in an analytically rigorous but lucid way.

The course begins with the analysis of the short run inflation and output dynamics, using the DAD/DAS model. Then, the lectures will discuss the long-run growth determinants in the neoclassical growth theories. The presentation of the microfoundations of consumers' and investors' behavior and monetary and fiscal policy conduct follows. Finally, the role of fiscal and monetary policies are discussed.

Winter semester 2023/24

• Classes - 60 hours
• Lecture - 60 hours

Winter semester 2024/25

• Classes - 60 hours
• Lecture - 60 hours

Multivariable differential calculus, measure and integration theory.

This is an extended course and therefore it may be harder and more comprehensive than the normal course of Mathematical Analysis II.1.

Summer semester 2023/24

• Classes - 45 hours
• Lecture - 30 hours

Summer semester 2024/25

• Classes - 45 hours
• Lecture - 30 hours

The lecture presents basic informations on existence, uniqueness and properties of ODE solutions. Elements of the qualitative analysis of solutions are also included. A number of important applications of ODE is discussed.

Summer semester 2023/24

• Classes - 45 hours
• Lecture - 30 hours

Summer semester 2024/25

• Classes - 45 hours
• Lecture - 30 hours

Kolmogorov axioms. Basic probabilities.

Random variables, probability distributions, and their parameters. Independence.

Convergence of random variables. Basic limit theorems: Poisson theorem, weak and strong laws of large numbers, de Moivre-Laplace theorem.

Winter semester 2023/24

• Classes - 45 hours
• Lecture - 30 hours

Winter semester 2024/25

• Classes - 45 hours
• Lecture - 30 hours

This course presents basic notions of topology: metric and topological spaces, continuous maps, homeomorphisms, Cartesian products, complete metric spaces, compactness, connectedness and path connectedness, homotopy of maps and loops, contractibility, quotient spaces.