The research and scientific topics performed at the Faculty include:
- design of algorithms and the use of probability based methods in engineering, physics and medicine
- modelling of economic problems
- selected problems of stability in dynamical systems
- mathematical aspects of identification of systems, computational complexities
- discrete mathematics with special attention to graph theory
- problems of division and decomposition
- analytical and topological methods in the field of dynamical systems
- applications to problems in mathematical physics, economy and control theory
- differential equations
- numerical methods
- computational methods
- non-linear differential and difference, functional equations (of hyperbolic, elliptic and parabolic types)
- geometric methods
- functional analysis, operator theory, Hilbert spaces
- theory of approximations, splines, wavelets, rational functions
- theories of colmatation and flows with mass transfer and stability of deformation processes in metal crystals
- mathematical analysis
- differential schemes for partial differential equations (numerical analysis)
- partial differential equations
- functional equations and inequalities
- descriptive and projective geometry and engineering graphics.

Since 1990 the Faculty staff members have been organizing the annual conference "Cracow Workshop on Graph Theory" with participation of mathematicians not only from other polish centers, but also from Slovakia, Czech Republic, Germany and other countries. The conference "Applied Mathematics" is also international in range and has been held in Krynica since 1994. Every four years the cyclic international conference entitled "Cracow Conference on Graph Theory" is organized.

The faculty participates in the programs of Ceepus, Socrates/Erasmus in which the following foreign institutions are involved: Technical University - Budapest (Hungary); Technical University - Graz (Austria); P.J.Safarik University - Ko?ice (Slovakia); Technical University - Ljubljana (Slovenia); Technical University - Prague and Charles University - Prague (Czech Republic); University Degli studi Di L'Aquila (Italy).
The Faculty staff members collaborate with their counterparts from foreign centers, in particular Sweden, Czech Republic, Switzerland, Germany, USA and Ukraine. The practical effect of the contacts can be seen in the form of scientific articles published in collaboration with foreign authors. The staff members participate in the following research programs:
- National Scientific Foundation (NSF) supported by a grant at the NJIT New York, New Jersey - USA
- in the Technical University of Prague.

The scientific collaboration is also carried out through the membership in foreign organizations: The American Mathematical Society, Society of Industrial and Applied Mathematics, Association of Phys. Mathematics and GAMM in Germany.