PhD Written Entrance Exam

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 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