MM845: Functional Analysis
The Study Board for 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: 12-03-2025
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.
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.
Content
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.
Literature
Examination regulations
Exam element a)
Timing
Autumn (week 44)
Tests
Oral examination
EKA
N310041102
Assessment
Second examiner: External
Grading
7-point grading scale
Identification
Student Identification Card - Name
Language
English
Duration
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
5
Additional information
Indicative number of lessons
Teaching Method
Planned lessons
Total number of planned lessons: 42
Hereof:
Common lessons in classroom/auditorium 42
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 actual data. In these lessons there is room for questions and discussions. In addition, the students work with data-based problems and discussion topics, related to the content of the previous lectures. In these hours there is a possibility of working specifically with selected difficult concepts.
Other planned teaching activities:
The students work independently with problems and the understanding of the terms and concepts of the topic. Questions from this activity can afterwards be presented in either the common lessons.
Teacher responsible
Timetable
Administrative Unit
Team at 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.