MATS220 Functional Analysis (10 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
Hilbert spaces and Banach spaces, bounded linear operators, Fourier series, Baire category, weak topology, the spectrum of an operator.
Learning outcomes
The student
- masters the basic fundamental results of the theory of Banach and Hilbert spaces.
- has obtained skills to apply the theory of Banach and Hilbert spaces in modern analysis.
Description of prerequisites
Metric spaces, Topology, Measure and integration theory 1 and 2.
Literature
- Andrew M. Bruckner, Judith B. Bruckner & Brian S. Thomson: Real Analysis, 2008, www.classicalrealanalysis.com
- Avner Friedman, Foundations of modern analysis, Dover Publications Inc. 1982; ISBN: 0-486-64062-0
- John B. Conway, A course in functional analysis (2nd edition), Springer, 1990; ISBN: 0-387-97245-5
- Lauri Kahanpää, Funktionaalianalyysi, luntomoniste 51, Matematiikan ja tilastotieteen laitos, Jyväskylän yliopisto, 2004.; ISBN: 951-39-1763-0
Completion methods
Method 1
Evaluation criteria:
Course exam and exercises
Time of teaching:
Period 3, Period 4
Select all marked parts
Method 2
Evaluation criteria:
final exam
Select all marked parts
Parts of the completion methods
x
Teaching (10 cr)
Type:
Participation in teaching
Grading scale:
0-5
Language:
English, Finnish
Study methods:
Lectures and exercises
Teaching
1/10–5/22/2022 Lectures
6/1–6/1/2022 Exam
x
Exam (10 cr)
Type:
Exam
Grading scale:
0-5
Language:
English, Finnish