MM562: Advanced Linear Algebra

Study Board of Science

Teaching language: Danish or English depending on the teacher
EKA: N300044102
Assessment: Second examiner: External
Grading: 7-point grading scale
Offered in: Odense
Offered in: Spring
Level: Bachelor

STADS ID (UVA): N300044101
ECTS value: 5

Date of Approval: 10-10-2019


Duration: 1 semester

Version: Archive

Comment


Entry requirements

None

Academic preconditions

Basic linear algebra equivalent to the content of MM540 or MM505

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.


In relation to the competence profile of the degree it is the explicit focus of the course to:

Knowledge: Give the students knowledge on concepts, constructions and theorems in linear algebra (dimension, tensor products, spectral theory, linear transformations).

Skills: Give the students the skills to solve concrete problems in linear algebra (find the dimension of a vector space, describe linear transformations with respect to different bases, find eigenvalues and eigenvectors for normal operators). Give the students the skills to work with different operations on vector spaces and to analyse the properties of concrete linear transformations.

Competences: Give the students the competences to 1) Discuss and collaborate with others around mathematical problems within the field of linear algebra, concerning solution methods and theory, while applying standard mathematical terminology. 2) Switch fluently between abstract theory and concrete mathematical examples and understand the interaction between abstract theory and concrete problems.

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 minor proofs within the curriculum

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 Blackboard for syllabus lists and additional literature references.

Examination regulations

Exam element a)

Timing

Spring

Tests

Written exam

EKA

N300044102

Assessment

Second examiner: External

Grading

7-point grading scale

Identification

Full name and SDU username

Language

Normally, the same as teaching language

Examination aids

To be announced during the course

ECTS value

5

Additional information

The examination form for re-examination may be different from the exam form at the regular exam.

Indicative number of lessons

42 hours per semester

Teaching Method

At the faculty of science, teaching is organized after the three-phase model ie. intro, training and study phase.

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 the study phase.

  • Read the literature for the course‚Ä®
  • Solve exercises

Teacher responsible

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

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