Mathematics

Program Description

 

The study program of doctoral studies in Mathematics is established by scientific staff capable for independent research in the mathematical sciences, as well as critical estimation of research in Mathematics and related fields. A key element in this regard is achieving a high level of knowledge and understanding of the latest trends in Mathematics, as well as introducing to the structure of the scientific research process and  skills which are necessary for effective preparation, publication and presentation of the results of scientific research, according to standards adopted in the Mathematical sciences.

 

The study program includes modern areas of Mathematics that are motivated by formulating and solving models for problems that arise in other scientific disciplines, for example in the natural sciences, in many areas of IT,  technical, technological, economic research, as well as medical, agricultural and human sciences. Therefore, in addition to research in the field of mathematical sciences, the study program provides to young scientists to gain knowledge for specific applications and integration into general social trends, with aim to use and apply Mathematics in raising of the general level of social development.

 

Students who complete the doctoral studies are young scientific researchers who possess modern scientific and technical knowledge required for inclusion in the global scientific trends in areas of interest. They have at least one published paper work or accepted for publication in leading international journals in the field of Mathematics of interest, and as a result confirmation that they will be able to continue successful scientific research independently and in collaboration with other researchers. These young doctors will acquire the necessary knowledge for inclusion in the university teaching process in the areas of Mathematics at the undergraduate and graduate studies in Mathematics, as well as studies in other areas. They will have knowledge and techniques needed for inclusion in the technical and scientific teams at other institutions of direct and indirect production, where they will contribute to the quality of scientific models with direct application. Successfull mastering of this program provides knowledge and methodological approach to the analysis of various problems thanks to the specifics of the mathematical formulation of evidence and assertions on which is particulary insisted in Mathematics.

 

The general structure of the curriculum of studies is very simple. It is anticipated that in the first four semesters the student passes 12 subjects, 3 per semester. Of these 12 subjects, 4 are seminar paperworks (one in each semester), while the remaining 8  are elective subjects that student choose from the available list (which has a total of 63 subjects), in consultation with his advisor.

 

Student chooses his advisor (tutor) or he is awarded to the student at the begining. Mentor takes over the role of advisor  at the time of application of doctoral dissertation.

 

In respect of seminar paperworks, the student (if it is necessary with help of his advisors) chooses the head of then seminar paperworks from the rank of teachers involved in the study program. In agreement with him he defines and processes the selected material. The results of  his work are public exposed at regular scientific seminars at Faculty of Science (in relevant fields), which are held once a week as part of the projects of the Ministry of Science of Republic of Serbia and other projects (international, regional, etc.).

 

All elective courses and seminars are equivalent to 10 ECTS, which makes a total of 120 ECTS in the first two years of study. The third year is entirely devoted to writing of doctoral dissertation that is 60 ECTS.

 

CURRICULUM  OF DOCTORAL STUDIES OF MATHEMATICS

 

Ordinal numberCourse codeCourse NameSemesterStatusClasses of active teachingECTS
LecturesSIR

First year

1.   Elective course 1 I I 4 2 10
2.   Elective course 2 I I 4 2 10
3. SR-01 Scientiffic essay 1 I O - 8 10
4.   Elective course 3 II I 4 2 10
5.   Elective course 4 II I 4 2 10
6. SR-02 Scientiffic essay 1 II O - 8 10
Total number of classes of active teaching: 40  
Total ECTS: 60

 Second year

1.   Elective course 5 III I 4 2 10
2.   Elective course 6 III I 4 2 10
3. SR-03 Scientiffic essay 3 III O - 8 10
4.   Elective course 7 IV I 4 2 10
5.   Elective course 8 IV I 4 2 10
6. SR-04 Scientiffic essay 4 IV O - 8 10
Total number of classes of active teaching: 40  
Total ECTS: 60

Third year

1. DD-01 Doctoral dissertation V O - 20 60
VI O - 20
Total number of classes of active teaching: 40  
Total ECTS: 60

 

THE LIST OF (ELECTIVE) SUBJECTS AT DOCTORAL STUDIES

 

Ordinal numberCourse codeCourse nameName(s) of teachersField of Academic Expertis
1. AN-01 Download Algebras of generalized functions (Serbian) dr Arpad Takači
dr Đurđica Takači
AiV
2. AN-02 Download Analysis on manifolds (Serbian) dr Stevan Pilipović AiV
3. AN-03 Download Classical measure theory (Serbian) dr Endre Pap AiV
4. AN-04 Download Linear partial differential equations (Serbian) dr Marko Nedeljkov AiV
5. AN-05a Download Small waves and Gabor’s analysis 1 (Serbian) dr Nenad Teofanov AiV
6. AN-05b Download Small waves and Gabor’s analysis 2 (Serbian) dr Nenad Teofanov AiV
7. AN-06 Download Non-additive measures (Serbian) dr Endre Pap
dr Ivana Štajner-Papuga
AiV
8. AN-07 Download Nonlinear Partial Differential Equations (Serbian) dr Marko Nedeljkov AiV
9. AN-08 Download Semigroups of operators (Serbian) dr Stavan Pilipović AiV
10. AN-09 Download Application of partial differential equations (Serbian) dr Marko Nedeljkov AiV
11. AN-10 Download Function spaces (Serbian) dr Arpad Takači
dr Dušanka Perišić
AiV
12. AN-11 Download Pseudo analysis (Serbian) dr Endre Pap AiV
13. AN-12a Download Pseudodifferential and Fourier integral operators 1 (Serbian) dr Nenad Teofanov AiV
14. AN-12b Download Pseudodifferential and Fourier integral operators 2 (Serbian) dr Nenad Teofanov AiV
15. AN-13 Download Accidental processes and chaos expansion (Serbian) dr Danijela Rajter-Ćirić
dr Dora Seleši
AiV
16. AN-13a Download General Stochastic Processes (Serbian) dr Danijela Rajter-Ćirić
dr Dora Seleši
AiV
17. AN-13b Download Stochastic differential equations (Serbian) dr Danijela Rajter-Ćirić
dr Dora Seleši
AiV
18. AN-14 Download Probability theory (Serbian) dr Zagorka Lozanov-Crvenković
dr Danijela Rajter-Ćirić
AiV
19. AN-15 Download Topology 1 (Serbian) dr Ljiljana Gajić AiV
20. AN-16 Download Topology 2 (Serbian) dr Olga Hadžić AiV
21. AN-17 Download Topology 3 (Serbian) dr Olga Hadžić AiV
22. AN-18 Download Topology 4 (Serbian) dr Miloš Kurilić AiV
23. AN-19 Download General  transformation and functions (Serbian) dr Arpad Takači
dr Dušanka Perišić
AiV
24. AN-20 Download Aggregation functions (Serbian) dr Endre Pap AiV
25. AN-21 Download Functional Analysis and Operator Theory 1 (Serbian) dr Stevan Pilipović AiV
26. AN-22 Download Functional Analysis and Operator Theory 2 (Serbian) dr Stevan Pilipović AiV
27. AN-23 Download General functions on manifolds (Serbian) dr Stevan Pilipović AiV
28. AN-24 Download Application of Lee groups to differential equations (Serbian) dr Stevan Pilipović AiV
29. AN-25 Download Semi-Riemann geometry (Serbian) dr Stevan Pilipović AiV
30. AL-01 Download Algebraic Logic (Serbian) dr Rozalia Madaras-Silađi AiML
31. AL-02 Download Boolean algebra (Serbian) dr Miloš Kurilić AiML
32. AL-03 Download Combinatorial group theory (Serbian) dr Petar Marković AiML
33. AL-04 Download Mathematical Logic (Serbian) dr Gradimir Vojvodić AiML
34. AL-05 Download General Algebra (Serbian) dr Siniša Crvenković AiML
35. AL-06 Download Model Theory I (Serbian) dr Milan Grulović AiML
36. AL-07 Download Model Theory II (Serbian) dr Milan Grulović AiML
37. AL-08 Download Network Theory I (Serbian) dr Andreja Tepavčević AiML
38. AL-09 Download Network Theory II (Serbian) dr Branimir Šešelja AiML
39. AL-10 Download SemigroupsTheory I (Serbian) dr Igor Dolinka AiML
40. AL-11 Download SemigroupsTheory II (Serbian) dr Igor Dolinka AiML
41. AL-12 Download Ring Theory (Serbian) dr Siniša Crvenković AiML
42. AL-13 Download The theory of fuzzy sets I (Serbian) dr Branimir Šešelja AiML
43. AL-14 Download The theory of fuzzy sets II (Serbian) dr Andreja Tepavčević AiML
44. AL-15 Download Set Theory I (Serbian) dr Kurilić Miloš AiML
45. AL-16 Download Set Theory II (Serbian) dr Kurilić Miloš AiML
46. AL-17 Download The theory of ordered sets (Serbian) dr Branimir Šešelja AiML
47. AL-18 Download Universal algebra I (Serbian) dr Petar Marković AiML
48. AL-19 Download Universal algebra II (Serbian) dr Petar Marković AiML
49. DM-01 Download Combinatorics (Serbian) dr Petrović Vojislav
dr Ivica Bošnjak
DM
50. DM-02 Download Graph Theory I (Serbian) dr Petrović Vojislav DM
51. DM-03 Download Graph Theory II (Serbian) dr Petrović Vojislav DM
52. MM-01 Download Mathematical models in engineering (Serbian) dr Marko Nedeljkov MM
53. MM-02 Download Mathematical models in finances (Serbian) dr Nataša Krejić MM
54. MM-03 Download Methods of functional analysis in the mechanics dr Teodor Atanacković MM
55. MM-04 Download Operations Research (Serbian) dr Nataša Krejić MM
56. NM-01 Download Iterative methods for linear problems (Serbian) dr Ljiljana Cvetković NM
57. NM-02 Download Numerical optimization (Serbian) dr Nataša Krejić
dr Zorana Lužanin
NM
58. NM-03 Download Numerical methods for mathematical models in economics (Serbian) dr Zorana Lužanin NM
59. NM-04 Download Numerical algorithms in linear algebra (Serbian) dr Ljiljana Cvetković NM
60. NM-05 Download Numerical solution of differential equations (Serbian) dr Dragoslav Herceg
dr Helena Zarin
NM
61. NM-06 Download Numerical solution of parabolic partial differential equations (Serbian) dr Dragoslav Herceg
dr Helena Zarin
NM
62. NM-07 Download Methods of finite elements for Partial Differential Equations (Serbian) dr Dragoslav Herceg
dr Helena Zarin
NM
63. NM-08 Download Scientific Computing (Serbian) dr Ljiljana Cvetković
dr Nataša Krejić
NM
64. TI-01 Download The theory of algorithms (Serbian) dr Siniša Crvenković TOI
65. TI-02 Download The theory of automation and formal languages (Serbian) dr Igor Dolinka TOI
Legend: AiV - Analysis and Probability, AIML - Algebra and Mathematical Logic, DM - Discrete Mathematics, MM - Mathematical Modeling, NM - Numerical Mathematics, TOI – Theoretical Basis of Informatics