Department of Mathematics

The subject of scientific research of the Mathematics Department is found within major mathematical disciplines– mathematical analysis, algebra, geometry, probability and statistics and methodology.

Research based on statistical analyses of various types of time series with a significant practical application, mostly in econometrics. Special importance is given to the research of stochastic properties of such series, as well as to the construction of new, mathematically based, stochastic financial models which can describe different properties of the dynamics of real financial series and sequences.

The problem of estimating the parameters of the obtained models is studied extensivelly and for that purpose new, modern statistical techniques are introduced, primarily based on numerical integration and the application of various software tools. The focus here is on the method of empirical characteristic functions (ECF-method) and the method of probabilistic functions of generatrise (PGF-method), which have proven to be very effective in modeling the so-called nonlinear time series with pronounced fluctuations.

Application of methods of homotopy perturbations (HPM), as well as methods of homotopy analysis (HAM) in finding (exact or approximate) solutions of equations and problems of different types. By applying these two mathematical methods, for example, approximate solutions of differential equations and systems of partial equations are obtained, which occur in a wide group of physically based problems. On the other hand, the HPM and HAM methods have also been applied in solving various stochastic problems, such as the approximation of stochastic distributions that do not have a closed form or the determination of invariant probability measures of different types of chaotic maps.

The concept of a fixed point, its existence in Menger spaces, as well as in ordered and partially arranged b-metric spaces. Namely, special attention is given to the fixed point theorem for increasing mappings, as well as its direct consequences in metric spaces. We work on the concept of statistical causality and stopped statistical causality, which includes stopping times as well as their application to martingale theory, weak solutions of stochastic differential equations generated by semimartingales and the application of obtained results in the field of financial mathematics. Namely, the given concept of causality can be related to the orthogonality of the martingale, the stability of space of right-continuous martingales, the predictable representation property, extreme measures, optional and predictable projections, as well as purely discontinuous martingales. Using the concept of causality, we can describe weak solutions and local weak solutions of stochastic differential equations generated by semimartingales, solutions of the martingale problem (MP), stopped MP and local MP. The weak uniqueness and local uniqueness of these solutions can also be described by the concept of causality. All these concepts have a wide application in practice, especially in econometrics, financial mathematics, risk minimization of optimal stock trading strategies. ...

Participation in the Realization of Teaching

No Course Code Course Name Sem. Number of Classes Other ECTS Compulsory/Elective Course Type
L E OFT SRW
FIRST YEAR
1 43111 Mathematical Analysis 1 1 3 3 8 Compulsory Scientific-Vocational
2 43112 Linear Algebra 1 3 3 7 Compulsory Scientific-Vocational
3 43113 Basic Computer Skills 1 3 3 7 Compulsory Academic-general education
4 Блок 1 Elective Courses 1 1 2 2 7
1 43114 Elementary Mathematics Elective Academic-general education
2 43115 Fundamentals of Physics Elective Academic-general education
5 43121 Mathematical Analysis 2 2 3 3 8 Compulsory Scientific-Vocational
6 43122 Algebra 1 2 3 3 7 Compulsory Scientific-Vocational
7 43123 Descriptive Geometry 2 2 2 4 Compulsory Scientific-Vocational
8 43124 Analytical Geometry 2 2 2 5 Compulsory Scientific-Vocational
9 Блок 2 Elective Courses 2 2 2 2 7
3 43125 Financial Mathematics Elective Academic-general education
4 43126 Basics of Combinatorics Elective Theoretical-Methodological
Total number of classes (L, E, OFT, SRW): 23 23    60
Total number of classes: 46
SECOND YEAR
10 43231 Mathematical Analysis 3 3 3 3 7 7 Compulsory Scientific-Vocational
11 43232 Discrete Mathematics 3 3 3 7 7 Compulsory Vocational-applicative
12 43233 Basics of Geometry 3 2 2 6 6 Compulsory Scientific-Vocational
13 43234 Algebra 2 3 3 3 6 6 Compulsory Scientific-Vocational
14 Блок 3 Elective Courses 3 3 1 1 4 4
5 43235 English Language 1 Elective Academic-general education
6 43236 Russian Language 1 Elective Academic-general education
15 43241 Mathematical Analysis 4 4 3 3 7 7 Compulsory Scientific-Vocational
16 43242 Algorithms and Data Structures 4 2 3 7 7 Compulsory Vocational-applicative
17 43243 Psychology 4 3 2 8 8 Compulsory Theoretical-Methodological
18 43244 Linear Programming 4 2 2 4 4 Compulsory Vocational-applicative
19 Блок 4 Elective Courses 4 4 1 1 4 4
7 43245 English Language 2 Elective Academic-general education
8 43246 Russian Language 2 Elective Academic-general education
Total number of classes (L, E, OFT, SRW): 23 23    60
Total number of classes: 46
THIRD YEAR
20 43351 Real Analysis 5 2 2 4 Compulsory Scientific-Vocational
21 43352 Object Oriented Programming 5 2 3 7 Compulsory Vocational-applicative
22 43353 Pedagogy 5 3 2 8 Compulsory Theoretical-Methodological
23 43354 Ordinary Differential Equations 5 2 2 4 Compulsory Vocational-applicative
24 Блок 5 Elective Courses 5 5 1 2 6
9 43355 History of Mathematics Elective Academic-general education
10 43356 Non-Euclidean Geometries Elective Scientific-Vocational
25 43361 Introduction to Differential Geometry 6 2 2 4 Compulsory Scientific-Vocational
26 43362 Numerical Analysis 6 3 3 7 Compulsory Vocational-applicative
27 43363 Complex Analysis 6 3 3 6 Compulsory Scientific-Vocational
28 43364 Mathematics Teaching Methodology 1 6 2 2 7 Compulsory Theoretical-Methodological
29 Блок 6 Elective Courses 6 6 2 2 7
11 43365 Mathematical Software Elective Vocational-applicative
12 43366 Databases Elective Vocational-applicative
Total number of classes (L, E, OFT, SRW): 22 23    60
Total number of classes: 45
FOURTH YEAR
30 43471 Introduction to Probability Theory 7 2 2 5 Compulsory Vocational-applicative
31 43472 Partial Equations 7 3 3 5 Compulsory Vocational-applicative
32 43473 Mathematics Teaching Methodology 2 7 2 2 7 Compulsory Theoretical-Methodological
33 43474 Mathematical Modelling 7 2 2 4 Compulsory Vocational-applicative
34 43475 Professional Practice 1 7 0 0 90 3 Compulsory Theoretical-Methodological
35 Блок 7 Elective Courses 7 7 2 2 7
13 43476 Numerical Methods Elective Vocational-applicative
14 43477 Nonlinear Optimization Elective Vocational-applicative
36 43481 Mathematical Statistics 8 2 2 5 Compulsory Vocational-applicative
37 43482 Functional Analysis 8 3 3 6 Compulsory Scientific-Vocational
38 43483 Topology 8 3 2 5 Compulsory Scientific-Vocational
39 43484 Professional Practice 2 0 0 90 3 Compulsory Theoretical-Methodological
40 Блок 8 Elective Courses 8 8 2 2 6
15 43485 Information and Communication Technologies in Education Elective Theoretical-Methodological
16 43486 Integral Equations Elective Scientific-Vocational
41 43487 Final Thesis 8 0 0 15 3 Compulsory/elective Vocational-applicative
43487 Final Thesis Writing and Defense 8 0 0 1 Compulsory/elective Academic-general education
Total number of classes (L, E, OFT, SRW): 21 20    195 60
Total number of classes: 41
Total number of classes, other classes and ECTS in all years of study: 178 195 240

No Course Code Course Name Sem. Lectures Practical classes ECTS
FIRST YEAR
1 42111 Mathematical Analysis 1 1 3 3 9
2 42112 Linear Algebra 1 3 3 8
3 42113 Basics of Computer Science Technics 1 3 3 7
4 Блок 1 Изборни блок 1 1
1 11155 English language 1 1 1 6
2 11156 Russian language 1 1 1 6
5 42121 Mathematical Analysis 2 2 3 3 9
6 42122 Algebra 1 2 3 3 7
7 42123 Analytic Geometry 2 3 3 8
8 Блок 2 Изборни блок 2 2
1 11254 English language 2 1 1 6
2 11255 Russian language 2 1 1 6
Total number of classes 20 20
Укупно ЕПСБ 60
SECOND YEAR
9 42231 Mathematical Analysis 3 3 3 3 9
10 42232 Discrete mathematics 3 3 3 7
11 42233 Geometry 1 3 2 2 7
12 42234 Algebra 2 3 3 3 7
13 42241 Mathematical Analysis 4 4 3 3 9
14 42242 Programming and Programming Languages 4 3 2 7
15 42243 Introduction to Probability Theory 4 2 2 6
16 42244 Ordinary Differential Equations 4 3 3 8
Total number of classes 22 21
Укупно ЕПСБ 60
THIRD YEAR
17 42351 Real Analysis 5 3 3 8
18 42352 Methodology of Teaching Mathematics 5 3 3 8
19 42353 Pedagogy and Psychology 5 2 2 6
20 Блок 3 Изборни блок 3 5
1 42354 Linear programming 2 2 8
2 42355 Mathematical Logic 2 2 8
21 42361 Complex analysis 6 3 3 8
21 42362 Numerical analysis 6 3 3 8
23 42363 History of mathematics 6 2 2 6
24 Блок 4 Изборни блок 4 6
1 42364 Geometry 2 2 2 8
2 42365 Algebra 3 2 2 8
Total number of classes 20 20
Укупно ЕПСБ 60
FOURTH YEAR
25 42471 Mathematical statistics 7 2 3 6
26 42472 Basic Principles of Mathematical Modeling 7 3 2 6
27 42473 Partial differential equations 7 3 3 7
28 Блок 5 Изборни блок 5 7
1 42474 Numerical methods 2 2 7
2 42475 Number theory 2 2 7
29 42481 Functional analysis 8 3 3 7
30 42482 Descriptive geometry 8 3 3 7
31 42483 Topology 8 3 3 7
32 Блок 6 Изборни блок 6 8
1 42484 Integral equations 2 2 7
2 42485 Software for mathematical computing 2 2 7
33 42486 Graduate Thesis 8 0 0 6
Total number of classes 21 21
Укупно ЕПСБ 60

No Course Code Course Name Sem. Number of Classes Other ECTS Compulsory/Elective Course type
L E OFT SRW
FIRST YEAR
1 43111 Contemporary Theories and Approaches to Mathematics Learning and Teaching 1 4 3 7 Compulsory Scientific-Vocational
2 43112 Professional Practice 1 1 0 0 90 3 Compulsory Vocational-applicative
3 Блок 1 Elective Courses 1 1 2 2 6
1 43113 Scientific Research Methodology Elective Vocational-applicative
2 43114 Methodology of Teaching Computer Science and Mathematics Elective Vocational-applicative
4 Блок 2 Elective Courses 2 1 2 2 6
3 43115 Selected Chapters in Operations Research Elective Vocational-applicative
4 43116 Selected Chapters in Mathematical Modelling Elective Vocational-applicative
5 43121 The Theory of Measure and Integration 2 4 3 8 Compulsory Scientific-Vocational
43122 Professional Practice 2 2 0 0 90 3 Compulsory Scientific-Vocational
6 Блок 3 Elective Courses 3 2 2 2 6
1 43123 Theory of The Generalised Inverse Elective Scientific-Vocational
2 43124 Fixed Point Theory Elective Scientific-Vocational
7 Блок 4 Elective Courses 4 2 2 2 6
3 43125 Selected Chapters in Geometry Elective Scientific-Vocational
4 43126 Selected Chapters in Probability and Statistics Elective Scientific-Vocational
8 43127 Student Research Work 2 9 5 Compulsory Theoretical-Methodological
9 43128 Master’s Thesis 2 2 60 8 Compulsory /Elective Theoretical-Methodological
43129 Master’s Thesis Writing and Defense 2 1 2 Compulsory /Elective Vocational-applicative
Total number of classes (L, E, OFT, SRW): 16 14 12 240 60
Total number of classes (L, E, OFT, SRW) and other classes: 16 14 12 240 60
Total number of classes: 42
Total number of classes, other classes and ECTS in all years of study: 42 240 60

Faculty members in the Department of Mathematics

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Full Professor

Jelena Z. Vujaković
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Associate Professor

Milena J. Petrović
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Associate Professor

Eugen Š. Ljajko
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Associate Professor

Nataša Z. Kontrec
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Associate Professor

Dragana J. Valjarević
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Assistant Professor

Marina Ž. Tošić Stojanović
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Assistant Professor

Marija S. Najdanović
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Teaching Assistant

Miroslav D. Maksimović
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Teaching Assistant

Milica R. Vučurović
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Teaching Assistant

Bojana S. Stojčetović
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Teaching Associate

Tanja D. Jovanović-Spasojević
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Teaching Associate

Kristina T. Tomović
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Teaching Associate

Mejrima Š. Ljajko
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