# MM539: Algebra 2

The Study Board for Science

Teaching language: Danish or English depending on the teacher

EKA: N300034102

Assessment: Second examiner: External

Grading: 7-point grading scale

Offered in: Odense

Offered in: Spring

Level: Bachelor

STADS ID (UVA): N300034101

ECTS value: 5

Date of Approval: 01-11-2022

Duration: 1 semester

Version: Archive

## Comment

DISCONTINUED - last offered spring 2022.

1. Exam attempts are held June 2022

1. Exam attempts are held June 2022

2. Exam attempts are held August 2022

3. Exam attempts will be held in January 2023

Programmes with examination period at the end of the spring semester: If you do not pass the ordinary exam, you can register for re-examination (2. examination attempt) in the same examination period or immediately thereafter, but no later than the last working day of August.

## Entry requirements

## Academic preconditions

Students taking the course are expected to:

- There are no concrete preconditions, but it is an advantage to have followed the course MM538.
- Be able to use 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 MM505 Linear

algebra MM551 Algebra 1 and gives academic basis for making a bachelor

project in algebra or take elective courses on the master level with

algebraic content.

course builds on the knowledge acquired in the course MM505 Linear

algebra MM551 Algebra 1 and gives academic basis for making a bachelor

project in algebra or take elective courses on the master level with

algebraic content.

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,

gives 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, 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.

## 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

N300034102

## 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

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 (lectures) - 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 Educational Law & 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.