SubjectsSubjects(version: 850)
Course, academic year 2019/2020
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Symmetry in algebra - OB2310062
Title in English: Symetrie v algebře
Guaranteed by: Katedra matematiky a didaktiky matematiky (41-KMDM)
Faculty: Faculty of Education
Actual: from 2017
Semester: both
E-Credits: 2
Hours per week, examination: 0/2 MC [hours/week]
Capacity: winter:unknown / unknown (999)
summer: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
you can enroll for the course in winter and in summer semester
Guarantor: prof. RNDr. Jarmila Novotná, CSc.
Class: Matematika 1. cyklus - povinné
Pre-requisite : OB2310009
Annotation -
Last update: STEHLIKO/PEDF.CUNI.CZ (27.03.2009)
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 (01.09.2008)

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 (31.08.2008)

? 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 (31.08.2008)

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 (31.08.2008)

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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