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Symmetry in algebra seminar - OKB1310106

Title:	Symetrie v algebře seminář
Guaranteed by:	Katedra matematiky a didaktiky matematiky (41-KMDM)
Faculty:	Faculty of Education
Actual:	from 2012
Semester:	summer
E-Credits:	1
Examination process:	summer s.:
Hours per week, examination:	summer s.:0/0, MC [HS]
Extent per academic year:	6 [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
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 :	OKB2310260
Pre-requisite :	OKB2310208
In complex interchangeability with:	OKB1310N01

Opinion survey results Examination dates Schedule Noticeboard

Annotation -

Last update: JANCARIK/PEDF.CUNI.CZ (04.06.2010)

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: JANCARIK/PEDF.CUNI.CZ (04.06.2010)

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: JANCARIK/PEDF.CUNI.CZ (04.06.2010)

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 (04.06.2010)

Seminar

Syllabus -

Last update: JANCARIK/PEDF.CUNI.CZ (04.06.2010)

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.