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Course, academic year 2023/2024
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Algebra I - NUMP019
Title: Algebra I
Guaranteed by: Department of Algebra (32-KA)
Faculty: Faculty of Mathematics and Physics
Actual: from 2019
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: NALG087
Additional information: http://www.karlin.mff.cuni.cz/~stanovsk/vyuka/zalg.htm
Classification: Mathematics > Algebra
Teaching > Mathematics
Incompatibility : NALG026, NALG027, NALG034, NALG087, NMAI062, NMUE033, NMUM206, NUMZ010
Interchangeability : NALG026, NALG027, NALG034, NALG087, NMAI062, NMUE033, NMUM206, NUMZ010
Is incompatible with: NMUE033
Is interchangeable with: NMUM206, 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 -

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: T_KA (20.05.2009)
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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