Faculty of Mathematics, Physics
and Informatics
Comenius University Bratislava

Mathematics

Doctoral Degree Program

Field:

Mathematics

Form:

full time / external

Usual duration:

full time form 4 years, external form 5 years

Program director:

prof. RNDr. Ján Filo, CSc.

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 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.

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.

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: 807,50 EUR (6th class, 1st level)
  • after successful completion of the qualification exam: 940,50 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 2022/2023

  • Numerical methods for differential inclusions
    (supervisor: prof. RNDr. Michal Fečkan, DrSc.)
  • Existence of a weak solution to a nonlinear fluid–structure interaction problem modeling the flow of an incompressible, viscous fluid in a cylinder with deformable walls
    (supervisor: prof. RNDr. Ján Filo, CSc.)
  • Modelling convection and solidification in multicomponent alloys
    (supervisor: doc. RNDr. Peter Guba, PhD.)
  • Highly Symmetric Maps
    (supervisor: prof. RNDr. Robert Jajcay, DrSc.)
  • Algorithms for graph embeddability into surfaces
    (supervisor: prof. RNDr. Martin Škoviera, DrSc.)