SubjectsSubjects(version: 875)
Course, academic year 2020/2021
  
Algebra 2 - NMAG202
Title: Algebra 2
Guaranteed by: Department of Algebra (32-KA)
Faculty: Faculty of Mathematics and Physics
Actual: from 2020
Semester: summer
E-Credits: 4
Hours per week, examination: summer s.:2/1 C+Ex [hours/week]
Capacity: unlimited
Min. number of students: unlimited
State of the course: not taught
Language: Czech
Teaching methods: full-time
Guarantor: doc. RNDr. Jan Šťovíček, 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
Interchangeability : NMAG206
Annotation -
Last update: T_KA (17.05.2012)
Introductory course for the second year students of mathematics. Commutative algebra and field theory.
Course completion requirements -
Last update: doc. RNDr. Jan Šťovíček, Ph.D. (30.04.2020)

The credit is granted automatically after passing the exam.

Depending on the situation, the exam can have either a classical or a distance form. A part of the score for the exam comes from solving homework problems which will be published and their solutions handed in during the semester.

The classical form will consist of a written test, typically supplemented by an oral examination.

The distance form will consist of a combination of an on-line test and a mandatory video call.

Detailed infromation for this semester (in Czech) available at https://www.karlin.mff.cuni.cz/~stovicek/index.php/cs/1920ls-nmag202. You will be informed about any changes due to the current development in a timely manner.

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. RNDr. Jan Šťovíček, Ph.D. (23.04.2020)

The requirements for the exam correspond to what has been done during lectures and problem sessions (including on-line lectures). Detailed information for this semester (in Czech) is available at https://www.karlin.mff.cuni.cz/~stovicek/index.php/cs/1920ls-nmag202.

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

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

 
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