|Level, degree of commitment in original study programme||Advanced module, compulsory elective module|
|Forms of teaching and learning,
|Lecture (4 SWS), recitation class (2 SWS), |
270 hours (90 h attendance, 180 h private study)
Course requirement: Successful completion of at least 50 percent of the points from the weekly exercises.
Examination type: Written or oral examination
|German,The grading is done with 0 to 15 points according to the examination regulations for study course M.Sc. Mathematics.|
|Original study programme||M.Sc. Mathematik / Vertiefungsbereich Mathematik|
|One semester, |
Regelmäßig im Wechsel mit anderen advanced moduleen im Gebiet Analysis
|Person in charge of the module's outline||Prof. Dr. Ilka Agricola, Prof. Dr. Stephan Dahlke, Prof. Dr. Pablo Ramacher|
- Banach and Hilbert spaces, their dual spaces
- strong and weak convergence, pre-compactness, convex sets and minimization problems
- continuous operators, dual operators, operator topologies, Fourier and Laplace transformations
- Standard theorems of functional analysis
- Spectrum of bounded operators, Fredholm alternative, Fredholm operators and their index, spectral decomposition of normal operators
- Unbounded operators: basic questions, differential operators
The students shall
- get to know typical problems of infinite-dimensional theory and their applications,
- learn on examples like minimization problems how pure and applied mathematics interact,
- practice mathematical work methods (development of mathematical intuition and its formal justification, training of the ability to abstract, proof techniques),
- improve their oral communication skills in the exercises by practicing free speech in front of an audience and during discussion.
None. The competences taught in the following modules are recommended: either Linear Algebra I and Linear Algebra II or Basic Linear Algebra, either Analysis I and Analysis II or Basic Real Analysis, Measure and Integration Theory.
- Friedrich Hirzebruch, Winfried Scharlau, Einführung in die
- Funktionalanalysis. BI-Wissenschaftsverlag, 1991.
- John B. Conway, A course in functional analysis. Springer-Verlag, 1990.
- Walter Rudin, Functional analysis. McGraw-Hill, 1991.
This page describes a module according to the latest valid module guide in Wintersemester 2021/22. Most rules valid for a module are not covered by the examination regulations and can therefore be updated on a semesterly basis. The following versions are available in the online module guide:
- WiSe 2016/17 (no corresponding element)
- SoSe 2018 (no corresponding element)
- WiSe 2018/19
- WiSe 2019/20
- WiSe 2020/21
- SoSe 2021
- WiSe 2021/22
- WiSe 2022/23
The module guide contains all modules, independent of the current event offer. Please compare the current course catalogue in Marvin.
The information in this online module guide was created automatically. Legally binding is only the information in the examination regulations (Prüfungsordnung). If you notice any discrepancies or errors, we would be grateful for any advice.