MM845: Functional Analysis

Study Board of Science

Teaching language: English
EKA: N310041102
Assessment: Second examiner: External
Grading: 7-point grading scale
Offered in: Odense
Offered in: Autumn
Level: Master

STADS ID (UVA): N310041101
ECTS value: 5

Date of Approval: 15-05-2023

Duration: 1 semester

Version: Approved - active

Entry requirements


Academic preconditions

Students taking the course are expected to:

  • Know material from MM548 Measure and Integration and Banach Spaces or equivalent.

Course introduction

This course introduces the students to fundamental methods and techniques of Functional Analysis, building on the knowledge acquired in the course on Hilbert and Banach Spaces.  

In relation to the competence profile of the degree it is the explicit focus of the course to:
  • Give the competence to take responsibility for the academic development and specialization.
  • Give the competence to develop an overview of the interplay between different mathematical disciplines.
  • Give skills to:
a.Apply the thinking and terminology from Functional Analysis.
b.Analyze and evaluate the theoretical and practical problems for the application of a suitable mathematical model.

  • Give knowledge and understanding of:
a.basic knowledge generation, theory and methods in aspects of pure mathematics taught in this course. to conduct analyses using mathematical methods and critically evaluate scientific theories. 

Expected learning outcome

The learning objectives of the course is that the student demonstrates the ability to:

  • Reproduce definitions and results, including their proofs, covered in the course.
  • Be able to use these results to analyse concrete examples.
  • Formulate and present definitions, proofs and calculations in a mathematically rigorous way.


The following main topics are contained in the course:
  • Banach space theory, including the Hahn-Banach Theorem, The Principle of Uniform Boundedness, The Open Mapping Theorem.
  • Supplementary topics from Topology, including nets and filters, weak topologies, Banach-Alaoglu Theorem, Ascoli-Arzela Theorem. 
  • Compact operators on a Hilbert space.


See itslearning for syllabus lists and additional literature references.

Examination regulations

Exam element a)


Autumn (week 44)


Oral examination




Second examiner: External


7-point grading scale


Student Identification Card




Exam consists of 30 minutes preparation time and 30 minutes actual exam

Examination aids

Allowed during preparation time, not allowed during the atual exam, a closer description of the rules will be posted in itslearning.

ECTS value


Additional information

Indicative number of lessons

42 hours per semester

Teaching Method

At the faculty of science, teaching is organized after the three-phase model ie. intro, training and study phase.
  • Intro phase (lectures) - 28 hours
  • Training phase: 14 hours, including 14 hours tutorials
In the intro phase a modified version of the classical lecture is employed, where the terms and concepts of the topic are presented, from theory as well as from examples based on examples. In these hours there is room for questions and discussions. In the training phase the students work with data-based problems and discussion topics, related to the content of the previous lectures in the intro phase. In these hours there is a possibility of working specifically with selected difficult concepts. In the study phase the students work independently with problems and the understanding of the terms and concepts of the topic. Questions from the study phase can afterwards be presented in either the intro phase hours or the training phase hours.

Study Phase Activities:
  • Discussing specific concepts introduced in lectures.
  • Working out some examples

Teacher responsible

Name E-mail Department
Wojciech Szymanski Analyse


Administrative Unit

Institut for Matematik og Datalogi (matematik)

Team at Educational Law & Registration


Offered in


Recommended course of study

Transition rules

Transitional arrangements describe how a course replaces another course when changes are made to the course of study. 
If a transitional arrangement has been made for a course, it will be stated in the list. 
See transitional arrangements for all courses at the Faculty of Science.