Doctoral Programme in Mathematics

Partner institutions: University of Osijek, University of Rijeka, University of Split, University of Zagreb

Coordinating institution: Department of Mathematics, Faculty of Science, University of Zagreb                          

Introduction: Doctoral program in mathematics gives modern education in pure and applied mathematics, which provides competence for performing work in research, professional and educational institutions, as well as in economy at jobs which require rather high degree of expert knowledge and innovation.

Requirements for admission:Entry requirement for doctoral program in mathematics is completion of an appropriate graduate (master) university program, which enables acquiring appropriate mathematical competencies necessary for the doctoral program. Mathematical competence of candidates shall be assessed by reviewing the curriculum of completed graduate courses. The minimum grade-point average of completed appropriate graduate courses required for the enrolment is 3.5. Applications for the enrolment shall be dealt with by the Council of the postgraduate course teaching staff.

The structure of the doctoral study program:The Faculty Council chooses up to four disciplines from pure mathematics and up to four disciplines from applied mathematics for which standard courses will be offered in next four years. There will be a qualifying exam for each of the chosen disciplines. Each year the Faculty Council approves up to 10 advanced courses which present recent mathematical discoveries or theories of fundamental importance for mathematics. A special care is taken in order to ensure that the advanced courses cover the most of major mathematical disciplines. Every year the Faculty Council announces a list of seminars. Furthermore, here is the list of ECTS points for doctoral program in mathematics: Standard course - 6 ECTS; Advanced course (2 semesters) - 8 ECTS; Advanced course (1 semester) - 4 ECTS; Introduction to scientific research - 24 ECTS; Seminar - 20 ECTS; Scientific Colloquium - 4 ECTS; Scientific research - 20 ECTS; PhD thesis - 28 ECTS. In the first year, students take two standard courses, Introduction to scientific research (for which the supervisor is responsible), Seminar and Scientific Colloquium. In the second year, students take advanced courses for 16 ECTS points, Scientific research, Seminar and Scientific Colloquium. In the third year, students take advanced courses for 8 ECTS points, Seminar and Scientific Colloquium, and write the PhD thesis. There is no essential difference in the organization of full-time and part-time studies. The difference is that expected duration of full-time study is 3-5 years, while for part-time study it is 5-7 years.

Conditions for completing the study program:The study program is completed by PhD thesis (dissertation) defence. The dissertation contains original mathematical discoveries by the author (it is allowed that a part of these discovering is already published by the author). In the procedure of the evaluation and defence of PhD thesis we follow the Regulations on Doctoral Studies at the University of Zagreb. 

Administrative and Academic Offices

Potential Supervisors and their Research Interests

Courses

Seminars

Regulations on Doctoral Studies at the University of Zagreb


Mathematics

1. semester, 1. year
ECTS Mandatory courses English level Semester workload Sem INFO
24.0 Introduction to scientific research (192552)
- 15
(15S)
1 INFO
4.0 Scientific colloquium 1 (192866)
- 15
(15S)
1 INFO
ECTS Required courses
=> Pristupni kolegiji
English level Semester workload Sem INFO
6.0 Algebra (155702)
Adamović, D.; Ciganović, I.
- 60
(60L)
1 INFO
6.0 Analysis (192256)
Antonić, N.
- 60
(60L)
1 INFO
6.0 Geometry and topology (155704)
Pandžić, P.; Resman, M.
- 60
(60L)
1 INFO
6.0 Numerical mathematics (208302)
Grubišić, L.
- 60
(60L)
1 INFO
6.0 Partial differential equations (155705)
Muha, B.; Tambača, J.
- 60
(60L)
1 INFO
6.0 Probability (155703)
Wagner, V.
- 60
(60L)
1 INFO
ECTS Seminar 1
=> Seminar 1
English level Semester workload Sem INFO
20.0 Seminar for algebra 1 (155732)
- 60
(60S)
1 INFO
20.0 Seminar for analysis 1 (155761)
- 60
(60S)
1 INFO
20.0 Seminar for analysis and algeba (Alpe Adria, Croatia-Slovenia) 1 (208557)
- 60
(60S)
1 INFO
20.0 Seminar for combinatorial and discrete mathematics 1 (155726)
- 60
(60S)
1 INFO
20.0 Seminar for differential equations and nonlinear analysis 1 (155717)
- 60
(60S)
1 INFO
20.0 Seminar for differential equations and numerical analysis 1 (155716)
- 60
(60S)
1 INFO
20.0 Seminar for differential geometry 1 (155728)
- 60
(60S)
1 INFO
20.0 Seminar for discrete mathematics 1 (155737)
- 60
(60S)
1 INFO
20.0 Seminar for dynamical systems 1 (192763)
- 60
(60S)
1 INFO
20.0 Seminar for finite geometry and groups 1 (155729)
- 60
(60S)
1 INFO
20.0 Seminar for finite mathematics 1 (155738)
- 60
(60S)
1 INFO
20.0 Seminar for functional analysis 1 (155720)
- 60
(60S)
1 INFO
20.0 Seminar for geometry 1 (155724)
- 60
(60S)
1 INFO
20.0 Seminar for inequalities and applications 1 (192764)
- 60
(60S)
1 INFO
20.0 Seminar for mathematical analysis and applications 1 (208561)
- 60
(60S)
1 INFO
20.0 Seminar for mathematical didactics 1 (155734)
- 60
(60S)
1 INFO
20.0 Seminar for mathematical logics and foundations of mathematics 1 (155719)
- 60
(60S)
1 INFO
20.0 Seminar for mathematical programming and game theory 1 (155725)
- 60
(60S)
1 INFO
20.0 Seminar for mathematical programming and game theory 1 (208550)
- 60
(60S)
1 INFO
20.0 Seminar for number theory and algebra 1 (155723)
- 60
(60S)
1 INFO
20.0 Seminar for numerical mathematics and scientific computing 1 (155727)
- 60
(60S)
1 INFO
20.0 Seminar for optimization and applications 1 (155735)
- 60
(60S)
1 INFO
20.0 Seminar for probability 1 (155721)
- 60
(60S)
1 INFO
20.0 Seminar for representation theory 1 (155722)
- 60
(60S)
1 INFO
20.0 Seminar for theoretical computer science 1 (155731)
- 60
(60S)
1 INFO
20.0 Seminar for topology 1 (155718)
- 60
(60S)
1 INFO
20.0 Seminar for topology 1 (155736)
- 60
(60S)
1 INFO
20.0 Seminar for unitary representations and automorphic forms 1 (155733)
- 60
(60S)
1 INFO
3. semester, 2. year
ECTS Mandatory courses English level Semester workload Sem INFO
4.0 Scientific colloquium 2 (192867)
- 15
(15S)
3 INFO
20.0 Scientific research (192876)
- 15
(15S)
3 INFO
ECTS Seminar 2
=> Seminar 2
English level Semester workload Sem INFO
20.0 Seminar for algebra 2 (192767)
- 60
(60S)
3 INFO
20.0 Seminar for analysis 2 (192768)
- 60
(60S)
3 INFO
20.0 Seminar for analysis and algeba (Alpe Adria, Croatia-Slovenia) 2 (208559)
- 60
(60S)
3 INFO
20.0 Seminar for combinatorial and discrete mathematics 2 (192776)
- 60
(60S)
3 INFO
20.0 Seminar for differential equations and nonlinear analysis 2 (192769)
- 60
(60S)
3 INFO
20.0 Seminar for differential equations and numerical analysis 2 (192770)
- 60
(60S)
3 INFO
20.0 Seminar for differential geometry 2 (192771)
- 60
(60S)
3 INFO
20.0 Seminar for discrete mathematics 2 (192773)
- 60
(60S)
3 INFO
20.0 Seminar for dynamical systems 2 (192772)
- 60
(60S)
3 INFO
20.0 Seminar for finite geometry and groups 2 (192777)
- 60
(60S)
3 INFO
20.0 Seminar for finite mathematics 2 (192778)
- 60
(60S)
3 INFO
20.0 Seminar for functional analysis 2 (192774)
- 60
(60S)
3 INFO
20.0 Seminar for geometry 2 (192775)
- 60
(60S)
3 INFO
20.0 Seminar for inequalities and applications 2 (192781)
- 60
(60S)
3 INFO
20.0 Seminar for mathematical analysis and applications 2 (208563)
- 60
(60S)
3 INFO
20.0 Seminar for mathematical didactics 2 (192780)
- 60
(60S)
3 INFO
20.0 Seminar for mathematical logics and foundations of mathematics 2 (192779)
- 60
(60S)
3 INFO
20.0 Seminar for mathematical programming and game theory 2 (192784)
- 60
(60S)
3 INFO
20.0 Seminar for mathematical programming and game theory 2 (208551)
- 60
(60S)
3 INFO
20.0 Seminar for number theory and algebra 2 (192786)
- 60
(60S)
3 INFO
20.0 Seminar for numerical mathematics and scientific computing 2 (192782)
- 60
(60S)
3 INFO
20.0 Seminar for optimization and applications 2 (192783)
- 60
(60S)
3 INFO
20.0 Seminar for probability 2 (192788)
- 60
(60S)
3 INFO
20.0 Seminar for representation theory 2 (192787)
- 60
(60S)
3 INFO
20.0 Seminar for theoretical computer science 2 (192785)
- 60
(60S)
3 INFO
20.0 Seminar for topology 2 (192789)
- 60
(60S)
3 INFO
20.0 Seminar for topology 2 (192791)
- 60
(60S)
3 INFO
20.0 Seminar for unitary representations and automorphic forms 2 (192790)
- 60
(60S)
3 INFO
5. semester, 3. year
ECTS Mandatory courses English level Semester workload Sem INFO
28.0 Doctoral dissertation (192877)
- 15
(15S)
5 INFO
4.0 Scientific colloquium 3 (192868)
- 15
(15S)
5 INFO
ECTS Seminar 3
=> Seminar 3
English level Semester workload Sem INFO
20.0 Seminar for algebra 3 (192793)
- 60
(60S)
5 INFO
20.0 Seminar for analysis 3 (192794)
- 60
(60S)
5 INFO
20.0 Seminar for analysis and algeba (Alpe Adria, Croatia-Slovenia) 3 (208560)
- 60
(60S)
5 INFO
20.0 Seminar for combinatorial and discrete mathematics 3 (192804)
- 60
(60S)
5 INFO
20.0 Seminar for differential equations and nonlinear analysis 3 (192795)
- 60
(60S)
5 INFO
20.0 Seminar for differential equations and numerical analysis 3 (192798)
- 60
(60S)
5 INFO
20.0 Seminar for differential geometry 3 (192799)
- 60
(60S)
5 INFO
20.0 Seminar for discrete mathematics 3 (192801)
- 60
(60S)
5 INFO
20.0 Seminar for dynamical systems 3 (192800)
- 60
(60S)
5 INFO
20.0 Seminar for finite geometry and groups 3 (192805)
- 60
(60S)
5 INFO
20.0 Seminar for finite mathematics 3 (192806)
- 60
(60S)
5 INFO
20.0 Seminar for functional analysis 3 (192802)
- 60
(60S)
5 INFO
20.0 Seminar for geometry 3 (192803)
- 60
(60S)
5 INFO
20.0 Seminar for inequalities and applications 3 (192809)
- 60
(60S)
5 INFO
20.0 Seminar for mathematical analysis and applications 3 (208564)
- 60
(60S)
5 INFO
20.0 Seminar for mathematical didactics 3 (192808)
- 60
(60S)
5 INFO
20.0 Seminar for mathematical logics and foundations of mathematics 3 (192807)
- 60
(60S)
5 INFO
20.0 Seminar for mathematical programming and game theory 3 (192812)
- 60
(60S)
5 INFO
20.0 Seminar for mathematical programming and game theory 3 (208552)
- 60
(60S)
5 INFO
20.0 Seminar for number theory and algebra 3 (192814)
- 60
(60S)
5 INFO
20.0 Seminar for numerical mathematics and scientific computing 3 (192810)
- 60
(60S)
5 INFO
20.0 Seminar for optimization and applications 3 (192811)
- 60
(60S)
5 INFO
20.0 Seminar for probability 3 (192816)
- 60
(60S)
5 INFO
20.0 Seminar for representation theory 3 (192815)
- 60
(60S)
5 INFO
20.0 Seminar for theoretical computer science 3 (192813)
- 60
(60S)
5 INFO
20.0 Seminar for topology 3 (192817)
- 60
(60S)
5 INFO
20.0 Seminar for topology 3 (192819)
- 60
(60S)
5 INFO
20.0 Seminar for unitary representations and automorphic forms 3 (192818)
- 60
(60S)
5 INFO
1. semester, 1. year
ECTS Mandatory courses English level Semester workload Sem INFO
24.0 Introduction to scientific research (192552)
- 15
(15S)
1 INFO
4.0 Scientific colloquium 1 (192866)
- 15
(15S)
1 INFO
ECTS Required courses
=> Pristupni kolegiji
English level Semester workload Sem INFO
6.0 Algebra (155702)
Adamović, D.; Ciganović, I.
- 60
(60L)
1 INFO
6.0 Analysis (192256)
Antonić, N.
- 60
(60L)
1 INFO
6.0 Geometry and topology (155704)
Pandžić, P.; Resman, M.
- 60
(60L)
1 INFO
6.0 Numerical mathematics (208302)
Grubišić, L.
- 60
(60L)
1 INFO
6.0 Partial differential equations (155705)
Muha, B.; Tambača, J.
- 60
(60L)
1 INFO
6.0 Probability (155703)
Wagner, V.
- 60
(60L)
1 INFO
ECTS Seminar 1
=> Seminar 1
English level Semester workload Sem INFO
20.0 Seminar for algebra 1 (155732)
- 60
(60S)
1 INFO
20.0 Seminar for analysis 1 (155761)
- 60
(60S)
1 INFO
20.0 Seminar for analysis and algeba (Alpe Adria, Croatia-Slovenia) 1 (208557)
- 60
(60S)
1 INFO
20.0 Seminar for combinatorial and discrete mathematics 1 (155726)
- 60
(60S)
1 INFO
20.0 Seminar for differential equations and nonlinear analysis 1 (155717)
- 60
(60S)
1 INFO
20.0 Seminar for differential equations and numerical analysis 1 (155716)
- 60
(60S)
1 INFO
20.0 Seminar for differential geometry 1 (155728)
- 60
(60S)
1 INFO
20.0 Seminar for discrete mathematics 1 (155737)
- 60
(60S)
1 INFO
20.0 Seminar for dynamical systems 1 (192763)
- 60
(60S)
1 INFO
20.0 Seminar for finite geometry and groups 1 (155729)
- 60
(60S)
1 INFO
20.0 Seminar for finite mathematics 1 (155738)
- 60
(60S)
1 INFO
20.0 Seminar for functional analysis 1 (155720)
- 60
(60S)
1 INFO
20.0 Seminar for geometry 1 (155724)
- 60
(60S)
1 INFO
20.0 Seminar for inequalities and applications 1 (192764)
- 60
(60S)
1 INFO
20.0 Seminar for mathematical analysis and applications 1 (208561)
- 60
(60S)
1 INFO
20.0 Seminar for mathematical didactics 1 (155734)
- 60
(60S)
1 INFO
20.0 Seminar for mathematical logics and foundations of mathematics 1 (155719)
- 60
(60S)
1 INFO
20.0 Seminar for mathematical programming and game theory 1 (155725)
- 60
(60S)
1 INFO
20.0 Seminar for mathematical programming and game theory 1 (208550)
- 60
(60S)
1 INFO
20.0 Seminar for number theory and algebra 1 (155723)
- 60
(60S)
1 INFO
20.0 Seminar for numerical mathematics and scientific computing 1 (155727)
- 60
(60S)
1 INFO
20.0 Seminar for optimization and applications 1 (155735)
- 60
(60S)
1 INFO
20.0 Seminar for probability 1 (155721)
- 60
(60S)
1 INFO
20.0 Seminar for representation theory 1 (155722)
- 60
(60S)
1 INFO
20.0 Seminar for theoretical computer science 1 (155731)
- 60
(60S)
1 INFO
20.0 Seminar for topology 1 (155718)
- 60
(60S)
1 INFO
20.0 Seminar for topology 1 (155736)
- 60
(60S)
1 INFO
20.0 Seminar for unitary representations and automorphic forms 1 (155733)
- 60
(60S)
1 INFO
2. semester, 1. year
3. semester, 2. year
ECTS Mandatory courses English level Semester workload Sem INFO
4.0 Scientific colloquium 2 (192867)
- 15
(15S)
3 INFO
20.0 Scientific research (192876)
- 15
(15S)
3 INFO
ECTS Seminar 2
=> Seminar 2
English level Semester workload Sem INFO
20.0 Seminar for algebra 2 (192767)
- 60
(60S)
3 INFO
20.0 Seminar for analysis 2 (192768)
- 60
(60S)
3 INFO
20.0 Seminar for analysis and algeba (Alpe Adria, Croatia-Slovenia) 2 (208559)
- 60
(60S)
3 INFO
20.0 Seminar for combinatorial and discrete mathematics 2 (192776)
- 60
(60S)
3 INFO
20.0 Seminar for differential equations and nonlinear analysis 2 (192769)
- 60
(60S)
3 INFO
20.0 Seminar for differential equations and numerical analysis 2 (192770)
- 60
(60S)
3 INFO
20.0 Seminar for differential geometry 2 (192771)
- 60
(60S)
3 INFO
20.0 Seminar for discrete mathematics 2 (192773)
- 60
(60S)
3 INFO
20.0 Seminar for dynamical systems 2 (192772)
- 60
(60S)
3 INFO
20.0 Seminar for finite geometry and groups 2 (192777)
- 60
(60S)
3 INFO
20.0 Seminar for finite mathematics 2 (192778)
- 60
(60S)
3 INFO
20.0 Seminar for functional analysis 2 (192774)
- 60
(60S)
3 INFO
20.0 Seminar for geometry 2 (192775)
- 60
(60S)
3 INFO
20.0 Seminar for inequalities and applications 2 (192781)
- 60
(60S)
3 INFO
20.0 Seminar for mathematical analysis and applications 2 (208563)
- 60
(60S)
3 INFO
20.0 Seminar for mathematical didactics 2 (192780)
- 60
(60S)
3 INFO
20.0 Seminar for mathematical logics and foundations of mathematics 2 (192779)
- 60
(60S)
3 INFO
20.0 Seminar for mathematical programming and game theory 2 (192784)
- 60
(60S)
3 INFO
20.0 Seminar for mathematical programming and game theory 2 (208551)
- 60
(60S)
3 INFO
20.0 Seminar for number theory and algebra 2 (192786)
- 60
(60S)
3 INFO
20.0 Seminar for numerical mathematics and scientific computing 2 (192782)
- 60
(60S)
3 INFO
20.0 Seminar for optimization and applications 2 (192783)
- 60
(60S)
3 INFO
20.0 Seminar for probability 2 (192788)
- 60
(60S)
3 INFO
20.0 Seminar for representation theory 2 (192787)
- 60
(60S)
3 INFO
20.0 Seminar for theoretical computer science 2 (192785)
- 60
(60S)
3 INFO
20.0 Seminar for topology 2 (192789)
- 60
(60S)
3 INFO
20.0 Seminar for topology 2 (192791)
- 60
(60S)
3 INFO
20.0 Seminar for unitary representations and automorphic forms 2 (192790)
- 60
(60S)
3 INFO
4. semester, 2. year
5. semester, 3. year
ECTS Mandatory courses English level Semester workload Sem INFO
28.0 Doctoral dissertation (192877)
- 15
(15S)
5 INFO
4.0 Scientific colloquium 3 (192868)
- 15
(15S)
5 INFO
ECTS Seminar 3
=> Seminar 3
English level Semester workload Sem INFO
20.0 Seminar for algebra 3 (192793)
- 60
(60S)
5 INFO
20.0 Seminar for analysis 3 (192794)
- 60
(60S)
5 INFO
20.0 Seminar for analysis and algeba (Alpe Adria, Croatia-Slovenia) 3 (208560)
- 60
(60S)
5 INFO
20.0 Seminar for combinatorial and discrete mathematics 3 (192804)
- 60
(60S)
5 INFO
20.0 Seminar for differential equations and nonlinear analysis 3 (192795)
- 60
(60S)
5 INFO
20.0 Seminar for differential equations and numerical analysis 3 (192798)
- 60
(60S)
5 INFO
20.0 Seminar for differential geometry 3 (192799)
- 60
(60S)
5 INFO
20.0 Seminar for discrete mathematics 3 (192801)
- 60
(60S)
5 INFO
20.0 Seminar for dynamical systems 3 (192800)
- 60
(60S)
5 INFO
20.0 Seminar for finite geometry and groups 3 (192805)
- 60
(60S)
5 INFO
20.0 Seminar for finite mathematics 3 (192806)
- 60
(60S)
5 INFO
20.0 Seminar for functional analysis 3 (192802)
- 60
(60S)
5 INFO
20.0 Seminar for geometry 3 (192803)
- 60
(60S)
5 INFO
20.0 Seminar for inequalities and applications 3 (192809)
- 60
(60S)
5 INFO
20.0 Seminar for mathematical analysis and applications 3 (208564)
- 60
(60S)
5 INFO
20.0 Seminar for mathematical didactics 3 (192808)
- 60
(60S)
5 INFO
20.0 Seminar for mathematical logics and foundations of mathematics 3 (192807)
- 60
(60S)
5 INFO
20.0 Seminar for mathematical programming and game theory 3 (192812)
- 60
(60S)
5 INFO
20.0 Seminar for mathematical programming and game theory 3 (208552)
- 60
(60S)
5 INFO
20.0 Seminar for number theory and algebra 3 (192814)
- 60
(60S)
5 INFO
20.0 Seminar for numerical mathematics and scientific computing 3 (192810)
- 60
(60S)
5 INFO
20.0 Seminar for optimization and applications 3 (192811)
- 60
(60S)
5 INFO
20.0 Seminar for probability 3 (192816)
- 60
(60S)
5 INFO
20.0 Seminar for representation theory 3 (192815)
- 60
(60S)
5 INFO
20.0 Seminar for theoretical computer science 3 (192813)
- 60
(60S)
5 INFO
20.0 Seminar for topology 3 (192817)
- 60
(60S)
5 INFO
20.0 Seminar for topology 3 (192819)
- 60
(60S)
5 INFO
20.0 Seminar for unitary representations and automorphic forms 3 (192818)
- 60
(60S)
5 INFO
6. semester, 3. year

  (*)Course is currently not active
(***)Course is active in other academic year