Symmetry in algebra - OKB2310260
Title: Symetrie v algebře
Guaranteed by: Katedra matematiky a didaktiky matematiky (41-KMDM)
Faculty: Faculty of Education
Actual: from 2022
Semester: winter
E-Credits: 2
Examination process: winter s.:
Hours per week, examination: winter s.:0/0, MC [HS]
Extent per academic year: 4 [hours]
Capacity: unknown / unknown (999)
Min. number of students: unlimited
4EU+: no
Virtual mobility / capacity: no
State of the course: not taught
Language: Czech
Teaching methods: full-time
Note: course can be enrolled in outside the study plan
enabled for web enrollment
priority enrollment if the course is part of the study plan
Guarantor: prof. RNDr. Jarmila Novotná, CSc.
Class: Matematika 1. cyklus - povinné
Pre-requisite : OKB2310N09
Is co-requisite for: OKB1310106
Opinion survey results   Examination dates   Schedule   Noticeboard   
Annotation -
The subject focuses on symmetry and polynomials, symmetry and relations, symmetry and groups, symmetry and matrices, symmetry and graphs.
Last update: NOVOTNAJ/PEDF.CUNI.CZ (27.09.2013)
Aim of the course -

The aim of the course is to broaden and deepen knowledge of students interested in algebra their knowledge by emphasizing connections in algebra as well as outside of algebra.

Last update: NOVOTNAJ/PEDF.CUNI.CZ (27.09.2013)
Literature -

Adámek, J.: Matematické struktury a kategorie. Praha: SNTL 1982.
Blažek, J. a kol.: ATA I, II. Praha, SPN 1983, 1985.
Boltjanskij, V.G. - Vilenkin, N.Ja.: Symmetrija v algebre. Moskva, Nauka 1967.
Fried, E.: O algebrze abstrakcyjnej. Varšava, WPN 1978.
Katriňák, T. a kol.: ATA I. Bratislava ? Praha, ALFA ? SNTL 1984.
Kopka, J.: Svazy a Booleovy algebry. Ústí n.L., UJEP 1991.
Kořínek, V.: Základy algebry. Praha, NČSAV 1956.
Birkhoff, G. ? Mac Lane, S.: Algebra. Bratislava, Alfa 1974
Nešetřil, J.: Teorie grafů. Praha, SNTL.
Novotná, J. - Trch, M.: ATA, sbírka příkladů, 2. část Polynomická algebra. Praha, SPN 1990.
Pondělíček, B.: Algebraické struktury s binárními operacemi. MS SNTL 10. Praha, SNTL 1977.
Rieger, L.: O grupách. Praha, MF 1974.
Svatokrížny, P. a kol.: Aritmetika a algebra pre pedagogické fakulty, II. Algebra. Bratislava, SPN 1978.
Šalát a kol.: Algebra a teooretická aritmetika 2. Bratislava, Alfa 1986. 
Šrejder, J.A.: Binární relace. Praha, SNTL 1978.

Last update: NOVOTNAJ/PEDF.CUNI.CZ (27.09.2013)
Teaching methods -

Seminar

Last update: NOVOTNAJ/PEDF.CUNI.CZ (27.09.2013)
Requirements to the exam - Czech

Vypracování seminární práce

Zápočtový test; pro test jsou možné dva opravné termíny

Last update: Novotná Jarmila, prof. RNDr., CSc. (22.09.2017)
Syllabus -

Symmetry and polynomials: Polynomials with several variables, symmetric polynomials; their use for solving algebraic equations with one variable.
Symmetry and relations: Symmetric and skew-symmetric relations, types of relations, their properties and applications.
Symmetry and groups: Alternating groups, their usage. Link to geometry.
Symmetry and matrices: Symmetric matrices, their link to systems of linear equations and quadratic forms.

Last update: NOVOTNAJ/PEDF.CUNI.CZ (27.09.2013)