MM539: Algebra 2
Study Board of 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: 28-10-2020
Duration: 1 semester
Version: Archive
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 (lecture, classroom teaching) - 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.