MA-432 Topics in modern analysis
- ECTS Credits:
- 15
- Responsible department:
- Faculty of Engineering and Science
- Course Leader:
- Inger Johanne Håland Knutson
- Lecture Semester:
- Spring
- Teaching language:
- Norwegian or English.
- Duration:
- 1 term
The course is connected to the following study programs
- Mathematics, Master's Programme
- Didactics of Mathematics, Joint Nordic Master's Programme
Teaching language
Norwegian or English.Recommended prerequisites
MA-304
Course contents
Introduction to the basics of topology, theory of measure and integration and functional analysis.
Learning outcomes
The student
-
can develop the theory of the topology in metric spaces including compactness and uniform continuity
-
knows and can explain the theory of continuous functions in metric spaces, including the Arzela-Ascoli theorem
-
can develop the theory of operators in linear spaces, including Baire’s category theorem and its consequences
-
has a good understanding of measures, measurable spaces and functions, and of the construction of the Lebesgue measure
-
can develop the theory of integration with respect to a positive measure and explain the important convergence theorems
-
has a good understanding of product measure and the Fubini/Tonelli theorem
Examination requirements
Required assignments and tests must be approved, se Canvas for more information.
Teaching methods
Lectures and work in small groups. The course has an expected workload of around 400 hours.
Evaluation
The person responsible for the course, in consultation with the student representative, decides the method of evaluation and whether the courses will have a midterm- or end of term evaluation, see also the Quality System, section 4.1. Information about evaluation method for the course will be posted on Canvas.
Offered as Single Standing Module
Yes. Subject to avalibility or capacity.
Assessment methods and criteria
Oral individual examination. Graded assessment.