Module 24-B-AL Algebra

Faculty

Faculty of Mathematics

Person responsible for module

Herr Prof. Dr. Henning Krause

Regular cycle (beginning)

Every winter semester

Credit points and duration

10 Credit points

For information on the duration of the modul, refer to the courses of study in which the module is used.

Competencies

Non-official translation of the module descriptions. Only the German version is legally binding.

The module introduces the concepts and methods of algebra. Students develop an understanding of the fundamental principles of algebra and are enabled to carry out mathematical proofs independently. They learn how to deal with basic algebraic concepts and Galois theory and acquire the knowledge and skills required in in-depth courses on algebra, algebraic geometry, algebraic topology or algebraic number theory. They are confident in applying the methods of algebra and can successfully transfer them to new problems in algebra.

In the tutorials, students demonstrate the acquisition of competences in the technologies of algebra, the ability to apply the methods, presentation and communication skills as well as perseverance as basic mathematical competences. The final exam demonstrates students' understanding of the relationships and concepts as well as their confidence in applying the methods to new problems.

Content of teaching

Fundamental knowledge of groups, rings, solids and modules over rings
Introduction to Galois theory: Understanding the basic connections between solving algebraic equations, the theory of algebraic extensions of solids and group theory.

Recommended previous knowledge

Knowledge of linear algebra

Necessary requirements

—

Explanation regarding the elements of the module

The module cannot be studied together with module 24-B-Al-5.

Module structure: 1 SL, 1 bPr ¹

Courses

Algebra I

Type lecture

Regular cycle WiSe

Workload⁵ 60 h (60 + 0)

LP 2 [Pr]

Tutorials for Algebra I

Type exercise

Regular cycle WiSe

Workload⁵ 90 h (30 + 60)

LP 3 [SL]

Study requirements

Allocated examiner	Workload	LP²
Teaching staff of the course Tutorials for Algebra I (exercise) Regular completion of the exercises, each with a recognisable solution approach, as well as participation in the exercise groups for the module's lecture. As a rule, participation in the exercise group includes presenting solutions to exercises twice after being asked to do so as well as regular contributions to the scientific discussion in the exercise group, for example in the form of comments and questions on the proposed solutions presented. The organiser may replace some of the exercises with face-to-face exercises.	see above	see above

Examinations

e-portfolio with final oral examination o. e-portfolio with final written examination o. portfolio with final oral examination o. portfolio with final written examination

Allocated examiner Teaching staff of the course Algebra I (lecture)

Weighting 1

Workload 150h

LP² 5

The (e-)portfolio is passed if

a sufficient number of correctly solved exercises, which are completed as part of the study requirements , are demonstrated, usually by at least 50% of the points achievable in the semester for solving the exercises, and
a final exam in the form of a final written exam (usually 90 min) or a final oral exam (usually 30 min) is passed. The final exam relates to the content of the lecture and the tutorial and is used for assessment.

A remote electronic written examination is not permitted as a final exam.

The module is used in these degree programmes:

Degree programme	Version	Profile	Recommended start ³	Duration	Mandatory option ⁴
Extension subject / Master of Education Erweiterungsfach [Prüfungsordnung vom 21.03.2023 mit Änderungen vom 30.11.2023 und 26.04.2024]	Mathematics (Subject-specific Regulations from 2019): Extension subject Master of Education Continuation Minor Subject (Advanced Secondary and Comprehensive Schools ('Gymnasium' and 'Gesamtschule'))		3. o. 4.	one semester	Compulsory optional subject
Mathematical and Theoretical Physics / Master of Science [FsB vom 26.04.2024 mit Änderungen vom 29.05.2024 und 10.12.2024 und der Berichtigung vom 01.04.2025]		Admission Track Profile B	1. o. 2.	one semester	Compulsory optional subject
Mathematics / Bachelor of Science [FsB vom 28.02.2025]	Major Subject (Academic)		3. o. 4.	one semester	Obligation
Mathematics / Bachelor [FsB vom 28.02.2025]	Minor Subject (Academic), 60 CPs		4. o. 5. o. 6.	one semester	Compulsory optional subject
Mathematics / Bachelor of Science [FsB vom 28.02.2025]	Major Subject (Advanced Secondary and Comprehensive Schools ('Gymnasium' and 'Gesamtschule'))		3. o. 4. o. 5. o. 6.	one semester	Compulsory optional subject
Mathematics / Bachelor of Science [FsB vom 30.09.2016 mit Änderung vom 10.12.2024]	Major Subject (Academic)		3. o. 4.	one semester	Compulsory optional subject
Mathematics / Bachelor of Science [FsB vom 30.09.2016 mit Änderung vom 10.12.2024]	Major Subject (Academic)	Strukturierte Ergänzung des fw Bachelor KF	3. o. 4. o. 5.	one semester	Compulsory optional subject
Mathematics / Bachelor [FsB vom 30.09.2016 mit Änderung vom 10.12.2024]	Minor Subject (Academic), 60 CPs		3. o. 4. o. 5.	one semester	Compulsory optional subject
Mathematics / Bachelor of Science [FsB vom 30.09.2016 mit Änderung vom 10.12.2024]	Major Subject (Advanced Secondary and Comprehensive Schools ('Gymnasium' and 'Gesamtschule'))		3. o. 4.	one semester	Compulsory optional subject
Mathematics / Master of Education [FsB vom 01.03.2019 mit Änderung vom 10.12.2024]	Continuation Major Subject (Advanced Secondary and Comprehensive Schools ('Gymnasium' and 'Gesamtschule'))		3. o. 4.	one semester	Compulsory optional subject
Mathematics / Master of Education [FsB vom 01.03.2019 mit Änderung vom 10.12.2024]	Continuation Minor Subject (Advanced Secondary and Comprehensive Schools ('Gymnasium' and 'Gesamtschule'))		3. o. 4.	one semester	Compulsory optional subject
Mathematical Economics / Bachelor of Science [FsB vom 28.02.2025 mit Berichtigung vom 30.04.2025]	Bachelor with One Core Subject (Academic)		3. o. 4. o. 5. o. 6.	one semester	Compulsory optional subject
Mathematical Economics / Bachelor of Science [FsB vom 30.09.2016 mit Berichtigung vom 10.01.2017 und Änderungen vom 15.05.2017, 01.03.2018, 01.03.2019, 16.09.2019, 02.03.2020 und 10.12.2024]	Bachelor with One Core Subject (Academic)	Business Administration	3. o. 4. o. 5.	one semester	Compulsory optional subject
Mathematical Economics / Bachelor of Science [FsB vom 30.09.2016 mit Berichtigung vom 10.01.2017 und Änderungen vom 15.05.2017, 01.03.2018, 01.03.2019, 16.09.2019, 02.03.2020 und 10.12.2024]	Bachelor with One Core Subject (Academic)	Political Economy	3. o. 4. o. 5.	one semester	Compulsory optional subject

Automatic check for completeness

The system can perform an automatic check for completeness for this module.

Previus version of this module

24-B-AL_ver1 Algebra

Legend

1: The module structure displays the required number of study requirements and examinations.
2: LP is the short form for credit points.
3: The figures in this column are the specialist semesters in which it is recommended to start the module. Depending on the individual study schedule, entirely different courses of study are possible and advisable.
4: Explanations on mandatory option: "Obligation" means: This module is mandatory for the course of the studies; "Optional obligation" means: This module belongs to a number of modules available for selection under certain circumstances. This is more precisely regulated by the "Subject-related regulations" (see navigation).
5: Workload (contact time + self-study)
SoSe: Summer semester
WiSe: Winter semester
SL: Study requirement
Pr: Examination
bPr: Number of examinations with grades
uPr: Number of examinations without grades
: This academic achievement can be reported and recognised.