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Algebra and Theoretical Arithmetic I - NUMZ010

Title:	Algebra a teoretická aritmetika I
Guaranteed by:	Department of Mathematics Education (32-KDM)
Faculty:	Faculty of Mathematics and Physics
Actual:	from 2016
Semester:	winter
E-Credits:	5
Hours per week, examination:	winter s.:2/2, C+Ex [HT]
Capacity:	unlimited
Min. number of students:	unlimited
4EU+:	no
Virtual mobility / capacity:	no
State of the course:	cancelled
Language:	Czech
Teaching methods:	full-time
Teaching methods:	full-time
Is provided by:	NMUM105

Guarantor:	RNDr. Eliška Pecinová, Ph.D.
Classification:	Mathematics > Algebra Teaching > Mathematics
Incompatibility :	NMUM105
Interchangeability :	NMUM105
Is incompatible with:	NUMP019, NMUE033
Is interchangeable with:	NUMP019, NMUE033

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Annotation -

Last update: STANOVSK/MFF.CUNI.CZ (25.01.2008)

An introductory course on general algebraic structures, based on number theory and modular arithmetics. General concepts and properties of groups and domains are presented.

Literature - Czech

Last update: STANOVSK/MFF.CUNI.CZ (25.01.2008)

D. Stanovský, Základy algebry, http://www.karlin.mff.cuni.cz/~stanovsk/vyuka/zalg.htm

Procházka a kol.: Algebra, Academia 1990.

L. Bican: Algebra (pro učitelské studium), Academia, Praha 2001, ISBN 80-200-0860-8

Syllabus -

Last update: STANOVSK/MFF.CUNI.CZ (25.01.2008)

1. Partial order

2. Elementary number theory

3. Integral domains - definition, examples

4. Divisibility in domains - unique factorization domains, Euclidean domains, Gaussian integers, roots of polynomials

5. Universal algebras

6. Groups - definition, examples, basic structure theory, cyclic groups, Lagrange theorem, Burnside theorem, factorgroups