MM570: Group theory
The Study Board for Science
Teaching language: Danish or English depending on the teacher
EKA: N300060102
Assessment: Second examiner: External
Grading: 7-point grading scale
Offered in: Odense
Offered in: Spring
Level: Bachelor
STADS ID (UVA): N300060101
ECTS value: 5
Date of Approval: 07-10-2022
Duration: 1 semester
Version: Archive
Entry requirements
The course cannot be chosen if you have passed, registered, or have followed MM539, or if MM539 is a constituent part of your Curriculum.
Academic preconditions
Students taking the course are expected to:
- Know the basics of linear algebra corresponding to the course MM568 (Logic and Linear Algebra).
- Be able to apply basic mathematical thinking.
Course introduction
The aim of the course is to introduce the student to the theory of groups. The course builds on the knowledge acquired in the course MM568 (Logic and Linear Algebra) and provides the foundation for more advanced courses in algebra.
In relation to the competence profile of the degree it is the explicit focus of the course to:
- Give the competence to reason within an abstract mathematical context, and understand this context through concrete examples. The course, moreover, trains the competence to understand and construct mathematical proofs.
- Give skills regarding proofs, mathematical thinking and understanding of abstract mathematical structures.
- Give knowledge and understanding of groups, homomorphisms, isomorphisms, subgroups, abelian groups og finite groups.
Expected learning outcome
The learning objective of the course is that the student demonstrates the ability to:
- Understand and carry out reasoning pertaining to groups and their homomorphisms.
- Have knowledge of concrete examples of various types of groups and their properties.
Content
The following main topics are contained in the course:
- Groups, subgroups, finite groups, quotient groups, abelian groups.
- Homomorphisms, isomorphisms, kernel, isomorphism theorems.
- Basic number theory and modular arithmetic
Literature
Thomas W Hungerford : Abstract Algebra: An introduction, third edition.
See itslearning for syllabus lists and additional literature references.
See itslearning for syllabus lists and additional literature references.
Examination regulations
Exam element a)
Timing
June
Tests
Oral exam
EKA
N300060102
Assessment
Second examiner: External
Grading
7-point grading scale
Identification
Student Identification Card - Name
Language
Normally, the same as teaching language
Duration
20 minutes
Examination aids
Exam aids allowed, a closer description of the exam rules will be posted in itslearning.
ECTS value
5
Indicative number of lessons
Teaching Method
Teaching activities result in an estimated indicative distribution of the work effort of an average student in the following way:
- Intro phase (lecture) - 28 hours
- Training phase: 21 hours
Classical lectures combined with exercise sessions.
Activities during the study phase
- Work with the new mathematical notions
- Deeper understanding of the topics covered in the lectures.
- Solution of relevant exercises.
Teacher responsible
Timetable
Administrative Unit
Team at Registration
Offered in
Recommended course of study
Transition rules
Transitional arrangements describe how a course replaces another course when changes are made to the course of study.
If a transitional arrangement has been made for a course, it will be stated in the list.
See transitional arrangements for all courses at the Faculty of Science.