|
Title
|
Probability and Statistics
|
||
|
Code
|
ÚMV/PST1b/04
|
Teacher
|
Skřivánková Valéria, Ohriska Ján
|
|
ECTS credits
|
6
|
Hrs/week
|
2/2
|
|
Assessment
|
Examination
|
Semester
|
1
|
|
T/L method
|
Lecture, Practical
|
||
|
Content
|
Random
vectors, their distributions and characteristics. Correlation and regression.
Random sample, sampling distributions and characteristics. Point estimates
and their properties. Maximum likelihood method. Interval estimates;
confidence interval construction. Testing of statistical hypothesis; critical
region and level of significance. Parametric and nonparametric tests.
|
||
|
Recommended reading
|
Mason-Lind.:Statistical Techniques in Business and
Economics, Irwin, Inc., 1990
Skřivánková, V:Pravdepodobnosť v príkladoch, UPJŠ,
Košice, 2006
Skřivánková, V.-Hančová, M.:Štatistika v príkladoch,
UPJŠ, Košice, 2005
|
||
|
Title
|
Game Theory
|
||
|
Code
|
ÚMV/TH1/04
|
Teacher
|
Cechlárová Katarína, Hajduková Jana
|
|
ECTS credits
|
6
|
Hrs/week
|
3/1
|
|
Assessment
|
Examination
|
Semester
|
1
|
|
T/L method
|
Lecture, Practical
|
||
|
Objective
|
To teach
the basic methods of game theory and to have students model situations from
everyday life as simple games.
|
||
|
Content
|
Examples of
games. Extensive form of a game, value of the game. Von Neumann Morgenstern
theory of utility. Matrix games and their solution. Bimatrix games.Theory of
negotiations. N-person games: core, Shapley value. Economic applications of
game theory.
|
||
|
Alternate courses
|
ÚMV/TH1/99
|
||
|
Recommended reading
|
K. Binmore, Fun and games, D.C. Heath, 1992.
M. Chobot, F. Turnovec, V. Ulašin, Teória hier a
rozhodovania, Alfa, Bratislava, 1991.
G. Owen, Game
Theory, Academic Press.
L.C. Thomas,
Games, Theory and Applications,
Wiley, New York.
H.S. Bierman, L.Fernandez, Game Theory with Economic
Applications, Addison-Wesley, 1998.
K. Cechlárová: Lecture notes in AIS
|
||
|
Title
|
Combinatorial Optimisation
|
||
|
Code
|
ÚMV/KOO/04
|
Teacher
|
Jendroľ Stanislav, Lacko
Vladimír
|
|
ECTS credits
|
6
|
Hrs/week
|
3/1
|
|
Assessment
|
Examination
|
Semester
|
2
|
|
T/L method
|
Lecture, Practical
|
||
|
Objective
|
To teach
students basic knowledge about the
methods of modelling and controlling and how to apply them to typical
problems using methods of discrete mathematics.
|
||
|
Content
|
Complexity
of combinatorial algorithms. Sorting problems. Searching algorithms. Greedy algorithm. Trees and
spanning trees: rooted trees. Minimal spanning tree problem. Optimal path
problems. Introduction to network analysis. Distribution problems. Flows.
Assignment problem. The Chinese Postman problem. The Travelling Salesman
problem. Transportation problems.
|
||
|
Exclusive courses
|
ÚMV/KOA1/04
|
||
|
Recommended reading
|
N. Christofides: Graph Theory - An Algorithmic
approach, Academic Press, New York 1975 (ruský preklad z r. 1978)
G. Chartrand, O.R. Vellermann: Applied and
Algorithmic Graph Theory, McGraw-Hill, Inc. New York 1993
|
||
|
Title
|
Classical and Quantum Computations
|
||
|
Code
|
ÚINF/KKV1/06
|
Teacher
|
Semanišin Gabriel
|
|
ECTS credits
|
6
|
Hrs/week
|
3/1
|
|
Assessment
|
Examination
|
Semester
|
3
|
|
T/L method
|
Lecture, Practical
|
||
|
Objective
|
To provide
students information on quantum computers and quantum computations. To allow
students to compare classical and quantum models and methods.
|
||
|
Content
|
The basics
of classical theory of computation: Turing machines, Boolean circuits,
parallel algorithms, probabilistic computation, NP-complete problems, and the
idea of complexity of an algorithm.
Introduction of general quantum formalism (pure states, density
matrices, and superoperators), universal gate sets and approximation
theorems. Grover's algorithm, Shor's factoring algorithm, and the Abelian
hidden subgroup problem. Parallel quantum computation, a quantum analogue of
NP-completeness, and quantum error-correcting codes.
|
||
|
Recommended reading
|
1 A. Yu. Kitaev, Classical and Quantum
Computation, American Mathematical Society, Graduate Studies in Mathematics
47 (2002), ISBN 0-8218-3229-8
1 Gruska, J: Quantum Computing. McGraw-Hill Londýn
1999
|
||
|
Title
|
Functional Analysis
|
||
|
Code
|
ÚMV/FAN/06
|
Teacher
|
Doboš Jozef
|
|
ECTS credits
|
6
|
Hrs/week
|
3/1
|
|
Assessment
|
Examination
|
Semester
|
2
|
|
T/L method
|
Lecture, Practical
|
||
|
Content
|
Metric
spaces and their fundamental properties. Complete metric space and the
contrary mapping principle. Normed linear spaces. Hilbert's space. Linear
operators. The spectrum of the operator.
|
||
|
Recommended reading
|
N. Dunford, J.T. Schwartz, Linear operators, Part I,
Generaly theory, New York, 1963
N. Dunford, J.T. Schwartz, Linear operators, Part II,
Spectral theory, New York, 1963
|
||
Compulsory elective courses
|
Title
|
Foundations of Knowledge Systems
|
||
|
Code
|
ÚINF/ZNA1/06
|
Teacher
|
Vojtáš Peter
|
|
ECTS credits
|
4
|
Hrs/week
|
2/-
|
|
Assessment
|
Examination
|
Semester
|
1
|
|
T/L method
|
Lecture
|
||
|
Content
|
Relations
of formal models: DBMS, SQL, and logic programming. Summary of different
formal models of computational processes, connections among them and
translations. Gentzenov systems, semantics and verification of programs.
Formal specifications, temporal logics: formulas, models, tableaux.
|
||
|
Recommended reading
|
M. Ben-Ari. Mathematical logic for Computer Science
2ed. Springer Verlag London 2001
J. Ullman. Principles of database and
knowledge based systems. Comp. Sci. Press 1988
J. W. Lloyd. Foundations of logic programming.
Springer Berlin 1987
|
||
|
Title
|
Mathematical Foundations of Cryptography
|
||
|
Code
|
ÚINF/MZK/06
|
Teacher
|
Geffert Viliam, Lacko
Vladimír
|
|
ECTS credits
|
6
|
Hrs/week
|
3/2
|
|
Assessment
|
Examination
|
Semester
|
1
|
|
T/L method
|
Lecture, Practical
|
||
|
Content
|
Classical
cryptography. Steganography. Conventional symmetric cryptography. Feistel
networks. Encryption modes: ECB, CBC, CFB, OFB. Security definitions. Models
of an adversary. Cryptoanalysis. Asymmetric cryptosystems. One-way functions
with trapdoors. RSA cryptosystem. El-Gamal cryptosystem. Generating large
prime numbers. Elliptic curves cryptography. Keyed Hash functions. Collision
resistant functions. Birthday paradox. SHA-1. Message authentication codes.
Password security. Digital signatures. Blind signatures. Key management.
X509. Certificates. Certification authorities. Electronic payments.
Electronic cash.
|
||
|
Exclusive courses
|
ÚINF/UKR1/03
|
||
|
Title
|
Graph Theory
|
||
|
Code
|
ÚMV/TGT/04
|
Teacher
|
Jendroľ Stanislav, Madaras
Tomáš
|
|
ECTS credits
|
4
|
Hrs/week
|
2/-
|
|
Assessment
|
Examination
|
Semester
|
1, 3
|
|
T/L method
|
Lecture
|
||
|
Objective
|
To provide
students deeper knowledge of graph theory.
|
||
|
Content
|
Connectivity
of graphs. Hamiltonian graphs. Colouring of graphs. Planar graphs. Oriented
graphs. Automorphism of graphs. Snarks. Minors of graphs.
|
||
|
Recommended reading
|
J. Bang-Jensen and G. Gutin, Digraphs: Theory,
Algorithms and Applications. Springer-Verlag London 2001
J. A. Bondy and U.S.R. Murty, Graph theory with
applications. North Holland, Amsterdam 1976.
R. Diestel, Graph Theory, Springer-Verlag. New
York 2000, 2nd edition.
|
||
|
Title
|
Theory of Information
|
||
|
Code
|
ÚMV/TIN1/03
|
Teacher
|
Bukovský Lev
|
|
ECTS credits
|
4
|
Hrs/week
|
2/-
|
|
Assessment
|
Examination
|
Semester
|
1, 3
|
|
T/L method
|
Lecture
|
||
|
Objective
|
To
introduce students to mathematical attempts at solving selected problems of
computer science.
|
||
|
Content
|
Measurement
of information. Entropy and its properties. Shanon’s theorems. Coding and
basic types of codes. Using of algebraic structures in construction of codes.
Kolmogorov complexity. Basic properties and relation to the notion of
entropy. Complexity and randomness.
|
||
|
Recommended reading
|
J.Adámek, Kódovaní a teorie informace, Vydavatelství
ČVUT, Praha 1994
J. Černý, Entrópia a informácia v kybernetike, Alfa
1981
M. Li and P. Vitanyi, Kolmogorov Complexity and its
Applications, Handbook of Theoretical Computer Science, Elsevier, 1990, p. 188-252.
|
||
|
Title
|
Theory of Codes
|
||
|
Code
|
ÚMV/TKO1/04
|
Teacher
|
Horňák Mirko
|
|
ECTS credits
|
6
|
Hrs/week
|
4/-
|
|
Assessment
|
Examination
|
Semester
|
1, 3
|
|
T/L method
|
Lecture
|
||
|
Objective
|
To acquaint
students with the basic principles and theoretical bases of text coding and
possibilities for their application.
|
||
|
Content
|
Monoids.
Basic notions of theory of codes. Examples of codes. Important classes of
codes. Maximal codes. Submonoids generated by codes. Stable submonoids. Group
codes. Free hull of a set of words. Test for recognising codes. Measure of a
code. Bernoulli distribution. Dyck code. Complete sets in monoids. Thin
codes. Composition of codes. Indecomposable codes.
|
||
|
Recommended reading
|
J. Berstel and D. Perrin, Theory of Codes, Academic
Press 1985
|
||
|
Title
|
Matroid theory
|
||
|
Code
|
ÚMV/TMT/04
|
Teacher
|
Horňák Mirko
|
|
ECTS credits
|
5
|
Hrs/week
|
3/-
|
|
Assessment
|
Examination
|
Semester
|
1, 3
|
|
T/L method
|
Lecture
|
||
|
Objective
|
To acquaint
students with basic notions of matroid theory and possibilities of using
matroids in various disciplines of discrete mathematics.
|
||
|
Content
|
Independent
sets and bases. Properties of rank function. Closure operator. Circuits.
Duality in matroids. Hyperplanes. Submatroids. Restriction, contraction,
minor of a matroid. Transversals. Radó-Hall's Theorem and its
generalisations. Greedy algorithm versus matroids.
|
||
|
Recommended reading
|
D. J. A. Welsh, Matroid Theory, Academic Press,
1976.
|
||
|
Title
|
Computational complexity
|
||
|
Code
|
ÚINF/VYZ1/04
|
Teacher
|
Geffert Viliam
|
|
ECTS credits
|
4
|
Hrs/week
|
2/-
|
|
Assessment
|
Examination
|
Semester
|
1, 3
|
|
T/L method
|
Lecture
|
||
|
Objective
|
To give
students background in the computational complexity and theory of
NP-completeness.
|
||
|
Content
|
Deterministic
and nondeterministic algorithms with polynomial time; NP-completeness.
Deterministic simulation of a nondeterministic Turing machine. Satisfiability
of Boolean formulae. Other NP-complete problems: satisfiability of a formula
in a conjunctive normal form, 3-satisfiability, 3-colorability of a graph,
3-colorability of a planar graph, knapsack problem, balancing, etc. Space
bounded computations, classes LOG-space and P-space. Deterministic
simulation: Savitch’s theorem. Closure under complement. Classification of
computational complexity of problems.
|
||
|
Alternate courses
|
ÚINF/VYZ1/03 orÚINF/VYZ1/00
|
||
|
Recommended reading
|
A.V.Aho and J.D.Ullman. The design and analysis of
computer algorithms. Addison-Wesley, 1974.
P.van Emde Boas. Machine models and simulations. In
J.van Leeuwen (ed.): Handbook of theoretical computer science. North-Holland,
1990.
Ch.K.Yap. Introduction to the theory of complexity
classes. To be published by Oxford Univ. Press. (Electronic version available
via anonymous ftp://cs.nyu.edu/pub/local/yap/complexity-bk).
|
||
|
Title
|
Fractal Geometry
|
||
|
Code
|
ÚMV/FRG1/03
|
Teacher
|
Bukovský Lev
|
|
ECTS credits
|
4
|
Hrs/week
|
2/-
|
|
Assessment
|
Examination
|
Semester
|
2
|
|
T/L method
|
Lecture
|
||
|
Objective
|
To
introduce students to the mathematical approach to analysing the concept of a
fractal with the possibility of using the results for the construction of
fractals.
|
||
|
Content
|
Concept of
a fractal. Basic topology of metric spaces. Self-similarity of a fractal.
Fractal as fixpoint of a mapping. Construction of a fractal by iteration.
Topological dimension and basic properties. Hausdorff measure and Hausdorff
dimension. Topological and Hausdorff dimension of particular fractals. Some
methods of construction of a fractal (topological dynamics).
|
||
|
Title
|
Theory of Groups
|
||
|
Code
|
ÚMV/TGR1/04
|
Teacher
|
Lihová Judita
|
|
ECTS credits
|
5
|
Hrs/week
|
2/1
|
|
Assessment
|
Examination
|
Semester
|
2
|
|
T/L method
|
Lecture, Practical
|
||
|
Content
|
Cyclic
groups; quotient groups. Finitely generated Abelian groups. Groups of
permutations and their applications.
|
||
|
Recommended reading
|
M.Hall: The Theory of Groups, New York, 1959
|
||
|
Title
|
Applied Statistics
|
||
|
Code
|
ÚMV/APS1/99
|
Teacher
|
Žežula Ivan
|
|
ECTS credits
|
6
|
Hrs/week
|
3/2
|
|
Assessment
|
Examination
|
Semester
|
2
|
|
T/L method
|
Lecture, Practical
|
||
|
Objective
|
To teach
students the most frequently applied statistical methods.
|
||
|
Content
|
Matrices
and geometry of linear space. One- and multidimensional normal distribution
and related distributions. General linear model. Regression. Analysis of
variance. Analysis of covariance.
|
||
|
Prerequisite courses
|
ÚMV/PST1b/04
|
||
|
Recommended reading
|
Seber: Linear regression analysis, Wiley, 1977
|
||
|
Title
|
Applied Linear Algebra
|
||
|
Code
|
ÚMV/ALA1/04
|
Teacher
|
Studenovská Danica
|
|
ECTS credits
|
5
|
Hrs/week
|
2/1
|
|
Assessment
|
Examination
|
Semester
|
2, 4
|
|
T/L method
|
Lecture, Practical
|
||
|
Objective
|
To teach
students basic knowledge about linear algebra; to make students able to apply
the theory in concrete excercises.
|
||
|
Content
|
Matrices
over Euclidean rings, canonical forms. Polynomial matrices. Similar matrices.
Jordan normal form. Functions of matrices, sequences, series. Inversion of
singular matrices, pseudoinverse matrices and their application.
|
||
|
Alternate courses
|
ÚMV/ALA1/99
|
||
|
Recommended reading
|
M. Fiedler: Speciálni matice a jejich použití v
numerické matematice,
|
||
|
Title
|
Universal Algebra
|
||
|
Code
|
ÚMV/UAL/04
|
Teacher
|
Studenovská Danica
|
|
ECTS credits
|
5
|
Hrs/week
|
3/-
|
|
Assessment
|
Examination
|
Semester
|
8, 10
|
|
T/L method
|
Lecture
|
||
|
Objective
|
To provide
basic knowledge of universal algebra and to make students able to apply this
knowledge in concrete situations.
|
||
|
Content
|
Algebraic
structures. Homomorphisms and congruences. Direct and subdirect products.
Terms. Free algebras. Birkhoff’s theorems about varieties.
|
||
|
Exclusive courses
|
ÚMV/KAL1/04
|
||
|
Recommended reading
|
M.Kolibiar a kol.: Algebra a príbuzné disciplíny.
Bratislava, 1991.
S.Burris, H.P.Sankappanavar: A Course in Universal
Algebra. Springer-Verlag, 1981.
|
||
Study programme Mathematics
(Full-time
master)
Code Title
ECTS Credit Hours/week
Assessment Recommended Year/Semester
Compulsory
courses
|
ÚMV/DPM1a/03
|
Diploma Work
|
2
|
-/-
|
Recognition
|
1/3
|
|
KFaDF/DF2p/07
|
History of Philosophy
|
4
|
2/1
|
Examination
|
1/1
|
|
ÚMV/TGT/01
|
Graph Theory
|
4
|
2/-
|
Examination
|
1/3
|
|
ÚMV/UAS/01
|
Ordered Algebraic Structures
|
5
|
2/1
|
Examination
|
1/3
|
|
ÚMV/TOP/03
|
Topology
|
4
|
2/-
|
Examination
|
1/3
|
|
ÚMV/UAL/01
|
Universal Algebra
|
5
|
3/-
|
Examination
|
1/2
|
|
ÚMV/POT1/01
|
Polyhedral Theory
|
4
|
2/-
|
Examination
|
1/2
|
|
ÚMV/TGR1/01
|
Theory of Groups
|
5
|
2/1
|
Examination
|
1/2
|
|
ÚMV/DPM1b/01
|
Diploma Work
|
2
|
-/-
|
Recognition
|
1/2
|
|
ÚMV/DSMa/04
|
Seminar on Diploma Work
|
2
|
-/2
|
Recognition
|
1/2
|
|
ÚMV/TMT/01
|
Matroid Theory
|
5
|
3/-
|
Examination
|
2/3
|
|
ÚMV/DPM1c/01
|
Diploma Work
|
2
|
-/-
|
Recognition
|
2/3
|
|
ÚMV/DSMb/04
|
Seminar on Diploma Work
|
2
|
-/2
|
Recognition
|
2/1
|
|
ÚMV/VKP1/01
|
Selected Topics in Probability
|
5
|
3/-
|
Examination
|
2/3
|
|
ÚMV/DIR/06
|
Differential and Integral Equations
|
6
|
3/1
|
Examination
|
2/3
|
|
ÚMV/KOO/01
|
Combinatorial Optimisation
|
6
|
3/1
|
Examination
|
2/4
|
|
ÚMV/DPM1d/01
|
Diploma Work
|
15
|
-/-
|
Recognition
|
2/4
|
|
ÚMV/DSMc/04
|
Seminar on Diploma Work
|
2
|
-/2
|
Recognition
|
2/2
|
|
ÚMV/FAN/06
|
Functional Analysis
|
6
|
3/1
|
Examination
|
1/2
|
Compulsory
elective courses
|
ÚINF/MZK/06
|
Mathematical Foundations of Cryptography
|
6
|
3/2
|
Examination
|
1/3
|
|
ÚMV/GZ/01
|
Geometric Transformations
|
5
|
2/1
|
Examination
|
1/1, 2/3
|
|
ÚMV/PST1b/01
|
Probability and Statistics
|
6
|
2/2
|
Examination
|
1/1, 2/3
|
|
ÚMV/TH1/01
|
Game Theory
|
6
|
3/1
|
Examination
|
1/1, 2/3
|
|
ÚMV/TKO1/01
|
Theory of Codes
|
6
|
1/-
|
Examination
|
1/1, 2/3
|
|
ÚMV/PMTG/01
|
Probability Method in Graph Theory
|
4
|
2/-
|
Examination
|
1/2
|
|
ÚMV/ALA1/01
|
Applied Linear Algebra
|
5
|
2/1
|
Examination
|
1/2, 2/4
|
|
ÚMV/FRG1/03
|
Fractal Geometry
|
4
|
2/-
|
Examination
|
1/2
|
|
ÚMV/TCI/01
|
Number Theory
|
4
|
2/-
|
Examination
|
1/2
|
|
ÚMV/SKA1/99
|
Combinatorial Algorithms Seminar
|
2
|
-/2
|
Assessment
|
2/4
|
|
ÚMV/TK/07
|
Theory of Categories
|
5
|
2/1
|
Examination
|
1/2
|
|
ÚMV/TRF/07
|
Real Functions Theory
|
5
|
2/1
|
Examination
|
1/1
|
Recommended
elective courses
|
ÚINF/ZNA1/06
|
Foundations of Knowledge Systems
|
4
|
2/-
|
Examination
|
2/3
|
|
ÚMV/TIN1/03
|
Theory of Information
|
4
|
2/-
|
Examination
|
1/1, 2/3
|
|
ÚMV/TS1/01
|
Control Theory
|
6
|
3/1
|
Examination
|
1/1, 2/3
|
|
ÚINF/VYZ1/01
|
Computational Complexity
|
4
|
2/-
|
Examination
|
1/1, 2/3
|
|
ÚMV/ANP/03
|
Algorithmically Unsolvable Problems
|
4
|
2/-
|
Examination
|
1/2
|
|
ÚMV/PME/04
|
Matching Models in Economics
|
5
|
2/1
|
Examination
|
1/2
|
|
ÚMV/SVK1/01
|
Student scientific conference
|
4
|
-/-
|
Assessment
|
1/2
|
Course units
Compulsory courses
|
Title
|
Graph Theory
|
||
|
Code
|
ÚMV/TGT/04
|
Teacher
|
Jendroľ Stanislav, Madaras
Tomáš
|
|
ECTS credits
|
4
|
Hrs/week
|
2/-
|
|
Assessment
|
Examination
|
Semester
|
1
|
|
T/L method
|
Lecture
|
||
|
Objective
|
To provide
students deeper knowledge of graph theory.
|
||
|
Content
|
Connectivity
of graphs. Hamiltonian graphs. Colouring of graphs. Planar graphs. Oriented
graphs. Automorphism of graphs. Snarks. Minors of graphs.
|
||
|
Recommended reading
|
J. Bang-Jensen and G. Gutin, Digraphs: Theory,
Algorithms and Applications. Springer-Verlag London 2001
J. A. Bondy and U.S.R. Murty, Graph Theory with
Applications. North Holland, Amsterdam 1976
R. Diestel, Graph Theory, Springer-Verlag. New
York 2000, 2nd edition.
|
||
|
Title
|
Ordered Algebraic Structures
|
||
|
Code
|
ÚMV/UAS/04
|
Teacher
|
Lihová Judita
|
|
ECTS credits
|
5
|
Hrs/week
|
2/1
|
|
Assessment
|
Examination
|
Semester
|
1
|
|
T/L method
|
Lecture, Practical
|
||
|
Content
|
Partially
ordered, linearly ordered, lattice ordered groups. Partially ordered and
linearly ordered rings, fields; lattice ordered rings.
|
||
|
Recommended reading
|
L.Fuchs: Partially ordered algebraic systems, Pergamon
Press, 1963
|
||
|
Title
|
Topology
|
||
|
Code
|
ÚMV/TOP/07
|
Teacher
|
Bukovský Lev
|
|
ECTS credits
|
4
|
Hrs/week
|
2/-
|
|
Assessment
|
Examination
|
Semester
|
1
|
|
T/L method
|
Lecture
|
||
|
Content
|
Basic
notions and results of set-theoretical topology. Connected and arcwise
connected space. Compactness. Čech-Stone compactification. Uniform space,
basic properties. The notion of a manifold and examples of manifolds.
Homotopy, homotopy group. Homotopy group of a simple manifold. Fix point
theorem proved by using properties of homotopy groups.
|
||
|
Recommended reading
|
I.M.Singer and J.A.Thorpe, Lecture Notes on
Elementary Topology and Geometry, Springer 1967
R. Engelking, General Topology, Heldermann 1999
|
||
|
Title
|
Universal Algebra
|
||
|
Code
|
ÚMV/UAL/04
|
Teacher
|
Studenovská Danica
|
|
ECTS credits
|
5
|
Hrs/week
|
3/-
|
|
Assessment
|
Examination
|
Semester
|
2
|
|
T/L method
|
Lecture
|
||
|
Objective
|
To provide
basic knowledge of universal algebra and to make students able to apply this
knowledge in concrete situations.
|
||
|
Content
|
Algebraic
structures. Homomorphisms and congruences. Direct and subdirect products.
Terms. Free algebras. Birkhoff’s theorems about varieties.
|
||
|
Exclusive courses
|
ÚMV/KAL1/04
|
||
|
Recommended reading
|
S.Burris, H.P.Sankappanavar: A Course in Universal
Algebra. Springer-Verlag, 1981
B. Jónsson: Topics in universal algebra, Springer-Verlag
1972
G. Grätzer: Universal Algebra, 2nd edition, Springer
Verlag, 1979
|
||
|
Title
|
Polyhedral Theory
|
||
|
Code
|
ÚMV/POT1/04
|
Teacher
|
Jendroľ Stanislav
|
|
ECTS credits
|
4
|
Hrs/week
|
2/-
|
|
Assessment
|
Examination
|
Semester
|
2
|
|
T/L method
|
Lecture
|
||
|
Objective
|
To teach
students basic knowledge of the theory of convex polyhedra and polyhedral
maps.
|
||
|
Content
|
Combinatorial
and geometric properties of three-dimensional convex polyhedra and their
analogues: polyhedral maps. Euler’s theorem; Steinitz’s theorem. Light
subgraphs. Face and vertex vectors. Groups of symmetries of polyhedra.
Applications in optimisation and chemistry.
|
||
|
Recommended reading
|
B. Grunbaum: Convex polytopes (2nd edition), Springer
New York 2003
G.M. Ziegler: Lectures on Polytopes, Springer-Verlag,
New York, 1996
|
||
|
Title
|
Theory of Groups
|
||
|
Code
|
ÚMV/TGR1/04
|
Teacher
|
Lihová Judita
|
|
ECTS credits
|
5
|
Hrs/week
|
2/1
|
|
Assessment
|
Examination
|
Semester
|
2
|
|
T/L method
|
Lecture, Practical
|
||
|
Content
|
Cyclic
groups; quotient groups. Finitely generated Abelian groups. Groups of
permutations and their applications.
|
||
|
Recommended reading
|
M.Hall: The Theory of Groups, New York, 1959
L.Fuchs: Abelian groups, Akadémiai Kiadó,Budapest,
1966
|
||
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