MM838: Selected topics in modern analysis (5 ECTS)

STADS: 13016201

Level
Master's level course approved as PhD course

Teaching period
The course is offered in the autumn semester.

Teacher responsible
Email: dkyed@imada.sdu.dk

Additional teachers
szymanski@imada.sdu.dk

Timetable
Show entire timetable
Show personal time table for this course.

Comment:
Ubegrænset deltagerantal.

Prerequisites:
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.

Subject overview
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

Meddeles ved kursets start.

Website
This course uses e-learn (blackboard).

Prerequisites for participating in the exam
None

Assessment and marking:
Mandatory assignments a an oral presentation. Internal marking by the Danish 7-mark scale.

Expected working hours
The teaching method is based on three phase model.
Intro phase: 28 hours
Skills training phase: 14 hours, hereof:
 - Tutorials: 14 hours

Educational activities

Educational form
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.

Language
This course is taught in Danish or English, depending on the lecturer. However, if international students participate, the teaching language will always be English.

Course enrollment
See deadline of enrolment.

Tuition fees for single courses
See fees for single courses.