31142
B
1-EFM-370
FMFI.KAMŠ/1-EFM-370/00
Financial Mathematics
5
Evaluation
lecture / practicals
2 / 2
26 / 26
1
(Single degree study, master II. deg., full time form)
Z
1
doc. Mgr. Igor Melicherčík, PhD., Mgr. Radoslav Hurtiš, PhD.
16.02.2026
20.06.2022
FMFI.KAMŠ/1-EFM-250/00 or FMFI.KAMŠ/1-DAV-102/20 or FMFI.KMANM/1-MAT-250/22
FMFI.KAMŠ/1-EFM-250/00 - Mathematical Analysis (4) or FMFI.KAMŠ/1-DAV-102/20 - Calculus (1) or FMFI.KMANM/1-MAT-250/22 - Mathematical Analysis (4)
1-EFM-250 - Mathematical Analysis (4) or 1-DAV-102 - Calculus (1) or 1-MAT-250 - Mathematical Analysis (4)
8
Person responsible for the delivery, development and quality of the study programme
prof. RNDr. Ján Filo, CSc.
filo1@uniba.sk
lecture
2
26
prezenčná
practicals
2
26
prezenčná
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Z
3
on-site learning
5
4889
DAV
Data Science
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3
on-site learning
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4891
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4
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1009661
1
P
lecturer
Igor
Melicherčík
doc. Mgr. Igor Melicherčík, PhD.
melichercik2@uniba.sk
Slovak
1184863
2
C
instructor
Radoslav
Hurtiš
Mgr. Radoslav Hurtiš, PhD.
hurtis3@uniba.sk
Slovak
SK
Slovak
Slovak
Z
1
<_C_>
Goal
Familiarize students with basic elements of the financial mathematics: theory of interest rates, portfolio theory and pricing of derivatives.
<_L_>
Recommended literature
Baxter M., Rennie A.: Financial Calculus
Hull J.: Options, Futures and Other Derivatives
Luenberger D.: Investment Science
<_P_>
Continuous assessment
Project, written test, activity during semester
<_PA_>
Conditions for completion of course
Evaluation during the semester: Project, written test, activity during exercises
Written exam. Voluntary oral examination to improve the final evaluation.
Informative evaluation scale: A 90%, B 80%, C 70%, D 60%, E 50%
<_PJ_>
Language, which knowledge is needed to pass the course
English, Slovak
<_SO_>
Brief outline of the course
Coupon and zero-coupon bonds, term structure of interest rates, bootstrap method, yield to maturity, forward rates, duration.
Risk aversion, properties of utility functions, utility functions and mean-variance analysis, the problem of Markowitz, Capital Asset Pricing Model (CAMP).
Binomial tree model, risk-neutral probabilities, risk-neutral pricing formula, Black-Scholes formula, pricing of american options.
<_VH_>
Weighting of course assessment (continuous/final)
50/50
<_VV_>
Learning outcomes
After completing the course, students will understand the basic principles of interest rate theory and bond investment management. They will also get acquainted with the principles of stock portfolio management. In the last part of the lecture, they will learn to price derivatives of the European and American type using binomial trees and will also get acquainted with Black-Scholes formulas for pricing put and call options.
<_Z_>
Final assessment
oral examination
A
445
58.86
B
157
20.77
C
81
10.71
D
46
6.08
E
21
2.78
FX
6
0.79
756
6
104340
B
1-FYZ-677
FMFI.KTF/1-FYZ-677/15
Mathematical Physics
7
Evaluation
lecture / practicals
4 / 2
52 / 26
1
(Single degree study, master II. deg., full time form)
Z
1
doc. RNDr. Marián Fecko, PhD.
16.02.2026
11.08.2022
8
Person responsible for the delivery, development and quality of the study programme
prof. RNDr. Ján Filo, CSc.
filo1@uniba.sk
lecture
4
52
prezenčná
practicals
2
26
prezenčná
B
4896
FYZ/k
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4
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7
2979
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Z
1
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1
4383
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1
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974
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3
on-site learning
5
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1014662
1
P
lecturer
Marián
Fecko
doc. RNDr. Marián Fecko, PhD.
fecko1@uniba.sk
Slovak
SK
Slovak
Slovak
Z
1
<_L_>
Recommended literature
Differential geometry and Lie groups for physicists / Marián Fecko. Cambridge : Cambridge University Press, 2006
Crampin,Pirani: Applicable differential geometry, CUP 1986
<_PA_>
Conditions for completion of course
Continuous assessment: homework
Examination: two written exams during the semester
Indicative rating scale: A 90%, B 80%, C 70%, D 60%, E 50%
<_PJ_>
Language, which knowledge is needed to pass the course
Slovak, English
<_SO_>
Brief outline of the course
Fundamentals of analysis on manifolds (tensor fields, Lie derivatives, Killing fields, ...) and introduction to the theory of Lie groups and Lie algebras and their representations. Group actions, homogeneous spaces.
<_URL_>
Course web page URL
http://davinci.fmph.uniba.sk/~fecko1/studenti.html
<_VH_>
Weighting of course assessment (continuous/final)
100/0
<_VV_>
Learning outcomes
After completing the course, students will be able to use the material contained
in the Brief syllabus.
A
41
48.81
B
14
16.67
C
14
16.67
D
5
5.95
E
5
5.95
FX
5
5.95
84
6
28192
B
1-MXX-161
FMFI.KJP/1-MXX-161/00
Russian Language (1)
2
Evaluation
practicals
2
26
1, 7
(Single degree study, master II. deg., full time form)
Z
1, 4
Viktoria Mirsalova
16.02.2026
20.06.2022
8
Person responsible for the delivery, development and quality of the study programme
prof. RNDr. Ján Filo, CSc.
filo1@uniba.sk
practicals
2
26
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on-site learning
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1317979
1
C
instructor
Viktoria
Mirsalova
Viktoria Mirsalova
mirsalova1@uniba.sk
Russian, Slovak
RJ
Russian
SK
Slovak
Russian, Slovak
Z
1
7
<_C_>
Goal
To master the fundamentals of general Russian. The language level is A1.
Learning the Cyrillic (Russian) alphabet, gaining basic language competence, building up skills and confidence in dealing with unfamiliar authentic and semi-authentic texts.
<_L_>
Recommended literature
The textbook: : Точка Ру A1 (Ольга Долматова, Екатерина Новачац), рracovné karty Падежи 1 (Л.С. Безкоровайная, В.Е. Штыленко).
<_P_>
Continuous assessment
test
<_SO_>
Brief outline of the course
To master the fundamentals of general Russian. The language level is A1.
Learning the Cyrillic (Russian) alphabet, gaining basic language competence, building up skills and confidence in dealing with unfamiliar authentic and semi-authentic texts.
The subject provides a course in Russian language for beginners.
<_VH_>
Weighting of course assessment (continuous/final)
100/0
<_VV_>
Learning outcomes
Basic communication in Russian, developing other Russian language skills - listening comprehension, reading and writing.
A
431
57.77
B
124
16.62
C
83
11.13
D
31
4.16
E
13
1.74
FX
64
8.58
746
6
28193
B
1-MXX-162
FMFI.KJP/1-MXX-162/00
Russian Language (2)
2
Evaluation
practicals
2
26
2, 8
(Single degree study, master II. deg., full time form)
L
1, 4
Viktoria Mirsalova
16.02.2026
20.06.2022
8
Person responsible for the delivery, development and quality of the study programme
prof. RNDr. Ján Filo, CSc.
filo1@uniba.sk
practicals
2
26
prezenčná
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1
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1
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L
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1
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4
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1
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I., I.II., II.
on-site learning
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I., II.
1317979
1
C
instructor
Viktoria
Mirsalova
Viktoria Mirsalova
mirsalova1@uniba.sk
Russian, Slovak
RJ
Russian
SK
Slovak
Russian, Slovak
L
2
8
<_C_>
Goal
To master the fundamentals of general Russian.
Learning the Cyrillic (Russian) alphabet, gaining basic language competence, building up skills and confidence in dealing with unfamiliar authentic and semi-authentic texts.
<_L_>
Recommended literature
Textbook: Точка Ру A1 (Ольга Долматова, Екатерина Новачац), рracovné karty Падежи 1 (Л.С. Безкоровайная, В.Е. Штыленко).
<_P_>
Continuous assessment
test
<_SO_>
Brief outline of the course
To master the fundamentals of general Russian.
Learning the Cyrillic (Russian) alphabet, gaining basic language competence, building up skills and confidence in dealing with unfamiliar authentic and semi-authentic texts.
The subject continues the program of Russian language (1) and provides a course of Russian for beginners.
<_VH_>
Weighting of course assessment (continuous/final)
100/0
<_VV_>
Learning outcomes
Basic communication in Russian, developing other Russian language skills - listening comprehension, reading and writing.
A
278
63.91
B
70
16.09
C
39
8.97
D
17
3.91
E
4
0.92
FX
27
6.21
435
6
95117
B
1-MXX-233
FMFI.KJP/1-MXX-233/13
English Conversation Course (1)
2
Evaluation
practicals
2
26
1, 3, 7, 9
(Single degree study, master II. deg., full time form)
Z
1, 2, 4, 5
Mgr. Aneta Barnes
16.02.2026
11.04.2024
8
Person responsible for the delivery, development and quality of the study programme
prof. RNDr. Ján Filo, CSc.
filo1@uniba.sk
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26
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I., I.II., II.
on-site learning
true
I., II.
1304488
1
C
instructor
Aneta
Barnes
Mgr. Aneta Barnes
barnes1@uniba.sk
English, Slovak
EN
English
SK
Slovak
English, Slovak
Z
1
3
7
9
<_C_>
Goal
Continual improvement of all language skills focused on communication/speaking, listening comprehension and writing. The emphasis is on discourse, lexicology and morphology, word-bank broadening of communicational English as well as English for specific purposes appropriate for university students. This course is a follow up of the previously taught ESP course.
<_L_>
Recommended literature
Appropriate study material is supplied based on the participants’level of English by the lecturer.(Sources- The Guardian, The Herald Morning Sun. The Nine News, The West Australian, BBC News and podcasts, CNN podcasts).
<_P_>
Continuous assessment
tests, oral presentations, essays
<_PA_>
Conditions for completion of course
tests, presentations, essays
Course prerequisites:
https://fmph.uniba.sk/microsites/kjp/katedra-jazykovej-pripravy/poziadavky-na-udelenie-priebezneho-hodnotenia-aj1aj2aj3-ostatne-kurzy/
<_SO_>
Brief outline of the course
This course’s focus is to broaden spoken/communicational English for students with B2/C1 level of English knowledge.
<_VH_>
Weighting of course assessment (continuous/final)
100/0
<_VV_>
Learning outcomes
Continual improvement of all language skills focused on communication/speaking, listening comprehension and writing. The emphasis is on discourse, lexicology and morphology, word-bank broadening of communicational English as well as English for specific purposes appropriate for university students. This course is a follow up of the previously taught ESP course.
<_Z_>
Final assessment
tests
A
246
77.36
B
28
8.81
C
14
4.4
D
4
1.26
E
3
0.94
FX
23
7.23
318
6
95118
B
1-MXX-234
FMFI.KJP/1-MXX-234/13
English Conversation Course (2)
2
Evaluation
practicals
2
26
2, 4, 8, 10
(Single degree study, master II. deg., full time form)
L
1, 2, 4, 5
Mgr. Aneta Barnes
16.02.2026
11.04.2024
8
Person responsible for the delivery, development and quality of the study programme
prof. RNDr. Ján Filo, CSc.
filo1@uniba.sk
practicals
2
26
prezenčná
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I., I.II., II.
on-site learning
true
I., II.
1304488
1
C
instructor
Aneta
Barnes
Mgr. Aneta Barnes
barnes1@uniba.sk
English, Slovak
EN
English
SK
Slovak
English, Slovak
L
2
4
8
10
<_C_>
Goal
Continual improvement of all language skills focused on communication/speaking, listening comprehension and writing. The emphasis is on discourse, lexicology and morphology, word-bank broadening of communicational/spoken English as well as English for specific purpose appropriate for university students. This course is a follow up of the Conversational English course 1.
<_L_>
Recommended literature
Appropriate study material is supplied based on the participants’level of English by the lecturer.(Sources- The Guardian, The Herald Morning Sun. The Nine News, The West Australian, BBC News and podcasts, CNN podcasts).
<_P_>
Continuous assessment
tests, oral presentations, essays
<_PA_>
Conditions for completion of course
tests, oral presentations, essays
Course prerequisites:
https://fmph.uniba.sk/microsites/kjp/katedra-jazykovej-pripravy/poziadavky-na-udelenie-priebezneho-hodnotenia-aj1aj2aj3-ostatne-kurzy/
<_SO_>
Brief outline of the course
This course’s focus is to broaden spoken/communicational English for students with B2/C1 level of English knowledge( Upper-Intermediate/Lower Advanced).
<_VH_>
Weighting of course assessment (continuous/final)
100/0
<_VV_>
Learning outcomes
Continual improvement of all language skills focused on communication/speaking, listening comprehension and writing. The emphasis is on discourse, lexicology and morphology, word-bank broadening of communicational/spoken English as well as English for specific purpose appropriate for university students. This course is a follow up of the Conversational English course 1.
<_Z_>
Final assessment
tests
A
165
82.09
B
18
8.96
C
5
2.49
D
2
1.0
E
0
0.0
FX
11
5.47
201
6
29712
B
1-MXX-261
FMFI.KJP/1-MXX-261/00
Russian Language (3)
2
Evaluation
practicals
2
26
3, 9
(Single degree study, master II. deg., full time form)
Z
2, 5
Viktoria Mirsalova
16.02.2026
20.06.2022
8
Person responsible for the delivery, development and quality of the study programme
prof. RNDr. Ján Filo, CSc.
filo1@uniba.sk
practicals
2
26
prezenčná
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2
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2
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1317979
1
C
instructor
Viktoria
Mirsalova
Viktoria Mirsalova
mirsalova1@uniba.sk
Russian, Slovak
RJ
Russian
SK
Slovak
Russian, Slovak
Z
3
9
<_C_>
Goal
Learning the handwritten Russian (Russian Cursive Cyrillic), developing further language skills, gaining knowledge of Russian culture, history and way of life, pre-intermediate to intermediate grammar and vocabulary.
<_L_>
Recommended literature
Точка Ру A2 (Ольга Долматова, Екатерина Новачац) a Short Stories in Russian (Olly Richards, Alex Rowlings)
<_P_>
Continuous assessment
test
<_SO_>
Brief outline of the course
Learning the handwritten Russian (Russian Cursive Cyrillic), developing further language skills, gaining knowledge of Russian culture, history and way of life, pre-intermediate to intermediate grammar and vocabulary.
The course "Russian for Intermediate Students" is a follow-up to "Russian for Beginners". The subject of the course is general Russian in the range appropriate to the given level.
<_VH_>
Weighting of course assessment (continuous/final)
100/0
<_VV_>
Learning outcomes
Basic communication in Russian, developing other Russian language skills - listening comprehension, reading and writing.
A
148
68.84
B
38
17.67
C
20
9.3
D
5
2.33
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0
0.0
FX
4
1.86
215
6
29714
B
1-MXX-262
FMFI.KJP/1-MXX-262/00
Russian Language (4)
2
Evaluation
practicals
2
26
4, 10
(Single degree study, master II. deg., full time form)
L
2, 5
Viktoria Mirsalova
16.02.2026
20.06.2022
8
Person responsible for the delivery, development and quality of the study programme
prof. RNDr. Ján Filo, CSc.
filo1@uniba.sk
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2596
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2
on-site learning
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3006
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L
5
on-site learning
10
3507
muMADG/k
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5
on-site learning
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5
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on-site learning
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I., I.II., II.
on-site learning
true
I., II.
1317979
1
C
instructor
Viktoria
Mirsalova
Viktoria Mirsalova
mirsalova1@uniba.sk
Russian, Slovak
RJ
Russian
SK
Slovak
Russian, Slovak
L
4
10
<_C_>
Goal
Learning the handwritten Russian (Russian Cursive Cyrillic), developing further language skills, gaining knowledge of Russian culture, history and way of life, pre-intermediate to intermediate grammar and vocabulary.
<_L_>
Recommended literature
Точка Ру A2 (Ольга Долматова, Екатерина Новачац) a Short Stories in Russian (Olly Richards, Alex Rowlings)
<_P_>
Continuous assessment
test
<_SO_>
Brief outline of the course
Learning the handwritten Russian (Russian Cursive Cyrillic), developing further language skills, gaining knowledge of Russian culture, history and way of life, pre-intermediate to intermediate grammar and vocabulary.
The course "Russian for Intermediate Students" is a follow-up to "Russian for Beginners". The subject of the course is general Russian in the range appropriate to the given level.
<_VH_>
Weighting of course assessment (continuous/final)
100/0
<_VV_>
Learning outcomes
Learning the handwritten Russian (Russian Cursive Cyrillic), developing further language skills, gaining knowledge of Russian culture, history and way of life, pre-intermediate to intermediate grammar and vocabulary.
A
114
74.51
B
22
14.38
C
11
7.19
D
4
2.61
E
1
0.65
FX
1
0.65
153
6
92161
B
2-EFM-117
FMFI.KAMŠ/2-EFM-117/12
Convex Optimisation
3
Evaluation
lecture
2
26
2
(Single degree study, master II. deg., full time form)
L
1
doc. RNDr. Mária Trnovská, PhD., Mgr. Jakub Hrdina, PhD.
16.02.2026
14.07.2025
8
Person responsible for the delivery, development and quality of the study programme
prof. RNDr. Ján Filo, CSc.
filo1@uniba.sk
lecture
2
26
prezenčná
B
4378
mINFa
Computer Science
L
1
on-site learning
2
954
mPMS
Probability and Mathematical Statistics
L
2
on-site learning
4
4383
mMATa
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L
1
on-site learning
2
4374
mEMMa
Mathematical Economics, Finance and Modelling
L
1
on-site learning
2
965
mINF/k
Computer Science (Conversion Programme)
L
1
on-site learning
2
954
mPMS
Probability and Mathematical Statistics
L
1
on-site learning
2
4387
mPMSa
Probability and Mathematical Statistics
L
2
on-site learning
4
968
mINF
Computer Science
L
1
on-site learning
2
2979
mMAT
Mathematics
L
1
on-site learning
2
4387
mPMSa
Probability and Mathematical Statistics
L
1
on-site learning
2
3965
mEMM
Mathematical Economics, Finance and Modelling
L
1
on-site learning
2
II.
on-site learning
true
II.
1051883
1
P
lecturer
Mária
Trnovská
doc. RNDr. Mária Trnovská, PhD.
trnovska2@uniba.sk
English, Slovak
1209058
2
P
lecturer
Jakub
Hrdina
Mgr. Jakub Hrdina, PhD.
hrdina8@uniba.sk
English, Slovak
EN
English
SK
Slovak
English, Slovak
L
2
<_C_>
Goal
Introduce the theory, methods and applications of convex optimization.
<_L_>
Recommended literature
M. Trnovská: Konvexná optimalizácia, elektronický text.
Boyd, Vandenberghe: Convex Optimization, Cambridge Univ.Press 2004
CVX: Matlab Software for Disciplined Convex Programming www.stanford.edu/~boyd/cvxbook
Ben-Tal, Nemirovski: Lectures on Modern Convex Optimization, SIAM 2001
<_O_>
Content prerequisite
Nonlinear programming, Linear programming
<_P_>
Continuous assessment
team homework, test
<_PA_>
Conditions for completion of course
Ongoing assessment: homework assignments (20%), in-class tests (30%)
Final assessment: semester project (20%), final exam (30%)
Grading A 91%, B 81%, C 71%, D 61%, E 51%
<_PJ_>
Language, which knowledge is needed to pass the course
Slovak, English
<_S_>
Course syllabus
Convex optimization problems in standard form
(Convex functions, problems, duality, KKT optimality conditions)
Generalization of standard convex problems
(Convex cones, conic programs, transformation of standard convex problems into a conic form)
Conic convex problems
(Basic conic linear programming classes, LP, SDP, SOCP,.. and relations between them, conic representable functions and problems)
Geometry of convex cones
(Proper cones, dual and self dual cones, properties)
Duality theory for conic linear programs
(Dual problem derivation, Generalized Farkas Lemma, Duality theory for conic linear problems, optimality conditions)
Applications of convex conic problems
(Portfolio optimization, Optimal experiment design, Minimal surface problem, Linear and quadratic discrimination)
Conic relaxations
(Non-convex quadratic problems relaxation, MAX-CUT)
Interior point methods
<_SO_>
Brief outline of the course
Convex optimization problems in standard form
Generalization of standard convex problems
Conic convex problems (SDP, SOCP,..)
Geometry of convex cones
Duality theory for conic linear programs
Applications of convex conic problems
Conic relaxations
Interior point methods
<_VH_>
Weighting of course assessment (continuous/final)
50% /50%
<_VV_>
Learning outcomes
Student learn the basic theory of convex analysis and convex (conic) optimization,
basic classes of convex conic programming, and methods for solving them, they learn the duality theory of conic linear programming. They are able to use Matlab and CVX (cvxopt) modeling system for solving convex problems, they are able to solve various practical problems and applications.
<_Z_>
Final assessment
Project
A
96
68.57
B
21
15.0
C
13
9.29
D
3
2.14
E
4
2.86
FX
3
2.14
140
6
104553
B
2-EFM-152
FMFI.KAMŠ/2-EFM-152/15
Principles of Mathematical Modelling in Science and Engineering
3
Evaluation
lecture
2
26
3
(Single degree study, master II. deg., full time form)
Z
2
doc. RNDr. Peter Guba, PhD.
16.02.2026
22.06.2022
8
Person responsible for the delivery, development and quality of the study programme
prof. RNDr. Ján Filo, CSc.
filo1@uniba.sk
lecture
2
26
prezenčná
B
2979
mMAT
Mathematics
Z
2
on-site learning
3
3965
mEMM
Mathematical Economics, Finance and Modelling
Z
1
on-site learning
1
4374
mEMMa
Mathematical Economics, Finance and Modelling
Z
1
on-site learning
1
4383
mMATa
Mathematics
Z
2
on-site learning
3
978
mFAA
Astronomy and Astrophysics
Z
1
on-site learning
1
II.
on-site learning
true
II.
1002422
1
P
lecturer
Peter
Guba
doc. RNDr. Peter Guba, PhD.
guba1@uniba.sk
English, Slovak
EN
English
SK
Slovak
English, Slovak
Z
3
<_L_>
Recommended literature
A. C. Fowler, Mathematical Models in the Applied Sciences, Cambridge University Press, 1997
A. Quarteroni, P. Gervasio, A Primer on Mathematical Modelling, Springer, 2020
<_PA_>
Conditions for completion of course
Interim assessment during the semester has a weight of 40% (homeworks 30%, bonus exercises 10%). The two semester exam papers have a total weight of 60% (the first paper taken in the middle of the semester, the second paper taken at the end of the semester). The student must obtain at least half of the points from each semester exam paper. The final evaluation can be adjusted by an oral exam (theoretical questions, written preparation).
Grading: A (100-91), B (90-81), C (80-71), D (70-61), E (60-51), FX (50-0)
<_PJ_>
Language, which knowledge is needed to pass the course
Slovak, English
<_SO_>
Brief outline of the course
Basic principles of modeling.
Principle of nondimensionalisation. Buckingham Pi-theorem. Dimensionless parameters.
Asymptotic expansion, convergence vs. divergence, uniformity. Matched asymptotic approximations.
Application of asymptotic methods: Van der Pol oscillator.
Heat transfer model. Degenerate diffusion.
Material derivative. Vorticity. Viscous flow.
Flow instability and transition to turbulence.
<_VH_>
Weighting of course assessment (continuous/final)
Weight of the intermediate / final evaluation: 40/60
<_VV_>
Learning outcomes
By completing this course, the student will gain knowledge of the principles of mathematical modeling of phenomena in the natural and technical sciences.
A
55
55.56
B
20
20.2
C
11
11.11
D
5
5.05
E
2
2.02
FX
6
6.06
99
6
117068
B
2-FTF-111
FMFI.KTF/2-FTF-111/16
Representations of Groups
7
Evaluation
lecture / practicals
4 / 1
52 / 13
4
(Single degree study, master II. deg., full time form)
L
2
Mgr. Martin Krššák, Dr.rer.nat.
16.02.2026
25.02.2022
8
Person responsible for the delivery, development and quality of the study programme
prof. RNDr. Ján Filo, CSc.
filo1@uniba.sk
lecture
4
52
prezenčná
practicals
1
13
prezenčná
B
955
mFTF
Theoretical Physics
L
1
on-site learning
2
4388
mFTFa
Theoretical Physics
L
1
on-site learning
2
2979
mMAT
Mathematics
L
2
on-site learning
4
4383
mMATa
Mathematics
L
2
on-site learning
4
II.
on-site learning
true
II.
1058782
1
P
lecturer
Martin
Krššák
Mgr. Martin Krššák, Dr.rer.nat.
krssak1@uniba.sk
English, Slovak
EN
English
SK
Slovak
English, Slovak
L
4
<_L_>
Recommended literature
Fulton, Harris - Representation Theory, A First Course, Springer, 1991.
Simon - Representations of Finite and Compact Groups, AMS, 1996.
Hall - Lie Groups, Lie Algebras, and Representations, Springer, 2003.
<_PA_>
Conditions for completion of course
Homework and exam.
<_SO_>
Brief outline of the course
Representations of finite groups, characters, Pontryagin's dual, Fourier analysis on finite groups, Frobeni's theory of representations of semi-direct products, representations of symmetric groups.
Representations of Lie groups, linearization, structure of Lie algebras, representations of simple Lie algebras, Clifford algebras, BCH formula, local and global integration of representations of Lie algebras, Peter-Weyl theorem and non-abelian Fourier analysis, Wigner theorem, projective representations, representations of Poincaré group, mass, spin, helicity, relationship of quantum fields and particles.
<_VH_>
Weighting of course assessment (continuous/final)
40/60
<_VV_>
Learning outcomes
Upon completion, students will understand the basics of the representation theory of finite and Lie groups and applications in theoretical physics.
A
23
65.71
B
2
5.71
C
6
17.14
D
1
2.86
E
2
5.71
FX
1
2.86
35
6
104807
B
2-INF-178
FMFI.KI/2-INF-178/15
Cryptology (1)
6
Evaluation
lecture
4
52
3
(Single degree study, master II. deg., full time form)
Z
2
doc. RNDr. Martin Stanek, PhD.
16.02.2026
28.06.2022
8
Person responsible for the delivery, development and quality of the study programme
prof. RNDr. Ján Filo, CSc.
filo1@uniba.sk
lecture
4
52
prezenčná
C
2979
mMAT
Mathematics
Z
2
on-site learning
3
965
mINF/k
Computer Science (Conversion Programme)
Z
1
on-site learning
1
4889
DAV
Data Science
Z
2
on-site learning
3
4378
mINFa
Computer Science
Z
1
on-site learning
1
4383
mMATa
Mathematics
Z
2
on-site learning
3
5539
INF/k
Computer Science (Conversion Programme)
Z
4
on-site learning
7
4891
DAV/k
Data Science (Conversion Programme)
Z
3
on-site learning
5
968
mINF
Computer Science
Z
1
on-site learning
1
969
INF
Computer Science
Z
3
on-site learning
5
I., II.
on-site learning
true
I., II.
1050087
1
P
lecturer
Martin
Stanek
doc. RNDr. Martin Stanek, PhD.
stanek2@uniba.sk
Slovak
SK
Slovak
Slovak
Z
3
<_L_>
Recommended literature
Douglas R. Stinson, Maura Paterson: Cryptography: Theory and Practice, Chapman and Hall/CRC; 4th edition, 2018
Nigel P. Smart: Cryptography Made Simple, Springer, 2016
Jean-Philippe Aumasson: Serious Cryptography: A Practical Introduction to Modern Encryption, 2017
Other on-line resources
<_PA_>
Conditions for completion of course
Homework assignments,
Condition for qualifying for the exam: timely and correctly solved all homework assignments,
Exam: written exam,
Approximate grading scale: A 92%, B 84%, C 76%, D 68%, E 60%
<_PJ_>
Language, which knowledge is needed to pass the course
Slovak, English
<_SO_>
Brief outline of the course
symmetric ciphers (block and stream ciphers), asymmetric ciphers, underlying problems for asymmetric constructions, hash functions, message authentication codes, digital signatures, passwords, secret sharing schemes, cryptographic protocols and related attacks, zero-knowledge proofs
<_VH_>
Weighting of course assessment (continuous/final)
20/80
<_VV_>
Learning outcomes
The students will have the knowledge of basic cryptographic constructions; they will understand security guarantees provided by these constructions, and assumptions required for their security. The students will be able to choose a suitable cryptographic construction for given application / information system.
A
15
10.34
B
15
10.34
C
23
15.86
D
25
17.24
E
36
24.83
FX
31
21.38
145
6
104834
B
2-MAT-111
FMFI.KMANM/2-MAT-111/15
Dynamical Systems
5
Evaluation
lecture / practicals
2 / 2
26 / 26
1
(Single degree study, master II. deg., full time form)
Z
1
RNDr. Michal Pospíšil, PhD., prof. RNDr. Milan Medveď, DrSc., RNDr. František Jaroš, PhD., prof. RNDr. Michal Fečkan, DrSc.
16.02.2026
17.06.2022
8
Person responsible for the delivery, development and quality of the study programme
prof. RNDr. Ján Filo, CSc.
filo1@uniba.sk
lecture
2
26
prezenčná
practicals
2
26
prezenčná
B
2979
mMAT
Mathematics
Z
1
on-site learning
1
4383
mMATa
Mathematics
Z
1
on-site learning
1
II.
on-site learning
true
II.
1044619
1
P
lecturer
Michal
Pospíšil
RNDr. Michal Pospíšil, PhD.
pospisil1@uniba.sk
Slovak
1008228
2
P
lecturer
Milan
Medveď
prof. RNDr. Milan Medveď, DrSc.
medved1@uniba.sk
Slovak
1038328
3
P
lecturer
František
Jaroš
RNDr. František Jaroš, PhD.
jaros2@uniba.sk
Slovak
1015751
4
P
lecturer
Michal
Fečkan
prof. RNDr. Michal Fečkan, DrSc.
feckan1@uniba.sk
Slovak
SK
Slovak
Slovak
Z
1
<_L_>
Recommended literature
Medveď, M. : Dynamické systémy, Bratislava, Univerzita Komenského, 2000.
Medveď, M. : Fundamentals of dynamical systems and bifurcation theory, 1992.
<_O_>
Content prerequisite
(1-MAT-801 Topology or 1-MAT-150 Mathematical Analysis (2)) and 1-MAT-310 Ordinary Differential Equations (1)
<_PA_>
Conditions for completion of course
Continuous assessment: 20 points for exercises
Final examination: written exam for 60 points and oral exam for 20 points
Indicative assessment scale: A 90%, B 80%, C 70%, D 60%, E 50%
<_SO_>
Brief outline of the course
Mathematical pendulum, gradient and Hamiltonian system, autonomous differential equations, phase portrait, local and global flow, continuous and discrete dynamical system (DS), invariant sets, asymptotic properties of DS, normal forms of DS, orbital equivalence, Hartmann's theorem, invariant manifolds, reduction to the central manifold, bifurcation, bifurcation equation. Basic bifurcations (Hopf, saddle-node type, period doubling type, Neimark-Sacker bifurcation, bifurcations around periodic trajectories).
<_VH_>
Weighting of course assessment (continuous/final)
20/80
<_VV_>
Learning outcomes
The graduate will acquire basic knowledge of the theory of dynamical systems, which will enable him to continue his education in this theory, for example in postgraduate studies, and will also gain the ability to apply this theory in solving problems in the field of natural and technical sciences.
A
12
48.0
B
2
8.0
C
5
20.0
D
4
16.0
E
0
0.0
FX
2
8.0
25
6
104835
B
2-MAT-112
FMFI.KMANM/2-MAT-112/15
Partial Differential Equations (1)
5
Evaluation
lecture / practicals
2 / 2
26 / 26
1
(Single degree study, master II. deg., full time form)
Z
1
doc. RNDr. Eugen Viszus, CSc.
16.02.2026
16.06.2022
8
Person responsible for the delivery, development and quality of the study programme
prof. RNDr. Ján Filo, CSc.
filo1@uniba.sk
lecture
2
26
prezenčná
practicals
2
26
prezenčná
B
2979
mMAT
Mathematics
Z
1
on-site learning
1
4383
mMATa
Mathematics
Z
1
on-site learning
1
II.
on-site learning
true
II.
1023881
1
P
lecturer
Eugen
Viszus
doc. RNDr. Eugen Viszus, CSc.
viszus1@uniba.sk
Slovak
SK
Slovak
Slovak
Z
1
<_L_>
Recommended literature
Partial differential equations / Lawrence C. Evans. Providence : American Mathematical Society, 1998
<_O_>
Content prerequisite
1-MAT-410 Functional analysis (1) AND 1-MAT-411 Functional analysis (2) AND 1-MAT-430 Classical methods of solving partial differential equations AND 1-MAT-785 Measure theory and integration
<_PA_>
Conditions for completion of course
Preliminary evaluation: 1 written partial exam (50%) and home work (50%)
Final exam: written (55%)/oral (45%)
Indicative evaluation scale: A 90%, B 80%, C 70%, D 65%, E 55%
<_PJ_>
Language, which knowledge is needed to pass the course
Slovak, English
<_SO_>
Brief outline of the course
Sobolev spaces: definition, elementary properties, approximation by smooth functions, traces, basic inequalities, imbeddings, some special properties. Linear second-order elliptic partial differential equations: weak solutions, existence and unicity, regularity, maximum principles, eigenvalues and eigenfunctions.
<_VH_>
Weighting of course assessment (continuous/final)
40/60
<_VV_>
Learning outcomes
After completing the course, students will gain basic knowledge and skills of theory of weak solutions to elliptic partial differential equations, boudary-value problems and elements of Sobolev spaces.
A
7
31.82
B
3
13.64
C
6
27.27
D
4
18.18
E
2
9.09
FX
0
0.0
22
6
92425
B
2-MAT-115
FMFI.KAMŠ/2-MAT-115/12
Functional Analysis
5
Evaluation
lecture / practicals
2 / 2
26 / 26
1
(Single degree study, master II. deg., full time form)
Z
1
prof. RNDr. Pavol Quittner, DrSc.
16.02.2026
19.06.2022
8
Person responsible for the delivery, development and quality of the study programme
prof. RNDr. Ján Filo, CSc.
filo1@uniba.sk
lecture
2
26
prezenčná
practicals
2
26
prezenčná
B
2979
mMAT
Mathematics
Z
1
on-site learning
1
4383
mMATa
Mathematics
Z
1
on-site learning
1
II.
on-site learning
true
II.
1008290
1
P
lecturer
Pavol
Quittner
prof. RNDr. Pavol Quittner, DrSc.
quittner1@uniba.sk
English, Slovak
EN
English
SK
Slovak
English, Slovak
Z
1
<_L_>
Recommended literature
W. Rudin: Functional Analysis, McGraw-Hill, New York 1973.
K. Yosida: Functional Analysis, Springer, Berlin, Heidelberg 1980.
A.E. Taylor: Introduction to Functional Analysis, John Wiley & Sons, New York 1958.
A.W. Naylor & G.R. Sell: Linear operator theory in engineering and science, Holt, Rinehart & Winston, New York, 1971.
<_PA_>
Conditions for completion of course
Preliminary grading: homeworks.
Exam: written and oral.
Grading: A 90%, B 80%, C 70%, D 60%, E 50%.
<_PJ_>
Language, which knowledge is needed to pass the course
English
<_SO_>
Brief outline of the course
Compact operators and Fredholm's alternative, spectrum of closed, continuous, compact and self-adjoint operators, locally convex spaces and continuous linear operators in these spaces, weak topologies and compactness in weak topologies, distributions.
<_VH_>
Weighting of course assessment (continuous/final)
20/80
<_VV_>
Learning outcomes
The students will learn to determine the spectrum of certain types of linear operators, the convergence of operators and functions in various topologies and function spaces, and perform basic operations with distributions.
A
18
58.06
B
5
16.13
C
6
19.35
D
1
3.23
E
1
3.23
FX
0
0.0
31
6
76155
B
2-MAT-121
FMFI.KAMŠ/2-MAT-121/09
Partial Differential Equations (2)
5
Evaluation
lecture / practicals
2 / 2
26 / 26
2
(Single degree study, master II. deg., full time form)
L
1
doc. Mgr. Richard Kollár, PhD.
16.02.2026
13.03.2022
8
Person responsible for the delivery, development and quality of the study programme
prof. RNDr. Ján Filo, CSc.
filo1@uniba.sk
lecture
2
26
prezenčná
practicals
2
26
prezenčná
B
4383
mMATa
Mathematics
L
1
on-site learning
2
2979
mMAT
Mathematics
L
1
on-site learning
2
II.
on-site learning
true
II.
1052723
1
P
lecturer
Richard
Kollár
doc. Mgr. Richard Kollár, PhD.
kollar53@uniba.sk
English, Slovak
EN
English
SK
Slovak
English, Slovak
L
2
<_C_>
Goal
A study of basic methods of advanced theory for evolution partial differential equations.
<_L_>
Recommended literature
Partial differential equations / Lawrence C. Evans. Providence : American Mathematical Society, 1998
<_P_>
Continuous assessment
homework sets and midterm test
<_PA_>
Conditions for completion of course
Continuous assessment: homework sets and midterm exam
Final exam: written and oral exam
Grade scale: A 90%, B 80%, C 70%, D 60%, E 50%
<_SO_>
Brief outline of the course
Heat conduction equation in one and more dimensions, self-similar solutions, fundamental solution, derivation of heat conduction equation from Brownian motion, maximum principle for parabolic problems, solution regularity, weak formulation of parabolic equations, regularity of weak solutions, wave equation, hyperbolic and dispersion waves, reaction-diffusion equations, existence and stability of traveling waves
<_VH_>
Weighting of course assessment (continuous/final)
65/35
<_VV_>
Learning outcomes
Upon successful completion of this course, students will gain knowledge of the basic properties of parabolic and hyperbolic partial differential equations with emphasis on the qualitative properties of their solutions, including rigorous derivation of the relevant theory. They will get acquainted with the concept of the weak solution of evolutionary partial differential equations. Students will also gain basic knowledge about the phenomena appearing in nonlinear partial equations - about dispersive and traveling waves and their stability.
<_Z_>
Final assessment
final exam: written and oral
A
14
35.9
B
10
25.64
C
4
10.26
D
5
12.82
E
6
15.38
FX
0
0.0
39
6
104837
B
2-MAT-122
FMFI.KMANM/2-MAT-122/15
Nonlinear Functional Analysis
5
Evaluation
lecture / practicals
2 / 2
26 / 26
2
(Single degree study, master II. deg., full time form)
L
1
prof. RNDr. Michal Fečkan, DrSc.
16.02.2026
12.03.2022
8
Person responsible for the delivery, development and quality of the study programme
prof. RNDr. Ján Filo, CSc.
filo1@uniba.sk
lecture
2
26
prezenčná
practicals
2
26
prezenčná
B
1078
dGTL
Geometry and Topology
L
-1
on-site learning
4383
mMATa
Mathematics
L
1
on-site learning
2
1080
dGTL/x
Geometry and Topology
L
-1
on-site learning
4403
dGTLa/x
Geometry and Topology
L
-1
on-site learning
4402
dGTLa
Geometry and Topology
L
-1
on-site learning
2979
mMAT
Mathematics
L
1
on-site learning
2
II., III.
on-site learning
true
II., III.
1015751
1
P
lecturer
Michal
Fečkan
prof. RNDr. Michal Fečkan, DrSc.
feckan1@uniba.sk
English, Slovak
EN
English
SK
Slovak
English, Slovak
L
2
<_L_>
Recommended literature
Lectures on nonlinear analysis / Pavel Drábek, Jaroslav Milota. Plzeň : Vydavateľstvo servis, 2004
Nonlinear differential equations and dynamical systems / Ferdinand Verhulst. Berlin : Springer, 1990
Nelineární diferenciální rovnice / Svatopluk Fučík, Alois Kufner. Praha : Státní nakladatelství technické literatury, 1978
<_PA_>
Conditions for completion of course
Continuous assessment: handwriting
Exam: oral
Original rating scale: A 90%, B 80%, C 70%, D 60%, E 50%
<_SO_>
Brief outline of the course
1. Differential calculus in Banach spaces.
2. Local nonlinear analysis: Uniform contraction theorem and implicit function theorem.
3. Bifurcation theory: Lyapunov - Schmidt reduction.
4. Continuous methods for solving nonlinear equations.
<_VH_>
Weighting of course assessment (continuous/final)
40/60
<_VV_>
Learning outcomes
Fundamentals of nonlinear analysis, differential calculus in Banach spaces, bifurcation theory and continuous methods.
A
12
85.71
ABS
0
0.0
B
0
0.0
C
0
0.0
D
0
0.0
E
0
0.0
FX
2
14.29
NEABS
0
0.0
14
8
104838
B
2-MAT-123
FMFI.KAMŠ/2-MAT-123/15
Calculus of Variations
6
Evaluation
lecture / practicals
2 / 2
26 / 26
2
(Single degree study, master II. deg., full time form)
L
1
prof. RNDr. Pavol Quittner, DrSc.
16.02.2026
19.06.2022
8
Person responsible for the delivery, development and quality of the study programme
prof. RNDr. Ján Filo, CSc.
filo1@uniba.sk
lecture
2
26
prezenčná
practicals
2
26
prezenčná
B
1078
dGTL
Geometry and Topology
L
-1
on-site learning
4383
mMATa
Mathematics
L
1
on-site learning
2
1080
dGTL/x
Geometry and Topology
L
-1
on-site learning
4403
dGTLa/x
Geometry and Topology
L
-1
on-site learning
4402
dGTLa
Geometry and Topology
L
-1
on-site learning
2979
mMAT
Mathematics
L
1
on-site learning
2
II., III.
on-site learning
true
II., III.
1008290
1
P
lecturer
Pavol
Quittner
prof. RNDr. Pavol Quittner, DrSc.
quittner1@uniba.sk
English, Slovak
EN
English
SK
Slovak
English, Slovak
L
2
<_L_>
Recommended literature
B. Dacorogna: Direct methods in the calculus of variations, Springer, Berlin - Heidelberg 2008.
M. Struwe: Variational methods, Springer, Berlin - Heidelberg 2008.
J.L. Troutman: Variational calculus and Optimal Control, Springer, New York 1996.
G. Buttazzo, M. Giaquinta, S. Hildebrandt: One-dimensional variational problems, Clarendon Press, Oxford 1998.
<_PA_>
Conditions for completion of course
Preliminary grading: homeworks.
Exam: written and oral.
Grading: A 90%, B 80%, C 70%, D 60%, E 50%.
<_PJ_>
Language, which knowledge is needed to pass the course
English
<_SO_>
Brief outline of the course
Differentiability of the Nemytskii mapping, basic existence theorem for global extrema, necessary and sufficient conditions for local extrema,
constrained extrema, the Euler and Jacobi equations, necessary and sufficient conditions for strong and weak extrema of one-dimensional integrals, investigation of critical points of particular functionals.
<_VH_>
Weighting of course assessment (continuous/final)
20/80
<_VV_>
Learning outcomes
The students will learn to differentiate variational integrals and related Nemytskii mappings, they will be able to verify necessary and sufficient conditions guaranteeing the existence of global and local extrema of particular functionals, to find extrema in the case of one-dimensional integrals and find out, whether these extrema are weak or strong.
A
6
50.0
ABS
0
0.0
B
3
25.0
C
0
0.0
D
1
8.33
E
0
0.0
FX
2
16.67
NEABS
0
0.0
12
8
104839
B
2-MAT-132
FMFI.KMANM/2-MAT-132/15
Selected Topics of Mathematical Physics
4
Evaluation
lecture / practicals
2 / 2
26 / 26
4
(Single degree study, master II. deg., full time form)
L
2
doc. RNDr. Michal Demetrian, PhD., doc. RNDr. Eugen Viszus, CSc.
16.02.2026
16.06.2022
8
Person responsible for the delivery, development and quality of the study programme
prof. RNDr. Ján Filo, CSc.
filo1@uniba.sk
lecture
2
26
prezenčná
practicals
2
26
prezenčná
B
2979
mMAT
Mathematics
L
2
on-site learning
4
4383
mMATa
Mathematics
L
2
on-site learning
4
II.
on-site learning
true
II.
1043923
1
P
lecturer
Michal
Demetrian
doc. RNDr. Michal Demetrian, PhD.
demetrian1@uniba.sk
Slovak
1023881
2
P
lecturer
Eugen
Viszus
doc. RNDr. Eugen Viszus, CSc.
viszus1@uniba.sk
Slovak
SK
Slovak
Slovak
L
4
<_L_>
Recommended literature
Mechanika / L. D. Landau, Je. M. Lifšic. Moskva : Nauka, 1973
Mechanika / Jozef Kvasnica ... [et al.]. Praha : Academia, 2004
Teoretická mechanika / Miroslav Brdička, Arnošt Hladík. Praha : Academia, 1987
Theoretical mechanics / T. C. Bradbury. New York : John Wiley, 1968
Úvod do teoretickej fyziky 1 : Mechanika, Elektrodynamika / Lev Davidovič Landau, Jevgenij Michajlovič Lifšic ; z ruského originálu preložil Juraj Šebesta. Bratislava : Alfa, 1980
<_PA_>
Conditions for completion of course
Interim evaluation: independent work, homework,
Grades: A (100-91), B (90-81), C (80-71), D (70-61), E (60-51), Fx (50-0).
<_PJ_>
Language, which knowledge is needed to pass the course
Slovak, English
<_SO_>
Brief outline of the course
Newton's laws. Lagrange's formulation of mechanics. Newton's / Coulomb's law. Electromagnetic field and Maxwell's equations.
<_VH_>
Weighting of course assessment (continuous/final)
100/0
<_VV_>
Learning outcomes
The student will be able to formulate mathematical models of problems of mechanics and electromagnetism.
A
10
83.33
B
2
16.67
C
0
0.0
D
0
0.0
E
0
0.0
FX
0
0.0
12
6
102583
B
2-MAT-142
FMFI.KMANM/2-MAT-142/14
Transport, conservation laws and equations of motion
4
Evaluation
lecture
2
26
3
(Single degree study, master II. deg., full time form)
Z
2
prof. RNDr. Ján Filo, CSc.
16.02.2026
21.06.2022
FMFI.KMANM/2-MAT-112/15 and FMFI.KAMŠ/2-MAT-121/09
FMFI.KMANM/2-MAT-112/15 - Partial Differential Equations (1) and FMFI.KAMŠ/2-MAT-121/09 - Partial Differential Equations (2)
2-MAT-112 - Partial Differential Equations (1) and 2-MAT-121 - Partial Differential Equations (2)
8
Person responsible for the delivery, development and quality of the study programme
prof. RNDr. Ján Filo, CSc.
filo1@uniba.sk
lecture
2
26
prezenčná
104835
FMFI.KMANM/2-MAT-112/15
2-MAT-112
Partial Differential Equations (1)
,
76155
FMFI.KAMŠ/2-MAT-121/09
2-MAT-121
Partial Differential Equations (2)
B
2979
mMAT
Mathematics
Z
2
on-site learning
3
4383
mMATa
Mathematics
Z
2
on-site learning
3
II.
on-site learning
true
II.
1042269
1
P
lecturer
Ján
Filo
prof. RNDr. Ján Filo, CSc.
filo1@uniba.sk
Slovak
SK
Slovak
Slovak
Z
3
<_L_>
Recommended literature
Partial differential equations / Lawrence C. Evans. Providence : American Mathematical Society, 1998
Miloslav Feistauer, Mathematical methods in fluid dynamics, Longman Scientific & Technical, 1993
John C. Neu, Training Manual on Transport and Fluids, Graduate Studies in Mathematics, Volume 109, AMS.
<_PA_>
Conditions for completion of course
Exam: The exam consists of a written and an oral part.
Indicative assessment scale: A 92%, B 84%, C 76%, D 68%, E 60%
<_PJ_>
Language, which knowledge is needed to pass the course
Slovak, English
<_SO_>
Brief outline of the course
Transport theorem, continuity equation, equation of motion, conservation law equations, Navier-Stokes equations
<_VH_>
Weighting of course assessment (continuous/final)
0/100
<_VV_>
Learning outcomes
The graduate of this course has knowledge of the mathematical theory of conservation laws and the equations of motion modeling fluid flow.
A
12
80.0
B
1
6.67
C
1
6.67
D
1
6.67
E
0
0.0
FX
0
0.0
15
6
104840
B
2-MAT-211
FMFI.KAG/2-MAT-211/15
General Topology
5
Evaluation
lecture
4
52
1
(Single degree study, master II. deg., full time form)
Z
1
RNDr. Martin Sleziak, PhD., doc. Mgr. Tibor Macko, PhD.
16.02.2026
18.06.2022
8
Person responsible for the delivery, development and quality of the study programme
prof. RNDr. Ján Filo, CSc.
filo1@uniba.sk
lecture
4
52
prezenčná
B
4403
dGTLa/x
Geometry and Topology
Z
-1
on-site learning
1078
dGTL
Geometry and Topology
Z
-1
on-site learning
2979
mMAT
Mathematics
Z
1
on-site learning
1
4383
mMATa
Mathematics
Z
1
on-site learning
1
4402
dGTLa
Geometry and Topology
Z
-1
on-site learning
1080
dGTL/x
Geometry and Topology
Z
-1
on-site learning
II., III.
on-site learning
true
II., III.
1040155
1
P
lecturer
Martin
Sleziak
RNDr. Martin Sleziak, PhD.
sleziak1@uniba.sk
Slovak
1237494
2
P
lecturer
Tibor
Macko
doc. Mgr. Tibor Macko, PhD.
macko58@uniba.sk
Slovak
SK
Slovak
Slovak
Z
1
<_L_>
Recommended literature
General topology / Stephen Willard. Mineola : Dover, 1970
Topology / James R. Munkres. Upper Saddle River : Prentice-Hall , 2000
<_PA_>
Conditions for completion of course
Final evaluation: oral exam
Rating scale: A 90%, B 80%, C 70%, D 60%, E 50%
<_PJ_>
Language, which knowledge is needed to pass the course
Slovak, English
<_SO_>
Brief outline of the course
Topological spaces and continuous functions. Basic topological constructions (subspace, topological sum and product, quotient space).
Countability axioms and separation axioms (Hausdorff, regular, completely regular and normal spaces). Connected and linearly connected spaces. Compact and locally compact spaces. Metric space, metrizable spaces.
<_URL_>
Course web page URL
http://msleziak.com/vyuka/vstop.html
<_VH_>
Weighting of course assessment (continuous/final)
100% final exam
<_VV_>
Learning outcomes
Students will understand basic notions of general topology, properties of topological spaces and their subsets, basic topological constructions. They will be able to apply topological results in further areas of mathematical analysis, topology and geometry.
A
20
80.0
ABS
0
0.0
B
4
16.0
C
0
0.0
D
0
0.0
E
0
0.0
FX
1
4.0
NEABS
0
0.0
25
8
135121
B
2-MAT-212
FMFI.KAG/2-MAT-212/22
Universal Algebras and Lattices (1)
3
Evaluation
seminar
2
26
2
(Single degree study, master II. deg., full time form)
L
1
doc. RNDr. Jaroslav Guričan, CSc.
16.02.2026
21.06.2022
FMFI.KAG/2-MAT-212/09
FMFI.KAG/2-MAT-212/09 - Universal Algebras and Lattices (1)
2-MAT-212 - Universal Algebras and Lattices (1)
8
Person responsible for the delivery, development and quality of the study programme
prof. RNDr. Ján Filo, CSc.
filo1@uniba.sk
seminar
2
26
prezenčná
76164
FMFI.KAG/2-MAT-212/09
2-MAT-212
Universal Algebras and Lattices (1)
B
4383
mMATa
Mathematics
L
1
on-site learning
2
2979
mMAT
Mathematics
L
1
on-site learning
2
II.
on-site learning
true
II.
1049553
1
P
lecturer
Jaroslav
Guričan
doc. RNDr. Jaroslav Guričan, CSc.
gurican1@uniba.sk
English, Slovak
EN
English
SK
Slovak
English, Slovak
L
2
<_O_>
Content prerequisite
FMFI.KAG/2-MAT-217/22 Seminar in Algebra
<_PA_>
Conditions for completion of course
presentations, quality and depth of understanding
A - 91%+
B - 81%-90%
C - 71%-80%
D - 61%-70%
E - 50%-60%
Fx - less than 50%
<_PJ_>
Language, which knowledge is needed to pass the course
slovak, english
<_SO_>
Brief outline of the course
Subdirect products.
Class operators H, S, P, varieties.
Free algebras, terms, fully invariant congruences.
Malcev conditions.
Defining formulas and constructions preservations.
<_VV_>
Learning outcomes
Students will gain experience in independent study of advanced mathematical topics and with the presentation of new knowledge. They will know the most important concepts, methods and results from the lattice theory and universal algebra and their connection with the methods and results of "classical" mathematical disciplines.
A
34
82.93
B
3
7.32
C
3
7.32
D
0
0.0
E
1
2.44
FX
0
0.0
41
6
76168
B
2-MAT-214
FMFI.KAG/2-MAT-214/09
Differential Topology
4
Evaluation
lecture
2
26
1
(Single degree study, master II. deg., full time form)
Z
1
doc. Mgr. Tibor Macko, PhD.
16.02.2026
21.06.2022
8
Person responsible for the delivery, development and quality of the study programme
prof. RNDr. Ján Filo, CSc.
filo1@uniba.sk
lecture
2
26
prezenčná
B
4403
dGTLa/x
Geometry and Topology
Z
-1
on-site learning
1078
dGTL
Geometry and Topology
Z
-1
on-site learning
2979
mMAT
Mathematics
Z
1
on-site learning
1
4383
mMATa
Mathematics
Z
1
on-site learning
1
4402
dGTLa
Geometry and Topology
Z
-1
on-site learning
1080
dGTL/x
Geometry and Topology
Z
-1
on-site learning
II., III.
on-site learning
true
II., III.
1237494
1
P
lecturer
Tibor
Macko
doc. Mgr. Tibor Macko, PhD.
macko58@uniba.sk
English, Slovak
EN
English
SK
Slovak
English, Slovak
Z
1
<_L_>
Recommended literature
M. Hirsch, Differential Topology. Springer-Verlag, New York 1976.
J. Milnor, Topology from the Differential Viewpoint, The Univ. Press of Virginia, Charlottesville 1965.
I. Singer, J. Thorpe, Lecture Notes on Elementary Topology and Geometry, Scott, Foresman and Co., Glenview, Illinois 1967.
F. Warner, Foundations of Differentiable Manifolds and Lie Groups. Springer-Verlag, Berlin 1983.
<_PA_>
Conditions for completion of course
Exam: written and oral
Indicative assessment scale: A 90%, B 80%, C 70%, D 60%, E 50%
<_PJ_>
Language, which knowledge is needed to pass the course
English
<_SO_>
Brief outline of the course
A review of selected basic notions of general topology. Differentiable manifolds and differentiable maps. Tangent vector space. The differential of a differentiable map at a point. Tangent bundles. Submanifolds. Immersions and embeddings of manifolds. Inverse Function Theorem and its corollaries; transversality. Regular and critical points, regular and critical values, Sard’s Theorem. Proof of the fundamental theorem of algebra.
<_VV_>
Learning outcomes
Subject aim: to acquaint students with basic ideas, methods and some applications of differential topology.
A
34
60.71
ABS
1
1.79
B
6
10.71
C
8
14.29
D
2
3.57
E
2
3.57
FX
3
5.36
NEABS
0
0.0
56
8
92426
B
2-MAT-215
FMFI.KAG/2-MAT-215/12
Field Theory (1)
3
Evaluation
lecture
2
26
1
(Single degree study, master II. deg., full time form)
Z
1
doc. RNDr. Martin Mačaj, PhD.
16.02.2026
14.03.2022
8
Person responsible for the delivery, development and quality of the study programme
prof. RNDr. Ján Filo, CSc.
filo1@uniba.sk
lecture
2
26
prezenčná
B
2979
mMAT
Mathematics
Z
1
on-site learning
1
4383
mMATa
Mathematics
Z
1
on-site learning
1
II.
on-site learning
true
II.
1040555
1
P
lecturer
Martin
Mačaj
doc. RNDr. Martin Mačaj, PhD.
macaj1@uniba.sk
English, Slovak
EN
English
SK
Slovak
English, Slovak
Z
1
<_C_>
Goal
Theory of fields and its applications.
<_L_>
Recommended literature
Birkhoff, G., MacLane, S: Prehľad modernej algebry
Lang, S.: Algebra
Niederreiter, H., Lidl, R.: Theory of fields
<_O_>
Content prerequisite
1-MAT-220 Algebra (1) OR 1-INF-156 Algebra (2)
<_P_>
Continuous assessment
individual tasks
<_PA_>
Conditions for completion of course
Exam: oral
Indicative evaluation scale: A 90%, B 80%, C 70%, D 60%, E 50%
<_SO_>
Brief outline of the course
Field extensions. Finite fields. Introduction to the Galois theory. Fundamental theorem of algebra. Radical extensions
<_VH_>
Weighting of course assessment (continuous/final)
10/90
<_VV_>
Learning outcomes
Mastering basic concepts and methods in the field of field theory. Studying the basic theorem of Galois theory for finite extensions and its consequences.
<_Z_>
Final assessment
examination
A
24
61.54
B
4
10.26
C
3
7.69
D
1
2.56
E
4
10.26
FX
3
7.69
39
6
133681
B
2-MAT-217
FMFI.KAG/2-MAT-217/22
Seminar in Algebra
3
Evaluation
seminar
2
26
1
(Single degree study, master II. deg., full time form)
Z
1
doc. RNDr. Jaroslav Guričan, CSc.
16.02.2026
21.06.2022
8
Person responsible for the delivery, development and quality of the study programme
prof. RNDr. Ján Filo, CSc.
filo1@uniba.sk
seminar
2
26
prezenčná
B
2979
mMAT
Mathematics
Z
1
on-site learning
1
4383
mMATa
Mathematics
Z
1
on-site learning
1
II.
on-site learning
true
II.
1049553
1
P
lecturer
Jaroslav
Guričan
doc. RNDr. Jaroslav Guričan, CSc.
gurican1@uniba.sk
Slovak
SK
Slovak
Slovak
Z
1
<_L_>
Recommended literature
Algebra (Third revised revision)/ S. Lang, Springer-Verlag New York 2002
Introduction to Commutative algebra / M. F. Atiyah, I. G. Macdonald, Addison-Wesley Publ. Company 1969
A course in Universal Algebra (Millenium Edition, 2012 Update) / S. Burris and H.P. Sankappanavar, free book
Teacher's electronic text, manuscript
<_O_>
Content prerequisite
FMFI.KAG/2-MAT-457/22 Algebra (4)
<_PA_>
Conditions for completion of course
presentations, quality and depth of understanding
A - 91%+
B - 81%-90%
C - 71%-80%
D - 61%-70%
E - 50%-60%
Fx - less than 50%
<_PJ_>
Language, which knowledge is needed to pass the course
slovak, english
<_SO_>
Brief outline of the course
Rings of integers, extensions of homomorphisms. Algebraic independence. Hilbert's theorem of zeros (Hilbert's Nullstellensatz).
Exact sequences, tensor product of modules.
Basic concepts of lattice theory, distributive and modular lattices, complete and algebraic lattices, closure operators. Basic concepts of universal algebra.
<_VV_>
Learning outcomes
Students will gain experience with some more advanced methods used in the field of polynomial rings of several variables and their ideals (algebraic geometry), with universal constructions in the form of tensor product of modules. They will also get acquainted with the introductory concepts of the lattice theory and universal algebra.
A
9
90.0
B
0
0.0
C
1
10.0
D
0
0.0
E
0
0.0
FX
0
0.0
10
6
135122
B
2-MAT-221
FMFI.KAG/2-MAT-221/22
Universal Algebras and Lattices (2)
3
Evaluation
seminar
2
26
3
(Single degree study, master II. deg., full time form)
Z
2
doc. RNDr. Jaroslav Guričan, CSc.
16.02.2026
21.06.2022
FMFI.KAG/2-MAT-221/09
FMFI.KAG/2-MAT-221/09 - Universal Algebras and Lattices (2)
2-MAT-221 - Universal Algebras and Lattices (2)
8
Person responsible for the delivery, development and quality of the study programme
prof. RNDr. Ján Filo, CSc.
filo1@uniba.sk
seminar
2
26
prezenčná
76165
FMFI.KAG/2-MAT-221/09
2-MAT-221
Universal Algebras and Lattices (2)
C
2979
mMAT
Mathematics
Z
2
on-site learning
3
4383
mMATa
Mathematics
Z
2
on-site learning
3
II.
on-site learning
true
II.
1049553
1
P
lecturer
Jaroslav
Guričan
doc. RNDr. Jaroslav Guričan, CSc.
gurican1@uniba.sk
English, Slovak
EN
English
SK
Slovak
English, Slovak
Z
3
<_O_>
Content prerequisite
FMFI.KAG/2-MAT-212/22 Universal Algebras and Lattices (1)
<_PA_>
Conditions for completion of course
presentations, quality and depth of understanding
A - 91%+
B - 81%-90%
C - 71%-80%
D - 61%-70%
E - 50%-60%
Fx - less than 50%
<_PJ_>
Language, which knowledge is needed to pass the course
slovak, english
<_SO_>
Brief outline of the course
Boolean algebras, topological representations, Stone's representation theorems.
Equational classes versus varieties, Birkhoff's theorems.
Ultraproducts and filtred products.
<_VV_>
Learning outcomes
Students will gain experience in independent study of advanced mathematical topics and with the presentation of new knowledge. They will know the most important concepts, methods and results from the lattice theory and universal algebra and their connection with the methods and results of "classical" mathematical disciplines. They will be able to follow current research in the field of lattice theory and universal algebra.
A
25
86.21
B
4
13.79
C
0
0.0
D
0
0.0
E
0
0.0
FX
0
0.0
29
6
76169
B
2-MAT-223
FMFI.KAG/2-MAT-223/09
Algebraic Topology
6
Evaluation
lecture
4
52
2
(Single degree study, master II. deg., full time form)
L
1
doc. Mgr. Tibor Macko, PhD.
16.02.2026
21.06.2022
8
Person responsible for the delivery, development and quality of the study programme
prof. RNDr. Ján Filo, CSc.
filo1@uniba.sk
lecture
4
52
prezenčná
B
1078
dGTL
Geometry and Topology
L
-1
on-site learning
4383
mMATa
Mathematics
L
1
on-site learning
2
1080
dGTL/x
Geometry and Topology
L
-1
on-site learning
4403
dGTLa/x
Geometry and Topology
L
-1
on-site learning
4402
dGTLa
Geometry and Topology
L
-1
on-site learning
2979
mMAT
Mathematics
L
1
on-site learning
2
II., III.
on-site learning
true
II., III.
1237494
1
P
lecturer
Tibor
Macko
doc. Mgr. Tibor Macko, PhD.
macko58@uniba.sk
English, Slovak
EN
English
SK
Slovak
English, Slovak
L
2
<_L_>
Recommended literature
A. Hatcher, Algebraic Topology. Cambridge University Press 2002
A. Kriegl, Algebraic Topology. Lecture Notes. University of Vienna, Vienna 2008, accessible at http://www.mat.univie.ac.at/~kriegl/Skripten/alg-top.pdf
W. Massey, A Basic Course in Algebraic Topology. Springer-Verlag, New York 1991
E. Spanier, Algebraic Topology. Springer-Verlag, New York 1995
<_PA_>
Conditions for completion of course
Exam: written and oral
Indicative assessment scale: A 90%, B 80%, C 70%, D 60%, E 50%
<_PJ_>
Language, which knowledge is needed to pass the course
English
<_SO_>
Brief outline of the course
The problem of homeomorphy. Constructions of new topological spaces by forming quotient spaces. Attaching a cell to a topological space. Surfaces and topological manifolds. Path-connectedness. Homotopy. Fundamental group. Basic homology theory. Homology groups of spheres and their applications. Cohomology groups, cohomology ring, and applications.
<_VV_>
Learning outcomes
Subject aim: to acquaint students with basic ideas, methods and some applications of algebraic topology.
A
32
62.75
ABS
0
0.0
B
10
19.61
C
4
7.84
D
3
5.88
E
2
3.92
FX
0
0.0
NEABS
0
0.0
51
8
76170
B
2-MAT-224
FMFI.KAG/2-MAT-224/09
Linear Codes
4
Evaluation
lecture
2
26
1
(Single degree study, master II. deg., full time form)
Z
1
prof. RNDr. Róbert Jajcay, DrSc.
16.02.2026
14.03.2022
8
Person responsible for the delivery, development and quality of the study programme
prof. RNDr. Ján Filo, CSc.
filo1@uniba.sk
lecture
2
26
prezenčná
B
2979
mMAT
Mathematics
Z
1
on-site learning
1
4383
mMATa
Mathematics
Z
1
on-site learning
1
II.
on-site learning
true
II.
1060451
1
P
lecturer
Róbert
Jajcay
prof. RNDr. Róbert Jajcay, DrSc.
jajcay6@uniba.sk
English, Slovak
EN
English
SK
Slovak
English, Slovak
Z
1
<_L_>
Recommended literature
Introduction to coding theory / Jacobus Hendricus van Lint. Berlin : Springer, 1999
J. Adámek: Coding theory, SNTL, Praha 1989 (in Czech)
Paul Garrett, The Mathematics of Coding Theory, Pearson Prentice Hall
Raymond Hill, A First Course in Coding Theory, Oxford
Steven Roman, Coding and Information Theory, Springer
<_PA_>
Conditions for completion of course
Ongoing evaluation during the semester: homeworks, midterm
Final exam: written and oral
Approximative grade scale: A 90%, B 80%, C 70%, D 60%, E 50%
<_PJ_>
Language, which knowledge is needed to pass the course
Slovak, English
<_SO_>
Brief outline of the course
Fundamental concepts ond examples from the theory of linear codes. Generating matrix and parity check matrix of a linear code. Error detection and correction. Standard decoding. Perfect codes. Hamming codes.
Cyclic codes. Generating polynome and parity check polynome. BCH codes. Reed-Solomon codes. Decoding of cyclic codes.
<_VH_>
Weighting of course assessment (continuous/final)
50/50
<_VV_>
Learning outcomes
After completing the course, students will be able to create and use basic linear codes designed to protect data against errors introduced via transmission and storage. They will also be able to evaluate the advantages and disadvantages of specific codes with regard to the conditions of their usage and the expected amount of transmitted information.
A
61
82.43
B
10
13.51
C
2
2.7
D
0
0.0
E
1
1.35
FX
0
0.0
74
6
104842
B
2-MAT-225
FMFI.KAG/2-MAT-225/15
Group Theory Applications in Discrete Mathematics
5
Evaluation
course
4
52
2
(Single degree study, master II. deg., full time form)
L
1
prof. RNDr. Róbert Jajcay, DrSc.
16.02.2026
14.03.2022
8
Person responsible for the delivery, development and quality of the study programme
prof. RNDr. Ján Filo, CSc.
filo1@uniba.sk
course
4
52
prezenčná
B
4383
mMATa
Mathematics
L
1
on-site learning
2
2979
mMAT
Mathematics
L
1
on-site learning
2
II.
on-site learning
true
II.
1060451
1
P
lecturer
Róbert
Jajcay
prof. RNDr. Róbert Jajcay, DrSc.
jajcay6@uniba.sk
English, Slovak
EN
English
SK
Slovak
English, Slovak
L
2
<_L_>
Recommended literature
Algebraic graph theory / Norman Biggs. Cambridge : Cambridge University Press, 1993
Discrete mathematics / Norman L. Biggs. Oxford : Clarendon Press, 1985
An Introduction to the theory of groups / Joseph J. Rotman. New York : Springer, 1995
Electronic texts prepared by the teacher made available at the course web page.
Selection of recenty articles published in the area.
<_PA_>
Conditions for completion of course
Ongoing evaluation during the semester: homeworks, midterm
Final exam: written and oral
Approximative grade scale: A 90%, B 80%, C 70%, D 60%, E 50%
<_PJ_>
Language, which knowledge is needed to pass the course
Slovak, English
<_SO_>
Brief outline of the course
Introduction to permutation group theory, group actions, transitive actions, primitive actions, point stabilizers, recursive constructions of groups, automorphism groups of combinatorial structures, vertex-, edge-, and arc-transitive graphs, automorphism groups of finite geometries, Cayley graphs, graphs with a prescribed abstract automorphism group, graphs with a prescribed permutation group for their automorphism group, the effect of recursive constructions on the automorphism groups of the resulting graphs.
<_VH_>
Weighting of course assessment (continuous/final)
50/50
<_VV_>
Learning outcomes
After completing the course, students will be familiar with the basic theory of permutation groups and will be able to use and apply the acquired information in determining the automorphism groups of various types of combinatorial structures. They will be able to construct structures with a prescribed automorphism group and symmetry level.
A
22
100.0
B
0
0.0
C
0
0.0
D
0
0.0
E
0
0.0
FX
0
0.0
22
6
102584
B
2-MAT-226
FMFI.KAG/2-MAT-226/14
Applications of set theory
3
Evaluation
lecture
2
26
2
(Single degree study, master II. deg., full time form)
L
1
RNDr. Martin Sleziak, PhD.
16.02.2026
18.06.2022
8
Person responsible for the delivery, development and quality of the study programme
prof. RNDr. Ján Filo, CSc.
filo1@uniba.sk
lecture
2
26
prezenčná
C
4383
mMATa
Mathematics
L
1
on-site learning
2
2979
mMAT
Mathematics
L
1
on-site learning
2
II.
on-site learning
true
II.
1040155
1
P
lecturer
Martin
Sleziak
RNDr. Martin Sleziak, PhD.
sleziak1@uniba.sk
Slovak
SK
Slovak
Slovak
L
2
<_C_>
Goal
Learn to apply more advanced set-theoretical techniques (most importantly Zorn lemma and transfinite induction0 on various mathematical problems.
<_L_>
Recommended literature
Combinatorial set theory : With a gentle introduction to forcing / Lorenz J. Halbeisen. London : Springer, 2012
<_P_>
Continuous assessment
homework, presentations
<_PA_>
Conditions for completion of course
homework, presentations
Grading: A 90%, B 80%, C 70%, D 60%, E 50%, Fx < 50%
<_S_>
Course syllabus
Axiom of choice and its equivalents. Zorn lemma and its applications. Ordinals, transfinite induction and its applications. Almost disjoints systems, infinite trees, ultrafilters.
<_SO_>
Brief outline of the course
Axiom of choice and its equivalents. Zorn lemma and its applications. Ordinals, transfinite induction and its applications. Almost disjoints systems, infinite trees, ultrafilters.
<_URL_>
Course web page URL
http://msleziak.com/vyuka/apliktm.html
<_VH_>
Weighting of course assessment (continuous/final)
Semester 100% (homework assignments)
<_VV_>
Learning outcomes
Students will be able to apply more advanced set-theoretic techniques (mainly Zorn's lemma and transfinite induction) to problems from various areas of mathematics.
A
12
92.31
B
0
0.0
C
0
0.0
D
0
0.0
E
0
0.0
FX
1
7.69
13
6
76171
B
2-MAT-231
FMFI.KAG/2-MAT-231/09
Selected Topics in Cryptology
4
Evaluation
lecture
2
26
3
(Single degree study, master II. deg., full time form)
Z
2
prof. RNDr. Róbert Jajcay, DrSc., doc. RNDr. Martin Mačaj, PhD.
16.02.2026
14.03.2022
8
Person responsible for the delivery, development and quality of the study programme
prof. RNDr. Ján Filo, CSc.
filo1@uniba.sk
lecture
2
26
prezenčná
B
2979
mMAT
Mathematics
Z
2
on-site learning
3
4383
mMATa
Mathematics
Z
2
on-site learning
3
II.
on-site learning
true
II.
1060451
1
P
lecturer
Róbert
Jajcay
prof. RNDr. Róbert Jajcay, DrSc.
jajcay6@uniba.sk
English, Slovak
1040555
2
P
lecturer
Martin
Mačaj
doc. RNDr. Martin Mačaj, PhD.
macaj1@uniba.sk
English, Slovak
EN
English
SK
Slovak
English, Slovak
Z
3
<_L_>
Recommended literature
Cryptography : Theory and practice / Douglas R. Stinson. Boca Raton, Fla. : Chapman & Hall, 2006
Algebraic aspects of cryptography / Neal Koblitz. Berlin : Springer, 1998
<_PA_>
Conditions for completion of course
Ongoing evaluation during the semester: homeworks, midterm
Final exam: written and oral
Approximative grade scale: A 90%, B 80%, C 70%, D 60%, E 50%
<_PJ_>
Language, which knowledge is needed to pass the course
Slovak, English
<_SO_>
Brief outline of the course
A brief historical introduction and examples of crypto systems. Summary of relevant basic facts from number theory and algebra (congruencies, rings of modulo arithmetic, the Chines remained theorem). Definition and examples of crypto systems. Symmetric and asymmetric crypto systems. Cryptanalysis. Affine block codes and their cryptanalysis. DES-algorithms. Public-key crypto systems and the RSA method (potentially other methods as well). Hash functions and their usage in digital signature.
<_VH_>
Weighting of course assessment (continuous/final)
50/50
<_VV_>
Learning outcomes
After completing the course, students will understand fundamental principles of cryptographic protocols, will be able to evaluate the required levels of secrecy with regard to the security situation requirements, they will be familair with the basic principles of cryptographic attacks and corresponding defenses. Students will be familiar with classical cryprographical set-ups and protocols and their respective strengths and weaknesses.
A
49
98.0
B
1
2.0
C
0
0.0
D
0
0.0
E
0
0.0
FX
0
0.0
50
6
76172
B
2-MAT-232
FMFI.KAG/2-MAT-232/09
Computer Algebra (1)
3
Evaluation
lecture
2
26
3
(Single degree study, master II. deg., full time form)
Z
2
doc. RNDr. Jaroslav Guričan, CSc.
16.02.2026
21.06.2022
8
Person responsible for the delivery, development and quality of the study programme
prof. RNDr. Ján Filo, CSc.
filo1@uniba.sk
lecture
2
26
prezenčná
B
2979
mMAT
Mathematics
Z
2
on-site learning
3
4383
mMATa
Mathematics
Z
2
on-site learning
3
II.
on-site learning
true
II.
1049553
1
P
lecturer
Jaroslav
Guričan
doc. RNDr. Jaroslav Guričan, CSc.
gurican1@uniba.sk
English, Slovak
EN
English
SK
Slovak
English, Slovak
Z
3
<_L_>
Recommended literature
The Art of computer programming : Volume 2. Seminumerical Algorithms / Donald E. Knuth. Reading : Addison-Wesley, 1969
Lecturer's electronic texts, manuscripts.
<_O_>
Content prerequisite
1-INF-156 Algebra (2) OR 1-MAT-260 Algebra (2)
<_PA_>
Conditions for completion of course
oral exam with presentation
A - 91%+
B - 81%-90%
C - 71%-80%
D - 61%-70%
E - 50%-60%
Fx - less than 50%
<_PJ_>
Language, which knowledge is needed to pass the course
slovak, english
<_SO_>
Brief outline of the course
Basic algorithms for numbers and polynomials and their complexity. Methods of calculations using homomorphic images, Chinese residue theorem for Euclidean rings. Discrete Fourier and inverse Fourier transform, use in fast multiplication of polynomials and large integers. Berlekamp's algorithm for polynomial factorization over finite fields. Polynomial factorization withinin the ring Z[x] and within the rings of polynomials over finite algebraic extensions of the field Q.
<_VV_>
Learning outcomes
Students will master the most important algorithms of computer algebra, know most of the details of their implementation and time complexity.
A
49
89.09
B
4
7.27
C
1
1.82
D
0
0.0
E
1
1.82
FX
0
0.0
55
6
76173
B
2-MAT-241
FMFI.KAG/2-MAT-241/09
Computer Algebra (2)
3
Evaluation
lecture
2
26
4
(Single degree study, master II. deg., full time form)
L
2
doc. RNDr. Jaroslav Guričan, CSc.
16.02.2026
21.06.2022
8
Person responsible for the delivery, development and quality of the study programme
prof. RNDr. Ján Filo, CSc.
filo1@uniba.sk
lecture
2
26
prezenčná
B
2979
mMAT
Mathematics
L
2
on-site learning
4
4383
mMATa
Mathematics
L
2
on-site learning
4
II.
on-site learning
true
II.
1049553
1
P
lecturer
Jaroslav
Guričan
doc. RNDr. Jaroslav Guričan, CSc.
gurican1@uniba.sk
English, Slovak
EN
English
SK
Slovak
English, Slovak
L
4
<_L_>
Recommended literature
Gröbner Bases : A computational approach to commutative Algebra / Thomas Becker, Volker Weispfenning, Heinz Kredel. New York : Springer, 1993
Lecturer's electronic texts, manuscripts.
<_O_>
Content prerequisite
1-INF-156 Algebra (2) OR 1-MAT-260 Algebra (2)
<_PA_>
Conditions for completion of course
oral exam with presentation
A - 91%+
B - 81%-90%
C - 71%-80%
D - 61%-70%
E - 50%-60%
Fx - less than 50%
<_PJ_>
Language, which knowledge is needed to pass the course
slovak, english
<_SO_>
Brief outline of the course
Data representation and data structures. The problem of simplification and growth of intermediate results. Groebner basis of the ideal of a ring of real polynomials of several variables, applications to solutions of finite systems of polynomial equations of several variables and automatic proof of theorems of classical geometry. Well-founded and Dickson's quasiorderings and their role in computer algebra.
<_VV_>
Learning outcomes
Students will know the advantages and disadvantages of the data structures used. They will master in detail the theoretical significance of Groebner bases and also the details of the algorithm for finding GB's for a given ideal and other related algorithms. They will also be able to use Groebner bases to solve some important problems in rings of multivariate polynomials.
A
46
85.19
B
3
5.56
C
4
7.41
D
0
0.0
E
1
1.85
FX
0
0.0
54
6
104843
B
2-MAT-311
FMFI.KAMŠ/2-MAT-311/15
Non-Linear Programming
5
Evaluation
lecture / practicals
2 / 2
26 / 26
1
(Single degree study, master II. deg., full time form)
Z
1
doc. RNDr. Mária Trnovská, PhD.
16.02.2026
14.07.2025
8
Person responsible for the delivery, development and quality of the study programme
prof. RNDr. Ján Filo, CSc.
filo1@uniba.sk
lecture
2
26
prezenčná
practicals
2
26
prezenčná
B
2979
mMAT
Mathematics
Z
1
on-site learning
1
4383
mMATa
Mathematics
Z
1
on-site learning
1
II.
on-site learning
true
II.
1051883
1
P
lecturer
Mária
Trnovská
doc. RNDr. Mária Trnovská, PhD.
trnovska2@uniba.sk
Slovak
SK
Slovak
Slovak
Z
1
<_L_>
Recommended literature
Nelineárne programovanie, teória a algoritmy / Milan Hamala, Mária Trnovská. Bratislava : EPOS, 2013
S. Boyd, L. Vandenberghe: Convex Optimization, Cambridge University Press, 2004.
<_PA_>
Conditions for completion of course
Continuous assessment: exercises 30%, project: 20%, Final exam: 50%. Grading: A (100-91), B (90-81), C (80-71), D (70-61), E (60-51), Fx (50-0).
<_SO_>
Brief outline of the course
Lagrange function and its properties, Lagrange duality, Transformations of optimization problems, Generalization of Lagrange function, Roode axioms, Min-max theorem, General principle of duality, Convex, quasiconvex and strong convex functions, Optimality conditions, Lagrange and Kuhn-Tucker theorem, Duality thoery in convex programming, Slater theorem, Interior point methods - introduction.
<_VH_>
Weighting of course assessment (continuous/final)
50% / 50%
<_VV_>
Learning outcomes
Student has mastered the basics of nonlinear programming theory and methods.
A
6
33.33
B
1
5.56
C
3
16.67
D
2
11.11
E
5
27.78
FX
1
5.56
18
6
124610
B
2-MAT-313
FMFI.KAG/2-MAT-313/19
Selected Topics of Numerical Algebra
5
Evaluation
course
3
39
2
(Single degree study, master II. deg., full time form)
L
1
doc. RNDr. Andrej Ferko, PhD., Mgr. Martin Niepel, PhD.
16.02.2026
22.06.2022
8
Person responsible for the delivery, development and quality of the study programme
prof. RNDr. Ján Filo, CSc.
filo1@uniba.sk
course
3
39
prezenčná
B
956
mMPG
Computer Graphics and Geometry
L
2
on-site learning
4
4383
mMATa
Mathematics
L
1
on-site learning
2
4037
mMPG/k
Computer Graphics and Geometry (Conversion Programme)
L
2
on-site learning
4
2979
mMAT
Mathematics
L
1
on-site learning
2
II.
on-site learning
true
II.
1021974
1
P
lecturer
Andrej
Ferko
doc. RNDr. Andrej Ferko, PhD.
ferko1@uniba.sk
English, Slovak
1031904
2
P
lecturer
Martin
Niepel
Mgr. Martin Niepel, PhD.
niepel2@uniba.sk
English, Slovak
EN
English
SK
Slovak
English, Slovak
L
2
<_L_>
Recommended literature
L. N. Trefethen, D. Bau: Numerical Linear Algebra, SIAM, 1997
P-G. Martinsson, J. A. Tropp: Randomized Numerical Linear Algebra: Foundations & Algorithms
Carl D. Meyer: Matrix Analysis and Applied Linear Algebra, SIAM, 2001
Gene Golub, Charles Van Loan: Matrix Computations, John Hopkins, 2012
<_O_>
Content prerequisite
1-MAT-530 Numerical Methods of Linear Algebra
<_PA_>
Conditions for completion of course
Semester: homework
<_PJ_>
Language, which knowledge is needed to pass the course
English, Slovak
<_SO_>
Brief outline of the course
Spectral theory: eigenvalue problems, Schur factorization, power method, QR-algorithm, eigenvalue problems for symmetric matrices - Min-max theorem, QR-algorithm for symmetric matrices, Rayleigh-Ritz projection, subspace iterations, Krylov methods, GMRES , Arnoldi and Lanczos iteration, Golub-Kahan-Lanczos bidiagonalization.
Randomized numerical linear algerba: current algorithms for big data processing based on a randomized sampling, accuracy estimates, parallelization of calculations, etc.
<_URL_>
Course web page URL
http://thales.doa.fmph.uniba.sk/niepel/MC/matice3.html
<_VH_>
Weighting of course assessment (continuous/final)
100/0
<_VV_>
Learning outcomes
Students will get acquainted with theoretical foundations of advanced techniques in numerical linear algebra and at the same time gain practical experience with programming computational algorithms.
A
2
33.33
B
2
33.33
C
1
16.67
D
1
16.67
E
0
0.0
FX
0
0.0
6
6
104844
B
2-MAT-314
FMFI.KMANM+KAMŠ/2-MAT-314/15
Handling of Modern Software in Numerical Mathematics
3
Evaluation
course
2
26
1
(Single degree study, master II. deg., full time form)
Z
1
doc. RNDr. Peter Guba, PhD., Mgr. Jela Babušíková, PhD.
16.02.2026
21.06.2022
8
Person responsible for the delivery, development and quality of the study programme
prof. RNDr. Ján Filo, CSc.
filo1@uniba.sk
course
2
26
prezenčná
B
2979
mMAT
Mathematics
Z
1
on-site learning
1
4383
mMATa
Mathematics
Z
1
on-site learning
1
II.
on-site learning
true
II.
1002422
1
P
lecturer
Peter
Guba
doc. RNDr. Peter Guba, PhD.
guba1@uniba.sk
Slovak
1036748
2
P
lecturer
Jela
Babušíková
Mgr. Jela Babušíková, PhD.
babusikova1@uniba.sk
Slovak
SK
Slovak
Slovak
Z
1
<_L_>
Recommended literature
R. E. Bank: A Software Package for Solving Elliptic Partial Differential Equations, Users' Guide 9.0, University of California at San Diego
G. H. Golub, J. M. Ortega: Scientific Computing and Differential Equations: An Introduction to Numerical Methods, Academic Press, 1992
<_PA_>
Conditions for completion of course
Continuous assessment: active work on lectures 30 points, 2x individual work 20 points each, project 30 points
Final evaluation: 100 - 90 A, 89 - 80 B, 79 - 70 C, 69 - 60 D, 59 - 50 E, less than 50 FX.
<_PJ_>
Language, which knowledge is needed to pass the course
Slovak, English
<_SO_>
Brief outline of the course
Solving one-dimensional differential equations of elliptical and parabolic type using MATLAB software, handling the numerical package PLTMG - defining own problems and modification to solve parabolic type problems.
<_VV_>
Learning outcomes
Handling the procedures of practical solution of differential equations.
A
22
88.0
B
3
12.0
C
0
0.0
D
0
0.0
E
0
0.0
FX
0
0.0
25
6
124612
B
2-MAT-315
FMFI.KMANM/2-MAT-315/19
Finite Difference Methods for Differential Equations
4
Evaluation
lecture / practicals
2 / 1
26 / 13
2
(Single degree study, master II. deg., full time form)
L
1
Mgr. Jela Babušíková, PhD., prof. RNDr. Ján Filo, CSc., RNDr. Patrik Mihala, PhD.
16.02.2026
21.06.2022
FMFI.KMANM/2-EFM-101/15
FMFI.KMANM/2-EFM-101/15 - Numerical Modelling
2-EFM-101 - Numerical Modelling
FMFI.KMANM/2-MAT-315/12
FMFI.KMANM/2-MAT-315/12 - Finite Difference Methods for Differential Equations
2-MAT-315 - Finite Difference Methods for Differential Equations
8
Person responsible for the delivery, development and quality of the study programme
prof. RNDr. Ján Filo, CSc.
filo1@uniba.sk
lecture
2
26
prezenčná
practicals
1
13
prezenčná
104540
FMFI.KMANM/2-EFM-101/15
2-EFM-101
Numerical Modelling
92445
FMFI.KMANM/2-MAT-315/12
2-MAT-315
Finite Difference Methods for Differential Equations
B
4383
mMATa
Mathematics
L
1
on-site learning
2
2979
mMAT
Mathematics
L
1
on-site learning
2
II.
on-site learning
true
II.
1036748
1
P
lecturer
Jela
Babušíková
Mgr. Jela Babušíková, PhD.
babusikova1@uniba.sk
Slovak
1042269
2
P
lecturer
Ján
Filo
prof. RNDr. Ján Filo, CSc.
filo1@uniba.sk
Slovak
1134035
3
C
instructor
Patrik
Mihala
RNDr. Patrik Mihala, PhD.
mihala1@uniba.sk
Slovak
SK
Slovak
Slovak
L
2
<_L_>
Recommended literature
E. Vitásek: Numerická matematika II : Numerické řešení diferenciálních rovnic, Praha : Univerzita Karlova, 1981
E. Vitásek: Numerické metody, Praha : Státní nakladatelství technické literatury, 1987
G. H. Golub, J. M. Ortega: Scientific Computing and Differential Equations: An Introduction to Numerical Methods, Academic Press, 1992
M. H. Holmes: An Introduction to Numerical Methods in Differential Equations, Springer, 2007
<_PA_>
Conditions for completion of course
Preliminary assessment: 2 written tests 10 points each, project 20 points
Final examination: written exam for 50 points and oral exam for 10 points
Grading scheme: A 90%, B 80%, C 70%, D 60%, E 50%
<_PJ_>
Language, which knowledge is needed to pass the course
Slovak, English
<_SO_>
Brief outline of the course
Numerical methods for ordinary differential equations.
Initial value problem, one-step and multistep methods of Runge-Kutta type.
Methods for Solving Ordinary Differential Equations.
Applications of ODR numerical methods in physics and biology.
Numerical solution of boundary value problems for ordinary differential equations, difference method, shooting method.
Partial differential equation: Finite difference method for parabolic, hyperbolic and elliptic problems in 2D, explicit and implicit methods, stability, alternating direction method.
Applications of PDR numerical methods in physics and biology.
Implementation of numerical algorithms in Matlab and Python.
<_VH_>
Weighting of course assessment (continuous/final)
40/60
<_VV_>
Learning outcomes
Student will be able to solve ordinary and partial differential equations by modern numerical methods.
A
16
48.48
B
4
12.12
C
5
15.15
D
5
15.15
E
3
9.09
FX
0
0.0
33
6
153222
B
2-MAT-323
FMFI.KMANM/2-MAT-323/25
Numerical Analysis of Partial Differential Equations (1)
4
Evaluation
lecture
2
26
2
(Single degree study, master II. deg., full time form)
L
1
Dr. Hana Šmitala Mizerová
16.02.2026
20.05.2025
FMFI.KMANM/2-MAT-325/12
FMFI.KMANM/2-MAT-325/12 - Variational Methods in Differential Equations
2-MAT-325 - Variational Methods in Differential Equations
FMFI.KMANM/2-MAT-323/09
FMFI.KMANM/2-MAT-323/09 - Finite Element Method (1)
2-MAT-323 - Finite Element Method (1)
8
Person responsible for the delivery, development and quality of the study programme
prof. RNDr. Ján Filo, CSc.
filo1@uniba.sk
lecture
2
26
prezenčná
92428
FMFI.KMANM/2-MAT-325/12
2-MAT-325
Variational Methods in Differential Equations
76180
FMFI.KMANM/2-MAT-323/09
2-MAT-323
Finite Element Method (1)
B
4383
mMATa
Mathematics
L
1
on-site learning
2
2979
mMAT
Mathematics
L
1
on-site learning
2
II.
on-site learning
true
II.
1007722
1
P
lecturer
Hana
Šmitala Mizerová
Dr. Hana Šmitala Mizerová
mizerova3@uniba.sk
English, Slovak
EN
English
SK
Slovak
English, Slovak
L
2
<_C_>
Goal
To master basic modern numerical methods for solving engineering problems.
<_L_>
Recommended literature
J. Kačur: Numerické metódy riešenia PDR (electronic version)
P. G. Ciarlet: The finite element method for elliptic problems, North Holland, 1978
C. Johnson: Numerical solution of PDE by finite element method. Cambridge University Press, 1988
<_P_>
Continuous assessment
individual task
<_SO_>
Brief outline of the course
Variational formulation for linear elliptic boundary value problems; Ritz and Galerkin methods (Lemma of Cea ); construction of basis functions for finite-dimensional approximation spaces; local and global variational formulation; assembling; convergence; error estimates for 1D and 2D linear interpolation.
<_VV_>
Learning outcomes
Completing the course students will acquire basic knowledge of classical numerical methods for solving elliptic, parabolic and hyperbolic partial differential equations with the focus on convergence analysis and error estimates.
A
20
43.48
B
12
26.09
C
8
17.39
D
4
8.7
E
0
0.0
FX
2
4.35
46
6
92428
B
2-MAT-325
FMFI.KMANM/2-MAT-325/12
Variational Methods in Differential Equations
4
Evaluation
lecture
2
26
1
(Single degree study, master II. deg., full time form)
Z
1
Dr. Hana Šmitala Mizerová
16.02.2026
15.03.2022
8
Person responsible for the delivery, development and quality of the study programme
prof. RNDr. Ján Filo, CSc.
filo1@uniba.sk
lecture
2
26
prezenčná
B
2979
mMAT
Mathematics
Z
1
on-site learning
1
4383
mMATa
Mathematics
Z
1
on-site learning
1
II.
on-site learning
true
II.
1007722
1
P
lecturer
Hana
Šmitala Mizerová
Dr. Hana Šmitala Mizerová
mizerova3@uniba.sk
English, Slovak
EN
English
SK
Slovak
English, Slovak
Z
1
<_L_>
Recommended literature
C.Johnson: Numerical solutions of PDE,Cambridge University Press Cambridge 1987
J.Kačur: Numerické metódy PDR (pdf v elektronickej podobe)
<_PA_>
Conditions for completion of course
Indicative assessment scale: A 90%, B 80%, C 70%, D 60%, E 50%
<_PJ_>
Language, which knowledge is needed to pass the course
Slovak, English
<_SO_>
Brief outline of the course
Weak solutions of problems, Sobolev space theory, traces of traces of Lax-Milgram lemma, theorem on equivalent norms, spectral theory, Fredholm's theorem, Galerkin method.
<_VH_>
Weighting of course assessment (continuous/final)
0/100
<_VV_>
Learning outcomes
After completing the course, students will be able to solve practical problems using modern methods of functional analysis and PDR.
A
12
37.5
B
6
18.75
C
4
12.5
D
3
9.38
E
6
18.75
FX
1
3.13
32
6
92430
B
2-MAT-327
FMFI.KMANM/2-MAT-327/12
Numerical Modelling in Optimization Problems
3
Evaluation
course
2
26
3
(Single degree study, master II. deg., full time form)
Z
2
prof. RNDr. Jozef Kačur, DrSc., RNDr. Patrik Mihala, PhD.
16.02.2026
15.03.2022
8
Person responsible for the delivery, development and quality of the study programme
prof. RNDr. Ján Filo, CSc.
filo1@uniba.sk
course
2
26
prezenčná
B
2979
mMAT
Mathematics
Z
2
on-site learning
3
4383
mMATa
Mathematics
Z
2
on-site learning
3
II.
on-site learning
true
II.
1035429
1
P
lecturer
Jozef
Kačur
prof. RNDr. Jozef Kačur, DrSc.
kacur1@uniba.sk
Slovak
1134035
2
P
lecturer
Patrik
Mihala
RNDr. Patrik Mihala, PhD.
mihala1@uniba.sk
Slovak
SK
Slovak
Slovak
Z
3
<_L_>
Recommended literature
R.Fletcher”Practical Methods of Optimization, Wiley,New York, 1987
S.J. Wright:Primal-Dual Interior –Point Methods. SIAM, Philadelphia, 1997
<_PA_>
Conditions for completion of course
Indicative assessment scale: A 90%, B 80%, C 70%, D 60%, E 50%
<_PJ_>
Language, which knowledge is needed to pass the course
Slovak, English
<_SO_>
Brief outline of the course
Solution (in matlab) by method: simplex, primary-dual, internal point, quadratic and convex programming, Frank-Wolfe, Rosen, penalty, berier.
<_VH_>
Weighting of course assessment (continuous/final)
50/50
<_VV_>
Learning outcomes
After completing the course, students will be able to solve practical problems by modern methods.
A
16
76.19
B
1
4.76
C
1
4.76
D
1
4.76
E
1
4.76
FX
1
4.76
21
6
153223
B
2-MAT-334
FMFI.KMANM/2-MAT-334/25
Numerical Analysis of Partial Differential Equations (2)
3
Evaluation
lecture
2
26
3
(Single degree study, master II. deg., full time form)
Z
2
Dr. Hana Šmitala Mizerová
16.02.2026
20.05.2025
FMFI.KMANM/2-MAT-323/25 or FMFI.KMANM/2-MAT-323/09
FMFI.KMANM/2-MAT-323/25 - Numerical Analysis of Partial Differential Equations (1) or FMFI.KMANM/2-MAT-323/09 - Finite Element Method (1)
2-MAT-323 - Numerical Analysis of Partial Differential Equations (1) or 2-MAT-323 - Finite Element Method (1)
FMFI.KMANM/2-MAT-334/10
FMFI.KMANM/2-MAT-334/10 - Finite Element Method (2)
2-MAT-334 - Finite Element Method (2)
8
Person responsible for the delivery, development and quality of the study programme
prof. RNDr. Ján Filo, CSc.
filo1@uniba.sk
lecture
2
26
prezenčná
153222
FMFI.KMANM/2-MAT-323/25
2-MAT-323
Numerical Analysis of Partial Differential Equations (1)
andlebo
76180
FMFI.KMANM/2-MAT-323/09
2-MAT-323
Finite Element Method (1)
81368
FMFI.KMANM/2-MAT-334/10
2-MAT-334
Finite Element Method (2)
B
2979
mMAT
Mathematics
Z
2
on-site learning
3
4383
mMATa
Mathematics
Z
2
on-site learning
3
II.
on-site learning
true
II.
1007722
1
P
lecturer
Hana
Šmitala Mizerová
Dr. Hana Šmitala Mizerová
mizerova3@uniba.sk
English, Slovak
EN
English
SK
Slovak
English, Slovak
Z
3
<_C_>
Goal
To extend the basics of finite element method used to solve various problems arising in engineering.
<_L_>
Recommended literature
J. Kačur: Numerické metódy riešenia PDR (v elektronickej forme)
C. Johnson: Numerical solution of PDE by the FEM, Cambridge University Press, 1987
P.G. Ciarlet: The Finite Element Method for Elliptic Problems, North-Holland, Amsterdam, 1978
G. Strang: Variational crimes in the FEM, The Mathematical Foundations of the Finite Element Method with Applications to Partial Differential Equations 1972, p. 689-710
S.C. Brenner, L.R. Scott: The mathematical theory of FEM, Springer New York, 2008
<_P_>
Continuous assessment
individual task
<_SO_>
Brief outline of the course
variational crimes (1. and 2. Strang's lemma; approximation of boundary conditions; nonconformal FEM); mixed FEM (approximation of saddle point problem, inf-sup condition); adaptive mesh-refinement method (a posteriori error estimates); finite volume method; fluid flow models
<_VH_>
Weighting of course assessment (continuous/final)
30/70
<_VV_>
Learning outcomes
Completing the course students will acquire basic knowledge of classical numerical methods for solving parabolic and hyperbolic partial differential equations with the focus on convergence analysis and error estimates.
<_Z_>
Final assessment
exam
A
16
51.61
B
1
3.23
C
7
22.58
D
3
9.68
E
3
9.68
FX
1
3.23
31
6
104845
B
2-MAT-341
FMFI.KMANM+KAMŠ/2-MAT-341/15
Solving of Engineering Problems by Numerical Software
3
Evaluation
course
2
26
4
(Single degree study, master II. deg., full time form)
L
2
doc. RNDr. Peter Guba, PhD., Mgr. Jela Babušíková, PhD.
16.02.2026
21.06.2022
8
Person responsible for the delivery, development and quality of the study programme
prof. RNDr. Ján Filo, CSc.
filo1@uniba.sk
course
2
26
prezenčná
B
2979
mMAT
Mathematics
L
2
on-site learning
4
4383
mMATa
Mathematics
L
2
on-site learning
4
II.
on-site learning
true
II.
1002422
1
P
lecturer
Peter
Guba
doc. RNDr. Peter Guba, PhD.
guba1@uniba.sk
Slovak
1036748
2
P
lecturer
Jela
Babušíková
Mgr. Jela Babušíková, PhD.
babusikova1@uniba.sk
Slovak
SK
Slovak
Slovak
L
4
<_L_>
Recommended literature
G. H. Golub, J. M. Ortega: Scientific Computing and Differential Equations: An Introduction to Numerical Methods, Academic Press, 1992
M. H. Holmes: An Introduction to Numerical Methods in Differential Equations, Springer, 2007
<_PA_>
Conditions for completion of course
Continuous assessment: active work on lectures 30 points, 2x individual work 20 points each, project 30 points
Final evaluation: 100 - 90 A, 89 - 80 B, 79 - 70 C, 69 - 60 D, 59 - 50 E, less than 50 FX.
<_PJ_>
Language, which knowledge is needed to pass the course
Slovak, English
<_SO_>
Brief outline of the course
An overview of numerical methods for solving engineering models and their program implementation, appling existing software when applied to specific tasks of mathematical physics and engineering practice, work with software LSODA, MATLAB, PLTMG.
<_VH_>
Weighting of course assessment (continuous/final)
100/0
<_VV_>
Learning outcomes
After completing the course, students should be able to practically solve various types of differential equations.
A
11
91.67
B
1
8.33
C
0
0.0
D
0
0.0
E
0
0.0
FX
0
0.0
12
6
76200
B
2-MAT-610
FMFI.KAG/2-MAT-610/09
Algebraic Number Theory
3
Evaluation
lecture
2
26
4
(Single degree study, master II. deg., full time form)
L
2
doc. RNDr. Martin Mačaj, PhD.
16.02.2026
14.03.2022
8
Person responsible for the delivery, development and quality of the study programme
prof. RNDr. Ján Filo, CSc.
filo1@uniba.sk
lecture
2
26
prezenčná
B
2979
mMAT
Mathematics
L
2
on-site learning
4
4383
mMATa
Mathematics
L
2
on-site learning
4
II.
on-site learning
true
II.
1040555
1
P
lecturer
Martin
Mačaj
doc. RNDr. Martin Mačaj, PhD.
macaj1@uniba.sk
English, Slovak
EN
English
SK
Slovak
English, Slovak
L
4
<_L_>
Recommended literature
Algebraic Number Theory and Fermat's Last Theorem/ Ian Stewart, David Tall. A. K. Peters 2001
<_O_>
Content prerequisite
2-MAT-213 Selected topics in algebra (1) AND 2-MAT-215 Field Theory (1)
<_PA_>
Conditions for completion of course
Exam: oral
Indicative evaluation scale: A 90%, B 80%, C 70%, D 60%, E 50%
<_PJ_>
Language, which knowledge is needed to pass the course
slovak, english
<_SO_>
Brief outline of the course
Algebraic numbers and algebraic integers. Quadratic and cyclotomic fields. Prime decomposition. Ramanujan-Nagel theorem. Ideals, norms, prime decomposition of ideals. Integral lattices. Minkowski theorem.
<_VH_>
Weighting of course assessment (continuous/final)
0/100
<_VV_>
Learning outcomes
Mastering basic concepts and methods from algebraic number theory. Awareness of the importance of uniqueness of prime decomposition in integral domains, Ability to solve some types of Diophantine equations.
A
15
75.0
B
1
5.0
C
3
15.0
D
1
5.0
E
0
0.0
FX
0
0.0
20
6
76202
B
2-MAT-617
FMFI.KAG/2-MAT-617/09
Category Theory (1)
3
Evaluation
lecture
2
26
3
(Single degree study, master II. deg., full time form)
Z
2
doc. Mgr. Tibor Macko, PhD., Mgr. Tomáš Rusin, PhD.
16.02.2026
21.06.2022
8
Person responsible for the delivery, development and quality of the study programme
prof. RNDr. Ján Filo, CSc.
filo1@uniba.sk
lecture
2
26
prezenčná
B
4403
dGTLa/x
Geometry and Topology
Z
-1
on-site learning
2979
mMAT
Mathematics
Z
2
on-site learning
3
1078
dGTL
Geometry and Topology
Z
-1
on-site learning
4383
mMATa
Mathematics
Z
2
on-site learning
3
4402
dGTLa
Geometry and Topology
Z
-1
on-site learning
1080
dGTL/x
Geometry and Topology
Z
-1
on-site learning
II., III.
on-site learning
true
II., III.
1237494
1
P
lecturer
Tibor
Macko
doc. Mgr. Tibor Macko, PhD.
macko58@uniba.sk
English, Slovak
1006036
2
P
lecturer
Tomáš
Rusin
Mgr. Tomáš Rusin, PhD.
rusin3@uniba.sk
English, Slovak
EN
English
SK
Slovak
English, Slovak
Z
3
<_L_>
Recommended literature
Algebra a príbuzné disciplíny / Milan Kolibiar ...[et al.]. Bratislava : Alfa, 1992
Categories for the working mathematician / Saunders Mac Lane. New York : Springer, 1997
Abstract and Concrete Categories/Jiří Adámek, Horst Herrlich, George E. Strecker. http://katmat.math.uni-bremen.de/acc/acc.pdf
<_PA_>
Conditions for completion of course
Continuous assessment: homework and 1 presentation
Indicative evaluation scale: A 90%, B 80%, C 70%, D 60%, E 50%
<_PJ_>
Language, which knowledge is needed to pass the course
Slovak, English
<_SO_>
Brief outline of the course
Categories, functors and natural transformations. Special morphisms and objects. Subcategories. Limits and colimits. Factorization systems.
<_VH_>
Weighting of course assessment (continuous/final)
100/0
<_VV_>
Learning outcomes
Students will master selected basic concepts and methods of category theory and will be able to apply them in topology and algebra.
A
36
97.3
ABS
0
0.0
B
0
0.0
C
0
0.0
D
0
0.0
E
0
0.0
FX
1
2.7
NEABS
0
0.0
37
8
135123
B
2-MAT-618
FMFI.KAG/2-MAT-618/22
Universal Algebras and Lattices (3)
3
Evaluation
seminar
2
26
4
(Single degree study, master II. deg., full time form)
L
2
doc. RNDr. Jaroslav Guričan, CSc.
16.02.2026
21.06.2022
FMFI.KAG/2-MAT-618/09
FMFI.KAG/2-MAT-618/09 - Universal Algebras and Lattices (3)
2-MAT-618 - Universal Algebras and Lattices (3)
8
Person responsible for the delivery, development and quality of the study programme
prof. RNDr. Ján Filo, CSc.
filo1@uniba.sk
seminar
2
26
prezenčná
76204
FMFI.KAG/2-MAT-618/09
2-MAT-618
Universal Algebras and Lattices (3)
C
2979
mMAT
Mathematics
L
2
on-site learning
4
4383
mMATa
Mathematics
L
2
on-site learning
4
II.
on-site learning
true
II.
1049553
1
P
lecturer
Jaroslav
Guričan
doc. RNDr. Jaroslav Guričan, CSc.
gurican1@uniba.sk
English, Slovak
EN
English
SK
Slovak
English, Slovak
L
4
<_O_>
Content prerequisite
FMFI.KAG/2-MAT-221/22 Universal Algebras and Lattices (2)
<_PA_>
Conditions for completion of course
presentations, quality and depth of understanding
A - 91%+
B - 81%-90%
C - 71%-80%
D - 61%-70%
E - 50%-60%
Fx - less than 50%
<_PJ_>
Language, which knowledge is needed to pass the course
slovak, english
<_SO_>
Brief outline of the course
We shall continue with the literature from previous semester. Topics are selected by students.
Few possibilities:
Free, injective and projective Boolean algebras.
Applications of Boolean algebras in relational systems (automatons, computer science).
Presentations of research papers from leading journals, e.g. Universal Algebra, Order, Semigroup forum.
<_VV_>
Learning outcomes
Students will gain experience in independent study of advanced mathematical topics and with the presentation of new knowledge. They will know the most important concepts, methods and results from the lattice theory and universal algebra and their connection with the methods and results of "classical" mathematical disciplines. They will be able to follow current research in the field of lattice theory and universal algebra.
A
13
100.0
B
0
0.0
C
0
0.0
D
0
0.0
E
0
0.0
FX
0
0.0
13
6
76206
B
2-MAT-619
FMFI.KAG/2-MAT-619/09
Selected Chapters in the Theory of Functions of Complex Variable
3
Evaluation
lecture
2
26
3
(Single degree study, master II. deg., full time form)
Z
2
Mgr. Martin Niepel, PhD.
16.02.2026
15.03.2022
8
Person responsible for the delivery, development and quality of the study programme
prof. RNDr. Ján Filo, CSc.
filo1@uniba.sk
lecture
2
26
prezenčná
C
2979
mMAT
Mathematics
Z
2
on-site learning
3
4383
mMATa
Mathematics
Z
2
on-site learning
3
II.
on-site learning
true
II.
1031904
1
P
lecturer
Martin
Niepel
Mgr. Martin Niepel, PhD.
niepel2@uniba.sk
English, Slovak
EN
English
SK
Slovak
English, Slovak
Z
3
<_L_>
Recommended literature
M. Ablowitz, A. Fokas: Complex variables. Introduction and Applications, Cambridge Texts in Applied Mathematics, 2003
L. V. Ahlfors: Complex Analysis, McGraw-Hill, New York, 1979.
E. Stein, R. Shakarchi: Complex Analysis, Princeton University Press, 2003
A. I. Markushevich: Theory of functions of complex variable, Chelsea, New York, 1977
<_O_>
Content prerequisite
1-MAT-416 or 1-FYZ-225 - introduction to methods of complex analysis
<_PA_>
Conditions for completion of course
Semester: homework, presentation
Approximate grade scheme: A 90%, B 80%, C 70%, D 60%, E 50%
<_PJ_>
Language, which knowledge is needed to pass the course
English, Slovak
<_PZ_>
Notes
The course can also be taught in English.
The course might not run every year.
<_SO_>
Brief outline of the course
Cauchy type integrals, principal value integral, Hilbert and Fourier transforms, analytic continuation, compactness for families of analytic functions, infinite series (Mittag-Leffler's theorem), infinite products (Weierstrass factorization), Gamma function, Stirling's formula, Riemann Zeta function, conformal maps, Riemann mapping theorem, elliptic functions, modular forms, Riemann surfaces and global analytic functions, branching points, Picard theorem, etc.
Covered topics could be customized to match students' interests.
<_URL_>
Course web page URL
http://thales.doa.fmph.uniba.sk/niepel/CA/complex.html
<_VH_>
Weighting of course assessment (continuous/final)
100/0
<_VV_>
Learning outcomes
Students will expand their knowledge of the theory of functions of complex variable with regard to applications in PDR, analytical number theory, special functions, geometry, topology, etc.
With the help of homework sets, they will gain practical skills in advanced computation techniques and proofs.
A
13
81.25
B
2
12.5
C
0
0.0
D
1
6.25
E
0
0.0
FX
0
0.0
16
6
76208
B
2-MAT-620
FMFI.KAG/2-MAT-620/09
Seminar in Algebraic and Differential Topology (1)
3
Evaluation
seminar
2
26
3
(Single degree study, master II. deg., full time form)
Z
2
Mgr. Martin Niepel, PhD., doc. Mgr. Tibor Macko, PhD.
16.02.2026
15.03.2022
8
Person responsible for the delivery, development and quality of the study programme
prof. RNDr. Ján Filo, CSc.
filo1@uniba.sk
seminar
2
26
prezenčná
C
2979
mMAT
Mathematics
Z
2
on-site learning
3
4383
mMATa
Mathematics
Z
2
on-site learning
3
II.
on-site learning
true
II.
1031904
1
P
lecturer
Martin
Niepel
Mgr. Martin Niepel, PhD.
niepel2@uniba.sk
English, Slovak
1237494
2
P
lecturer
Tibor
Macko
doc. Mgr. Tibor Macko, PhD.
macko58@uniba.sk
English, Slovak
EN
English
SK
Slovak
English, Slovak
Z
3
<_L_>
Recommended literature
Handbook of Algebraic Topology (edited by I. James), Elsevier, Amsterdam 1995.
Handbook of Global Analysis (edited by D. Krupka and D. Saunders), Elsevier, Amsterdam 2007/2008.
<_PA_>
Conditions for completion of course
Semester: talk/presentation
Indicative grading scheme: A 90%, B 80%, C 70%, D 60%, E 50%
<_PJ_>
Language, which knowledge is needed to pass the course
English, Slovak
<_SO_>
Brief outline of the course
Algebraic topology. Theory of manifolds and cellular complexes.
Global analysis, analysis on manifolds.
<_VH_>
Weighting of course assessment (continuous/final)
100/0
<_VV_>
Learning outcomes
Students will gain qualified understanding of ideas, approaches, methods and results in selected topics of algebraic and differential topology.
A
7
100.0
B
0
0.0
C
0
0.0
D
0
0.0
E
0
0.0
FX
0
0.0
7
6
76203
B
2-MAT-622
FMFI.KAG/2-MAT-622/09
Category Theory (2)
3
Evaluation
lecture
2
26
4
(Single degree study, master II. deg., full time form)
L
2
doc. Mgr. Tibor Macko, PhD.
16.02.2026
21.06.2022
8
Person responsible for the delivery, development and quality of the study programme
prof. RNDr. Ján Filo, CSc.
filo1@uniba.sk
lecture
2
26
prezenčná
C
1078
dGTL
Geometry and Topology
L
-1
on-site learning
1080
dGTL/x
Geometry and Topology
L
-1
on-site learning
4403
dGTLa/x
Geometry and Topology
L
-1
on-site learning
2979
mMAT
Mathematics
L
2
on-site learning
4
4383
mMATa
Mathematics
L
2
on-site learning
4
4402
dGTLa
Geometry and Topology
L
-1
on-site learning
II., III.
on-site learning
true
II., III.
1237494
1
P
lecturer
Tibor
Macko
doc. Mgr. Tibor Macko, PhD.
macko58@uniba.sk
English, Slovak
EN
English
SK
Slovak
English, Slovak
L
4
<_L_>
Recommended literature
Algebra a príbuzné disciplíny / Milan Kolibiar ...[et al.]. Bratislava : Alfa, 1992
Categories for the working mathematician / Saunders Mac Lane. New York : Springer, 1997
Abstract and Concrete Categories/Jiří Adámek, Horst Herrlich, George E. Strecker. http://katmat.math.uni-bremen.de/acc/acc.pdf
<_PA_>
Conditions for completion of course
Continuous assessment: homework and 1 presentation
Indicative evaluation scale: A 90%, B 80%, C 70%, D 60%, E 50%
<_PJ_>
Language, which knowledge is needed to pass the course
Slovak, English
<_SO_>
Brief outline of the course
Adjoint functors, existence theorems, reflective and coreflective subcategories. Generators and cogenerators of categories and subcategories. Application of category theory methods in topology and algebra.
<_VH_>
Weighting of course assessment (continuous/final)
100/0
<_VV_>
Learning outcomes
Students will master selected basic concepts and methods of category theory and will be able to apply them in topology and algebra.
A
14
100.0
ABS
0
0.0
B
0
0.0
C
0
0.0
D
0
0.0
E
0
0.0
FX
0
0.0
NEABS
0
0.0
14
8
76210
B
2-MAT-624
FMFI.KAG/2-MAT-624/09
Number Theory (2)
3
Evaluation
lecture
2
26
2
(Single degree study, master II. deg., full time form)
L
1
RNDr. Martin Sleziak, PhD.
16.02.2026
18.06.2022
8
Person responsible for the delivery, development and quality of the study programme
prof. RNDr. Ján Filo, CSc.
filo1@uniba.sk
lecture
2
26
prezenčná
B
4383
mMATa
Mathematics
L
1
on-site learning
2
2979
mMAT
Mathematics
L
1
on-site learning
2
II.
on-site learning
true
II.
1040155
1
P
lecturer
Martin
Sleziak
RNDr. Martin Sleziak, PhD.
sleziak1@uniba.sk
Slovak
SK
Slovak
Slovak
L
2
<_L_>
Recommended literature
Elementary number theory / Gareth A. Jones, J. Mary Jones. London : Springer, 1998
<_PA_>
Conditions for completion of course
Homework and an oral exam
Grading: A 90%, B 80%, C 70%, D 60%, E 50%, Fx < 50%
<_SO_>
Brief outline of the course
Various types of densities (Schnirelman, asymptotic and logarithmic density). Diophantine equations and Pythagorean triples. Results on expressing integers as sums of squares. Minkowski theorem. Cantor's expansions of real numbers. Proofs of rrationality of some real numbers.
<_VH_>
Weighting of course assessment (continuous/final)
Semester 20% (homework assignments) / 80% final exam (oral exam).
<_VV_>
Learning outcomes
Students will learn to solve basic types of Diophantine equations. They will be able to use various types of densities to compare various subsets of the set of positive integers.
A
40
90.91
B
2
4.55
C
0
0.0
D
1
2.27
E
0
0.0
FX
1
2.27
44
6
76209
B
2-MAT-625
FMFI.KAG/2-MAT-625/09
Seminar in Algebraic and Differential Topology (2)
3
Evaluation
seminar
2
26
4
(Single degree study, master II. deg., full time form)
L
2
Mgr. Martin Niepel, PhD., doc. Mgr. Tibor Macko, PhD.
16.02.2026
15.03.2022
8
Person responsible for the delivery, development and quality of the study programme
prof. RNDr. Ján Filo, CSc.
filo1@uniba.sk
seminar
2
26
prezenčná
C
2979
mMAT
Mathematics
L
2
on-site learning
4
4383
mMATa
Mathematics
L
2
on-site learning
4
II.
on-site learning
true
II.
1031904
1
P
lecturer
Martin
Niepel
Mgr. Martin Niepel, PhD.
niepel2@uniba.sk
English, Slovak
1237494
2
P
lecturer
Tibor
Macko
doc. Mgr. Tibor Macko, PhD.
macko58@uniba.sk
English, Slovak
EN
English
SK
Slovak
English, Slovak
L
4
<_L_>
Recommended literature
Handbook of Algebraic Topology (edited by I. James), Elsevier, Amsterdam 1995.
Handbook of Global Analysis (edited by D. Krupka and D. Saunders), Elsevier, Amsterdam 2007/2008.
<_PA_>
Conditions for completion of course
Semester: talk/presentation
Indicative grading scheme: A 90%, B 80%, C 70%, D 60%, E 50%
<_PJ_>
Language, which knowledge is needed to pass the course
English, Slovak
<_SO_>
Brief outline of the course
Algebraic topology. Theory of manifolds and cellular complexes.
Global analysis, analysis on manifolds.
<_VH_>
Weighting of course assessment (continuous/final)
100/0
<_VV_>
Learning outcomes
Students will gain qualified understanding of ideas, approaches, methods and results in selected
topics of algebraic and differential topology.
A
4
100.0
B
0
0.0
C
0
0.0
D
0
0.0
E
0
0.0
FX
0
0.0
4
6
124609
B
2-MAT-626
FMFI.KAG/2-MAT-626/19
Selected Topics of Algebraic Topology
3
Evaluation
lecture
2
26
3
(Single degree study, master II. deg., full time form)
Z
2
doc. Mgr. Tibor Macko, PhD.
16.02.2026
21.06.2022
FMFI.KAG/2-MAT-223/09
FMFI.KAG/2-MAT-223/09 - Algebraic Topology
2-MAT-223 - Algebraic Topology
8
Person responsible for the delivery, development and quality of the study programme
prof. RNDr. Ján Filo, CSc.
filo1@uniba.sk
lecture
2
26
prezenčná
76169
FMFI.KAG/2-MAT-223/09
2-MAT-223
Algebraic Topology
C
2979
mMAT
Mathematics
Z
2
on-site learning
3
4383
mMATa
Mathematics
Z
2
on-site learning
3
II.
on-site learning
true
II.
1237494
1
P
lecturer
Tibor
Macko
doc. Mgr. Tibor Macko, PhD.
macko58@uniba.sk
English, Slovak
EN
English
SK
Slovak
English, Slovak
Z
3
<_L_>
Recommended literature
A. Hatcher: Algebraic Topology
<_PA_>
Conditions for completion of course
Continuous assessment: homework, presentation
Indicative evaluation scale: A 90%, B 80%, C 70%, D 60%, E 50%
<_PJ_>
Language, which knowledge is needed to pass the course
Slovak, English
<_PZ_>
Notes
The course may be taught in English. It may not be offered every year.
<_SO_>
Brief outline of the course
Homological algebra: universal coefficient theorems, Kuenneth's theorem. Cohomology ring, calculations in some specific cases. Poincaré's duality and its application to manifolds. Higher homotopy groups. Fibrations and cofibrations. Hurewicz's theorem. Whitehead's theorem. Moore-Postnikov's towers. Blakers-Massey theorem. Stable homotopy groups. Spectra in the sense homotopy theory. Generalized homology and cohomology theories. Spectral sequences. Cobordisms. Characteristic classes. K-theory. Morse theory. Surgery.
The choice of topics can be tailored to the interests of students.
<_VH_>
Weighting of course assessment (continuous/final)
100/0
<_VV_>
Learning outcomes
Students will expand their knowledge of algebraic topology with topics that could not be covered within the course Algebraic topology, such as homological algebra, Poincaré duality and basics of homotopy theory.
A
5
100.0
B
0
0.0
C
0
0.0
D
0
0.0
E
0
0.0
FX
0
0.0
5
6
133678
Z
2-MAT-910
FMFI.KMANM/2-MAT-910/22
Individual Work on Final Thesis (1)
5
Evaluation
independent work
100s
2
(Single degree study, master II. deg., full time form)
L
1
prof. RNDr. Ján Filo, CSc.
16.02.2026
15.03.2022
FMFI.KMANM/2-MAT-910/15
FMFI.KMANM/2-MAT-910/15 - Individual Work on Final Thesis (1)
2-MAT-910 - Individual Work on Final Thesis (1)
8
Person responsible for the delivery, development and quality of the study programme
prof. RNDr. Ján Filo, CSc.
filo1@uniba.sk
independent work
100s
prezenčná
104848
FMFI.KMANM/2-MAT-910/15
2-MAT-910
Individual Work on Final Thesis (1)
A
4383
mMATa
Mathematics
L
1
on-site learning
2
2979
mMAT
Mathematics
L
1
on-site learning
2
II.
on-site learning
true
II.
1042269
1
P
lecturer
Ján
Filo
prof. RNDr. Ján Filo, CSc.
filo1@uniba.sk
Slovak
SK
Slovak
Slovak
L
2
<_L_>
Recommended literature
Ako písať vysokoškolské a kvalifikačné práce : Ako písať seminárne práce, ročníkové práce, práce študentskej vedeckej a odbornej činnosti, diplomové práce, záverečné a atestačné práce, dizertácie / Dušan Katuščák. Bratislava : Stimul, 1998
<_PA_>
Conditions for completion of course
Continuous assessment: individual work under the supervision of the thesis supervisor, evaluation based on the recommendation of the thesis supervisor
Indicative assessment scale: A 90%, B 80%, C 70%, D 60%, E 50%
<_PJ_>
Language, which knowledge is needed to pass the course
Slovak, English
<_SO_>
Brief outline of the course
A typical diploma thesis usually contains: title page with title, content, introduction, historical overview of the issue, theory, main results, conclusion, list of used literature, or appendices and appendices.
<_VH_>
Weighting of course assessment (continuous/final)
100/0
<_VV_>
Learning outcomes
The student will gain an overview of the available literature in the field of the assigned topic of his thesis and will prepare its introductory part.
Together with the thesis supervisor, they will specify the goals for the next stage of the thesis.
A
32
88.89
B
1
2.78
C
0
0.0
D
1
2.78
E
2
5.56
FX
0
0.0
36
6
133679
Z
2-MAT-911
FMFI.KMANM/2-MAT-911/22
Individual Work on Final Thesis (2)
5
Evaluation
independent work
100s
3
(Single degree study, master II. deg., full time form)
Z
2
prof. RNDr. Ján Filo, CSc.
16.02.2026
15.03.2022
FMFI.KMANM/2-MAT-911/15
FMFI.KMANM/2-MAT-911/15 - Individual Work on Final Thesis (2)
2-MAT-911 - Individual Work on Final Thesis (2)
8
Person responsible for the delivery, development and quality of the study programme
prof. RNDr. Ján Filo, CSc.
filo1@uniba.sk
independent work
100s
prezenčná
104849
FMFI.KMANM/2-MAT-911/15
2-MAT-911
Individual Work on Final Thesis (2)
A
2979
mMAT
Mathematics
Z
2
on-site learning
3
4383
mMATa
Mathematics
Z
2
on-site learning
3
II.
on-site learning
true
II.
1042269
1
P
lecturer
Ján
Filo
prof. RNDr. Ján Filo, CSc.
filo1@uniba.sk
Slovak
SK
Slovak
Slovak
Z
3
<_L_>
Recommended literature
Ako písať vysokoškolské a kvalifikačné práce : Ako písať seminárne práce, ročníkové práce, práce študentskej vedeckej a odbornej činnosti, diplomové práce, záverečné a atestačné práce, dizertácie / Dušan Katuščák. Bratislava : Stimul, 1998
<_PA_>
Conditions for completion of course
Continuous assessment: individual work under the supervision of the thesis supervisor, evaluation based on the recommendation of the thesis supervisor
Indicative assessment scale: A 90%, B 80%, C 70%, D 60%, E 50%
<_PJ_>
Language, which knowledge is needed to pass the course
Slovak, English
<_SO_>
Brief outline of the course
A typical diploma thesis usually contains: title page with title, content, introduction, historical overview of the issue, theory, main results, conclusion, list of used literature, or appendices and appendices.
<_VH_>
Weighting of course assessment (continuous/final)
100/0
<_VV_>
Learning outcomes
The student will work out the basis of his / her diploma thesis and together with the supervisor of his / her diploma thesis he / she will specify the goals for the last stage of the work on the final thesis.
A
29
82.86
B
2
5.71
C
4
11.43
D
0
0.0
E
0
0.0
FX
0
0.0
35
6
133680
B
2-MAT-920
FMFI.KMANM/2-MAT-920/22
Diploma Thesis Seminar
3
Evaluation
seminar
3
39
4
(Single degree study, master II. deg., full time form)
L
2
prof. RNDr. Ján Filo, CSc., doc. RNDr. Eugen Viszus, CSc.
16.02.2026
16.06.2022
FMFI.KMANM/2-MAT-920/15
FMFI.KMANM/2-MAT-920/15 - Diploma Thesis Seminar
2-MAT-920 - Diploma Thesis Seminar
8
Person responsible for the delivery, development and quality of the study programme
prof. RNDr. Ján Filo, CSc.
filo1@uniba.sk
seminar
3
39
prezenčná
104850
FMFI.KMANM/2-MAT-920/15
2-MAT-920
Diploma Thesis Seminar
A
2979
mMAT
Mathematics
L
2
on-site learning
4
4383
mMATa
Mathematics
L
2
on-site learning
4
II.
on-site learning
true
II.
1042269
1
P
lecturer
Ján
Filo
prof. RNDr. Ján Filo, CSc.
filo1@uniba.sk
Slovak
1023881
2
P
lecturer
Eugen
Viszus
doc. RNDr. Eugen Viszus, CSc.
viszus1@uniba.sk
Slovak
SK
Slovak
Slovak
L
4
<_L_>
Recommended literature
Ako písať vysokoškolské a kvalifikačné práce : Ako písať seminárne práce, ročníkové práce, práce študentskej vedeckej a odbornej činnosti, diplomové práce, záverečné a atestačné práce, dizertácie / Dušan Katuščák. Bratislava : Stimul, 1998
<_PA_>
Conditions for completion of course
Mid-term evaluation: compulsory participation in presentations of your classmates (20%) and two presentation of your obtained results (80%).
Indicative assessment scale: A 90%, B 80%, C 70%, D 60%, E 50%
<_PJ_>
Language, which knowledge is needed to pass the course
Slovak. English
<_SO_>
Brief outline of the course
Each student will present (twice a semester) partial results of his/her diploma thesis.
<_VH_>
Weighting of course assessment (continuous/final)
100/0
<_VV_>
Learning outcomes
Students will gain skills of formal writing of scientific text and modern methods of presentation of their own results.
A
28
90.32
B
1
3.23
C
0
0.0
D
0
0.0
E
1
3.23
FX
1
3.23
31
6
104847
B
2-MMN-140
FMFI.KMANM/2-MMN-140/15
Unconventional Application of Mathematical Analysis
3
Evaluation
seminar
2
26
3
(Single degree study, master II. deg., full time form)
Z
2
prof. RNDr. Jaroslav Jaroš, CSc.
16.02.2026
16.06.2022
8
Person responsible for the delivery, development and quality of the study programme
prof. RNDr. Ján Filo, CSc.
filo1@uniba.sk
seminar
2
26
prezenčná
C
2979
mMAT
Mathematics
Z
2
on-site learning
3
4383
mMATa
Mathematics
Z
2
on-site learning
3
964
mMMN
Managerial Mathematics
Z
2
on-site learning
3
4382
mMMNa
Managerial Mathematics
Z
2
on-site learning
3
II.
on-site learning
true
II.
1021533
1
P
lecturer
Jaroslav
Jaroš
prof. RNDr. Jaroslav Jaroš, CSc.
jaros1@uniba.sk
Slovak
SK
Slovak
Slovak
Z
3
<_PA_>
Conditions for completion of course
Continuous assessment: individual work, presentation on a given topic.
<_PJ_>
Language, which knowledge is needed to pass the course
Slovak, English
<_SO_>
Brief outline of the course
1. Discrete and continuous models of interactions of biological populations (competitive systems, system "predator-prey", symbiotic systems).
2. Mathematical model of the detection of diabetes.
3. Discrete dynamical systems of mathematical genetics.
4. Epidemic models and dynamics of infectious diseases.
<_VH_>
Weighting of course assessment (continuous/final)
100/0
<_VV_>
Learning outcomes
The purpose of the course is to present to students some uncommon applications of modern mathematical analysis, mainly in biology, medicine and social sciences.
A
80
93.02
B
6
6.98
C
0
0.0
D
0
0.0
E
0
0.0
FX
0
0.0
86
6
127849
B
2-MPG-104
FMFI.KAG/2-MPG-104/20
Algebraic Geometry (1)
5
Evaluation
course
3
39
2
(Single degree study, master II. deg., full time form)
L
1
RNDr. Jana Chalmovianská, PhD., doc. RNDr. Martin Mačaj, PhD.
16.02.2026
21.06.2022
8
Person responsible for the delivery, development and quality of the study programme
prof. RNDr. Ján Filo, CSc.
filo1@uniba.sk
course
3
39
prezenčná
B
4385
mMPGa
Computer Graphics and Geometry
L
1
on-site learning
2
4383
mMATa
Mathematics
L
1
on-site learning
2
4386
mMPGa/k
Computer Graphics and Geometry (Conversion Programme)
L
1
on-site learning
2
4037
mMPG/k
Computer Graphics and Geometry (Conversion Programme)
L
1
on-site learning
2
956
mMPG
Computer Graphics and Geometry
L
1
on-site learning
2
2979
mMAT
Mathematics
L
1
on-site learning
2
II.
on-site learning
true
II.
1030199
1
P
lecturer
Jana
Chalmovianská
RNDr. Jana Chalmovianská, PhD.
pilnikova1@uniba.sk
English, Slovak
1040555
2
P
lecturer
Martin
Mačaj
doc. RNDr. Martin Mačaj, PhD.
macaj1@uniba.sk
English, Slovak
EN
English
SK
Slovak
English, Slovak
L
2
<_PA_>
Conditions for completion of course
Preliminary assessment: homework
Final assessment: oral exam
Grading: A 90%, B 80%, C 70%, D 60%, E 50%
<_SO_>
Brief outline of the course
- ideals and varieties in affine space, Hilbert's basis theorem
- Nullstellensatz
- elements of algebraic geometry:
- Zariski topology,
- coordinate rings, morphisms and rational maps
- computational methods of algebraic geometry: Gröbner bases, resultants
- Sturm sequences (calculations in real algebraic geometry)
<_VV_>
Learning outcomes
The student gains an overview of the basic concepts of algebraic geometry as well as the most common computational methods there.
A
15
78.95
B
0
0.0
C
1
5.26
D
3
15.79
E
0
0.0
FX
0
0.0
19
6
133824
B
2-MPG-108
FMFI.KAG/2-MPG-108/22
Differential Geometry
4
Evaluation
lecture
3
39
1
(Single degree study, master II. deg., full time form)
Z
1
doc. RNDr. Pavel Chalmovianský, PhD.
16.02.2026
22.06.2022
8
Person responsible for the delivery, development and quality of the study programme
prof. RNDr. Ján Filo, CSc.
filo1@uniba.sk
lecture
3
39
prezenčná
B
4386
mMPGa/k
Computer Graphics and Geometry (Conversion Programme)
Z
1
on-site learning
1
956
mMPG
Computer Graphics and Geometry
Z
1
on-site learning
1
4385
mMPGa
Computer Graphics and Geometry
Z
1
on-site learning
1
2979
mMAT
Mathematics
Z
1
on-site learning
1
4383
mMATa
Mathematics
Z
1
on-site learning
1
4037
mMPG/k
Computer Graphics and Geometry (Conversion Programme)
Z
1
on-site learning
1
II.
on-site learning
true
II.
1003473
1
P
lecturer
Pavel
Chalmovianský
doc. RNDr. Pavel Chalmovianský, PhD.
chalmovians1@uniba.sk
English, Slovak
EN
English
SK
Slovak
English, Slovak
Z
1
<_L_>
Recommended literature
Analytická a diferenciální geometrie / Bruno Budinský. Praha : Státní nakladatelství technické literatury, 1983
Lectures on classical differential geometry / Dirk J. Struik. Cambridge : Addison-Wesley Press, 1950
Electronic texts by the teacher, published on the WWW page of the subject.
<_PA_>
Conditions for completion of course
Homeworks (written solutions of problems and their consulting 20%), final exam (oral exam with written preparation 80%). Rough evaluation scale: A 90%, B 80%, C 70%, D 60%, E 50%
<_PJ_>
Language, which knowledge is needed to pass the course
Slovak and English
<_SO_>
Brief outline of the course
Curves: Torsion of a curve, the Frenet formulas. Envelopes of a one-parameter family of curves. Singular points of plane curves. The oriented curvature of plane curves. Some special curves (evolutes, evolvents, equidistants).
Surfaces: Developable ruled surfaces. The first fundamental form of a surface and measuring on a surface. Mappings of surfaces. The Dupin indicatrix, directions at a point. Principal directions and principal curvatures. The Gaussian curvature. Geodesics. Semi-geodesic coordinates. Extremal properties of geodesics. Surfaces of constant Gaussian curvature.
<_VH_>
Weighting of course assessment (continuous/final)
20/80
<_VV_>
Learning outcomes
By completing this subject, the students will deepen the knowledge of curves in Euclidean plane and Euclidean 3-space, as well as the knowledge of surfaces, needed in advanced computer graphics, geometric modeling and their applications.
A
6
37.5
B
1
6.25
C
3
18.75
D
1
6.25
E
2
12.5
FX
3
18.75
16
6
31053
B
2-MXX-110
FMFI.KTV/2-MXX-110/00
Physical Education and Sport (1)
2
Evaluation
practicals
2
26
1, 7
(Single degree study, master II. deg., full time form)
Z
1, 4
PaedDr. Dana Mašlejová, Mgr. Ladislav Mókus, Mgr. Jana Leginusová, Mgr. Tomáš Kuchár, PhD., PaedDr. Mikuláš Ortutay, Mgr. Martin Dovičák, PhD., Mgr. Júlia Raábová, PhD., Mgr. Branislav Nedbálek, PhD., Mgr. Tomáš Lovecký, Mgr. Martina Maheľová, PaedDr. Lucia Ondrušová
16.02.2026
15.03.2022
8
Person responsible for the delivery, development and quality of the study programme
prof. RNDr. Ján Filo, CSc.
filo1@uniba.sk
practicals
2
26
prezenčná
C
955
mFTF
Theoretical Physics
Z
4
on-site learning
7
968
mINF
Computer Science
Z
4
on-site learning
7
1018
muMAIN
Teaching Mathematics and Computer Science
Z
1
on-site learning
1
1019
mAIN
Applied Computer Science
Z
1
on-site learning
1
3006
muFYIN
Teaching Physics and Computer Science
Z
1
on-site learning
1
3507
muMADG/k
Teaching Mathematics and Descriptive Geometry (Conversion Programme)
Z
1
on-site learning
1
3510
muMAIN/k
Teaching Mathematics and Computer Science (Conversion Programme)
Z
1
on-site learning
1
3510
muMAIN/k
Teaching Mathematics and Computer Science (Conversion Programme)
Z
4
on-site learning
7
3965
mEMM
Mathematical Economics, Finance and Modelling
Z
1
on-site learning
1
4384
mFOSa
Optics, Lasers and Optical Spectroscopy
Z
4
on-site learning
7
4386
mMPGa/k
Computer Graphics and Geometry (Conversion Programme)
Z
1
on-site learning
1
5123
muINAN
Teaching Computer Science and English Language and Literature
Z
4
on-site learning
7
5688
mBIN
Bioinformatics
Z
1
on-site learning
1
956
mMPG
Computer Graphics and Geometry
Z
1
on-site learning
1
964
mMMN
Managerial Mathematics
Z
1
on-site learning
1
1018
muMAIN
Teaching Mathematics and Computer Science
Z
4
on-site learning
7
2979
mMAT
Mathematics
Z
4
on-site learning
7
2980
mFOS
Optics, Lasers and Optical Spectroscopy
Z
4
on-site learning
7
4374
mEMMa
Mathematical Economics, Finance and Modelling
Z
4
on-site learning
7
4375
mEOMa
Environmental Physics, Renewable Energy Sources and Meteorology and Climatology
Z
4
on-site learning
7
4381
mIKVa
Cognitive Science
Z
4
on-site learning
7
4383
mMATa
Mathematics
Z
4
on-site learning
7
4384
mFOSa
Optics, Lasers and Optical Spectroscopy
Z
1
on-site learning
1
5574
muINGE
Teaching Computer Science and Geography
Z
1
on-site learning
1
5620
mBMF
Biomedical Physics
Z
4
on-site learning
7
5687
mDAV
Data Science
Z
1
on-site learning
1
965
mINF/k
Computer Science (Conversion Programme)
Z
1
on-site learning
1
978
mFAA
Astronomy and Astrophysics
Z
4
on-site learning
7
2980
mFOS
Optics, Lasers and Optical Spectroscopy
Z
1
on-site learning
1
3006
muFYIN
Teaching Physics and Computer Science
Z
4
on-site learning
7
3007
muINBI
Teaching Computer Science and Biology
Z
4
on-site learning
7
3966
mEOM
Environmental Physics, Renewable Energy Sources and Meteorology and Climatology
Z
4
on-site learning
7
3971
mFPE
Physics of the Earth
Z
4
on-site learning
7
4037
mMPG/k
Computer Graphics and Geometry (Conversion Programme)
Z
4
on-site learning
7
4371
mAINa
Applied Computer Science
Z
4
on-site learning
7
4374
mEMMa
Mathematical Economics, Finance and Modelling
Z
1
on-site learning
1
4385
mMPGa
Computer Graphics and Geometry
Z
1
on-site learning
1
5688
mBIN
Bioinformatics
Z
4
on-site learning
7
970
mFFP
Plasma Physics
Z
1
on-site learning
1
971
mFTL
Solid State Physics
Z
4
on-site learning
7
2604
muMATV
Teaching Mathematics and Physical Education
Z
1
on-site learning
1
2604
muMATV
Teaching Mathematics and Physical Education
Z
4
on-site learning
7
3508
muFYIN/k
Teaching Physics and Computer Science (Conversion Programme)
Z
4
on-site learning
7
3966
mEOM
Environmental Physics, Renewable Energy Sources and Meteorology and Climatology
Z
1
on-site learning
1
4375
mEOMa
Environmental Physics, Renewable Energy Sources and Meteorology and Climatology
Z
1
on-site learning
1
4376
mFFPa
Plasma Physics
Z
1
on-site learning
1
4376
mFFPa
Plasma Physics
Z
4
on-site learning
7
4382
mMMNa
Managerial Mathematics
Z
4
on-site learning
7
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1005342
1
C
instructor
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Mašlejová
PaedDr. Dana Mašlejová
maslejova1@uniba.sk
Slovak
1009061
2
C
instructor
Ladislav
Mókus
Mgr. Ladislav Mókus
mokus2@uniba.sk
Slovak
1045838
3
C
instructor
Jana
Leginusová
Mgr. Jana Leginusová
leginusova1@uniba.sk
Slovak
1049011
4
C
instructor
Tomáš
Kuchár
Mgr. Tomáš Kuchár, PhD.
kuchar1@uniba.sk
Slovak
1045754
5
C
instructor
Mikuláš
Ortutay
PaedDr. Mikuláš Ortutay
ortutay1@uniba.sk
Slovak
1003472
6
C
instructor
Martin
Dovičák
Mgr. Martin Dovičák, PhD.
dovicak1@uniba.sk
Slovak
1017460
7
C
instructor
Júlia
Raábová
Mgr. Júlia Raábová, PhD.
raabova1@uniba.sk
Slovak
1230273
8
C
instructor
Branislav
Nedbálek
Mgr. Branislav Nedbálek, PhD.
nedbalek2@uniba.sk
Slovak
1051507
9
C
instructor
Tomáš
Lovecký
Mgr. Tomáš Lovecký
lovecky3@uniba.sk
Slovak
1060552
10
C
instructor
Martina
Maheľová
Mgr. Martina Maheľová
Slovak
1367237
11
P
lecturer
Lucia
Ondrušová
PaedDr. Lucia Ondrušová
Slovak
SK
Slovak
Slovak
Z
1
7
<_C_>
Goal
Basic practicing and improvement of locomotion skills in various selected sports: aerobics, basketball, volleyball, football, floorball, hockey, badminton, tennis, table tennis, swimming, body building, trampoline jumping, paddling. Development of a harmonic personality in the sense of “kalokagatia” – to cultivate the students´ mental and physical values.
<_PJ_>
Language, which knowledge is needed to pass the course
Slovak, English
<_SO_>
Brief outline of the course
Practicing of the students´ game skills in collective sports: basketball, volleyball, football, floorball and hockey. Mastering of the basic technique of a particular sport discipline in other sports. In paddling, basic training on still and slightly flowing water. Development of coordination skills, improvement of articular mobility and cardiovascular system.
<_VH_>
Weighting of course assessment (continuous/final)
100/0
A
1955
97.41
B
12
0.6
C
2
0.1
D
0
0.0
E
0
0.0
FX
38
1.89
2007
6
118709
B
2-MXX-115
FMFI.KTV/2-MXX-115/17
Sports in Natur (1)
2
Evaluation
1, 7
(Single degree study, master II. deg., full time form)
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16.02.2026
16.06.2022
8
Person responsible for the delivery, development and quality of the study programme
prof. RNDr. Ján Filo, CSc.
filo1@uniba.sk
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1003472
1
C
instructor
Martin
Dovičák
Mgr. Martin Dovičák, PhD.
dovicak1@uniba.sk
Slovak
1049011
2
P
lecturer
Tomáš
Kuchár
Mgr. Tomáš Kuchár, PhD.
kuchar1@uniba.sk
Slovak
1045838
3
C
instructor
Jana
Leginusová
Mgr. Jana Leginusová
leginusova1@uniba.sk
Slovak
1005342
4
C
instructor
Dana
Mašlejová
PaedDr. Dana Mašlejová
maslejova1@uniba.sk
Slovak
1009061
5
C
instructor
Ladislav
Mókus
Mgr. Ladislav Mókus
mokus2@uniba.sk
Slovak
1045754
6
C
instructor
Mikuláš
Ortutay
PaedDr. Mikuláš Ortutay
ortutay1@uniba.sk
Slovak
1017460
7
C
instructor
Júlia
Raábová
Mgr. Júlia Raábová, PhD.
raabova1@uniba.sk
Slovak
1051507
8
C
instructor
Tomáš
Lovecký
Mgr. Tomáš Lovecký
lovecky3@uniba.sk
Slovak
SK
Slovak
Slovak
Z
1
7
<_PA_>
Conditions for completion of course
Grades: A 90%, B 80%, C 70%, D 60%, E 50%
The condition for the award of 1 or 2 credits is the completion of a multi-day course in its full scope, or the completion of one-day courses in the scope of 4 days. Candidates can apply to the leaders of individual courses. From the presented offer of courses, you can choose the one that suits your interests, abilities and deadlines.
<_PJ_>
Language, which knowledge is needed to pass the course
Slovak
<_PZ_>
Notes
KTVŠ does not rent ski equipment.
<_SO_>
Brief outline of the course
The student can sign up for the outdoor sports courses offered by the department: skiing, snowboarding. The lessons in the courses are focused on the development of basic and special movement skills and mastering the techniques needed for the sports.
<_VV_>
Learning outcomes
Acquisition and development of basic motor skills and abilities in selected sports: skiing and snowboarding. Mastering the correct technique of performing individual movements, which are necessary for skiing and snowboarding.
A
184
98.92
B
0
0.0
C
0
0.0
D
0
0.0
E
0
0.0
FX
2
1.08
186
6
122252
B
2-MXX-116
FMFI.KTV/2-MXX-116/18
Sports in Natur (2)
2
Evaluation
2, 8
(Single degree study, master II. deg., full time form)
L
1, 4
Mgr. Martin Dovičák, PhD., Mgr. Tomáš Kuchár, PhD., Mgr. Jana Leginusová, PaedDr. Dana Mašlejová, Mgr. Ladislav Mókus, PaedDr. Mikuláš Ortutay, Mgr. Júlia Raábová, PhD., Mgr. Tomáš Lovecký
16.02.2026
16.06.2022
8
Person responsible for the delivery, development and quality of the study programme
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filo1@uniba.sk
C
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on-site learning
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Applied Computer Science (Conversion Programme)
L
4
on-site learning
8
2980
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Optics, Lasers and Optical Spectroscopy
L
1
on-site learning
2
3966
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Environmental Physics, Renewable Energy Sources and Meteorology and Climatology
L
1
on-site learning
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Solid State Physics
L
4
on-site learning
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4
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L
4
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L
1
on-site learning
2
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1
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Nuclear and Sub-nuclear Physics
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4
on-site learning
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Applied Computer Science
L
1
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L
1
on-site learning
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Environmental Physics, Renewable Energy Sources and Meteorology and Climatology
L
4
on-site learning
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Applied Computer Science
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1
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4
on-site learning
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L
1
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Biomedical Physics
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Bioinformatics
L
1
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Bioinformatics
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Plasma Physics
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Solid State Physics
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1
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1
on-site learning
2
1018
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Teaching Mathematics and Computer Science
L
4
on-site learning
8
3007
muINBI
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L
4
on-site learning
8
3510
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L
1
on-site learning
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mFPE
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L
4
on-site learning
8
4037
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on-site learning
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4380
mFJFa
Nuclear and Sub-nuclear Physics
L
1
on-site learning
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4
on-site learning
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L
1
on-site learning
2
5123
muINAN
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L
4
on-site learning
8
956
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Computer Graphics and Geometry
L
1
on-site learning
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L
1
on-site learning
2
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3006
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1
on-site learning
2
3006
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L
4
on-site learning
8
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L
4
on-site learning
8
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L
4
on-site learning
8
3965
mEMM
Mathematical Economics, Finance and Modelling
L
4
on-site learning
8
4037
mMPG/k
Computer Graphics and Geometry (Conversion Programme)
L
4
on-site learning
8
4378
mINFa
Computer Science
L
4
on-site learning
8
956
mMPG
Computer Graphics and Geometry
L
4
on-site learning
8
968
mINF
Computer Science
L
1
on-site learning
2
976
mFBM
Biomedical Physics
L
4
on-site learning
8
978
mFAA
Astronomy and Astrophysics
L
1
on-site learning
2
2979
mMAT
Mathematics
L
1
on-site learning
2
2979
mMAT
Mathematics
L
4
on-site learning
8
3507
muMADG/k
Teaching Mathematics and Descriptive Geometry (Conversion Programme)
L
4
on-site learning
8
3509
muMAFY/k
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L
1
on-site learning
2
3965
mEMM
Mathematical Economics, Finance and Modelling
L
1
on-site learning
2
3971
mFPE
Physics of the Earth
L
1
on-site learning
2
4382
mMMNa
Managerial Mathematics
L
4
on-site learning
8
4384
mFOSa
Optics, Lasers and Optical Spectroscopy
L
4
on-site learning
8
4387
mPMSa
Probability and Mathematical Statistics
L
1
on-site learning
2
4388
mFTFa
Theoretical Physics
L
4
on-site learning
8
5574
muINGE
Teaching Computer Science and Geography
L
1
on-site learning
2
I.II., II.
on-site learning
true
1003472
1
C
instructor
Martin
Dovičák
Mgr. Martin Dovičák, PhD.
dovicak1@uniba.sk
Slovak
1049011
2
P
lecturer
Tomáš
Kuchár
Mgr. Tomáš Kuchár, PhD.
kuchar1@uniba.sk
Slovak
1045838
3
C
instructor
Jana
Leginusová
Mgr. Jana Leginusová
leginusova1@uniba.sk
Slovak
1005342
4
C
instructor
Dana
Mašlejová
PaedDr. Dana Mašlejová
maslejova1@uniba.sk
Slovak
1009061
5
C
instructor
Ladislav
Mókus
Mgr. Ladislav Mókus
mokus2@uniba.sk
Slovak
1045754
6
C
instructor
Mikuláš
Ortutay
PaedDr. Mikuláš Ortutay
ortutay1@uniba.sk
Slovak
1017460
7
C
instructor
Júlia
Raábová
Mgr. Júlia Raábová, PhD.
raabova1@uniba.sk
Slovak
1051507
8
C
instructor
Tomáš
Lovecký
Mgr. Tomáš Lovecký
lovecky3@uniba.sk
Slovak
SK
Slovak
Slovak
L
2
8
<_PA_>
Conditions for completion of course
Grades: A 90%, B 80%, C 70%, D 60%, E 50%.
The condition for the award of 1 or 2 credits is the completion of a multi-day course in its full scope, or the completion of one-day courses in the scope of 4 days. Candidates can apply to the leaders of individual courses. From the presented offer of courses, you can choose the one that suits your interests, abilities and deadlines.
<_PJ_>
Language, which knowledge is needed to pass the course
Slovak
<_PZ_>
Notes
KTVŠ will provide sports equipment.
<_SO_>
Brief outline of the course
The student can sign up for the outdoor sports courses offered by the department: water tourism - river rafting, windsurfing, beach volleyball, hiking and other hobby sports. The lessons in the courses are focused on the development of basic and special movement skills and, mastering the techniques needed for the sports.
<_VV_>
Learning outcomes
Creating a positive and lasting relationship with physical activity. Acquisition and mastery of basic motor skills and abilities in outdoor sports: windsurfing, beach volleyball, water tourism - river rafting, hiking and other sports according to interest. Training and improving the technique needed for the sports.
A
104
95.41
B
0
0.0
C
0
0.0
D
0
0.0
E
0
0.0
FX
5
4.59
109
6
130637
B
2-MXX-130
FMFI.KAI/2-MXX-130/21
Elements of AI
2
Evaluation
independent work
25
325
2, 8
(Single degree study, master II. deg., full time form)
L
1, 4
doc. RNDr. Mária Markošová, PhD., prof. Ing. Igor Farkaš, Dr., doc. RNDr. Martin Takáč, PhD.
16.02.2026
22.08.2021
8
Person responsible for the delivery, development and quality of the study programme
prof. RNDr. Ján Filo, CSc.
filo1@uniba.sk
independent work
25
325
prezenčná
C
955
mFTF
Theoretical Physics
L
4
on-site learning
8
965
mINF/k
Computer Science (Conversion Programme)
L
4
on-site learning
8
2604
muMATV
Teaching Mathematics and Physical Education
L
4
on-site learning
8
3507
muMADG/k
Teaching Mathematics and Descriptive Geometry (Conversion Programme)
L
1
on-site learning
2
4375
mEOMa
Environmental Physics, Renewable Energy Sources and Meteorology and Climatology
L
1
on-site learning
2
4375
mEOMa
Environmental Physics, Renewable Energy Sources and Meteorology and Climatology
L
4
on-site learning
8
4376
mFFPa
Plasma Physics
L
1
on-site learning
2
4378
mINFa
Computer Science
L
1
on-site learning
2
4385
mMPGa
Computer Graphics and Geometry
L
1
on-site learning
2
4387
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Probability and Mathematical Statistics
L
4
on-site learning
8
5687
mDAV
Data Science
L
1
on-site learning
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mDAV
Data Science
L
4
on-site learning
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mPMS
Probability and Mathematical Statistics
L
4
on-site learning
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Applied Computer Science
L
4
on-site learning
8
2980
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Optics, Lasers and Optical Spectroscopy
L
4
on-site learning
8
3007
muINBI
Teaching Computer Science and Biology
L
1
on-site learning
2
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L
4
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L
1
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4
on-site learning
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1
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mMPGa/k
Computer Graphics and Geometry (Conversion Programme)
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L
4
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mFAA
Astronomy and Astrophysics
L
4
on-site learning
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muMADG
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1
on-site learning
2
1017
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1104
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L
1
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3508
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L
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Applied Computer Science
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on-site learning
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1
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955
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on-site learning
2
964
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Managerial Mathematics
L
1
on-site learning
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968
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Computer Science
L
4
on-site learning
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1104
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Teaching Mathematics and Physics
L
4
on-site learning
8
2596
mAIN/k
Applied Computer Science (Conversion Programme)
L
1
on-site learning
2
2596
mAIN/k
Applied Computer Science (Conversion Programme)
L
4
on-site learning
8
2980
mFOS
Optics, Lasers and Optical Spectroscopy
L
1
on-site learning
2
3966
mEOM
Environmental Physics, Renewable Energy Sources and Meteorology and Climatology
L
1
on-site learning
2
4377
mFTLa
Solid State Physics
L
4
on-site learning
8
4380
mFJFa
Nuclear and Sub-nuclear Physics
L
4
on-site learning
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mMMNa
Managerial Mathematics
L
1
on-site learning
2
4384
mFOSa
Optics, Lasers and Optical Spectroscopy
L
1
on-site learning
2
5574
muINGE
Teaching Computer Science and Geography
L
4
on-site learning
8
5620
mBMF
Biomedical Physics
L
4
on-site learning
8
954
mPMS
Probability and Mathematical Statistics
L
1
on-site learning
2
965
mINF/k
Computer Science (Conversion Programme)
L
1
on-site learning
2
967
mFJF
Nuclear and Sub-nuclear Physics
L
4
on-site learning
8
1019
mAIN
Applied Computer Science
L
1
on-site learning
2
2604
muMATV
Teaching Mathematics and Physical Education
L
1
on-site learning
2
3966
mEOM
Environmental Physics, Renewable Energy Sources and Meteorology and Climatology
L
4
on-site learning
8
4371
mAINa
Applied Computer Science
L
1
on-site learning
2
4376
mFFPa
Plasma Physics
L
4
on-site learning
8
4381
mIKVa
Cognitive Science
L
4
on-site learning
8
5123
muINAN
Teaching Computer Science and English Language and Literature
L
1
on-site learning
2
5620
mBMF
Biomedical Physics
L
1
on-site learning
2
5688
mBIN
Bioinformatics
L
1
on-site learning
2
5688
mBIN
Bioinformatics
L
4
on-site learning
8
964
mMMN
Managerial Mathematics
L
4
on-site learning
8
970
mFFP
Plasma Physics
L
1
on-site learning
2
970
mFFP
Plasma Physics
L
4
on-site learning
8
971
mFTL
Solid State Physics
L
1
on-site learning
2
1018
muMAIN
Teaching Mathematics and Computer Science
L
1
on-site learning
2
1018
muMAIN
Teaching Mathematics and Computer Science
L
4
on-site learning
8
3007
muINBI
Teaching Computer Science and Biology
L
4
on-site learning
8
3510
muMAIN/k
Teaching Mathematics and Computer Science (Conversion Programme)
L
1
on-site learning
2
3971
mFPE
Physics of the Earth
L
4
on-site learning
8
4037
mMPG/k
Computer Graphics and Geometry (Conversion Programme)
L
1
on-site learning
2
4380
mFJFa
Nuclear and Sub-nuclear Physics
L
1
on-site learning
2
4385
mMPGa
Computer Graphics and Geometry
L
4
on-site learning
8
4388
mFTFa
Theoretical Physics
L
1
on-site learning
2
5123
muINAN
Teaching Computer Science and English Language and Literature
L
4
on-site learning
8
956
mMPG
Computer Graphics and Geometry
L
1
on-site learning
2
967
mFJF
Nuclear and Sub-nuclear Physics
L
1
on-site learning
2
976
mFBM
Biomedical Physics
L
1
on-site learning
2
3006
muFYIN
Teaching Physics and Computer Science
L
1
on-site learning
2
3006
muFYIN
Teaching Physics and Computer Science
L
4
on-site learning
8
3508
muFYIN/k
Teaching Physics and Computer Science (Conversion Programme)
L
4
on-site learning
8
3510
muMAIN/k
Teaching Mathematics and Computer Science (Conversion Programme)
L
4
on-site learning
8
3965
mEMM
Mathematical Economics, Finance and Modelling
L
4
on-site learning
8
4037
mMPG/k
Computer Graphics and Geometry (Conversion Programme)
L
4
on-site learning
8
4378
mINFa
Computer Science
L
4
on-site learning
8
956
mMPG
Computer Graphics and Geometry
L
4
on-site learning
8
968
mINF
Computer Science
L
1
on-site learning
2
976
mFBM
Biomedical Physics
L
4
on-site learning
8
978
mFAA
Astronomy and Astrophysics
L
1
on-site learning
2
2979
mMAT
Mathematics
L
1
on-site learning
2
2979
mMAT
Mathematics
L
4
on-site learning
8
3507
muMADG/k
Teaching Mathematics and Descriptive Geometry (Conversion Programme)
L
4
on-site learning
8
3509
muMAFY/k
Teaching Mathematics and Physics (Conversion Programme)
L
1
on-site learning
2
3965
mEMM
Mathematical Economics, Finance and Modelling
L
1
on-site learning
2
3971
mFPE
Physics of the Earth
L
1
on-site learning
2
4382
mMMNa
Managerial Mathematics
L
4
on-site learning
8
4384
mFOSa
Optics, Lasers and Optical Spectroscopy
L
4
on-site learning
8
4387
mPMSa
Probability and Mathematical Statistics
L
1
on-site learning
2
4388
mFTFa
Theoretical Physics
L
4
on-site learning
8
5574
muINGE
Teaching Computer Science and Geography
L
1
on-site learning
2
I.II., II.
on-site learning
true
II.
1020529
1
P
lecturer
Mária
Markošová
doc. RNDr. Mária Markošová, PhD.
markosova1@uniba.sk
Slovak
1029976
2
P
lecturer
Igor
Farkaš
prof. Ing. Igor Farkaš, Dr.
farkas3@uniba.sk
Slovak
1045892
3
P
lecturer
Martin
Takáč
doc. RNDr. Martin Takáč, PhD.
takac1@uniba.sk
Slovak
SK
Slovak
Slovak
L
2
8
<_L_>
Recommended literature
Russell S., Norwig P. (2010). Artificial Intelligence: A Modern Approach, (3rd ed.), Prentice Hall. Available in faculty library.
Marsland S. (2015). Machine Learning: An Algorithmic Perspective, (2nd ed.), CRC Press.
<_PA_>
Conditions for completion of course
Passing the online course https://course.elementsofai.com/ (in Enlish or Slovak version).
<_PJ_>
Language, which knowledge is needed to pass the course
Slovak or English
<_PZ_>
Notes
The course consists of 20 numerical and 5 text-based tasks. Numerical tasks are checked automatically, text-based tasks are evaluated anonymously by students.
<_SO_>
Brief outline of the course
1. What is artificial intelligence: related areas, AI philosophy.
2. Troubleshooting and UI: Browsing and troubleshooting, browsing and games
3. Probability and chance, Bayes' theorem, naive Bayesian classification.
4. Machine learning: nearest neighbor classifier, regression.
5. Neural networks: basics, creation, modern techniques.
6. Consequences: on predicting the future, the effects of AI on society, summary.
<_VV_>
Learning outcomes
The student will get acquainted with selected basic concepts of artificial intelligence and their use in solving various practical tasks.
A
95
100.0
B
0
0.0
C
0
0.0
D
0
0.0
E
0
0.0
FX
0
0.0
95
6
130637
B
2-MXX-130
FMFI.KAI/2-MXX-130/21
Elements of AI
2
Evaluation
independent work
25
325
1, 7
(Single degree study, master II. deg., full time form)
Z
1, 4
doc. RNDr. Mária Markošová, PhD.
16.02.2026
22.08.2021
8
Person responsible for the delivery, development and quality of the study programme
prof. RNDr. Ján Filo, CSc.
filo1@uniba.sk
independent work
25
325
prezenčná
C
955
mFTF
Theoretical Physics
Z
4
on-site learning
7
968
mINF
Computer Science
Z
4
on-site learning
7
1018
muMAIN
Teaching Mathematics and Computer Science
Z
1
on-site learning
1
1019
mAIN
Applied Computer Science
Z
1
on-site learning
1
3006
muFYIN
Teaching Physics and Computer Science
Z
1
on-site learning
1
3507
muMADG/k
Teaching Mathematics and Descriptive Geometry (Conversion Programme)
Z
1
on-site learning
1
3510
muMAIN/k
Teaching Mathematics and Computer Science (Conversion Programme)
Z
1
on-site learning
1
3510
muMAIN/k
Teaching Mathematics and Computer Science (Conversion Programme)
Z
4
on-site learning
7
3965
mEMM
Mathematical Economics, Finance and Modelling
Z
1
on-site learning
1
4384
mFOSa
Optics, Lasers and Optical Spectroscopy
Z
4
on-site learning
7
4386
mMPGa/k
Computer Graphics and Geometry (Conversion Programme)
Z
1
on-site learning
1
5123
muINAN
Teaching Computer Science and English Language and Literature
Z
4
on-site learning
7
5688
mBIN
Bioinformatics
Z
1
on-site learning
1
956
mMPG
Computer Graphics and Geometry
Z
1
on-site learning
1
964
mMMN
Managerial Mathematics
Z
1
on-site learning
1
1018
muMAIN
Teaching Mathematics and Computer Science
Z
4
on-site learning
7
2979
mMAT
Mathematics
Z
4
on-site learning
7
2980
mFOS
Optics, Lasers and Optical Spectroscopy
Z
4
on-site learning
7
4374
mEMMa
Mathematical Economics, Finance and Modelling
Z
4
on-site learning
7
4375
mEOMa
Environmental Physics, Renewable Energy Sources and Meteorology and Climatology
Z
4
on-site learning
7
4381
mIKVa
Cognitive Science
Z
4
on-site learning
7
4383
mMATa
Mathematics
Z
4
on-site learning
7
4384
mFOSa
Optics, Lasers and Optical Spectroscopy
Z
1
on-site learning
1
5574
muINGE
Teaching Computer Science and Geography
Z
1
on-site learning
1
5620
mBMF
Biomedical Physics
Z
4
on-site learning
7
5687
mDAV
Data Science
Z
1
on-site learning
1
965
mINF/k
Computer Science (Conversion Programme)
Z
1
on-site learning
1
978
mFAA
Astronomy and Astrophysics
Z
4
on-site learning
7
2980
mFOS
Optics, Lasers and Optical Spectroscopy
Z
1
on-site learning
1
3006
muFYIN
Teaching Physics and Computer Science
Z
4
on-site learning
7
3007
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1
on-site learning
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on-site learning
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1
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1
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4
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1
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1
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1
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1
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1
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1
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1
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Z
1
on-site learning
1
4386
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4
on-site learning
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1
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1
on-site learning
1
954
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Probability and Mathematical Statistics
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4
on-site learning
7
955
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1
on-site learning
1
976
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1
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4
on-site learning
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4371
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1
on-site learning
1
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1
on-site learning
1
4382
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1
on-site learning
1
5574
muINGE
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Z
4
on-site learning
7
956
mMPG
Computer Graphics and Geometry
Z
4
on-site learning
7
968
mINF
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Z
1
on-site learning
1
970
mFFP
Plasma Physics
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4
on-site learning
7
978
mFAA
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Z
1
on-site learning
1
1017
muMADG
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4
on-site learning
7
2596
mAIN/k
Applied Computer Science (Conversion Programme)
Z
4
on-site learning
7
3007
muINBI
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Z
1
on-site learning
1
3507
muMADG/k
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4
on-site learning
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3509
muMAFY/k
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4
on-site learning
7
3971
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1
on-site learning
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4
on-site learning
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4
on-site learning
7
4388
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1
on-site learning
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4
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5687
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4
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I.II., II.
on-site learning
true
II.
1020529
1
P
lecturer
Mária
Markošová
doc. RNDr. Mária Markošová, PhD.
markosova1@uniba.sk
Slovak
SK
Slovak
Slovak
Z
1
7
<_L_>
Recommended literature
Russell S., Norwig P. (2010). Artificial Intelligence: A Modern Approach, (3rd ed.), Prentice Hall. Available in faculty library.
Marsland S. (2015). Machine Learning: An Algorithmic Perspective, (2nd ed.), CRC Press.
<_PA_>
Conditions for completion of course
Passing the online course https://course.elementsofai.com/ (in Enlish or Slovak version).
<_PJ_>
Language, which knowledge is needed to pass the course
Slovak or English
<_PZ_>
Notes
The course consists of 20 numerical and 5 text-based tasks. Numerical tasks are checked automatically, text-based tasks are evaluated anonymously by students.
<_SO_>
Brief outline of the course
1. What is artificial intelligence: related areas, AI philosophy.
2. Troubleshooting and UI: Browsing and troubleshooting, browsing and games
3. Probability and chance, Bayes' theorem, naive Bayesian classification.
4. Machine learning: nearest neighbor classifier, regression.
5. Neural networks: basics, creation, modern techniques.
6. Consequences: on predicting the future, the effects of AI on society, summary.
<_VV_>
Learning outcomes
The student will get acquainted with selected basic concepts of artificial intelligence and their use in solving various practical tasks.
A
95
100.0
B
0
0.0
C
0
0.0
D
0
0.0
E
0
0.0
FX
0
0.0
95
6
130832
B
2-MXX-131
FMFI.KDMFI+KAI/2-MXX-131/21
International Team-based Research Project
5
Evaluation
course / independent work
3
39 / 30s
1, 7
(Single degree study, master II. deg., full time form)
Z
1, 4
prof. RNDr. Zuzana Kubincová, PhD., doc. RNDr. Martin Homola, PhD.
16.02.2026
22.06.2022
8
Person responsible for the delivery, development and quality of the study programme
prof. RNDr. Ján Filo, CSc.
filo1@uniba.sk
course
3
39
prezenčná
independent work
30s
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4384
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4
on-site learning
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on-site learning
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1
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1
on-site learning
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1
on-site learning
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1
on-site learning
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3006
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on-site learning
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on-site learning
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on-site learning
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Computer Graphics and Geometry
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1
on-site learning
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5688
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4
on-site learning
7
5123
muINAN
Teaching Computer Science and English Language and Literature
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1
on-site learning
1
965
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Computer Science (Conversion Programme)
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2
on-site learning
3
970
mFFP
Plasma Physics
Z
1
on-site learning
1
971
mFTL
Solid State Physics
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4
on-site learning
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2604
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1
on-site learning
1
2604
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4
on-site learning
7
3508
muFYIN/k
Teaching Physics and Computer Science (Conversion Programme)
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4
on-site learning
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3966
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Environmental Physics, Renewable Energy Sources and Meteorology and Climatology
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1
on-site learning
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1
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Plasma Physics
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4382
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1
on-site learning
1
976
mFBM
Biomedical Physics
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4
on-site learning
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1017
muMADG
Teaching Mathematics and Descriptive Geometry
Z
1
on-site learning
1
1104
muMAFY
Teaching Mathematics and Physics
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4
on-site learning
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2596
mAIN/k
Applied Computer Science (Conversion Programme)
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1
on-site learning
1
2979
mMAT
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Z
1
on-site learning
1
3509
muMAFY/k
Teaching Mathematics and Physics (Conversion Programme)
Z
1
on-site learning
1
3965
mEMM
Mathematical Economics, Finance and Modelling
Z
4
on-site learning
7
4373
mFBMa
Biomedical Physics
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4
on-site learning
7
4377
mFTLa
Solid State Physics
Z
1
on-site learning
1
4378
mINFa
Computer Science
Z
4
on-site learning
7
4380
mFJFa
Nuclear and Sub-nuclear Physics
Z
1
on-site learning
1
4385
mMPGa
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4
on-site learning
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4
on-site learning
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1
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2
on-site learning
3
965
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4
on-site learning
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967
mFJF
Nuclear and Sub-nuclear Physics
Z
1
on-site learning
1
967
mFJF
Nuclear and Sub-nuclear Physics
Z
4
on-site learning
7
1104
muMAFY
Teaching Mathematics and Physics
Z
1
on-site learning
1
3508
muFYIN/k
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Z
1
on-site learning
1
4037
mMPG/k
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Z
1
on-site learning
1
4383
mMATa
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Z
1
on-site learning
1
4386
mMPGa/k
Computer Graphics and Geometry (Conversion Programme)
Z
4
on-site learning
7
4387
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Probability and Mathematical Statistics
Z
1
on-site learning
1
954
mPMS
Probability and Mathematical Statistics
Z
1
on-site learning
1
954
mPMS
Probability and Mathematical Statistics
Z
4
on-site learning
7
955
mFTF
Theoretical Physics
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1
on-site learning
1
976
mFBM
Biomedical Physics
Z
1
on-site learning
1
1019
mAIN
Applied Computer Science
Z
4
on-site learning
7
4371
mAINa
Applied Computer Science
Z
1
on-site learning
1
4373
mFBMa
Biomedical Physics
Z
1
on-site learning
1
4382
mMMNa
Managerial Mathematics
Z
1
on-site learning
1
5574
muINGE
Teaching Computer Science and Geography
Z
4
on-site learning
7
3007
muINBI
Teaching Computer Science and Biology
Z
1
on-site learning
1
968
mINF
Computer Science
Z
1
on-site learning
1
956
mMPG
Computer Graphics and Geometry
Z
4
on-site learning
7
970
mFFP
Plasma Physics
Z
4
on-site learning
7
978
mFAA
Astronomy and Astrophysics
Z
1
on-site learning
1
1017
muMADG
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Z
4
on-site learning
7
2596
mAIN/k
Applied Computer Science (Conversion Programme)
Z
4
on-site learning
7
3507
muMADG/k
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Z
4
on-site learning
7
3509
muMAFY/k
Teaching Mathematics and Physics (Conversion Programme)
Z
4
on-site learning
7
3971
mFPE
Physics of the Earth
Z
1
on-site learning
1
4377
mFTLa
Solid State Physics
Z
4
on-site learning
7
4380
mFJFa
Nuclear and Sub-nuclear Physics
Z
4
on-site learning
7
4388
mFTFa
Theoretical Physics
Z
1
on-site learning
1
4388
mFTFa
Theoretical Physics
Z
4
on-site learning
7
5687
mDAV
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4
on-site learning
7
I.II., II.
on-site learning
true
II.
1033993
1
P
lecturer
Zuzana
Kubincová
prof. RNDr. Zuzana Kubincová, PhD.
kubincova1@uniba.sk
English, Slovak
1033776
2
P
lecturer
Martin
Homola
doc. RNDr. Martin Homola, PhD.
homola1@uniba.sk
English, Slovak
EN
English
SK
Slovak
English, Slovak
Z
1
7
<_L_>
Recommended literature
- Teachers' own electronic study materials published on the course website or in the Moodle system
- Gavora, Peter a kol. 2010. Elektronická učebnica pedagogického výskumu. [online]. Bratislava : Univerzita Komenského, 2010. Dostupné na: http://www.e-metodologia.fedu.uniba.sk/ ISBN 978–80–223–2951–4.
- Tharenou, P., Donohue, R. and Cooper, B., 2007. Management research methods. Cambridge University Press.
- Topping, A., 2015: The Quantitative-Qualitative Continium. In: Gerrish, K. and Lathlean, J., The Research Process in Nursing, p. 159-172
- Williamson, K. and Johanson, G. eds., 2017. Research methods: Information, systems, and contexts. Chandos Publishing.
<_PA_>
Conditions for completion of course
Continuous assessment: active participation in research in an international student team (25%), presentation of work in a workshop (25%), scientific article (50%)
Indicative evaluation scale: A 90 %, B 80 %, C 70 %, D 60 %, E 50 %
<_PJ_>
Language, which knowledge is needed to pass the course
English
<_SO_>
Brief outline of the course
- Research methodology
- Design and implementation of a research project in an international group (preferably interdisciplinary)
- Methods and tools for collaboration in virtual space, collaboration in science and practice
- Academic writing, presentation of research results through scientific articles; objectives, content and structure of scientific articles; forms of academic publication, publication forums and evaluation of their quality
- Quality assurance and feedback - peer review
- Communication of results through posters or conference presentations
<_VH_>
Weighting of course assessment (continuous/final)
100/0
<_VV_>
Learning outcomes
Students will learn in the team to agree on a common research topic, formulate research questions, determine research methods for the problem, collect and evaluate data, discuss their findings, present research results to the professional public, analyze and evaluate the scientific work of their colleagues, prepare a scientific article suitable for publication
A
7
70.0
B
0
0.0
C
0
0.0
D
0
0.0
E
3
30.0
FX
0
0.0
10
6
156729
B
2-MXX-134
FMFI.CENAM/2-MXX-134/26
Innovation and Entrepreneurship in Natural and Technical Sciences
3
Evaluation
lecture / independent work
2 / 1
26 / 13
1, 7
(Single degree study, master II. deg., full time form)
Z
1, 4
doc. RNDr. Tomáš Plecenik, PhD., Mgr. Veronika Hidaši Turiničová, PhD.
25.02.2026
13.03.2026
8
Person responsible for the delivery, development and quality of the study programme
prof. RNDr. Ján Filo, CSc.
filo1@uniba.sk
lecture
2
26
prezenčná
independent work
1
13
prezenčná
C
955
mFTF
Theoretical Physics
Z
4
on-site learning
7
968
mINF
Computer Science
Z
4
on-site learning
7
1018
muMAIN
Teaching Mathematics and Computer Science
Z
1
on-site learning
1
1019
mAIN
Applied Computer Science
Z
1
on-site learning
1
3006
muFYIN
Teaching Physics and Computer Science
Z
1
on-site learning
1
3507
muMADG/k
Teaching Mathematics and Descriptive Geometry (Conversion Programme)
Z
1
on-site learning
1
3510
muMAIN/k
Teaching Mathematics and Computer Science (Conversion Programme)
Z
1
on-site learning
1
3510
muMAIN/k
Teaching Mathematics and Computer Science (Conversion Programme)
Z
4
on-site learning
7
3965
mEMM
Mathematical Economics, Finance and Modelling
Z
1
on-site learning
1
4384
mFOSa
Optics, Lasers and Optical Spectroscopy
Z
4
on-site learning
7
4386
mMPGa/k
Computer Graphics and Geometry (Conversion Programme)
Z
1
on-site learning
1
5123
muINAN
Teaching Computer Science and English Language and Literature
Z
4
on-site learning
7
5688
mBIN
Bioinformatics
Z
1
on-site learning
1
956
mMPG
Computer Graphics and Geometry
Z
1
on-site learning
1
964
mMMN
Managerial Mathematics
Z
1
on-site learning
1
1018
muMAIN
Teaching Mathematics and Computer Science
Z
4
on-site learning
7
2979
mMAT
Mathematics
Z
4
on-site learning
7
2980
mFOS
Optics, Lasers and Optical Spectroscopy
Z
4
on-site learning
7
4374
mEMMa
Mathematical Economics, Finance and Modelling
Z
4
on-site learning
7
4375
mEOMa
Environmental Physics, Renewable Energy Sources and Meteorology and Climatology
Z
4
on-site learning
7
4381
mIKVa
Cognitive Science
Z
4
on-site learning
7
4383
mMATa
Mathematics
Z
4
on-site learning
7
4384
mFOSa
Optics, Lasers and Optical Spectroscopy
Z
1
on-site learning
1
5574
muINGE
Teaching Computer Science and Geography
Z
1
on-site learning
1
5620
mBMF
Biomedical Physics
Z
4
on-site learning
7
5687
mDAV
Data Science
Z
1
on-site learning
1
965
mINF/k
Computer Science (Conversion Programme)
Z
1
on-site learning
1
978
mFAA
Astronomy and Astrophysics
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4
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1029748
1
P
lecturer
Tomáš
Plecenik
doc. RNDr. Tomáš Plecenik, PhD.
plecenik2@uniba.sk
Slovak
1220569
2
P
lecturer
Veronika
Hidaši Turiničová
Mgr. Veronika Hidaši Turiničová, PhD.
turinicova8@uniba.sk
Slovak
SK
Slovak
Slovak
Z
1
7
<_DI_>
Type, volume, methods and workload of the student - additional information
2/1 (lecture / individual work)
<_L_>
Recommended literature
Clark, Timothy R., et al. Business Model Generation. Wiley, 2010
<_PA_>
Conditions for completion of course
The condition for admission to the exam is active participation in at least 80% of the lessons.
The final assessment consists of a presentation of the semester project. To successfully complete the course, it is necessary to achieve at least 50% of the overall score.
<_PJ_>
Language, which knowledge is needed to pass the course
Slovak
<_SO_>
Brief outline of the course
1. Commercialization of scientific research.
2. Fundamentals of entrepreneurship and startup terminology.
3. Identification of problems and customer needs analysis (design thinking).
4. Technology transfer. Technology Readiness Levels (TRL).
5. Intellectual property and its protection.
6. Market, customer, and market potential of a technological solution.
7. Business Model Canvas. Revenue models.
8. Sources of financing for technological projects.
9. Pitching and communication of the solution.
10. Fundamentals of management and leadership.
11. Innovation support and incubation structures at national and international levels.
<_VH_>
Weighting of course assessment (continuous/final)
0/100
<_VV_>
Learning outcomes
After completing the course, students can describe the possibilities for commercialization of scientific and technological research. They can identify market needs, assess the market potential of a technological solution, and are familiar with the terminology of entrepreneurship, technology transfer, and intellectual property protection. They understand the overall structure of a business plan and the main forms of financing for technological projects. They are familiar with the principles of communication, teamwork, and team leadership and can apply them appropriately in project work and its presentation.
A
0
0.0
B
0
0.0
C
0
0.0
D
0
0.0
E
0
0.0
FX
0
0.0
0
6
124583
B
2-PMS-116
FMFI.KAMŠ/2-PMS-116/19
Cluster analysis and data classification
5
Evaluation
lecture / practicals
2 / 2
26 / 26
4
(Single degree study, master II. deg., full time form)
L
2
prof. Mgr. Radoslav Harman, PhD., Mgr. Samuel Rosa, PhD.
16.02.2026
10.03.2022
8
Person responsible for the delivery, development and quality of the study programme
prof. RNDr. Ján Filo, CSc.
filo1@uniba.sk
lecture
2
26
prezenčná
practicals
2
26
prezenčná
B
4378
mINFa
Computer Science
L
1
on-site learning
2
4374
mEMMa
Mathematical Economics, Finance and Modelling
L
1
on-site learning
2
965
mINF/k
Computer Science (Conversion Programme)
L
1
on-site learning
2
954
mPMS
Probability and Mathematical Statistics
L
1
on-site learning
2
2979
mMAT
Mathematics
L
2
on-site learning
4
4383
mMATa
Mathematics
L
2
on-site learning
4
968
mINF
Computer Science
L
1
on-site learning
2
4387
mPMSa
Probability and Mathematical Statistics
L
1
on-site learning
2
3965
mEMM
Mathematical Economics, Finance and Modelling
L
1
on-site learning
2
II.
on-site learning
true
II.
1018338
1
P
lecturer
Radoslav
Harman
prof. Mgr. Radoslav Harman, PhD.
harman1@uniba.sk
Slovak
1046621
2
P
lecturer
Samuel
Rosa
Mgr. Samuel Rosa, PhD.
rosa2@uniba.sk
Slovak
SK
Slovak
Slovak
L
4
<_L_>
Recommended literature
Izenman A: Modern Multivariate Statistical Techniques: Regression, Classification, and Manifold Learning (Springer Texts in Statistics) 1st ed., 2nd printing 2013; James G, Witten D, Hastie T, Tibshirani R: An Introduction to Statistical Learning: with Applications in R (Springer Texts in Statistics) 2nd ed., Springer 2021; Harman R: Multivariate Statistical Analysis (Selected Lecture Notes), study materials of the lecturer, 2021.
<_PA_>
Conditions for completion of course
Evaluation based on: project (teaching period), oral exam
Approximate grade thresholds: A 90%, B 80%, C 70%, D 60%, E 50%
<_PJ_>
Language, which knowledge is needed to pass the course
Slovak, English
<_PZ_>
Notes
The knowledge of the software R is recommended. Enrollment limit: 40 students
<_SO_>
Brief outline of the course
Selected multivariate data visualization methods, partitional clustering (k-means, k-medoids, DBSCAN, OPTICS, clustering based on the mixture of Gaussian distributions, spectral clustering), hierarchical clustering, general introduction to the statistical classification methods, Bayes classifier, k nearest neighbors, linear and quadratic discrimination, classification trees and forests, bagging and boosting, support vector machines, multinomial regression as a classification method
<_VH_>
Weighting of course assessment (continuous/final)
50/50
<_VV_>
Learning outcomes
The students understand the principles and practical realization of selected methods of cluster analysis and statistical data classification.
A
103
59.54
B
41
23.7
C
16
9.25
D
2
1.16
E
3
1.73
FX
8
4.62
173
6
133637
B
2-PMS-118
FMFI.KAMŠ/2-PMS-118/22
Markov Models (1)
5
Evaluation
lecture / practicals
2 / 2
26 / 26
1
(Single degree study, master II. deg., full time form)
Z
1
doc. RNDr. Katarína Janková, CSc., Mgr. Ján Veselý
16.02.2026
22.06.2022
FMFI.KAMŠ/2-PMS-118/10
FMFI.KAMŠ/2-PMS-118/10 - Markov Processes (1)
2-PMS-118 - Markov Processes (1)
8
Person responsible for the delivery, development and quality of the study programme
prof. RNDr. Ján Filo, CSc.
filo1@uniba.sk
lecture
2
26
prezenčná
practicals
2
26
prezenčná
86099
FMFI.KAMŠ/2-PMS-118/10
2-PMS-118
Markov Processes (1)
B
3965
mEMM
Mathematical Economics, Finance and Modelling
Z
1
on-site learning
1
4374
mEMMa
Mathematical Economics, Finance and Modelling
Z
1
on-site learning
1
2979
mMAT
Mathematics
Z
1
on-site learning
1
4383
mMATa
Mathematics
Z
1
on-site learning
1
4387
mPMSa
Probability and Mathematical Statistics
Z
1
on-site learning
1
954
mPMS
Probability and Mathematical Statistics
Z
1
on-site learning
1
II.
on-site learning
true
II.
1039018
1
P
lecturer
Katarína
Janková
doc. RNDr. Katarína Janková, CSc.
jankova1@uniba.sk
English, Slovak
1224799
2
C
instructor
Ján
Veselý
Mgr. Ján Veselý
vesely18@uniba.sk
English, Slovak
EN
English
SK
Slovak
English, Slovak
Z
1
<_C_>
Goal
To give an introduction to discrete time Markov chains
<_L_>
Recommended literature
Kalas, J: Markovove reťazce, skriptá MFF UK
Norris, J.R.: Markov chains (1998)
Ross, S.M.: Introduction to probability models (2006)
<_P_>
Continuous assessment
test
<_PA_>
Conditions for completion of course
Preliminary semester evaluation: test(20%) and homeworks(50%)
Examination: written examination(30%)
Approximate grade thresholds: A 90%, B 80%, C 70%, D 60%, E 50%
<_SO_>
Brief outline of the course
Markov property, transition probabilities, transition matrix, Chapman Kolmogorov equation, irreducibility of a chain. Classification of states, recurrent states, transient states, null recurrent states and positive recurrent states, periodicity. Existence of stationary distribution, ergodic distribution, necessary and sufficient conditions for ergodicity. Random walks, branching processes, absorbtion probabilities, mean time to absorbtion. Markov reward chains algorithms and Markov Chain Monte Carlo.
<_VV_>
Learning outcomes
After completing the course the student will master elementary discrete time Markov chains models. He will be able to classify states of a Markov chain and calculate stationary probability distributions.
<_Z_>
Final assessment
exam
A
73
24.33
B
68
22.67
C
75
25.0
D
58
19.33
E
23
7.67
FX
3
1.0
300
6
133645
B
2-PMS-119
FMFI.KAMŠ/2-PMS-119/22
Markov Models (2)
5
Evaluation
lecture / practicals
2 / 2
26 / 26
2
(Single degree study, master II. deg., full time form)
L
1
doc. RNDr. Katarína Janková, CSc.
16.02.2026
22.06.2022
FMFI.KAMŠ/2-PMS-119/15
FMFI.KAMŠ/2-PMS-119/15 - Markov Processes(2)
2-PMS-119 - Markov Processes(2)
8
Person responsible for the delivery, development and quality of the study programme
prof. RNDr. Ján Filo, CSc.
filo1@uniba.sk
lecture
2
26
prezenčná
practicals
2
26
prezenčná
104882
FMFI.KAMŠ/2-PMS-119/15
2-PMS-119
Markov Processes(2)
B
4383
mMATa
Mathematics
L
1
on-site learning
2
954
mPMS
Probability and Mathematical Statistics
L
1
on-site learning
2
2979
mMAT
Mathematics
L
1
on-site learning
2
4387
mPMSa
Probability and Mathematical Statistics
L
1
on-site learning
2
II.
on-site learning
true
II.
1039018
1
P
lecturer
Katarína
Janková
doc. RNDr. Katarína Janková, CSc.
jankova1@uniba.sk
Slovak
SK
Slovak
Slovak
L
2
<_L_>
Recommended literature
Janková, K., Kilianová, S., Brunovský, P., Bokes, P.: Markovove reťazce a ich aplikácie. Epos 2014.
Norris, J.:Markov Chains.Cambridge University Press 1997.
<_PA_>
Conditions for completion of course
20% test(teaching period), 30% homeworks(teaching period), 50% examination
Approximate grade thresholds: A 90%, B 80%, C 70%, D 60%, E 50%
<_SO_>
Brief outline of the course
Markov property for continuous time chains, probabilities of transition, initial distribution, Chapman Kolmogorov equation. Forces of transition and their properties, backward and forward systems of Kolmogorov differential equations. Statioanary and ergodic distribution of the chain. Models of linear growth, birth and death chains, Poisson process. Characterization of processes using jump chain and holding times. Queueing systems: M/M/n, M/M/infinity. Imbedded chain technique for M/G/1. Pollaczek Chinchin formula.
<_VV_>
Learning outcomes
After completing the course students will know properties of homogeneous Markov chains with continuous time. They will be able to use models based on these chains.
A
36
28.13
B
20
15.63
C
33
25.78
D
30
23.44
E
7
5.47
FX
2
1.56
128
6
81386
B
2-PMS-123
FMFI.KAMŠ/2-PMS-123/10
Stochastic Simulation Methods
3
Evaluation
lecture
2
26
3
(Single degree study, master II. deg., full time form)
Z
2
doc. Mgr. Pavol Bokes, PhD.
16.02.2026
10.03.2022
8
Person responsible for the delivery, development and quality of the study programme
prof. RNDr. Ján Filo, CSc.
filo1@uniba.sk
lecture
2
26
prezenčná
B
2979
mMAT
Mathematics
Z
2
on-site learning
3
3965
mEMM
Mathematical Economics, Finance and Modelling
Z
1
on-site learning
1
954
mPMS
Probability and Mathematical Statistics
Z
2
on-site learning
3
4374
mEMMa
Mathematical Economics, Finance and Modelling
Z
1
on-site learning
1
965
mINF/k
Computer Science (Conversion Programme)
Z
2
on-site learning
3
4387
mPMSa
Probability and Mathematical Statistics
Z
2
on-site learning
3
4378
mINFa
Computer Science
Z
2
on-site learning
3
4383
mMATa
Mathematics
Z
2
on-site learning
3
968
mINF
Computer Science
Z
2
on-site learning
3
II.
on-site learning
true
II.
1079006
1
P
lecturer
Pavol
Bokes
doc. Mgr. Pavol Bokes, PhD.
bokes3@uniba.sk
Slovak
SK
Slovak
Slovak
Z
3
<_L_>
Recommended literature
Ross S: Simulation, Elsevier Academic Press 2006; Study materials of the lecturer.
<_PA_>
Conditions for completion of course
Evaluation based on: project (teaching period), oral exam
Approximate grade thresholds: A 90%, B 80%, C 70%, D 60%, E 50%
<_PJ_>
Language, which knowledge is needed to pass the course
Slovak, English
<_PZ_>
Notes
Enrollment limit: 40 students
<_SO_>
Brief outline of the course
Generating random numbers, testing of random number generators, Sampling discrete random variables and vectors, Sampling continuous random variables and vectors, Statistical analysis of simulated data, Classical Monte Carlo methods.
<_VH_>
Weighting of course assessment (continuous/final)
50/50
<_VV_>
Learning outcomes
The students understand the basic methods of computer sampling of random variables and vectors, apply them to the computation of Monte Carlo estimates and use them for the simulation of complex stochastic systems.
A
222
44.85
B
119
24.04
C
65
13.13
D
42
8.48
E
29
5.86
FX
18
3.64
495
6