Subjects

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Symmetry in Algebra - OKBM2M114A

Title:	Symetrie v algebře
Guaranteed by:	Katedra matematiky a didaktiky matematiky (41-KMDM)
Faculty:	Faculty of Education
Actual:	from 2019
Semester:	winter
E-Credits:	2
Examination process:	winter s.:
Hours per week, examination:	winter s.:0/0, C [HT]
Extent per academic year:	8 [hours]
Capacity:	unknown / unknown (unknown)
Min. number of students:	unlimited
4EU+:	no
Virtual mobility / capacity:	no
State of the course:	taught
Language:	Czech
Teaching methods:	combined
Is provided by:	OKBM1M129A
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.
Pre-requisite :	OKBM2M101A

Opinion survey results Examination dates WS schedule Noticeboard

Annotation -

The subject focuses on symmetry and polynomials, symmetry and relations, symmetry and groups, symmetry and matrices, symmetry and graphs.

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

Aim of the course -

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.

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

Descriptors - Czech

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

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

Literature -

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.

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

Teaching methods -

Seminar

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

Requirements to the exam -

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

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

Syllabus -

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.

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