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Course, academic year 2019/2020
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Algebra (CŽV) - NMUM809
Title in English: Algebra (CŽV)
Guaranteed by: Department of Mathematics Education (32-KDM)
Faculty: Faculty of Mathematics and Physics
Actual: from 2018
Semester: winter
E-Credits: 4
Hours per week, examination: winter s.:1/1 colloquium [hours/week]
summer s.:1/1 colloquium [hours/week]
Capacity: unlimited
Min. number of students: unlimited
State of the course: cancelled
Language: Czech
Teaching methods: full-time
Is provided by: NMUM206
Additional information: http://www.karlin.mff.cuni.cz/~stanovsk/vyuka/zalg.htm
Guarantor: RNDr. Eliška Pecinová, Ph.D.
doc. RNDr. Jindřich Bečvář, CSc.
Classification: Mathematics > Mathematics, Algebra, Differential Equations, Potential Theory, Didactics of Mathematics, Discrete Mathematics, Math. Econ. and Econometrics, External Subjects, Financial and Insurance Math., Functional Analysis, Geometry, General Subjects, , Real and Complex Analysis, Mathematics General, Mathematical Modeling in Physics, Numerical Analysis, Optimization, Probability and Statistics, Topology and Category
Is incompatible with: NMUM206
Is interchangeable with: NMUM206
Annotation -
Last update: JUDr. Dana Macharová (10.10.2012)
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 -
Last update: JUDr. Dana Macharová (10.10.2012)

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: JUDr. Dana Macharová (10.10.2012)

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

 
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