Subjects

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Algebra 2 - NMAG202

Title:	Algebra 2
Guaranteed by:	Department of Algebra (32-KA)
Faculty:	Faculty of Mathematics and Physics
Actual:	from 2024
Semester:	summer
E-Credits:	4
Hours per week, examination:	summer s.:2/1, C+Ex [HT]
Capacity:	unlimited
Min. number of students:	unlimited
4EU+:	no
Virtual mobility / capacity:	no
State of the course:	not taught
Language:	Czech
Teaching methods:	full-time
Teaching methods:	full-time
Is provided by:	NMAG206
Additional information:	https://sites.google.com/site/vitakala/teaching/20alg

Guarantor:	doc. Mgr. Vítězslav Kala, Ph.D.
Class:	M Bc. MMIB M Bc. MMIB > Povinné M Bc. MMIB > 2. ročník M Bc. MMIT M Bc. MMIT > Povinné M Bc. OM M Bc. OM > Povinné M Bc. OM > 2. ročník
Classification:	Mathematics > Algebra
Pre-requisite :	{One course in Linear Algebra}
Co-requisite :	NMAG201
Incompatibility :	NALG027
Is interchangeable with:	NALG027
In complex interchangeability with:	NMAG206

Opinion survey results Examination dates Schedule Noticeboard

Annotation -

Introductory course for the second year students of mathematics. Commutative algebra and field theory.

Last update: T_KA (17.05.2012)

Course completion requirements -

The course will be taught in Spring as part of NMAG206; the requirements will correspond to this course.

Last update: Kala Vítězslav, doc. Mgr., Ph.D. (11.02.2021)

Literature -

Video recorded lectures (in Czech)
D. Stanovský, Základy algebry, Matfyzpress, Praha 2010.
J. Rotman, A First Course in Abstract Algebra
L. Rowen, Algebra: Groups, Rings, and Fields
S. Lang, Algebra, Revised 3rd ed., GTM 211, Springer, New York, 2002.
N. Lauritzen, Concrete Abstract Algebra, Cambridge Univ. Press, Cambridge 2003.

Last update: Šťovíček Jan, doc. RNDr., Ph.D. (28.10.2019)

Requirements to the exam -

The course will be taught in Spring as part of NMAG206; the requirements will correspond to this course.

Last update: Kala Vítězslav, doc. Mgr., Ph.D. (11.02.2021)

Syllabus -

4. Group theory - Lagrange's theorem, group action and Burnside's theorem, the structure of cyclic groups, homomorphisms, factorgroups, solvability

5. Field extensions - dimension, ruler and compass constructions, splitting fields and finite fields

6. Galois theory - Galois groups, solving polynomial equations vs. field extensions vs. properties of Galois groups, Abel-Ruffini theorem

Last update: Stanovský David, doc. RNDr., Ph.D. (01.03.2019)

Registration requirements - Czech

Tento předmět se otevírá pouze pro studenty OM a MIT, kteří začali studovat před rokem 2019-2020 a kteří studují podle staré akreditace. Ostatním studentům bude případný zápis zrušen. Místo tohoto předmětu si mohou zapsat předmět Algebra NMAG206.

Výuka bude probíhat v rámci předmětu Algebra NMAG206 v letním semestru.

Last update: Kaplický Petr, doc. Mgr., Ph.D. (30.09.2020)