312.140 (17W) Algebra

Wintersemester 2017/18

Registration deadline has expired.

First course session
03.10.2017 12:00 - 13:30 N.0.07 On Campus
... no further dates known

Overview

Lecturer
Course title german Algebra
Type Lecture
Hours per Week 2.0
ECTS credits 3.0
Registrations 15
Organisational unit
Language of instruction English
possible language(s) of the assessment German , English , French
Course begins on 03.10.2017
eLearning Go to Moodle course

Time and place

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Course Information

Intended learning outcomes

After successful completion of this course, students know and understand the theory in the areas of algebra listed below. They are able to apply this knowledge to solving pertinent problems.

Teaching methodology including the use of eLearning tools

Lecture

Course content

  • Group actions
  • Sylow's theorems
  • Structure of finitely generated abelian groups
  • Simple and solvable groups
  • Field extensions and splitting fields
  • Galois theory
  • Cyclotomic fields
  • Radical extensions
  • Solvability of algebraic equations

Prior knowledge expected

Basic course on algebra (groups, quotient groups, congruence relations, symmetric and cyclic groups, rings, ideals, divisibility in ideals, principal ideal domains, factorial rings, simple algebraic field extensions). 

Literature

See lecture notes

Examination information

Im Fall von online durchgeführten Prüfungen sind die Standards zu beachten, die die technischen Geräte der Studierenden erfüllen müssen, um an diesen Prüfungen teilnehmen zu können.

Examination methodology

Oral exam (approx. 30 minutes).

Examination topic(s)

Contents of the lecture.

Grading scheme

Grade / Grade grading scheme

Position in the curriculum

  • Thematic Doctoral Programme Modeling-Analysis-Optimization of discrete, continuous and stochastic systems (SKZ: ---, Version: 16W.1)
    • Subject: Modeling-Analysis-Optimization of discrete, continuous and stochastic systems (Compulsory subject)
      • Modeling-Analysis - Optimization of discrete, continuous and stochastic systems ( 0.0h XX / 0.0 ECTS)
        • 312.140 Algebra (2.0h VO / 3.0 ECTS)
  • Master's degree programme Technical Mathematics (SKZ: 401, Version: 13W.1)
    • Subject: Diskrete Mathematik (Compulsory subject)
      • Algebra ( 2.0h VO / 3.0 ECTS)
        • 312.140 Algebra (2.0h VO / 3.0 ECTS)

Equivalent courses for counting the examination attempts

Wintersemester 2023/24
  • 312.140 VO Algebra (2.0h / 3.0ECTS)
Wintersemester 2022/23
  • 312.140 VO Algebra (2.0h / 3.0ECTS)
Wintersemester 2021/22
  • 312.140 VO Algebra (2.0h / 3.0ECTS)
Wintersemester 2020/21
  • 312.140 VO Algebra (2.0h / 3.0ECTS)
Wintersemester 2019/20
  • 312.140 VO Algebra (2.0h / 3.0ECTS)
Wintersemester 2018/19
  • 312.140 VO Algebra (2.0h / 3.0ECTS)
Wintersemester 2016/17
  • 312.140 VO Algebra (2.0h / 3.0ECTS)
Wintersemester 2015/16
  • 312.140 VO Algebra (2.0h / 3.0ECTS)
Wintersemester 2014/15
  • 312.140 VO Algebra (2.0h / 3.0ECTS)