Structure of the PhD School of Mathematics program

No	Code	Course	Sem.	Status	Active classes per week			ECTS
					Lec.	Res. S.	Other
The first year
1	MDS0I1	Elective course 1	1	И	5			12
2	MDS0I2	Elective course 2	1	И	5			12
3	MDS001	Seminar work 1 – Research study	1	О	2	10		6
4	MDS0I3	Elective course 3	2	И	5			12
5	MDS0I4	Elective course 4	2	И	5			12
6	MDS002	Seminar work 2 – Research study	2	О	2	10		6
Total number of classes per week/ECTS in the first year					24	20		60
The second year
7	MDS0I5	Elective course 5	3	И	5			12
8	MDS0I6	Elective course 6	3	И	5			12
9	MDS003	Seminar work 3 – Research study	3	О	2	10		6
10	MDS004	Scientific work 1 – Research work	4	O	0	10		12
11	MDS005	Scientific work 2 – Research work	4	O	0	10		12
12	MDS006	Seminar work – Research work	4	О	0	8		6
Total number of classes per week/ECTS in the second year					12	38		60
The third year
13	MDS007	Scientific paper 1 – Research paper	5	О		20		30
14	MDS008	Scientific paper 2 – Research paper	6	О		20		15
15	MDS009	PhD Theses	6	О		10		15
Total number of classes per week/ECTS in the third year						50		60
Total number of classes per week/ECTS					36	108		180

Elective courses

No	Code	Title	Teacher	Sem.	ECTS	Scientific topic	Type
Mycrolocal analysis
1	MDSMA1	Analysis on manifolds	To be assigned for every school year	1	12	Mathematics	Elect.
2	MDSMA2	Locally convex spaces		1	12	Mathematics	Elect.
3	MDSMA3	Time frequency analysis		2	12	Mathematics	Elect.
4	MDSMA4	Generalized functions		2	12	Mathematics	Elect.
5	MDSMA5	Integral transforms		2	12	Mathematics	Elect.
6	MDSMA6	Microlocal analysis		3	12	Mathematics	Elect.
7	MDSMA7	Pseudodifferential and Fourier integral operators		3	12	Mathematics	Elect.
Operator theory
8	MDSTO1	Measure and integration		1	12	Mathematics	Elect.
9	MDSTO2	Functional analysis		1	12	Mathematics	Elect.
10	MDSTO3	Banach algebras and spectral theory		2	12	Mathematics	Elect.
11	MDSTO4	Generalized inveres		2	12	Mathematics	Elect.
12	MDSTO5	Functional analysis 2		2	12	Mathematics	Elect.
13	MDSTO6	Unbounded linear operators		3	12	Mathematics	Elect.
14	MDSTO7	Fredholm theory		3	12	Mathematics	Elect.
15	MDSTO8	Functional analysis 3		3	12	Mathematics	Elect.
16	MDSTO9	Operator algebras and Hilbert C*-modules		3	12	Mathematics	Elect.
Partial differential equations
17	MDSPD1	Linear partial differential equations		1	12	Mathematics	Elect.
18	MDSPD2	Numerical solutions of partial differential equations		1	12	Mathematics	Elect.
19	MDSPD3	Hyperbolic partial differential equations		2	12	Mathematics	Elect.
20	MDSPD4	Finite elements method		2	12	Mathematics	Elect.
21	MDSPD5	Mathematical method in the mechanics of continuum		2	12	Mathematics	Elect.
22	MDSPD6	Mathematical aspects of quantum mechanics		3	12	Mathematics	Elect.
23	MDSPD7	Symmetry groups		3	12	Mathematics	Elect.
24	MDSPD8	Nonlinear partial differential equations		3	12	Mathematics	Elect.
25	MDSPD9	Mathematical methods in the kinetic theory of gases		3	12	Mathematics	Elect.
Dynamical systems and differential geometry
26	MDSD01	Lie groups and algebras		1	12	Mathematics	Elect.
27	MDSD02	Differential geometry		1	12	Mathematics	Elect.
28	MDSD03	Riemannian manifolds		2	12	Mathematics	Elect.
29	MDSD04	Semi-Riemannian geometry		2	12	Mathematics	Elect.
30	MDSD05	Riemannian surfaces and algebraic curves		2	12	Mathematics	Elect.
31	MDSD06	Symplectic geometry and analytical mechanics		3	12	Mathematics	Elect.
32	MDSD07	Generalized Riemannian spaces		3	12	Mathematics	Elect.
33	MDSD08	Geodesic mappings		3	12	Mathematics	Elect.
34	MDSD09	Dynamical systems		1	12	Mathematics	Elect.
35	MDSD10	Regularly varying functions and differential equations		2	12	Mathematics	Elect.
Mathematical logic
36	MDSL01	Nonclassical logics		1	12	Mathematics	Elect.
37	MDSL02	Mathematical logic		1	12	Mathematics	Elect.
38	MDSL03	Cryptology 1		1	12	Mathematics	Elect.
39	MDSL04	Model theory		2	12	Mathematics	Elect.
40	MDSL05	Automatic and interactive proofers		2	12	Mathematics	Elect.
41	MDSL06	Formalization of reasoning in the presence of uncertainty		2	12	Mathematics	Elect.
42	MDSL07	Cryptology 2		2	12	Mathematics	Elect.
43	MDSL08	Blockchain		3	12	Mathematics	Elect.
44	MDSL09	Proof theory and category theory		3	12	Mathematics	Elect.
45	MDSL10	Computability		3	12	Mathematics	Elect.
Numerical analysis and optimization
46	MDSN01	Approximation theory		1	12	Mathematics	Elect.
47	MDSN02	Linear programming and optimization		1	12	Mathematics	Elect.
48	MDSN03	Numerical optimization		1	12	Mathematics	Elect.
49	MDSN10	Graph theory		1	12	Mathematics	Elect.
50	MDSN04	Numerical linear algebra		2	12	Mathematics	Elect.
51	MDSN05	Numerical integration		2	12	Mathematics	Elect.
52	MDSN06	Multicriteria optimization		2	12	Mathematics	Elect.
53	MDSN07	Metaheuristic methods		2	12	Mathematics	Elect.
54	MDSN08	Distributed optimization		3	12	Mathematics	Elect.
55	MDSN09	Nonlinear optimization in time		3	12	Mathematics	Elect.
56	MDSN11	Stochastic optimization		3	12	Mathematics	Elect.
57	MDSN12	Introduction to the machine learning		3	12	Mathematics	Elect.
58	MDSN13	Artificial neuron networks		3	12	Mathematics	Elect.
Set theory and topology
59	MDST01	Algebraic topology		1	12	Mathematics	Elect.
60	MDST02	Introduction to the set theory		1	12	Mathematics	Elect.
61	MDST03	Torus topology		2	12	Mathematics	Elect.
62	MDST04	Models of the set theory		2	12	Mathematics	Elect.
63	MDST05	Set theoretic topology		2	12	Mathematics	Elect.
64	MDST06	Descriptive combinatorics		3	12	Mathematics	Elect.
65	MDST07	Polytope theory		3	12	Mathematics	Elect.
66	MDST08	Regularity and combinatorial strustures		3	12	Mathematics	Elect.
67	MDST09	Boolean algebras		3	12	Mathematics	Elect.
Algebra
68	MDSA01	General algebra		1	12	Mathematics	Elect.
69	MDSA02	Theory of ordered sets		1	12	Mathematics	Elect.
70	MDSA03	Semigroup theory		1	12	Mathematics	Elect.
71	MDSA04	Universal algebgra		1	12	Mathematics	Elect.
72	MDSA05	Ordered algebraic structures		2	12	Mathematics	Elect.
73	MDSA06	Semiring theory		2	12	Mathematics	Elect.
74	MDSA07	Network theory		2	12	Mathematics	Elect.
75	MDSA08	Fuzzy sets and systems		3	12	Mathematics	Elect.
76	MDSA09	Group theory		3	12	Mathematics	Elect.
77	MDSA10	Relational systems		3	12	Mathematics	Elect.
Stochastics and mathematical statistics
78	MDSS01	Mathematical statistics		1	12	Mathematics	Elect.
79	MDSS02	Stochastic analysis		1	12	Mathematics	Elect.
80	MDSS03	Probability theory and stochastic processes		1	12	Mathematics	Elect.
81	MDSS04	Stochastic differetinal equations		2	12	Mathematics	Elect.
82	MDSS05	Time series analysis		2	12	Mathematics	Elect.
83	MDSS06	Theory of stability of stochastic differential equations		2	12	Mathematics	Elect.
84	MDSS07	Generalized stochastic processes		2	12	Mathematics	Elect.
85	MDSS08	Statistical modeling		3	12	Mathematics	Elect.
86	MDSS09	Singular stochastic partial differential equations		3	12	Mathematics	Elect.
87	MDSS10	Monte Carlo method		3	12	Mathematics	Elect.