Functional Analysis (FunkAn)
Course content
This course will cover a number of fundamental topics within the area of Functional Analysis. These topics include:
- Banach spaces: The Hahn-Banach theorem, including its versions as separation theorem, weak and weak* toplogies, the Banach-Alaoglu theorem, fundamental results connected to the Baire Category theory (the open mapping theorem, the closed graph theorem and the Uniform Boundedness Principle), as well as convexity topics, including the Krein-Milman theorem and the Markov-Kakutani fixed point theorem.
- Operators on Hilbert spaces, Spectral theorem for self-adjoint compact operators.
- Fourier transform on R^n and the Plancherel Theorem.
- Radon measures and the Riesz representation theorem for positive linear functionals.
MSc Programme in Mathematics
MSc Programme in Statistics
MSc Programme in Mathematics with a minor subject
MSc Programme in Quantum Information Science
After completing the course, the student will have:
Knowledge about the subjects mentioned in the
description of the content.
Skills to solve problems concerning the material
covered.
The following Competences:
- Have a good understanding of the fundamental concepts and results presented in lectures, including a thorough understanding of various proofs.
- Establish connections between various concepts and results, and use the results discussed in lecture for various applications.
- Be in control of the material discussed in the lectures to the extent of being able to solve problems concerning the material covered.
- Be prepared to work with abstract concepts (from analysis and measure theory).
- Handle complex problems concerning topics within the area of Functional Analysis.
5 hours lectures (3+2) and 3 hours of exercises per week for 8 weeks.
Analyse 0 (An0), Analyse 1 (An1), Analyse 2 (An2) or
Lebesgueintegralet og målteori (LIM), Topology (Top) and AdVec.
Academic qualifications equivalent to a BSc degree is
recommended.
- ECTS
- 7,5 ECTS
- Type of assessment
-
Oral examination, 25 minutes under invigilation
- Type of assessment details
- An oral exam, 25 minutes under invigilation, with 30 minutes preparation time
- Examination prerequisites
-
The student must hand in a written assignment to able to partricipate in the oral exam.
The written assignment must be handed in and approved three weeks prior to the oral examination.
For the written assignment all aids are allowed.
- Aid
- All aids allowed except Generative AI and internet access
- Marking scale
- 7-point grading scale
- Censorship form
- External censorship
- Re-exam
-
Same as the ordinary exam.
If the student has not met the exam prerequisites for the ordinary exam, the student must hand in the written assignments to be able to participate in the oral reexam.
The written assignments must be handed in and approved three weeks prior to the oral reexamination.
Criteria for exam assessment
The student should convincingly and accurately demonstrate the knowledge, skills and competences described under Intended learning outcome.
Single subject courses (day)
- Category
- Hours
- Lectures
- 40
- Preparation
- 116
- Theory exercises
- 24
- Exam
- 26
- English
- 206
Kursusinformation
- Language
- English
- Course number
- NMAK10008U
- ECTS
- 7,5 ECTS
- Programme level
- Full Degree Master
- Duration
-
1 block
- Placement
- Block 2
- Schedulegroup
-
A
- Capacity
- No limitation – unless you register in the late-registration period (BSc and MSc) or as a credit or single subject student.
- Studyboard
- Study Board of Mathematics and Computer Science
Contracting department
- Department of Mathematical Sciences
Contracting faculty
- Faculty of Science
Course Coordinator
- Magdalena Elena Musat (5-6f77756376426f63766a306d7730666d)
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