NMAK10008U Functional Analysis (FunkAn)

Volume 2026/2027
Education

MSc Programme in Mathematics

MSc Programme in Statistics

MSc Programme in Mathematics with a minor subject

MSc Programme in Quantum Information Science

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.
Learning Outcome

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.
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.
5 hours lectures (3+2) and 3 hours of exercises per week for 8 weeks.
  • Category
  • Hours
  • Lectures
  • 40
  • Preparation
  • 116
  • Theory exercises
  • 24
  • Exam
  • 26
  • Total
  • 206
Continuous feedback during the course of the semester
Credit
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 assesment

The student should convincingly and accurately demonstrate the knowledge, skills and competences described under Intended learning outcome.