NMAK10008U Functional Analysis (FunkAn)

Volume 2024/2025

MSc Programme in Mathematics

MSc Programme in Statistics

MSc Programme in Mathematics with a minor subject

MSc Programme in Quantum Information Science



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
7,5 ECTS
Type of assessment
On-site written exam, 3 hours under invigilation
Continuous assessment
Type of assessment details
Two written assignments and a Final 3 hours written exam, under invigilation. Each of the written assignments count 25% towards the final grade; the students will be given 5 days to work on each. The Final written exam counts 50% towards the final grade, and it takes place in week 9.
All aids allowed
Marking scale
7-point grading scale
Censorship form
External censorship

Written exam, 3 hours, under invigilation. All aids allowed.

The final grade is the largest of the following two numbers: 1) Written exam counts 100% and 2) Written exam counts 50% and the two written assignments count 25% each.

Criteria for exam assesment

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