The areas of the scientific activity of the Faculty of Mathematics and Informatics include various researches of the Institute of Mathematics ( as well as the Institute of Informatics

The Institute of Mathematics focuses on the topics such as: ALGEBRA - group theory, ring and algebra theory: finite groups; radical theory of rings; filial rings; Hopf algebras.; FOUNDATIONS OF GEOMETRY - projective geometry and its generalizations: Grassmann spaces, quadratic Grassmann spaces, Veronese products, Segre products, spine spaces; FUNCTIONAL ANALYSIS - the theory of non-local or singular operators and equations associated to them: operator algebras associated to authomorphisms and endomorphisms, ergodic theory and entropy, stochastic analysis, dynamical systems; MATHEMATICAL ANALYSIS - the theory of ordinary and partial differential equations: group-theoretical analysis of differential equations, spectral and asymptotic analysis of differential operators, harmonic analysis, special functions; MATHEMATICAL LOGIC - applications of logic in computer science and artificial intelligence: computational complexity; formalization and automatization of mathematical reasoning: rough sets, approximate reasoning; MATHEMATICAL PHYSISCS - orthogonal polynomials in quantum optics, infinite dimensional integrable systems, Banach Lie-Poisson geometry, quantization and coherent states, reproducing kernels, quantum logics (; APPLIED MATHEMATICS - statistical physics, Quantum game theory, econophysics.

The scientific research areas of the Institute of Informatics mainly concentrate on: ARTIFICIAL INTELLIGENCE - natural speech synthesis systems and one or two dimensional signal recognition methods for speech and images; NUMERICAL METHODS - modeling and simulation of various technical problems in the precise and fuzzy way applying currently developed parametric integral equation system as non-element method; PROGRAMMING AND FORMAL METHODS - the Mizar project: further development of the Mizar system for computer-aided formalization of mathematics, maintenance of the repository of formal texts written in the Mizar language (; SIGNAL ANALYSIS - medical image and signal processing (dental radiographic and USG images, EEG, ECG, signals representing the uterine contractions activity); NANOMATERIALS - Ab-initio band structure calculations and computer simulations of the nanomaterials, magnetooptical spectroscopy, ultrafast laser induced dynamics, nonlinear effects; MATERIALS INFORMATICS - informatic technologies in the materials science, computer modelling of manufacturing techniques of electronic components; FORMAL LOGIC - the logic, informatics and philosophy of science (automated deduction, relations between formal and commonsense reasoning), topics in epistemic and in temporal logic; E-LEARNING - effectiveness of technology aided education, individualization of learning in intelligent tutoring systems.