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).