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This entry is from Winter semester 2016/17 and might be obsolete. You can find a current equivalent here.

Galois Theory
(dt. Galoistheorie)

Level, degree of commitment Specialization module, compulsory elective module
Forms of teaching and learning,
workload		 Lecture (4 SWS), recitation class (2 SWS),
270 hours (90 h attendance, 180 h private study)
Credit points,
formal requirements		 9 CP
Course requirement(s): Written or oral examination
Examination type: Successful completion of at least 50 percent of the points from the weekly exercises.
Language,
Grading		 German,
The grading is done with 0 to 15 points according to the examination regulations for the degree program M.Sc. Mathematics.
Duration,
frequency		 One semester,
Regularly alternating with other specialization modules in Algebra
Person in charge of the module's outline Prof. Dr. István Heckenberger

Contents

  • polynomials in several variables,
  • splitting fields, algebraic closure, Steinitz's theorem,
  • Normal, separable and inseparable field extensions,
  • Galois extensions, fundamental theorem of Galois theory,
  • Computation of the Galois group, translation theorem,
  • Finite fields, roots of unity, cyclotomic polynomials,
  • Pure equations, cyclic Galois groups,
  • solubility of algebraic equations by radicals (in any characteristic), constructions with compass and ruler, regular n-gons

Qualification Goals

Students will

1. become familiar with Galois theory with its applications and be able to evaluate its historical significance in particular,

2. learn how elementary problems about geometric constructions and solving equations can be solved by using abstract algebraic methods,

3. train the use of algebraic methods by means of many concrete examples.

4. practice mathematical ways of working (developing mathematical intuition and its formal justification, training the ability to abstract, reasoning)

5. improve their oral communication skills in the exercises by practicing free speech in front of an audience and in discussion.


Prerequisites

Translation is missing. Here is the German original:

Keine. Empfohlen werden die Kompetenzen, die in den Basismodulen und im Aufbaumodul Algebra vermittelt werden


Applicability

Module imported from M.Sc. Mathematics.

It can be attended at FB12 in study program(s)

  • B.Sc. Mathematics
  • M.Sc. Computer Science
  • M.Sc. Mathematics
  • LAaG Mathematics

When studying M.Sc. Computer Science, this module can be attended in the study area Minor subject Mathematics.


Recommended Reading

  • Cigler, J.: Körper, Ringe, Gleichungen, Spektrum.
  • Stewart, I.: Galois Theory, London.



Please note:

This page describes a module according to the latest valid module guide in Winter semester 2016/17. Most rules valid for a module are not covered by the examination regulations and can therefore be updated on a semesterly basis. The following versions are available in the online module guide:

The module guide contains all modules, independent of the current event offer. Please compare the current course catalogue in Marvin.

The information in this online module guide was created automatically. Legally binding is only the information in the examination regulations (Prüfungsordnung). If you notice any discrepancies or errors, we would be grateful for any advice.