The department provides education in mathematical and physical disciplines at both the bachelor's and master's levels, with the emphasis on mathematical modelling, operations research, and statistics. The goal of teaching at the master's level is to deepen students' knowledge of applied mathematics (numerical mathematics and statistics) in higher years and to create a coherent cycle of subjects for modelling linear stationary and non-stationary systems and processes, signal processing, classification of random processes, prediction algorithms, and analysis of large systems.

The department's research focus is mainly on the applications of mathematics in transportation, from rail and road to air transport. It includes modelling and identification of transport systems, dimensionality reduction of transport data and traffic prediction, approximation theory and special functions for processing non-stationary signals, optimization methods including optimization of planned infrastructure for clean mobility, modelling environmental impacts, algorithms for autonomous mobility, and more. We participate in a number of interesting projects aimed at contributing to proposals for improving efficiency and passenger satisfaction, smart cities, and motivational measures.

In addition to transportation issues, we also focus on the history of mathematics, logic, cryptography, theoretical physics, and various interdisciplinary areas. We often collaborate with doctors in clinical studies or with biologists, which demonstrates the main strength of mathematical modelling – its universal applicability. Whether it is a doctor, biologist, or transport engineer, they all use methods such as linear regression in the same way. At the same time, they usually need to process and evaluate data of various kinds.

The department also develops individual work with young people, both in leading student projects at the bachelor's and master's levels and in training doctoral students for scientific research work.