List of examination subjects for applicants to the PhD program
0. | (BMA) | BASIC MATHEMATICS |
1. | (ALG) | ALGEBRA |
2. | (ANA) | ANALYSIS (REAL AND COMPLEX) |
3. | (COM) | COMBINATORICS |
4. | (GEO) | GEOMETRY |
5. | (PRO) | PROBABILITY THEORY |
6. | (DEQ) | DIFFERENTIAL EQUATIONS |
7. | (DGT) | DIFFERENTIAL GEOMETRY / TOPOLOGY |
8. | (FAM) | FUNCTIONAL ANALYSIS / MEASURE THEORY |
9. | (NUM) | NUMERICAL ANALYSIS |
10. | (OPR) | OPERATIONS RESEARCH |
11. | (SET) | SET THEORY |
- The test for subject 0 (BMA) consists of 10 multiple choice questions. No explanation is needed in this part.
- Tests for subjects 1-11 consist of 4-5 questions. Each subject will be marked out of 100. Here you have to show your work for full mark – results without explanation may earn you very few marks.
- Here is a sample exam from 2018.
- Here is the detailed list of conditions of the exam together with topics for the subjects.
- While preparing for the exam, you may also find helpful the table containing the description of BSc courses.
The stucture of the written entrance exam
When applying for PhD studies, applicants must choose a wider area of studies in which they would want to pursue research. Note that under certain conditions, changes are possible later, during the studies. However, for the purpose of the entrance examination one such area should be chosen from the list below (see below). Once the choice is made, the tests of the entrance examination should be chosen according to the following rules:
- Each applicant has to write the test from 0. (BMA) BASIC MATHEMATICS.
- Applicants have to write the mandatory test for the chosen area (subjects 1-7).
- Applicants have to choose one test marked as elective for the chosen area (subjects 1-11).
- Applicants should choose one test from the remaining subjects (not excluding the remaining elective subjects).
- Thus altogether each exam will consist of four different subjects.
- The tests will be sent electronically to the applicant and the scanned solutions should be sent back within 6 hours to the address given on the cover sheet of the exam. In order to assess your work accurately, please, make sure that your solution pages are numbered and each page contains your name and country plus the subject and the number of problem.
- In case the applicant is not sure about the chosen research topic, a secondary choice may be taken into account by choosing for free subject the mandatory subject of the second choice.
Areas and the corresponding mandatory and elective subjects for the entrance exam
Area | Subjects of the exam | |||
Basic | Mandatory | Elective | Free | |
A. ALGEBRA / NUMBER THEORY | 0. BMA | 1. ALG | 2. ANA or 3. COM | free |
B. ANALYSIS | 0. BMA | 2. ANA | 6. DEQ or 8. FAM | free |
C. APPLIED ANALYSIS | 0. BMA | 2. ANA | 6. DEQ or 9. NUM | free |
D. DISCRETE MATHEMATICS | 0. BMA | 3. COM | 10. OPR or 11. SET | free |
E. GEOMETRY / TOPOLOGY | 0. BMA | 4. GEO | 7. DGT or 8. FAM | free |
F. OPERATIONS RESEARCH | 0. BMA | 10. OPR | 2. ANA or 3. COM | free |
G. PROBABILITY AND STATISTICS | 0. BMA | 5. PRO | 2. ANA or 8. FAM | free |
F. SET THEORY / MATHEMATICAL LOGIC | 0. BMA | 11. SET | 1. ALG or 2. ANA | free |