Bayesian machine learning, in particular deep learning and Bayesian optimization (including model hyperparameter optimization). We believe that applying the Bayesian paradigm to the modelling of random phenomena holds significant potential for development. However, at present, these applications are still largely at the research stage, offering substantial opportunities for scientific achievements

Data mining, in particular using soft computing methods and privacy-preserving data publishing techniques. The development of such areas is especially important in the context of growing volumes of personalized data. Additional attention is given to building recommendation systems that respect user privacy, as well as methods for detecting fraudulent activities in contextual advertising systems. Non-dyadic wavelet transforms present a promising tool for preprocessing complex signals in classification and anomaly detection tasks. All these topics are currently in an active research phase, offering broad opportunities for scientific achievements

The programme stands out for its interdisciplinarity, modernity, and practical orientation across various fields. In particular, it develops critical competencies in working with biomedical and clinical data, modelling complex processes at different levels — from molecules to populations — analyzing uncertainty, assessing risks, and making informed decisions. The use of modern mathematical modelling tools, combined with in-depth knowledge of biomedical research objects, enables graduates to master powerful methods for analytics and forecasting in medicine and related fields. As a result, the programme prepares highly qualified specialists capable of working with experimental and observational data, participating in clinical trials, conducting epidemiological analysis, and implementing advanced medical technologies — all of which are especially important in the current era of personalized medicine and evidence-based healthcare

The course covers both classical and original methods for interpolation and smoothing, including the construction of linear and surface splines such as Bézier curves, B-splines, and NURBS, as well as the original corotational beam and surface splines developed by Prof. I. Orynyak. It addresses problems such as shape completion (when part of a contour is missing), blending (inserting the smoothest possible surface between existing ones), and determining optimal trajectories between two points with given positions, directions, and curvatures. The course also explores principles of motion and trajectory modeling for ground, aerial, and underwater drones. In addition, attention is given to the processing of visual and color data obtained using scanners

In this course, students study the fundamentals of supervised and unsupervised learning, including relevant models, methods, and evaluation metrics. Topics covered include classification metrics, decision trees, metric-based, linear, Bayesian, and kernel methods, as well as the support vector machine (SVM) approach. Special attention is given to clustering, association rules, model ensembles, dimensionality reduction, and reinforcement learning. The course also introduces the foundations of statistical learning theory according to Vapnik and Chervonenkis, causal inference in machine learning, and learning with guaranteed accuracy

The course explores methods for solving complex branched technical systems (electrical, hydraulic, mechanical, geometric) whose components are described by ordinary differential equations. Students learn how to construct the equations governing such systems and how to formulate boundary conditions. The course examines solution methods in cases where the relationships may be nonlinear. It also introduces approaches to optimizing the system structure (the connections between components) to minimize losses

The course covers the finite difference method, the finite element method, the method of weighted residuals, the (Fourier) method of separation of variables, as well as the original method of matched sections developed by Prof. I. Orynyak. These methods are compared using examples of one- and two-dimensional problems of heat conduction and wave propagation in rods and plates, as well as problems of vibration and dynamics of beams and plates

This course establishes working knowledge of the Big Data infrastructure and corresponding cloud based services. The focus is given on the cloud based Big Data infrastructure and analytics solutions and how cloud based services can be integrated into company’s IT and data infrastructure. Hands-on exercises (practice) aim to provide insight into how the cloud based services and tools can simplify processing of Big Data by using cloud based services for Hadoop, Machine Learning and general data analytics, with a specific attention on Apache Hadoop ecosystem, MapReduce, Spark, HBase, Hive, Pig, and supported programming languages Pig Latin and Hive. Practical exercises are done on the real cloud platform and Hadoop cluster either AWS, Azure, or locally provided by the university. The course describes industry best practices and models for enterprise data architectures to ensure effective data management and governance. The course also provides sufficient insight into Big Data security and compliance issues including those that are related to EU General Data Protection Regulation (GDPR)

This course introduces students to methods of clustering and visualizing large-scale data. It covers a range of clustering algorithms, including BIRCH, Batch K-means, DBScan, Cure, WaveCluster, CLARA, and Clarans, as well as Borůvka’s and Forel’s algorithms, and Kohonen maps. Special attention is given to modern data visualization techniques such as Tufte’s principles, Chernoff faces, parallel coordinates, and radial (petal) diagrams. The course emphasizes the practical application of these methods for analyzing complex patterns in large datasets

This course covers modern methods and approaches for formalizing a wide range of biomedical processes: from intermolecular interactions (ligand–receptor), pharmacokinetics and pharmacodynamics (PK/PD) of drugs, to the spread of infectious diseases, vaccination effectiveness, and population behavioral strategies. Mathematical tools such as stochastic Petri nets, decision trees, Markov and Bayesian networks, and differential equations are examined. Significant emphasis is placed on simulation and probabilistic approaches under uncertainty, sensitivity analysis of parameters, and the assessment of the value of additional information. The practical component focuses on applying models to analyze real experimental and observational biomedical data for informed decision-making. The course develops students’ abilities to think systemically, manage uncertainty, build well-founded models, and make balanced decisions in medicine

This course is designed to develop practical skills in constructing, analyzing, and applying mathematical models to solve complex applied problems. It covers all key stages of modeling: problem formulation, data collection and processing, model development, calibration, verification, result analysis, and interpretation. Various types of models are addressed, including deterministic and stochastic, static and dynamic, discrete and continuous. Core mathematical tools include systems of differential equations, Markov models, regression analysis, optimization methods, and statistical and parametric modeling. The practical component focuses on implementing models in software environments and applying them to real-world problems in technical, economic, biomedical, and social domains. The course cultivates logical thinking, data handling skills, and the ability to select and effectively use relevant mathematical models as tools for practical analysis and decision-making

The course explores science in general as both fundamental and applied, alongside pure and applied mathematics, and their roles within fundamental and technical sciences. Master’s students are introduced to the concept of rankings for institutions, journals, and researchers, including rankings across various disciplines, as well as issues related to manipulation, falsification, and plagiarism. Current trends in applied mathematics are analyzed through the examination of articles published in leading international journals. The preparation of master’s theses involves public discussions of research topics, evaluation of data source reliability, literature review, and verification of results