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Symmetry in algebra - O02310062

Title:	Symetrie v algebře
Guaranteed by:	Katedra matematiky a didaktiky matematiky (41-KMDM)
Faculty:	Faculty of Education
Actual:	from 2017
Semester:	winter
E-Credits:	5
Examination process:	winter s.:
Hours per week, examination:	winter s.:2/1, C+Ex [HT]
Capacity:	unknown / unknown (999)
Min. number of students:	unlimited
4EU+:	no
Virtual mobility / capacity:	no
State of the course:	taught
Language:	Czech
Teaching methods:	full-time
Teaching methods:	full-time
Old code:	SYAL
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.
Classification:	Mathematics > Algebra
Pre-requisite :	O0231SOUB

Opinion survey results Examination dates WS schedule Noticeboard

Annotation -

Last update: NOVOTNAJ/PEDF.CUNI.CZ (01.09.2008)

This optinal subject covers the following topics: 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 (31.08.2008)

The goal of this course is to enlarge participants' knowledge of algebra by emphasising relationships in algebra and outside it.

Literature -

Last update: NOVOTNAJ/PEDF.CUNI.CZ (31.08.2008)

Blažek, J. a kol.: Algebra a teoretická aritmetika, I., II. díl. Praha, SPN 1985. (1, 2)

Boltjanskij, V.G. - Vilenkin, N.Ja.: Symmetrija v algebre. Moskva, Nauka 1967.

Demel, J.: Grafy. MVŠT, svazek XXXIV. Praha, SNTL 1988. (5)

Fried, E.: O algebrze abstrakcyjnej. Varšava, WPN 1978. (3)

Katriňák, L. a kol.: Algebra a teoretická aritmetika 1. Bratislava-Praha, Alfa-SNTL 1985. (2, 3, 5)

Kopka, J.: Svazy a Booleovy algebry. Ústí n.L., UJEP 1991. (2)

Kořínek, V.: Základy algebry. Praha, NČSAV 1956.

Mac Lane, S. - Birkhoff, G.: Algebra. Bratislava, Alfa 1974. (2, 3, 4)

Nešetřil, J.: Teorie grafů. Praha, SNTL 19??. (5)

Novotná, J. - Trch, M.: ATA, sbírka příkladů, 2. část Polynomická algebra. Praha, SPN 1990. (1)

Pondělíček, B.: Algebraické struktury s binárními operacemi. MS SNTL 10. Praha, SNTL 1977. (3)

Rieger, L.: O grupách. Praha, MF 1974. (3)

Svatokrížny, P. a kol.: Aritmetika a algebra pre pedagogické fakulty, II. Algebra. Bratislava, SPN 1978. (1)

Šalát a kol.: Algebra a teooretická aritmetika 2. Bratislava, Alfa 1986. (2, 5)

Šrejder, J.A.: Binární relace. Praha, SNTL 1978. (2)

Teaching methods -

Last update: NOVOTNAJ/PEDF.CUNI.CZ (31.08.2008)

Lecture & 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.

Symmetry and graphs: Symmetric graphs, symmetrization of a graph.