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

None

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

See itslearning for syllabus lists and additional literature references.

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

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: 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

Name E-mail Department
Jens Kaad kaad@imada.sdu.dk Analyse

Timetable

Administrative Unit

Institut for Matematik og Datalogi (matematik)

Team at Educational Law & Registration

NAT

Offered in

Odense

Recommended course of study

Profile Education Semester Offer period

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.