MA-449 Topology and Measure Theory
- ECTS Credits:
- 10
- Responsible department:
- Faculty of Engineering and Science
- Course Leader:
- Olav Kristian Gunnarson Dovland
- Lecture Semester:
- Autumn
- Teaching language:
- Norwegian or English
- Duration:
- 1 term
The course is connected to the following study programs
Teaching language
Norwegian or EnglishCourse contents
Metric spaces, convergence, completeness and compactness in metric spaces. Spaces of continuous functions, types of convergence, conservation of continuity, the Arzela-Ascoli theorem and the Stone-Weierstrass theorem. Measure space and measurable functions, integrable functions, convergence theorems, sign measures and the Radon-Nikodym theorem. Product goals and Tonelli-Fubini's rates.
Learning outcomes
After successful completion of the course the student is able to
-
explain and apply key terms in the theory of metric spaces.
-
account for important results and connections between concepts in this theory, especially completeness and compactness.
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analyze topological phenomena in spaces of continuous functions.
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deduce and apply the main results of the integration theory.
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apply Fubini's theorem and the Radon-Nikodym theorem.
Examination requirements
Approved compulsory hand-ins. See Canvas for more information.
Teaching methods
Seminar, group work, and compulsory hand-ins. Estimated workload of the course is 267 hours.
Evaluation
The person responsible for the course decides, in cooperation with student representative, the form of student evaluation and whether the course is to have a midway or end of course evaluation in accordance with the quality system for education, chapter 4.1.
Reduction of Credits
This course’s contents overlap with the following courses. A reduction of credits will occur if one of these courses is taken in addition:
| Course | Reduction of Credits |
|---|---|
| MA-432 – Topics in modern analysis | 10 |