MM838: Selected topics in modern analysis

Study Board of Science

Teaching language: Danish or English depending on the teacher, but English if international students are enrolled
EKA: N310037102
Censorship: Second examiner: Internal
Grading: 7-point grading scale
Offered in: Odense
Offered in: Spring
Level: Master's level course approved as PhD course

STADS ID (UVA): N310037101
ECTS value: 5

Date of Approval: 27-10-2018


Duration: 1 semester

Version: Approved - active

Comment

13016201 (former UVA) is identical with this course description.

Entry requirements

A bachelor’s degree in mathematics or applied mathematics.

Academic preconditions

Students taking the course are expected to:

  • Have a basic knowledge of topology and functional analysis, corresponding to the contents of the courses MM535 and MM543.

  • Be able to use basic arguments from topology.

  • Be able to work independently with linear algebra.

  • Have a basic knowledge of the theory of groups and rings and be able to work comfortably with these objects.

Course introduction

The aim of the course is to introduce the student to one or more topics in modern analysis and present them with the relevant tools and techniques. This will prepare the student for writing a master’s thesis within modern analysis.

The course primarily builds on the knowledge acquired in the course MM543 (Measure and integration and Banach spaces) and gives the student a broad insight into the many aspects of analysis.


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



  • Give the competence to take responsibility for the academic development and specialization.

  • Give the competence to develop an overview of the interplay between different mathematical disciplines.

  • Give skills to work concretely with new mathematical tools and objects.

  • Give skills to learn and understand advanced mathematical theories at a more independent level.

  • Give knowledge and understanding of one or more concrete disciplines within analysis

  • Bring perspective into the students mathematical knowledge.

Expected learning outcome

The learning objectives of the course are that the student demonstrates the ability to:

  • Reproduce definitions and results, including their proofs, covered in the course.

  • Be able to use these results to analyse concrete examples.

  • Formulate and present definitions, proofs and calculations in a mathematically rigorous way.

Content

The following main topics are contained in the course: Introduction to one or more topics in analysis. This could, for example, be:

  • Representation theory for groups

  • Cohomology theory for groups and/or algebras

  • Introduction to K-theory

  • Important classes of discrete groups

  • Von Neumann algebras

Literature

See Blackboard for syllabus lists and additional literature references.

Examination regulations

Exam element a)

Timing

Spring

Tests

Mandatory assignments a an oral presentation

EKA

N310037102

Censorship

Second examiner: Internal

Grading

7-point grading scale

Identification

Student Identification Card

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 week

Teaching Method

The teaching method is based on three phase model.

Intro phase: 28 hours

Skills training phase: 14 hours, hereof:

 - Tutorials: 14 hours

Activities during the study phase:

  • The students are expected to familiarize themselves with the material covered in the lectures.
  • To acquire knowledge of selected topics independently.

Teacher responsible

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

Additional teachers

Name E-mail Department City
Wojciech Szymanski szymanski@imada.sdu.dk

Timetable

Administrative Unit

Institut for Matematik og Datalogi (matematik)

Team at Registration & Legality

NAT

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