Doctoral Programme Mathematics and Physics - subprogramme Mathematics

The main goal and the most important activity of doctoral study is the doctoral dissertation, which must include original scientific results and result in at least one publication in a scientific journal. The student prepares this under the guidance of their mentor whom they choose before enrolment into the first year of study.

Individual research work towards the doctoral dissertation counts for 174 credit points, and the submission and defence of the dissertation for 6 credit points. The remaining 60 credit points of the doctoral degree are obtained from the following study obligations:

• A first-year Predoctoral exam (6 credit points). This is a pass/fail exam, which the student must pass. The aim of the exam is to check the basic understanding of mathematical concepts. Students with a solid mathematical background should not need to prepare for this exam. Three sample past exams are: 2018, 2019, 2020.
• Successfully completing five courses in the first two years of study (each subject contributes 6 credit points, making a total of 30 credit points). These are the only study obligations in the doctoral programme for which the student receives a numerical grade. At least three of the courses must be organised taught courses on the taught doctoral programme in mathematics. In addition, at most two of the courses can be taken as consultation courses, chosen with the help of the supervisor, who may not themself be the teacher of the consultation course. The names of the subjects are sufficiently general (e.g., "Selected topics in analysis"), that they can encompass any mathematical topic
• Individual studies in the first two years (in each year worth 6 credit points, making a total of 12 credit points). Under the guidance of their mentor, the student is introduced to the broader area around their research field (for example, by studying graduate textbooks from the area, solving exercises, etc.). This does not however include the study of scientific papers directly related to the topic of PhD research.
• Active participation in one of the seminars of the department of mathematics, in the first two years of study (in each year worth 6 credit points, making a total of 12 credit points).

Mathematics:

For enrolment in higher years it is necessary to meet the following conditions:

• For enrolment in the second year, it is necessary to obtain at least 48 ECTS from the programme requirements. This must include the predoctoral exam and at least an additional 24 ECTS from organised forms of study (courses, seminars, individual study) during the first year.
• For enrolment in the third year of study it is necessary to obtain at least 90 ECTS from the first two years. This must include the predoctoral exam and at least an additional 48 ECTS from organised forms of study (courses, seminar or disposition, individual study). In addition, before enrolment in the 3rd year, the student must obtain ratification by the senate of the Faculty (UL FMF) of a positive evaluation of the suitability of the subject of the doctoral dissertation from the Committee for monitoring the doctoral student (KSDŠ).
• For enrolment in the fourth year of study, it is necessary to meet all study requirements from the first three years and to obtain approval of the subject of the doctoral dissertation from the Senate of the University (UL).

• KLASIUS-SRV: Education leading to doctorate of science (third Bologna cycle)/Doctorate of science (third Bologna cycle)
• ISCED: Teacher training and education science, Physical sciences, Mathematics and statistics
• KLASIUS-P: Science (broad programmes)
• KLASIUS-P-16: Physics, Mathematics
• Frascati: Natural Sciences
• SOK level: 10
• EOK level: 8
• EOVK level: Third cycle

Description of courses for 2026/27