SubjectsSubjects(version: 850)
Course, academic year 2019/2020
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Symmetry in algebra - OB2310260
Title in English: Symetrie v algebře
Guaranteed by: Katedra matematiky a didaktiky matematiky (41-KMDM)
Faculty: Faculty of Education
Actual: from 2019
Semester: winter
E-Credits: 2
Examination process: winter s.:
Hours per week, examination: winter s.:1/0 MC [hours/week]
Capacity: unknown / unknown (999)
Min. number of students: unlimited
State of the course: taught
Language: Czech
Teaching methods: full-time
Is provided by: OPBM2M114A
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 : OB2310N009
Annotation -
Last update: NOVOTNAJ/PEDF.CUNI.CZ (27.09.2013)
The subject focuses on symmetry and polynomials, symmetry and relations, symmetry and groups, symmetry and matrices, symmetry and graphs.
Aim of the course -
Last update: NOVOTNAJ/PEDF.CUNI.CZ (27.09.2013)

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.

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

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.

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

Seminar

Requirements to the exam - Czech
Last update: prof. RNDr. Jarmila Novotná, CSc. (08.09.2017)

Vypracování seminární práce

Zápočtový test; pro test jsou možné dva opravné pokusy

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

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.

 
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