MM570: Group theory

Study Board of 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.

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

Language

Normally, the same as teaching language

Duration

20 minutes

Examination aids

To be announced during the course

ECTS value

5

Indicative number of lessons

49 hours per semester

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

Name E-mail Department
David Kyed dkyed@imada.sdu.dk Analyse

Timetable

Administrative Unit

Institut for Matematik og Datalogi (matematik)

Team at Educational Law & Registration

NAT

Offered in

Odense

Recommended course of study

Profile Education Semester Offer period

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.