MM849: 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: N310034102
Assessment: Second examiner: Internal
Grading: 7-point grading scale
Offered in: Odense
Offered in: Spring
Level: Master

STADS ID (UVA): N310034101
ECTS value: 10

Date of Approval: 12-10-2023


Duration: 1 semester

Version: Approved - active

Comment

-

Entry requirements

The course cannot be taken, MM838 has previously been followed or passed.

Academic preconditions

 Students taking the course are expected to:

  • Have a basic knowledge of topology and basic functional analysis, corresponding to the contents of the courses MM535 and MM543, and ideally also MM845.
  • 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 is 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
  • Introduction to index theory

Literature

See itslearning for syllabus lists and additional literature references.

Examination regulations

Exam element a)

Timing

Spring

Tests

Mandatory assignment

EKA

N310034102

Assessment

Second examiner: Internal

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

10

Additional information

With 3 or fewer students the format of the reexam will change to oral exam.
Duration: 30 minutes (including questions). All normal aids allowed.
• Topics are given before the exam date
• Students draw a topic just prior to the exam
• The exam is without preparation

Indicative number of lessons

84 hours per semester

Teaching Method

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

  • Intro phase (lectures)  56 hours
  • Training phase: 28 hours, including 28 hours tutorials
The lectures (intro phase) consist of classical lectures. In the skills training phase he students are expected to solve exercises selected with the purpose of familiarising them with the material covered in the lectures.  

Activitites 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 Analyse

Additional teachers

Name E-mail Department City
Are Austad are@sdu.dk Analyse

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

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.