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Symmetry in algebra seminar - OB1310106

Title:	Symetrie v algebře seminář
Guaranteed by:	Katedra matematiky a didaktiky matematiky (41-KMDM)
Faculty:	Faculty of Education
Actual:	from 2018
Semester:	summer
E-Credits:	1
Examination process:	summer s.:
Hours per week, examination:	summer s.:0/1, MC [HT]
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
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
Co-requisite :	OB2310260
Pre-requisite :	OB2310009
In complex interchangeability with:	OB1310N001

Opinion survey results Examination dates Schedule Noticeboard

Annotation -

Last update: NOVOTNAJ/PEDF.CUNI.CZ (27.02.2012)

The subject focuses on symmetry and polynomials, symmetry and relations, symmetry and groups, symmetry and matrices, symmetry and graphs. Offers additional and deeper knowledge from the course Symmetry in algebra.

Aim of the course -

Last update: JANCARIK/PEDF.CUNI.CZ (11.03.2010)

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 (27.02.2012)

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: JANCARIK/PEDF.CUNI.CZ (11.03.2010)

Seminar

Requirements to the exam - Czech

Last update: NOVOTNAJ/PEDF.CUNI.CZ (27.02.2012)

Vypracování seminárních prací a úspěšné vyřešení testu

Syllabus -

Last update: JANCARIK/PEDF.CUNI.CZ (11.03.2010)

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.