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Course, academic year 2023/2024
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Fundamentals of Algebra - NALG087
Title: Základy algebry
Guaranteed by: Department of Algebra (32-KA)
Faculty: Faculty of Mathematics and Physics
Actual: from 2018
Semester: winter
E-Credits: 6
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
Guarantor: doc. Mgr. Jan Šaroch, Ph.D.
Classification: Mathematics > Algebra
Interchangeability : NALG026, NALG034, NMAI062
Is co-requisite for: NALG090
Is incompatible with: NUMP019, NMUE033
Is pre-requisite for: NMIB020
Is interchangeable with: NUMP019, NALG026, NMUE033
Annotation -
An introductory course on general algebraic structures, based on number theory and modular arithmetics. General concepts and properties of groups and domains are presented.
Last update: STANOVSK/MFF.CUNI.CZ (25.01.2008)
Literature - Czech

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

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

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

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