MM573: Metric spaces
Study Board of Science
Teaching language: Danish or English depending on the teacher, but English if international students are enrolled
EKA: N300063102
Assessment: Second examiner: Internal
Grading: 7-point grading scale
Offered in: Odense
Offered in: Spring
Level: Bachelor
STADS ID (UVA): N300063101
ECTS value: 5
Date of Approval: 11-10-2023
Duration: 1 semester
Version: Approved - active
Entry requirements
Academic preconditions
Students taking the course are expected to have knowledge of basic mathematical analysis corresponding to the content of the courses MM536 and MM533
Course introduction
The aim of the course is to introduce the student to the theory of metric spaces, which is an important tool in many areas of mathematics and are applied in e.g. combinatorics and computer science.
The course builds on the knowledge acquired in the courses MM536 and MM533, and gives an academic basis for studying more advanced courses in analysis, for example MM845 and MM819. The course moreover complements the courses MM548 and MM549 and is therefore very suitable to follow simultaneously with these two courses (or a subset hereof).
In relation to the competence profile of the degree it is the explicit focus of the course to:
- Give the competence to reason within an abstract mathematical context, and understand this context through concrete examples.
- Give skills regarding proofs, mathematical thinking and understanding of abstract mathematical structures.
- Give knowledge and understanding of metric spaces in particular regarding convergence, completeness and compactness, as well as continuity of maps.
Expected learning outcome
The learning objective of the course is that the student demonstrates the ability to:
- Understand and carry out reasoning pertaining to convergence in metric spaces, completeness and compactness of metric spaces, as well as continuity of maps between metric spaces.
- Have knowledge of concrete examples of metric spaces and their properties.
Content
The following main topics are contained in the course:
- Metric spaces
- Convergence in metric spaces
- Completeness of metric spaces
- Compactness of metric spaces
- Continuity of maps between metric spaces
Literature
Examination regulations
Exam element a)
Timing
June
Tests
Oral exam
EKA
N300063102
Assessment
Second examiner: Internal
Grading
7-point grading scale
Identification
Full name and SDU username
Language
Normally, the same as teaching language
Duration
1 time inkl. forberedelse
Examination aids
All aids allowed, i.e books, notes and computer programs that are not using the internet
ECTS value
5
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: 28 hours
- Training phase: 14 hours, hereof tutorials: 14 hours
Activities during the study phase:
- Solution of weekly assignments in order to discuss these in the exercise sections
- Self study of various parts of the course material
- Reflection upon the intro and training sections
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.