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Introduction to Algebra - NALG034

Title:	Úvod do algebry
Guaranteed by:	Department of Algebra (32-KA)
Faculty:	Faculty of Mathematics and Physics
Actual:	from 2018
Semester:	winter
E-Credits:	8
Hours per week, examination:	winter s.:4/2, 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
Additional information:	http://www.karlin.mff.cuni.cz/~stanovsk/vyuka/zalg.htm

Guarantor:	doc. Mgr. Jan Šaroch, Ph.D.
Classification:	Mathematics > Algebra
Pre-requisite :	{NALG001 v NALG086 v NALG002}
Interchangeability :	{ALG026 a ALG027}, NMAI062
Is incompatible with:	NUMP019
Is interchangeable with:	NUMP019, NALG026, NALG087

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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, rings and fields are presented. The course is aimed on students of mathematical methods in information security.

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.

S. Mac Lane, G.Birkhoff: Algebra (Macmillan, New York, 1985)

Syllabus -

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

Partial order.

Integral domains - elementary number theory, unique factorization domains and Eucleidean domains, Gaussian integers, roots of polynomials.

Unversal algebras.

Groups - cyclic groups, discrete logarithm, Lagrange's theorem, Burnside's theorem, factorgroups.

Rings, factorization

Fields - finite extensions, constructions with straightedge and compass, splitting fields, algebraic closure.