Faculty of Mathematics, Physics
and Informatics
Comenius University Bratislava


Doctoral Degree Program




full time / external

Usual duration:

full time form 4 years, external form 5 years

Language of courses:


Program director:

prof. RNDr. Ján Filo, CSc.


prof. RNDr. Pavol Quittner, DrSc.
doc. RNDr. Eugen Viszus, CSc.
doc. RNDr. Róbert Jajcay, DrSc.
prof. RNDr. Pavol Zlatoš, PhD.

Related study programs: The program is considered a continuation of the Master's program in Mathematics; in case of dissertation topics selected from the area of Discrete Mathematics students who completed the Master's program in Computer Science are also eligible for admission.

Description of the Study Program

The main goal of the third-degree program in the Mathematics study program is to prepare students for independent scientific or development work in the academic environment, or in highly scientifically specialized companies. Graduates of the doctoral study program in Mathematics have deep theoretical and methodological knowledge of one of the key areas of mathematics: Discrete Mathematics, Mathematical Analysis or Numerical Mathematics at the current state of world research, master scientific research methods and creatively apply the acquired knowledge in practice. The graduate is able to analyze non-standard problems from various scientific fields and design their discrete or continuous mathematical models. He/she is able to work independently scientifically and to present the results of his/her research work at domestic and foreign scientific conferences. He/she is able to lead a professional team and throughout his/her career is able to follow the new developments and trends in his/her field of interest.

What to Expect

The student, in cooperation with the tutor, will compile an individual study plan, which is designed to meet the requirements of the "FMFI UK Study Regulations" and the submitted study program.

The individual study plan consists of three parts: studies-related, scientific and supplementary.

Studies part

The focus of the studies part is the individual studies of literature designated by the supervisor. Part of the studies is also successful completion of lectures in selected subjects. Another part of the studies is active participation in regular scientific seminars, the selection of which for the doctoral student will be determined by the supervisor. At the same time, the participation of a doctoral student in domestic and international conferences and summer / winter schools can also be a part of the evaluation.

Scientific part

The content of the scientific part is preparation of a dissertation. The work should prove the doctoral student's readiness to work scientifically by bringing either an original mathematical result or an original application of mathematical theory in a selected scientific discipline such as physics, informatics or biomathematics. The result of the work should be presented either in a peer-reviewed scientific journal in the field of mathematics or the subject area of its application.

Dissertation exam

The sufficiency and suitability of the study plan is assessed by the dissertation examination committee, which evaluates the depth and scope of the doctoral student's knowledge. The commission is appointed by the FMFI dean on the proposal of the guarantor and the supervisor in accordance with the FMFI study regulations. Part of the exam is the presentation of the dissertation project, in which the doctoral student acquaints the commission with the intentions of his work, resp. with the results already achieved. The doctoral student submits the dissertation project in writing. The project is assessed by at least one opponent who is also a member of the dissertation examination committee.

Elaboration of dissertation work

The doctoral student will prepare a dissertation within the deadline set for the given type of study, i.e., 4 years for the daily form we propose. The doctoral student consults with his / her supervisor on the elaboration, content and form of the dissertation. A summary of published doctoral student articles supplemented by an introduction and a summary of the achieved results can also be considered a dissertation.

Dissertation defense

The defense of the dissertation takes place before a commission, the composition of which will be determined by the dean of FMFI on the proposal of the guarantor of the doctoral studies of Mathematics. The work is being assessed by three scientific opponents.

Teaching activities

The study plan can be supplemented with elective courses. In the case of full-time students, pedagogical activities of up to four hours per week on average per academic year are required.

The study plan consists of a block of compulsory subjects, a block of compulsory elective subjects and a block of elective subjects. The compulsory and optional subjects include subjects that form the core of the given field of study and at the same time profiling subjects fulfilling the profile of the graduate determined by us.

Graduates' Career Opportunities

The rules for admitting students for doctoral studies in mathematics alone are set so that admitted students are immediately considered employees of the relevant departments and successfully completed doctoral students are of such high quality that they have not had a problem with applicability within the country or abroad. This is due to the fact that there is only a very small number of students, and these studies can only be managed by the best graduates of the master's degree program. These students are also confirmed during the selection by their future supervisor.

Doctoral Scholarships

Full-time doctoral students who have permanent residency in the European Union are entitled to receive a scholarship for the entire standard duration of their studies. The scholarships are paid starting on the date of enrollment. The scholarship is determined in accordance with the tables included in the Law no. 553/2003 Z.z. as follows: 

  • prior to completion of the qualification exam: 1025,50 EUR (6th class, 1st level)
  • after successful completion of the qualification exam: 1 194 EUR (7th class, 1st level)

Scholarships are not subject to taxes or other fees.

Doctoral studies are considered an equivalent to full time employment and in the majority of cases cannot be combined with another employment. Job holding applicants who intend to keep their job are advised to apply for the external (distance) form of doctoral studies. Doctoral students enrolled in the regular form are expected to participate in teaching activities such as conducting recitations or exam grading, in accordance with the needs of their corresponding departments.

Thesis Topics for Academic Year 2024/2025

  • Inference of stochastic dynamics in biological processes
    (supervisor: Mgr. Katarína Boďová, PhD.)
  • Propagation of waves of pathogen variants in epidemiological models
    (supervisor: doc. Mgr. Richard Kollár, PhD.) 
  • Asymptotic properties of solutions of differential equations
    (supervisor: RNDr. Michal Pospíšil, PhD.)
  • Combinatorial properties of algebraically defined graphs
    (supervisor: prof. RNDr. Robert Jajcay, DrSc.)
  • Properties of Primitive Permutation Groups
    (supervisor: doc. RNDr. Martin Mačaj, PhD.)
  • Convergence analysis of higher-order schemes in compressible fluid dynamics
    (supervisor: Dr. Hana Šmitala Mizerová)