MM838: Selected topics in modern analysis
- 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.
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
- 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.
- Representation theory for groups
- Cohomology theory for groups and/or algebras
- Introduction to K-theory
- Important classes of discrete groups
- Von Neumann algebras
Exam element a)
Mandatory assignments a an oral presentation
Indicative number of lessons
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.