MATS213 Metric Spaces (5 cr)
Study level:
Advanced studies
Grading scale:
0-5
Language:
English, Finnish
Responsible organisation:
Department of Mathematics and Statistics
Curriculum periods:
2020-2021, 2021-2022, 2022-2023
Description
Metric spaces, continuity and limits, completeness, compactness and connectedness
Learning outcomes
After passing the course the student:
- knows and understands the definitions of a metric, a metric space, and open and closed sets
- knows how handle sequences and functions in metric spaces
- knows what the completeness of a metric space means
- knows and understands the definitions of compact and connected sets in abstract metric spaces
- can apply the methods and proofs of the course to different problems
- has improved his/her abilities to understand course related concepts in applications
Description of prerequisites
Introduction to mathematical analysis 2, vector analysis 1
Study materials
Applicable parts of J. Väisälä: Topology 1
M. Bruckner, J. B. Bruckner, and B. S. Thomson: Real analysis. 2nd edition, 2008. chapter 9.
Literature
- M. Bruckner, J. B. Bruckner, and B. S. Thomson: Real analysis. 2nd edition, 2008.
- John B. Conway: A first course in analysis
Completion methods
Method 1
Evaluation criteria:
Course exam and exercises
Time of teaching:
Period 1
Select all marked parts
Method 2
Evaluation criteria:
Final exam
Select all marked parts
Parts of the completion methods
x
Teaching (5 cr)
Type:
Participation in teaching
Grading scale:
0-5
Evaluation criteria:
Hyväksyttyyn suoritukseen vaaditaan riittävä määrä pisteitä kurssitentistä ja laskuharjoitusten hyvityspisteistä.
Language:
Finnish
Study methods:
Lectures and homework. Course exam.
Study materials:
Soveltuvin osin J. Väisälä: Topologia I
Teaching
9/2–10/28/2020 Lectures
11/4–11/4/2020 Exam
11/18–11/18/2020 Exam
x
Exam (5 cr)
Type:
Exam
Grading scale:
0-5
Evaluation criteria:
Hyväksyttyyn suoritukseen vaaditaan riittävä pistemäärä lopputentissä.
Language:
English, Finnish
Study materials:
Soveltuvin osin J. Väisälä: Topologia I