MM853: Advanced Linear Algebra

The Study Board for Science

Teaching language: Danish or English depending on the teacher
EKA: N310050102
Assessment: Second examiner: External
Grading: 7-point grading scale
Offered in: Odense
Offered in: Spring
Level: Master

STADS ID (UVA): N310050101
ECTS value: 5

Date of Approval: 03-11-2025


Duration: 1 semester

Version: Approved - active

Comment

Lectures and exercises combined with MM562: Advanced Linear Algebra ( 5 ECTS).

Entry requirements

None

Academic preconditions

Basic linear algebra equivalent to the content of MM540, MM505 eller MM568

Course introduction

The aim of the course is that the student acquires a deeper understanding of linear algebra, which is a central topic in both pure and applied mathematics. The techniques developed in linear algebra are in fact of fundamental importance throughout the natural sciences.

Expected learning outcome

The learning objective of the course is that the student demonstrates the ability to:

  • Apply mathematical theory and results and methods to solve concrete problems in advanced linear algebra.
  • Argue in a mathematically correct way concerning the steps and techniques applied in the solution of given problems within advanced linear algebra.
  • Assess whether achieved results are correct.
  • Present mathematical arguments in written form.
  • master complex proofs within the curriculum
  • independently construct proofs within the field of linear algebra

Content

The following main topics are contained in the course:

  • operations on vector spaces (dual spaces, tensor products, direct sums, quotient spaces, determinants)
  • spectral theory for normal operators
  • linear transformations and their properties 

Literature

See itslearning for syllabus lists and additional literature references.

Examination regulations

Exam element a)

Timing

June

Tests

Written exam

EKA

N310050102

Assessment

Second examiner: External

Grading

7-point grading scale

Identification

Student Identification Card - Name

Language

Normally, the same as teaching language

Duration

4 hours

Examination aids

To be announced during the course

ECTS value

5

Indicative number of lessons

42 hours per semester

Teaching Method

Planned lessons:
Total number of planned lessons: 42
Hereof:
Common lessons in classroom/auditorium: 42

The lectures, where the literature (curriculum) for the course will be explained, will be supplemented by exercise classes, where relevant exercises, relating to the lectures, will be solved and explained. Both of these events are supported by the students' independent work (or group-work) on the material as described in other planned teaching activities.

Other planned teaching activities:
  • Read the literature for the course

  • Solve 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 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.