The professional title obtained is Doctor of Mathematical Sciences or Doctor of Computer Science
Doctor of Mathematical Sciences
The main objective of the program is to prepare candidates for independent, original and internationally recognized scientific research in the mathematical sciences. During their studies, candidates deepen their knowledge of selected areas of mathematics and develop the ability to independently identify and precisely define research problems, to formulate and rigorously prove mathematical statements, and to select, develop and apply appropriate theoretical, analytical and computational methods.
A further objective is to develop the ability to connect advanced mathematical concepts, to critically evaluate results and to disseminate them through scientific publications, conferences and collaboration in national and international research settings.
Doctor of Computer Science
The main objective of the program is to prepare candidates for independent, original and internationally recognized scientific research in computer science. During their studies, candidates deepen their knowledge of selected areas of computer science and develop the ability to independently identify and precisely define research problems, and to select, develop and apply appropriate theoretical, experimental and computational methods.
A further objective is to develop the ability to design and evaluate new algorithms, models, methods and software solutions, with critical evaluation of results, responsible application of research ethics and dissemination of results through scientific publications and international collaboration.
Competences specific to mathematics
Diploma holders are able to:
- systematically understand and interpret the fields of the mathematical sciences and master advanced research skills and methods in the mathematical sciences,
- identify and define relevant research problems, and plan and carry out research using appropriate methods of the mathematical sciences,
- conduct original research and make their own scientific contribution that extends existing knowledge in the mathematical sciences,
- communicate research results clearly and with sound arguments to the professional and the wider scientific community,
- relate the results of their own research to current international developments and critically assess their scientific significance and limitations,
- develop and apply new theoretical, analytical or computational approaches to solve complex research problems in their field,
- formulate new mathematical statements, develop rigorous proofs and critically evaluate the assumptions, methods and scope of the results obtained.
Competences specific to computer science
Diploma holders are able to:
- systematically understand the fields of computer science and master advanced research skills and methods in computer science,
- identify and define relevant research problems, and plan and carry out research using appropriate methods of computer science,
- conduct original research and make their own scientific contribution that extends the frontiers of existing knowledge in computer science,
- communicate research results clearly and with sound arguments to the professional and the wider scientific community,
- relate the results of their own research to current international developments and critically assess their scientific significance and limitations,
- develop, theoretically analyze and experimentally evaluate new algorithms, computational models and artificial intelligence methods, including machine learning and deep learning, as well as software solutions for complex research problems in their field,
- verify and critically evaluate computational methods and systems, taking into account the reliability, reproducibility and scientific soundness of research results.
Generic competences
Diploma holders are expected to:
- have a systematic understanding of the field of study and master research skills and methods,
- critically analyze, evaluate and synthesize new and complex ideas,
- independently prepare scientific papers for publication in relevant scientific publications and present the results of their research at national and international scientific conferences,
- communicate with colleagues, the wider scientific community and society as a whole in their area of expertise,
- understand and apply recognized codes of ethics in their research,
- contribute to the development of science, education, innovation and knowledge transfer, and promote technological, social and cultural progress in a knowledge-based society.
Doctor of Mathematical Sciences
The degree of Doctor of Mathematical Sciences qualifies the holder for independent scientific research and, subject to the applicable legal requirements, for teaching theoretical and applied mathematics at university level, as well as for work in research institutes. The holder is also qualified for professional, analytical and development work in institutions and organizations that require advanced theoretical and applied knowledge of mathematics.
Professional engagement may include the development and analysis of mathematical models and methods, interdisciplinary research, higher education and research projects, and expert and advisory work based on advanced mathematical competences.
Doctor of Computer Science
The degree of Doctor of Computer Science qualifies the holder for independent scientific research and, subject to the applicable legal requirements, for teaching computer science at university level and for work in research institutes. The holder is also qualified for research, development, professional and expert work in institutions and organizations that require advanced knowledge of computer science.
Professional engagement may include the development and evaluation of algorithms, models, methods and complex software systems, leading research and development projects, interdisciplinary research, and expert and advisory work in the academic, public and private sectors.
Curriculum for the 3rd cycle of study “Doctoral Studies in Mathematical and Computer Science” (valid for students enrolled from the academic year 2026/27)
(Curricula that were valid for students enrolled until the academic year 2020/2021)
(Curricula that were valid for students enrolled from the academic year 2021/2022 to 2025/2026)
Admission requirements
The requirements for admission to the program are:
a. At least 50% overlap of the content of mathematics and computer science courses, in both the first and the second cycle of study, with the corresponding study program at the Department;
b. A grade point average of at least 8 in the first cycle and at least 8.5 in the second cycle of study;
c. Candidates who do not meet requirement a. or b. may take an entrance examination. The Doctoral Study Council determines the content of the entrance examination for each candidate individually, and the examination is conducted by a committee appointed by the Council.
d. Candidates are advised to submit, together with their application for the doctoral program, a letter of motivation and a letter of recommendation from a potential academic advisor/mentor.
| Code | Course Title | No. contact hours | ECTS |
|---|---|---|---|
| EDU 605 | Research Methodology and Academic Skills | 30 | 10 |
| Elective Course 1 | 30 | 10 | |
| Elective Course 2 | 30 | 10 |
| Code | Course Title | No. contact hours | ECTS |
|---|---|---|---|
| Elective Course 3 | 30 | 10 | |
| Elective Course 4 | 30 | 10 | |
| Elective Course 5 | 30 | 10 |
| Code | Course Title | No. contact hours | ECTS |
|---|---|---|---|
| Work on Doctoral Thesis – Doctoral Seminar | 30 |
| Code | Course Title | No. contact hours | ECTS |
|---|---|---|---|
| Work on Doctoral Thesis | 30 |
| Code | Course Title | No. contact hours | ECTS |
|---|---|---|---|
| Work on Doctoral Thesis | 30 |
| Code | Course Title | No. contact hours | ECTS |
|---|---|---|---|
| Defense of Doctoral Thesis | 30 |
Courses with exclusively elective status
Two courses must be chosen from those listed below. One of the chosen courses must be from the candidate’s chosen research area:
| Code | Course Title |
|---|---|
| PMAT 601 | Advanced Topics in Mathematical Analysis |
| PMAT 701 | Advanced Topics in Algebra |
| PMAT 702 | Advanced Topics in Geometry |
| AMAT 601 | Advanced Methods of Applied Mathematics |
| CS 601 | Advanced Topics in Computer Science |
Courses with exclusively elective status
Three courses must be chosen, of which at least two must be from the group of courses of the chosen research area, and at most one may be from any other research area:
(G1) Mathematical Analysis
| Code | Course Title |
|---|---|
| PMAT 602 | Time-Scale Calculus and Special Functions |
| PMAT 603 | Heat and Wave Kernels on Manifolds and Discrete Structures: Analytical and Combinatorial Aspects |
| PMAT 604 | Spectral and Topological Graph Descriptors |
| PMAT 606 | Theory of L-Functions: Analytical and Numerical Approaches |
| PMAT 620 | Harmonic Function Theory |
| PMAT 625 | Generalised Functions |
| PMAT 645 | Algebraic Number Theory |
| PMAT 660 | Harmonic Analysis |
| PMAT 665 | Spectral Theory of Automorphic Forms |
| PMAT 670 | Spectral Graph Theory |
| PMAT 675 | Analysis on Manifolds |
| PMAT 686 | Selected Areas of Analytic Number Theory |
| PMAT 700 | Statistical Convergence |
(G2) Algebra, Geometry and Topology
| Code | Course Title |
|---|---|
| PMAT 615 | Finite Fields and Applications |
| PMAT 630 | Algebraic Topology I |
| PMAT 651 | Selected Areas of Combinatorics |
| PMAT 680 | Noncommutative Rings |
| PMAT 690 | Algebraic Topology II |
| PMAT 696 | Theory of Semigroups |
| PMAT 705 | Toric Varieties |
| PMAT 710 | Convex Polytopes |
(G3) Applied Mathematics
| Code | Course Title |
|---|---|
| AMAT 602 | Mathematical Biology |
| AMAT 603 | Selected Topics in Mathematical Statistics |
| AMAT 616 | Discrete Dynamical Systems |
| AMAT 625 | Numerical Methods for Solving Linear and Nonlinear Eigenvalue Problems |
| AMAT 655 | Continuous Dynamical Systems |
| AMAT 671 | Selected Areas of Cryptology |
| AMAT 676 | Chaos Theory |
| AMAT 680 | Stochastic Processes II |
(G4) Computer Science
Rules of study in the 3rd cycle of studies
In line with their research interests and in agreement with their academic advisor, a candidate enrolled in the Doctoral Studies in Mathematical and Computer Science at the Department of Mathematical and Computer Sciences chooses one of four areas of academic research: Mathematical Analysis (G1), Algebra, Geometry and Topology (G2), Applied Mathematics (G3) or Computer Science (G4).
In the first semester, the candidate takes one compulsory course, Research Methodology and Academic Skills, and chooses two elective courses from the list of courses offered for the first semester. One of the chosen courses must be from the candidate’s chosen research area.
In the second semester, the candidate chooses three elective courses, of which at least two must be from the group of courses of the chosen research area, and at most one may be from any other research area.
When choosing courses, the rule is that a candidate may take at most two courses with the same teacher, not counting the course Research Methodology and Academic Skills.
The list of courses for each candidate is confirmed by the Doctoral Study Council.
Activities in semesters III–VI consist of work on the doctoral dissertation and are aligned with the 2024 Rules of Study for the Third Cycle of Studies at the University of Sarajevo:
- In semester III, the candidate prepares and submits the application for the doctoral dissertation topic (form DS1).
- During semester IV, the candidate submits the application for the doctoral dissertation project. The candidate must take the public defense of the doctoral dissertation project by the end of the fifth semester.
- During semester V, the candidate prepares the working version of the doctoral dissertation and submits it for approval (form DS7).
- In semester VI, provided that all previous obligations have been fulfilled, the candidate may take the defense of the doctoral dissertation.