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Algebraic structures - O02310011

Title:	Algebraické struktury
Guaranteed by:	Katedra matematiky a didaktiky matematiky (41-KMDM)
Faculty:	Faculty of Education
Actual:	from 2012
Semester:	summer
E-Credits:	4
Examination process:	summer s.:
Hours per week, examination:	summer s.:2/1, C [HT]
Capacity:	unknown / unknown (100)
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
Explanation:	Rok3
Old code:	ALST
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.
Classification:	Mathematics > Algebra
Pre-requisite :	O02310010

Opinion survey results Examination dates Schedule Noticeboard

Annotation -

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.

Last update: STEHLIKO/PEDF.CUNI.CZ (13.03.2009)

Aim of the course -

Subject aiming to acquaint students with the construction and properties of number systems and with basic algebraic structures.

Last update: STEHLIKO/PEDF.CUNI.CZ (13.03.2009)

Literature -

BLAŽEK, J. a kol.: Algebra a teoretická aritmetika 1, 2. Praha: SPN, 1983, 1985.

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

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

NOVOTNÁ, J. ? TRCH, M.: Algebra a teoretická aritmetika, Sbírka příkladů. Část 3, Základy algebry. 2. Vyd. Praha: UK-PedF, 2004.

KUBÍNOVÁ, M. ? NOVOTNÁ, J.: Posloupnosti a řady. Matematická analýza, teoretická aritmetika. Praha: Karolinum, 1997.

Last update: STEHLIKO/PEDF.CUNI.CZ (13.03.2009)

Teaching methods -

Lecture & seminar

Last update: STEHLIKO/PEDF.CUNI.CZ (13.03.2009)

Requirements to the exam - Czech

vypracování seminární práce

2 testy

minimálně 80% účast na cvičeních či adekvátní náhrada řešenými úlohami v případě odůvodněné neúčasti

aktivita ve cvičeních během celého semestru

Last update: NOVOTNAJ/PEDF.CUNI.CZ (31.08.2008)

Syllabus -

# 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.

Last update: STEHLIKO/PEDF.CUNI.CZ (13.03.2009)

Entry requirements - Czech

vypracování seminární práce

2 testy

minimálně 80% účast na cvičeních či adekvátní náhrada řešenými úlohami v případě odůvodněné neúčasti

aktivita ve cvičeních během celého semestru

Last update: NOVOTNAJ/PEDF.CUNI.CZ (31.08.2008)