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Course, academic year 2023/2024
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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 2021
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
Interchangeability : NALG027, NMAG206
Is interchangeable with: NALG027
In complex interchangeability with: NMAG206
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)
 
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