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Numerical and algebraic structures - OKBM2M107A

Title:	Číselné a algebraické struktury
Guaranteed by:	Katedra matematiky a didaktiky matematiky (41-KMDM)
Faculty:	Faculty of Education
Actual:	from 2022
Semester:	winter
E-Credits:	4
Examination process:	winter s.:
Hours per week, examination:	winter s.:0/0, Ex [HT]
Extent per academic year:	12 [hours]
Capacity:	unknown / unknown (unknown)
Min. number of students:	unlimited
4EU+:	no
Virtual mobility / capacity:	no
State of the course:	not taught
Language:	Czech
Teaching methods:	combined
Teaching methods:	combined
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 Schedule Noticeboard

Annotation -

Last update: prof. RNDr. Jarmila Novotná, CSc. (06.09.2019)

The course covers two domains of algebra and theoretical arithmetic useful for lower and upper secondary mathematics teachers. It deals with the construction of number systems (natural, whole, rational, real and complex numbers), and broadens and deepens the knowledge that students gained during their previous study. The second part covers algebraic structures focusing mainly on the structures with one and two binary operations. Knowledge of structures that students gained in previous courses is generalised and broadened.

Aim of the course -

Last update: prof. RNDr. Jarmila Novotná, CSc. (06.09.2019)

The aim is to acquaint students with the construction and properties of number systems and with basic algebraic structures.

Descriptors - Czech

Last update: JUDr. Mgr. Filip Beran (21.10.2020)

Komunikace se uskutečňuje a materiály sdílí přes Moodle zde: https://dl1.cuni.cz/course/view.php?id=6051. Živé konzultace probíhají v MS Teams.

Literature -

Last update: doc. RNDr. Antonín Jančařík, Ph.D. (28.10.2019)

BLAŽEK, J. a kol.: Algebra a teoretická aritmetika 1, 2. Praha: SPN, 1983, 1985.14-514-83, 14-470-85.

KATRIŇÁK, T. a kol.: Algebra a teoretická aritmetika 1. Bratislava, Praha: ALFA, SNTL, 1985. 63-568-85.

ŠALÁT, T. a kol.: Algebra a teoretická aritmetika 2. Bratislava, Praha: ALFA, SNTL, 1986. 63-554-86.

NOVOTNÁ, J. – TRCH, M.: Algebra a teoretická aritmetika, Sbírka příkladů část 3, Základy algebry. 2. vyd. Praha: UK-PedF, 2004. ISBN 80-7290-190-7.

Kubínová, M. – Novotná, J.: Posloupnosti a řady. Matematická analýza, teoretická aritmetika. Praha: Karolinum, 1997. ISBN 80-7184-564-7.

http://ocw.mit.edu/courses/find-by-topic/#cat=mathematics&subcat=algebraandnumbertheory

http://www.zam.fme.vutbr.cz/~martisek/Vyuka%5CPrij%5Cskripta2.pdf

http://www.math.sk/skripta/skripta.pdf

Requirements to the exam -

Last update: doc. RNDr. Antonín Jančařík, Ph.D. (28.10.2019)

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

Syllabus -

Last update: prof. RNDr. Jarmila Novotná, CSc. (06.09.2019)

Revision of basic concept related to algebraic structures

Peano arithmetic: Natural numbers as an algebraic structure, Positional representation of natural numbers

Construction of the whole numbers system. Embedding of semigroups into groups

Construction of the field of rational numbers; Positional representation of rational numbers

Construction of the field of real numbers

Construction of the field of complex numbers; geometrical model of the field of complex numbers.

Basic properties of groups. Lagrange Theorem, quotient groups. Group homomorphisms.

Basic properties of rings.