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Symmetry in algebra - OB2310260

Title:	Symetrie v algebře
Guaranteed by:	Katedra matematiky a didaktiky matematiky (41-KMDM)
Faculty:	Faculty of Education
Actual:	from 2022
Semester:	winter
E-Credits:	2
Examination process:	winter s.:
Hours per week, examination:	winter s.:1/0, 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
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
Is co-requisite for:	OB1310106

Opinion survey results Examination dates Schedule Noticeboard

Annotation -

Last update: prof. RNDr. Jarmila Novotná, CSc. (10.09.2020)

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: prof. RNDr. Jarmila Novotná, CSc. (11.09.2021)

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.

Descriptors - Czech

Last update: prof. RNDr. Jarmila Novotná, CSc. (11.09.2021)

V případě online výuky: bude organizována online výuka v ZOOM, přičemž bude vyžadována aktivní účast na této výuce, jejímž předpokladem je přítomnost kamery a mikrofonu na straně studenta.

Předpokládá se, že online výuka bude probíhat v době, kdy je plánována v rozvrhu prezenční výuka předmětu.

Jarmila Novotná is inviting you to a scheduled Zoom meeting.

Topic: Symetrie v algebře
Time: This is a recurring meeting Meet anytime

Join Zoom Meeting
https://cuni-cz.zoom.us/j/7534626575?pwd=RElKaUZSUDgvb1hzMTM1bnI1Q0VOZz09

Meeting ID: 753 462 6575
Passcode: f09ZYx

Literature -

Last update: prof. RNDr. Jarmila Novotná, CSc. (11.09.2021)

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: prof. RNDr. Jarmila Novotná, CSc. (11.09.2021)

Seminar

Requirements to the exam -

Last update: prof. RNDr. Jarmila Novotná, CSc. (11.09.2021)

The course is taught only in Czech, so the requirements are only in Czech.

Syllabus -

Last update: prof. RNDr. Jarmila Novotná, CSc. (11.09.2021)

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.