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Course, academic year 2022/2023
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Algebra 1 - NMAG201
Title: Algebra 1
Guaranteed by: Department of Algebra (32-KA)
Faculty: Faculty of Mathematics and Physics
Actual: from 2021
Semester: winter
E-Credits: 4
Hours per week, examination: winter s.:2/1, C+Ex [HT]
Capacity: unlimited
Min. number of students: unlimited
Virtual mobility / capacity: no
State of the course: not taught
Language: Czech
Teaching methods: full-time
Is provided by: NMAG206
Additional information: https://sites.google.com/site/vitakala/teaching/20alg
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}
Incompatibility : NALG026
Interchangeability : NALG026, NMAG206
Is co-requisite for: NMAG202
Is interchangeable with: NALG026
In complex interchangeability with: NMAG206
Annotation -
Last update: T_KA (17.05.2012)
Introductory course for the second year students of mathematics. Introduction to the theory of groups and commutative algebra.
Course completion requirements -
Last update: doc. Mgr. Vítězslav Kala, Ph.D. (19.10.2020)

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

Literature -
Last update: doc. RNDr. Jan Šťovíček, Ph.D. (28.10.2019)
  • 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.
Requirements to the exam -
Last update: doc. Mgr. Vítězslav Kala, Ph.D. (19.10.2020)

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

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

1. Abstract theory of division - number domains, polynomial domains, fundamental theorem of arithmetics for general domains, Euclid's algorithm, principal ideals

2. Algebra of polynomials - multiple roots, multivariate polynomials, symmetric polynomials, splitting fields, the fundametal theorem of algebra

3. Field extensions - finite extensions, algebraic extensions, degree, constructions with ruler and compass

Registration requirements - Czech
Last update: doc. Mgr. Petr Kaplický, Ph.D. (30.09.2020)

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.

 
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