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: 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.
b.how 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.
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
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
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
Timetable
Administrative Unit
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.