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This entry is from Summer semester 2018 and might be obsolete. No current equivalent could be found.
Functional Analysis
(dt. Funktionalanalysis)
Level, degree of commitment | Specialization module, compulsory elective module |
Forms of teaching and learning, workload |
Lecture (4 SWS), recitation class (2 SWS), 270 hours (90 h attendance, 180 h private study) |
Credit points, formal requirements |
9 CP Course requirement(s): Written or oral examination Examination type: Successful completion of at least 50 percent of the points from the weekly exercises. |
Language, Grading |
German,The grading is done with 0 to 15 points according to the examination regulations for the degree program M.Sc. Mathematics. |
Duration, frequency |
One semester, Regularly alternating with other specialization modules im Gebiet Analysis |
Person in charge of the module's outline | Prof. Dr. Ilka Agricola, Prof. Dr. Stephan Dahlke, Prof. Dr. Pablo Ramacher |
Contents
- 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
Qualification Goals
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.
Prerequisites
Translation is missing. Here is the German original:
Keine. Empfohlen werden die Kompetenzen, die in den Basismodulen Analysis und Lineare Algebra sowie im Modul Maß- und Integrationstheorie vermittelt werden.
Applicability
Module imported from M.Sc. Mathematics.
It can be attended at FB12 in study program(s)
- B.Sc. Computer Science
- B.Sc. Mathematics
- B.Sc. Business Mathematics
- M.Sc. Computer Science
- M.Sc. Mathematics
- M.Sc. Business Mathematics
- LAaG Mathematics
When studying B.Sc. Computer Science, this module can be attended in the study area Minor subject Mathematics.
Recommended Reading
- 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.
Please note:
This page describes a module according to the latest valid module guide in Summer semester 2018. 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:
- Winter 2016/17
- Summer 2018
- Winter 2018/19
- Winter 2019/20
- Winter 2020/21
- Summer 2021 (no corresponding element)
- Winter 2021/22 (no corresponding element)
- Winter 2022/23 (no corresponding element)
- Winter 2023/24 (no corresponding element)
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.