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:
2024-2025, 2025-2026, 2026-2027, 2027-2028
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
Andrew M. Bruckner, Judith B. Bruckner ja Brian S. Thomson: Real analysis, 2008; www.classicalrealanalysis.com (in particular chapter 9)
Applicable parts of J. Väisälä: Topology 1
Literature
- 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
Language:
English, Finnish
Teaching
9/4–10/27/2024 Lectures
11/6–11/6/2024 Exam
11/20–11/20/2024 Course Exam
x
Exam (5 cr)
Type:
Exam
Grading scale:
0-5
Language:
English, Finnish