PhD - Mathematics

- The studies last 3 years and have the extent of 180 ECTS 
- This Study Program became active since the 2015/16. school year

1st Year


1st Semester
  Course name No. of hours
ECTS
1. A course 1 from optional block 
 4+6  9
2. A course 2 from optional block  4+6  9
3. Preparation of Doctoral Dissertation
 0+0  12
2nd Semester
  Course name No. of hours
ECTS
1. A course 3 from optional block  4+6  9
2. A course 4 from optional block  4+6  9
3. Preparation of Doctoral Dissertation  0+0  12
Total  40  60


2nd Year


3rd Semester
  Course name No. of hours
ECTS
1. A course 5 from optional block  4+6  9
2. A course 6 from optional block  4+6  9
3. Preparation of Doctoral Dissertation  0+0  12
4th Semester
  Course name No. of hours
ECTS
1. A course 7 from optional block  4+6  9
2. Special Course  4+6  9
3. Preparation of Doctoral Dissertation  0+0  12
Total  40  60


3rd Year


5th Semester
  Course name No. of hours ECTS
1. Scientific Paper 1  0+20  4
2. Preparation of Doctoral Dissertation  0+0  26
6th Semester
  Course name No. of hours
ECTS
1. Scientific Paper 2
 0+20  4
2. Preparation of Doctoral Dissertation  0+0  26
Total  40  60



Optional block - M3
  Course name No. of hours
ECTS
1. Algebra 4 4+6 9
2. Universal Algebra 4+6 9
3. Commutative Algebra 4+6 9
4. Rings and Modules 4+6 9
5. Algebraic Geometry 4+6 9
6. Homological Methods in Algebra 4+6 9
7. Model Theoretical Algebra 4+6 9
8. Noncommutative Algebra 4+6 9
9. Introduction to Hopf Algebras 4+6 9
10. Discrete Mathematics
4+6 9
11. Introduction to Representation Theory 4+6 9
12. Number Theory 4+6 9
13. Automorphic Forms and Representations 4+6 9
14. Special Course - Algebra 4+6 9
15. Analysis 4 4+6 9
16. Complex Analysis 2
4+6 9
17. Manifold Theory 4+6 9
18. Global Analysis 4+6 9
19. Morse Theory 4+6 9
20. Symplectic Manifolds 4+6 9
21. Hardy and Bergman Spaces 4+6 9
22. Enitre Functions 4+6 9
23.
Integral Operators 4+6
9
24.
Interpolation of Linear Operators 4+6
9

25.

Matrix Analysis 4+6
9
26. Operator Algebras 4+6
9
27.
Noncommutative Dynamics and Geometry 4+6
9
28.
Spectral Theory 4+6
9
29.
Harmonic Analysis 2 4+6
9
30.
Quasiconformal and Harmonic Mappings 4+6
9
31.
Differential Operators 4+6
9
32.
Pseudodifferential Operators 4+6
9
33.
Compact and Nonselfadjoint Operators 4+6
9
34.
Banach Algebras 4+6
9
35.
Linear Topological Spaces 4+6
9
36.
Theory of Distributions 4+6
9
37.
Functional Analysis 4+6
9
38.
Nonlinear Functional Analysis 4+6
9
39.
Stability of a Solution of Ordinary Differential Equations 4+6
9
40.
Qualitative Analysis of Ordinary Differential Equations 4+6
9
41.
Complex Dynamic Systems 4+6
9
42.
Asymptotic Analysis 4+6
9
43.
Fixed Point Theory 4+6
9
44.
Geometric function theory 2 4+6
9
45. Analysis on Manifolds 4+6 9
46.
Special Course - Analysis 4+6
9
47.
Riemannian Geometry A 4+6
9
48.
Riemannian Geometry B 4+6
9
49.
Groups in Geometry A 4+6
9
50.
Groups in Geometry B 4+6
9
51.
Non-Euclidian Geometries 4+6
9
52.
Regular polytopes 4+6
9
53.
The Geometry of Discrete Groups 4+6
9
54.
Complex Manifolds 4+6
9
55.
Spectral Geometry 4+6
9
56.
Differential Geometry of Vector Bundles 4+6
9
57.
Methods of Differential Geometry in Statistics 4+6
9
58.
Discrete Differential Geometry 4+6
9
59.
Geometry in Informatics 4+6
9
60.
Geometric Modeling and Design in Industry 4+6
9
61.
Symmetric Groups 4+6
9
62.
Transformation Groups 4+6
9
63.
Homogeneous Spaces 4+6
9
64.
Representations of Lie Groups and Algebras 4+6
9
65.
Symplectic geometry 4+6
9
66.
Stochastic Differential Geometry 4+6
9
67.
Theory of Submanifolds 4+6
9
68.
Special Course - Geometry 4+6
9
69.
Model Theory 4+6
9
70.
Computability theory 4+6
9
71.
Proof Theory 4+6
9
72.
Set Theory 4+6
9
73. Mathematical Logic in Computer Science 4+6
9
74.
Non-classical Logic 4+6
9
75.
Theoretical Computer Science 4+6
9
76.
Theory of Automata and Formal Languages 4+6
9
77.
Boolean Algebras 4+6
9
78.
Applicable Logic Theories 4+6
9
79.
Non-standard Analysis 4+6
9
80.
Special Course - Mathematical Logic and Theoretical Computer Science 4+6
9
81.
Selected Chapters of the Theory of Extremal Problems 4+6
9
82.
Numerical Analysis 3 4+6
9
83.
Finite Element Method and Applications 4+6
9
84.
Finite Difference Method 4+6
9
85.
Approximation Theory with Applications 4+6 9
86.
Game Theory 4+6
9
87.
Regularization Methods 4+6
9
88.
Discrete Optimization 4+6 9
89.
Pontryagin Maximum Principle 4+6
9
90.
Theory of Location Problems with Applications 4+6
9
91.
Metaheuristic Methods 4+6
9
92.
Spectral Graph Theory with Applications 4+6
9
93.
Graph Algorithms and their Applications 4+6
9
94.
Combinatorial Graph Theory with Applications 4+6
9
95.
Special Course – Applied Mathematics 4+6
9
96. Algebraic Combinatorics, Computability Theory and Computational Complexity Theory 4+6 9
97. Dynamical Systems 4+6 9
98. Optimization
4+6 9
99. Data Structures and High Level Computation
4+6 9
100.
Algebraic Topology 4+6
9
101.
Differential Topology 4+6 9
102.
Topological Combinatorics 4+6 9
103.
Discrete and Computational Topology
4+6
9
104.
Function Spaces 4+6
9
105.
PL Topology 4+6
9
106.
K - Theory 4+6
9
107.
Vector Bundles and Characteristic Classes 4+6
9
108.
Homotopy Theory 4+6
9
109.
Low - dimensional Topology 4+6
9
110.
Cohomology of Groups 4+6
9
111.
Spectral Sequences 4+6
9
112.
Selected Topics of General Topology 4+6
9
113.
Selected Topics of Algebraic Topology 4+6
9
114.
Cohomology Operations 4+6
9
115.
Theory of Cobordisms 4+6
9
116.
Equivariant Topology and Applications 4+6
9
117.
Special Course - Topology 4+6
9
118.
Mathematical Statistics
4+6
9
119.
Theory of Stochastic Processes 4+6
9
120.
Reliability Theory 4+6
9
121.
Queueing Theory 4+6
9
122.
Spectral Theory of Stochastic Processes 4+6
9
123.
Gaussian Stochastic Processes 4+6
9
124.
Stationary Stochastic Processes 4+6 9
125.
Time Series Analysis 4+6
9
126.
Statistics of Stochastic Processes 4+6
9
127.
Stochastic Differential Equations 4+6
9
128.
Stochastic  Financial Mathematics 4+6
9
129.
Testing Statistical Hypotheses 4+6
9
130.
Linear Statistical Models 4+6
9
131.
Nonparametric  Statistics 4+6
9
132.
Information Theory 4+6
9
133.
Coding Theory 4+6
9
134.
Ergodic Theory 4+6
9
135.
Stochastic Analysis 4+6
9
136.
Probability Measures in Metric Spaces 4+6
9
137.
Extreme Value Theory 4+6
9
138.
Risk Theory 4+6
9
139.
Special Course - Probability and Statistics 4+6 9
140.
Fluid Mechanics 4+6
9
141.
Integrable Dynamical Systems and Solitons 4+6
9
142. General Theory of Relativity and Cosmological Models 4+6 9
143.
Dynamics of the Systems of Bodies 4+6 9
144. Analytical Mechanics 4+6 9
145. Theory of Learning and  Teaching with  History of School and Pedagogical Ideas 4+6 9
146. Research Methodology in Teaching of Mathematics and Computer Science with Practicum 4+6 9
147. Teaching Methodology for Programming Courses
4+6 9
148. Internet and Software in Education 4+6 9