312.140 (18W) Algebra

Wintersemester 2018/19

Registration deadline has expired.

First course session
01.10.2018 12:00 - 14:00 N.2.01 On Campus
... no further dates known

Overview

Lecturer
Course title german Algebra
Type Lecture
Hours per Week 2.0
ECTS credits 3.0
Registrations 11
Organisational unit
Language of instruction English
Course begins on 01.10.2018
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.

Modified examination information (exceptional COVID-19 provisions)

Für den Zeitraum, in dem Präsenzprüfungen nur eingeschränkt möglich sind oder von der Universitätsleitung davon abgeraten wird, werden Prüfungen für diese Lehrveranstaltung online via BigBlueButton gemäß den Richtlinien auf https://www.aau.at/corona/pruefungen und der Verordnung https://www.ris.bka.gv.at/Dokumente/BgblAuth/BGBLA_2020_II_171/BGBLA_2020_II_171.html abgehalten. Jedenfalls wird auch ein Präsenzprüfungstermin angeboten werden, wenn die Maßnahmen aufgehoben sind.

Examination methodology

Oral exam (approx. 30 minutes).

Examination topic(s)

Contents of the lecture.

Assessment criteria / Standards of assessment for examinations

Emphasis is laid on reasonable knowledge of the definitions and facts and thorough understanding of the material of the course including the proofs. In case of partial fulfillment, the grade will be awarded freely depending on the deficiencies shown. 

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)
  • Masterstudium Mathematics (SKZ: 401, Version: 18W.1)
    • Subject: Discrete Mathematics (Compulsory subject)
      • 2.1 Algebra ( 2.0h VO / 3.0 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)
  • Doctoral programme Doctoral programme in Technical Sciences (SKZ: 786, Version: 12W.4)
    • Subject: Studienleistungen gem. § 3 Abs. 2a des Curriculums (Compulsory subject)
      • Studienleistungen gem. § 3 Abs. 2a des Curriculums ( 16.0h XX / 32.0 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 2017/18
  • 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)