SubjectsSubjects(version: 850)
Course, academic year 2019/2020
   Login via CAS
Numerical and algebraic structures - OKBM2M107A
Title in English: Číselné a algebraické struktury
Guaranteed by: Katedra matematiky a didaktiky matematiky (41-KMDM)
Faculty: Faculty of Education
Actual: from 2019
Semester: winter
E-Credits: 4
Examination process: winter s.:
Hours per week, examination: winter s.:0/0 Ex [hours/week]
Extent per academic year: 12 [hours]
Capacity: unknown / unknown (unknown)
Min. number of students: unlimited
State of the course: taught
Language: Czech
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.
Teacher(s): prof. RNDr. Jarmila Novotná, CSc.
Pre-requisite : OKBM2M101A
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.

Literature - Czech
Last update: doc. RNDr. Antonín Jančařík, Ph.D. (03.09.2018)

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 - Czech
Last update: doc. RNDr. Antonín Jančařík, Ph.D. (03.09.2018)

Student prokáže schopnost dokázat základní vlastnosti číselných oborů v rámci písemné části zkoušky. Při ústní zkoušce bude testována znalost pojmů, základních definic a tvrzení bez potřeby jejich důkazu.

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.

 
Charles University | Information system of Charles University | http://www.cuni.cz/UKEN-329.html