312.140 (18W) Algebra
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
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
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 schemePosition 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)
-
Modeling-Analysis - Optimization of discrete, continuous and stochastic systems (
0.0h XX / 0.0 ECTS)
-
Subject: Modeling-Analysis-Optimization of discrete, continuous and stochastic systems
(Compulsory subject)
- 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)
-
2.1 Algebra (
2.0h VO / 3.0 ECTS)
-
Subject: Discrete Mathematics
(Compulsory subject)
- 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)
-
Algebra (
2.0h VO / 3.0 ECTS)
-
Subject: Diskrete Mathematik
(Compulsory subject)
- 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)
-
Studienleistungen gem. § 3 Abs. 2a des Curriculums (
16.0h XX / 32.0 ECTS)
-
Subject: Studienleistungen gem. § 3 Abs. 2a des Curriculums
(Compulsory subject)
Equivalent courses for counting the examination attempts
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Wintersemester 2023/24
- 312.140 VO Algebra (2.0h / 3.0ECTS)
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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)