Lecture courses

Courses which are created and taught by LSRDA staff.

Bachelor level course annotations:

• MateB016: Probability Theory (6 ECTS);
  • The aim of the course is to introduce students to the basics of probability theory. Students are provided with the necessary knowledge for the mathematical statistics course and other lecture courses that use the concepts of probability theory.
  • The course objectives are:
    • to present the basics of probability theory, including the classical principle of calculating probability and the Bernoulli scheme of independent events;
    • to describe the concept of a random variable and its numerical characteristics, to provide various examples of applications;
    • to illustrate transformations of random variables and their examples;
    • to define multidimensional random variables and the concept of dependence of random variables.
• MateB015: Mathematical Statistics (6 ECTS);
  • The aim of the course is to learn the basic concepts and methods of mathematical statistics, which can be divided into:
    • descriptive statistics;
    • estimation of population parameters;
    • interval construction;
    • hypothesis testing;
    • construction of correlation and regression models.
  • In addition to classical statistical methods, the course will provide a brief overview of non-parametric statistical methods, which are used when the conditions for classical methods are not met.
  • Statistical methods will be implemented in the popular program R, looking at various real data problems, as well as performing simulations..
• MateK003: Introductory course working with data (3 ECTS);
  • Course objective: to learn how to collect and process data using Microsoft tools, as well as to familiarize yourself with data protection regulations.
  • Course objectives:
    • During the course, students independently master Microsoft Excel and Power BI tools;
    • become familiar with public data sources and legislative issues related to data analysis, especially the General Data Protection Regulation.
• MateB018: Mathematical Foundations of Econometric Analysis (6 ECTS);
  • The aim of the course is to learn the formulation of the linear regression model, its economic interpretation, and the assumptions underlying the model.
  • The course objectives are:
    • to learn the estimations of the least squares method, their statistical properties and hypothesis tests;
    • to introduce extensions of the classical model (model with heteroskedastic and autocorrelated errors, model for binary and multinomial dependent variables);
    • to demonstrate the applications of the methods to real economic data using the statistical software R.
• MateB014: Time Series Analysis  (6 ECTS);
  • The course aims to provide students with basic knowledge in time series analysis, starting with concepts such as time series process, trend, stationarity, seasonality, spectrum and finally defining the popular ARMA processes, with the help of which many real time series are modeled. A large part of the course will be devoted to ARMA processes, examining their properties, fitting them to data, estimating process coefficients and calculating forecasts and corresponding errors. Nonparametric statistical methods will also be used in both time series trend approximation and spectral analysis. The conclusion of the course is devoted to an insight into financial time series as ARCH and GARCH processes as well as mixed processes that describe dependence in a general form.
  • The R programming language will be used in the practical exercises.
• MateB029: Random processes (6 ECTS);
  • The aim of the course is to introduce students to the theory of random or stochastic processes, which is an extension of the concept of a random variable..
  • The course objectives are:
    • to define and describe the main types of stochastic processes, which include random walk, discrete and continuous-time Markov chains, their applications in crowd-sourcing models, Poisson process and Wiener process or Brownian motion;
    • to provide knowledge for solving theoretical and practical problems;
    • to provide insight into the main applications of processes;
    • to illustrate processes with the help of simulations in the computer program R.
• MateB057: Introduction to Probability Theory (6 ECTS);
  • The aim of the course is to introduce students to the concepts of probability theory. The basics of probability theory will be presented, starting with events, actions with them and the classical probability calculation probability and continuing with the concept of probability space, the Moivre-Laplace theorems, the concept of a random variable, its numerical characteristics, functions of random variables. Finally, at the end of the course, an insight into the concept of stochastic convergence will be given, the law of large numbers and the central limit theorem will be defined.
  • The objectives of the course are:
    • to provide in-depth knowledge in probability theory, which will allow understanding the essence of formulas and, consequently, to explain this knowledge more clearly to students to form an understanding of the main concepts of probability theory;
    • to teach how to choose appropriate methods for solving problems and facilitate the process of independent problem-solving;
    • to develop skills in performing calculations by choosing appropriate programs and tools.
• SDSKB059: Mathematical Statistics and Its Methodology (6 ECTS);
  • The aim of the course is to introduce the concepts of mathematical statistics, data processing in the R program and various statistical procedures and methods. This includes descriptive statistics and random sample characteristics. Inferential statistical methods will be learned, including population parameter estimation, hypothesis testing, and analysis of the dependence of random variables, and finally the course will conclude with regression analysis methods. Classical statistical methods will be supplemented with non-parametric and robust statistical methods. Special attention will be paid to explaining the relationship between probability theory and mathematical statistics.
  • Practical classes will be conducted using the statistical program R.
  • The objectives of the course are:
    • to provide in-depth knowledge in mathematical statistics, which will allow understanding the essence of formulas and corresponding procedures and, consequently, it will be more understandable to explain this knowledge to students;
    • to develop an understanding of the main concepts of mathematical statistics;
    • to teach how to choose appropriate methods for statistical data analysis;
    • to develop skills in performing data analysis by choosing appropriate programs and tools.
• MateB012: Mathematical and statistical software packages (3 ECTS);
  • The course introduces students to the main principles that must be mastered in order to be able to use the computer program packages SPSS, LaTeX and Python in the scientific, research and practical work of a mathematician, statistician, economist, financier, etc. An overview is given of the functions and possibilities of using the corresponding computer program packages, mainly focusing on the needs of students to develop various internships, bachelor's and other scientific works. The basic functions and possibilities of SPSS and Python will be shown, comparing them with the program R, which has already been mastered in practical work in mathematical statistics.
  • The goal of the course is to be able to use the computer programs SPSS and Python in data processing, to know the main advantages and disadvantages of R, SPSS and Python in order to be able to choose the most suitable program for data analysis or solving scientific problems, as well as to master the program LaTeX in order to be able to format diploma theses and mathematical texts.
  • The course objectives are:
    • to identify the advantages and disadvantages of various computer programs;
    • to learn the application of statistical methods in SPSS and Python;
    • to learn the basics of LaTeX and the use of style files.
• MateK005: Course work using the package R (3 ECTS);
  • The goal of the course is to independently implement the steps of a modern data analysis project to find answers to practical questions using publicly available data, the R programming language, and the RStudio programming environment.
  • The course objectives are:
    • to learn the methods available in the R programming language ecosystem for data import, export, data cleaning, data exploration with graphical and non-graphical techniques;
    • methods for presenting results in publication quality;
    • to introduce some elements of machine learning.
• MateB004: Statistics and Epidemiology (6 ECTS);
  • The aim of the study course is to develop scientific research skills in obtaining measurements, analyzing data, using various statistical methods, as well as to provide insight into epidemiology and the interpretation of obtained data.
  • The course objectives are:
    • to develop the first skills of scientific research work, which will help to develop a bachelor's thesis;
    • to develop skills in processing and presenting the obtained results; to provide knowledge about the basics of probability theory and mathematical statistical methods, on which hypothesis testing, regression analysis and analysis of variance are based;
    • to provide skills and abilities in collecting, processing and graphical visualization of statistical data;
    • to provide skills and abilities in the application of the most frequently used medical statistical methods;
    • to provide skills in analyzing statistical data with software tools using the R program;
    • to introduce the principles of epidemiological research, their design types and the concept of screening studies.
• MateB003: Mathematics for Optometry (6 ECTS).
  • The aim of the studies is to acquire the basics of mathematics, which allows to describe both the eye model and the light flows through the surface of the eye. The main objects of mathematical analysis to be studied or analyzed are, first of all, functions. The course covers the following basic topics:
    • real number;
    • differential and integral calculus of single-argument functions.
  • The course objectives are:
    • to introduce students to the above topics;
    • to introduce topics to be able to read modern scientific literature in optometry that uses mathematical techniques.

Master level course annotations:

• MateM013: Stochastic Processes (6 ECTS);
  • The aim of the study course is to learn the theoretical foundations of random processes, examining their various applications in probability theory, mathematical statistics, physics, chemistry, biology and other fields and practically implementing them with the help of the program R. In the study course, the student examines in depth the random walk process, discrete and continuous-time Markov processes, Brownian motion, Poisson process, as well as general diffusion processes; applications both in financial mathematics, describing the famous Black-Scholes model, and in physics, describing the Fokker-Planck and Langevin equations.
  • The course objectives are:
    • to become familiar with the theory of random processes;
    • to study in detail the processes of random walk and Brownian motion;
    • to become familiar with stochastic integrals and differential equations and their applications in various fields;
    • to calculate both theoretical problems and to use the program R in simulations of random processes and other applications.
• MateM002: Modern statistics and data science (6 ECTS);
  • The aim of this course is to introduce students to modern statistical concepts necessary for data processing and analysis. The course not only covers classical statistical problems such as parameter estimation, confidence intervals and hypothesis testing, correlation and regression models, but also shows how to apply these methods to big data. The second part of this course is devoted to data science concepts, which include big data analysis, data visualization and also statistical learning methods.
  • The course objectives are:
    • to provide an overview of classical statistics and data science problems;
    • to show the application of classical methods in the context of data science, where an important concept is big data and various algorithms as an alternative to statistical methods.
  • The course tasks are:
    • to provide the main classical statistical methods and the most important problems and methods of data science;
    • to show the relationship between data science methods, algorithms and classical statistical methods;
    • to analyze various real data examples as well as to perform simulations in the programming languages ​​R or Python.
• MateM012: Nonparametric Statistics (6 ECTS);
  • The aim of the course is to provide knowledge about nonparametric statistical methods that solve mathematical statistical problems without parametric assumptions about the type of data distributions. For independent and dependent samples, the currently widely used bootstrap methods, nonparametric regression, kernel density function smoothing, and empirical reliability function will be analyzed.
  • The course objectives are:
    • to understand theoretical methods and the main proof techniques;
    • to be able to apply nonparametric methods in the analysis of statistical data simulation;
    • to verify the correctness of theoretical methods with the help of simulations and compare them with other known methods;
    • to master methods using the program R.
• MateM009: Bayesian statistics (6 ECTS);
  • Bayesian statistics is an approach to statistical inference that uses prior assumptions in the form of prior distributions and updates them to given information based on Bayes' theorem.
  • The aim of the course is to provide students with an understanding of Bayesian statistics and its advantages.
  • The objectives of the course are:
    • to introduce students to the main concepts and methods of Bayesian statistics;
    • to teach them to implement them in the program R.
• MateM048: Selected topics in mathematical statistics for computer science (6 ECTS);
  • The first part of the course is devoted to the repetition and summary of the main methods of probability theory and mathematical statistics, dividing each lesson into two parts: the first part is theory, the second - testing and application of methods to both generated and real data. The second part of the course emphasizes the comparison and application of various methods, distinguishing between non-parametric, parametric, and robust procedures, paying great attention to the interpretation of results and testing of conditions.
  • The aim of the course is to provide students with an understanding of probability theory and mathematical statistical methods and their applications to data.
  • The course objectives are:
    • to clarify the main concepts of mathematical statistics;
    • to perform simulations and real data analysis;
    • to learn and know in which cases classical, non-parametric and robust statistical methods should be used.
• MateM015: Business intelligence tools and data visualization (6 ECTS);
  • Business Intelligence (BI) combines business analytics, data mining, data visualization, data tools and infrastructure, and best practices to help organizations make data-driven decisions.
  • The course aims to provide students with an understanding of business intelligence, as well as practical skills in using the most popular business intelligence tools.
  • The course objectives are:
    • to clarify the main concepts, terms and project flow of business intelligence;
    • to process and transform various data formats with selected business intelligence tools;
    • to realize visualization of various combinations of categorical, discrete, continuous and geospatial data;
    • to master data analysis expressions.
• MateM001: Asymptotic Statistics (6 ECTS);
  • The course will cover the theoretical foundations of modern asymptotic statistics, which are necessary to develop new methods in mathematical statistics, to understand the theoretical basis and justification for many mathematical statistical procedures. During the course, students will analyze publications in the field of mathematical statistics, study asymptotic methods and delve into scientific problems. Finally, using the R program, students will learn to verify theoretical asymptotic results with the help of simulations, as well as to apply theoretical methods in practice.
  • The aim of the course is to introduce asymptotic statistical methods, which will help both to conduct scientific research and to understand courses related to probability theory and mathematical statistics in depth.
  • The course objectives are:
    • to learn asymptotic methods, on which statistical procedures are based;
    • to use the program R with the help of simulations, helping to understand the essence of theoretical methods, also comparing them with each other;
    • to delve into the proofs and applications of specific asymptotic methods in practice by delving into and analyzing scientific publications.
• MateM011: Timeseries and signal analysis (6 ECTS).
  • The course aims to provide students with an introduction to modern time series analysis methods and their applications in financial analysis and engineering, as well as to signal analysis methods, especially digital signal analysis. The theoretical methods discussed will be implemented practically with the help of statistical software (R and Matlab).
  • The course objectives are:
    • to learn time series models for one-dimensional and multidimensional data;
    • to learn spectral analysis of signals.
• MateM052: Linear models in data science (6 ECTS).
  • The course aims to provide broad and in-depth knowledge of linear statistical models important in data science and their practical use for various factorial research designs, including single or multi-factor ANOVA, repeated measures ANOVA, analysis of covariance or ANCOVA, mixed design ANOVA methods, as well as linear and generalized linear mixed or random effects models.
  • The course objectives are:
    • to provide theoretical and practical knowledge of classical ANOVA methods, which are widely used for data analysis in practical research;
    • to expand students' knowledge of the most important linear and generalized linear models with mixed or random effects;
    • to illustrate data analysis of factorial research designs with various linear models in the R program;
    • to promote students' skills in developing their own research design, as well as processing and analyzing factorial design data collected during the research, and visualizing and interpreting the results of fitting linear models.