SubjectsSubjects(version: 875)
Course, academic year 2020/2021
  
Algebra 1 - NMAG201
Title: Algebra 1
Guaranteed by: Department of Algebra (32-KA)
Faculty: Faculty of Mathematics and Physics
Actual: from 2020
Semester: winter
E-Credits: 4
Hours per week, examination: winter 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}
Interchangeability : NMAG206
P//Is pre-requisite for: NMMB208
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. 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/1920zs-nmag201. 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. (28.10.2019)

The requirements for the exam correspond to what has been done during lectures and problem sessions. Detailed information for this semester (in Czech) is available at https://www.karlin.mff.cuni.cz/~stovicek/index.php/cs/1920zs-nmag201.

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

 
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