Research work carried out within the department is centered around two scientific disciplines: computer science and mathematics. The department is divided into two departments: Computer Science and Applied Mathematics. Faculty members collaborate with many top research institutions, both in the country and abroad. They participate in a number of national and international research grants, and actively publish their research results in international journals.

**DEPARTMENT OF COMPUTER SCIENCE**

The scientific and research activities of the Department of Computer Science cover computer science in the broadest sense, including computational science. The development of various computational methods and the algorithms used in them should be mentioned first and foremost.

The main issue intensively developed at the Department is the methods of artificial intelligence such as evolutionary algorithms, artificial immune systems used, among other things, for classification and data analysis, and for solving single- and multi-criteria optimization problems. The resulting methods are used in a wide variety of fields, including biological data analysis, bioinformatics and atomic cluster analysis. There is also advanced research in the fields of artificial neural networks, agent systems, fuzzy and neural-fuzzy inference systems and their application to modeling of various technical issues and in economic informatics.

A group of employees is involved in computer modeling of landscapes, such as digital maps, digital analysis of visibility of landscapes and objects in them, simulation of illumination or obscuration of objects and computer algorithms and programs for this purpose. They are also developing innovative solutions within the framework of virtual and augmented reality.

Another area of development of the method is algorithms for high-performance computing. Parallel and distributed programming algorithms are also being developed to increase the efficiency of computation and the area of their application to tasks that exceed the previous capabilities of numerical modeling. Scientific research is carried out on the operation of cloud and edge-computing systems. Security aspects of such systems are also analyzed.

Another important object of research is the finite element method (FEM). In the Department, research is being carried out on new methods and adaptive algorithms that make it possible to solve issues that exceed the capabilities of large computers with the use of a laptop, and thus to analyze data on the spot, such as in the field for geological surveys, in the doctor’s office for disease diagnosis, in the workshop for material damage diagnosis, and in many other situations. Computer methods are also being developed in solving the equations of electromagnetism and in multi-scale modeling of systems. The Department is also working on computer modeling of civil and mechanical objects such as shell structures. The strongly nonlinear models of large deformations used in their description are an important area of research for scientists working in this field.

The Department’s research collaborations include Jyvaskyla Polytechnic (Finland), University of Texas at Austin, MTS Minneapolis (USA), University of Alberta, University of Calgary (Canada), Ecole Nationale Superieure de Lyon, Ecole d’Architecture de Marseille (France), University of Ghent (Belgium), Universitaet Stuttgart (Germany), Swedish Defence Research Agency (Sweden).

**DEPARTMENT OF APPLIED MATHEMATICS**

Employees in research and teaching positions in the Department of Applied Mathematics conduct scientific research mainly in the field of science in the discipline of mathematics. This research focuses on algebra (group theory, nonconvex ring theory), functional analysis and operator theory, differential equations (in particular, differential equations of mathematical physics and fuzzy and multivalued stochastic equations) and differential geometry. There is also research in real and complex algebraic geometry, subanalytic geometry, the theory of o-minimal structures, topology (generalized topologies in the sense of Delphs-Knebusch), multiplicity theory and the foundations of mathematics, number theory, statistics and its applications in economics, fluid mechanics, complex analysis, approximation theory and graph theory. In recent years, work in the history of mathematics has intensified.

**SCIENTIFIC ACTIVITY**

**Department of Computer Science**

- machine learning and artificial intelligence
- computational intelligence
- optimization metaheuristics
- optimization in logistics and scheduling problems
- deep learning
- image analysis
- medical data analysis
- cybersecurity and cryptography
- blockchain technology
- complex systems modelling
- financial time series analysis
- computer graphics and modelling
- human-computer communication
- virtual and augmented reality
- high performance computing
- theoretical computer science
- embedded machine learning
- grid and cloud computing
- finite element method
- agent modelling

**Department of Applied Mathematics**

- differential geometry
- differential equations of mathematical physics
- fuzzy and multivalued stochastic differential equations
- algebra, including group theory, non-commutative ring theory
- functional analysis
- operator theory