Subjects

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Symmetry in Algebra - OPBM2M114A

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.:0/2, C [HT]
Capacity:	unknown / unknown (unknown)
Min. number of students:	unlimited
4EU+:	no
Virtual mobility / capacity:	no
State of the course:	taught
Language:	Czech
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.
Pre-requisite :	OPBM2M101A

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. The student will broaden and deepen the knowledge of algebra acquired in previous studies. The student will apply the knowledge and skills acquired in specific areas of algebra The student will give examples of the interrelationships of the parts of algebra included in the syllabus.

Last update: Novotná Jarmila, prof. RNDr., CSc. (07.09.2024)

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.

The student will broaden and deepen the knowledge of algebra acquired in previous studies.

The lstudentr will apply the knowledge and skills acquired in specific areas of algebra

The studentl will give examples of the interrelationships of the parts of algebra included in the syllabus. and solves problems

The studentr will solve problems in the areas of algebra covered in the syllabus.

Last update: Novotná Jarmila, prof. RNDr., CSc. (07.09.2024)

Descriptors - Czech

K předmětu jsou materiály k dispozici v kurzu v LMS Moodle s názvem Symetrie v algebře (https://dl1.cuni.cz/course/view.php?id=6001).

Další kurz v LMS Moodle: https://dl1.cuni.cz/course/view.php?id=7775

Celkem kreditů: 5 .... 150 h

Přímá výuka:

- prezenční forma studia: 24 h

- kombinovaná forma studia. 10 h

Příprava na výuku, plnění domácích úkolů:

- prezenční forma studia: 56 h

- kombinovaná forma studia: 70 h

Příprava na závěrečný test:

- prezenční forma studia: 70 h

- kombinovaná forma studia 70 h

Last update: Novotná Jarmila, prof. RNDr., CSc. (06.10.2023)

Course completion requirements -

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

Last update: Novotná Jarmila, prof. RNDr., CSc. (11.07.2022)

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. (11.07.2022)

Teaching methods -

seminar

Last update: Novotná Jarmila, prof. RNDr., CSc. (11.07.2022)

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. (07.09.2024)

Learning resources - Czech

K předmětu je vytvořen e-leaningový kurz https://dl1.cuni.cz/course/view.php?id=7775

Last update: Novotná Jarmila, prof. RNDr., CSc. (11.07.2022)

Learning outcomes -

Learners
- master the theory in the area of Symmetry and Polynomials (Polynomials of multiple variables, symmetric polynomials, product of simple symmetric polynomials, Main theorem of symmetric polynomials and its applications, use of symmetric polynomials in solving algebraic equations of one unknown) so as to be able to solve problems in this area including application problems
- master the theory of Symmetry and Relation (properties, representation, equivalence and tolerance, posets, semi-bundles and unions, Boolean algebras) including their applications in order to be able to solve problems in this area including application problems
- master the theory of Symmetry and Groups (symmetry groups of plane and space figures, symmetry group and its use in applications) including solving problems iand application problems
- master the theory of Symmetry and Matrices (symmetric matrices, their relation to the solution of systems of linear equations and to quadratic forms) in order to be able to solve problems including application problems

Last update: Novotná Jarmila, prof. RNDr., CSc. (07.09.2024)