- Hahn-Banach theorem and its applications,
- Baire category theorem and its applications (uniform boundedness principle, Banach-Steinhaus-Theorem, open mapping theorem, inverse mapping theorem, closed graph theorem),
- Weak convergence (Banach-Alaoglu theorem, reflexive Banach spaces, Mazur lemma and its applications),
- Projections (closed complement theorem),
- Bounded operators (adjoint operator, spectrum, resolvent, normal operators),
- Compact operators (Fredholm operators, Fredholm alternative and its applications, spectral theorem(Riesz-Schauder) and its application to normal operators),
- Unbounded operators (graph, symmetric and self-adjoint operators).
Functional Analysis (M, 9.0 LP)
|Module Number||Module Name||CP (Effort)|
|MAT-70-11-M-4||Functional Analysis||9.0 CP (270 h)|
|CP, Effort||9.0 CP = 270 h|
|Position of the semester||1 Sem. in SuSe|
|Level|| Bachelor (Specialization)|
|Area of study||[MAT-SPAS] Analysis and Stochastics|
|Reference course of study||[MAT-88.105-SG] M.Sc. Mathematics|
|Type/SWS||Course Number||Title||Choice in |
|SL||SL is |
required for exa.
|P||84 h||186 h||
- About [MAT-70-11-K-4]: Title: "Functional Analysis"; Presence-Time: 84 h; Self-Study: 186 h
- About [MAT-70-11-K-4]: The study achievement [U-Schein] proof of successful participation in the exercise classes (ungraded) must be obtained.
Examination achievement PL1
- Form of examination: oral examination (20-30 Min.)
- Examination Frequency: each semester
- Examination number: 84210 ("Functional Analysis")
Evaluation of grades
The grade of the module examination is also the module grade.
Competencies / intended learning achievements
By completing exercises, the students have developed a skilled, precise and independent handling of the terms, propositions and techniques taught in the lecture. In addition, they have learnt how to apply these techniques to new problems, analyze them and develop solution strategies.
- H.-W. Alt: Lineare Funktionalanalysis,
- H. Heuser: Funktionalanalysis,
- M. Reed, M, B. Simon: Functional Analysis I,
- D. Werner: Funktionalanalysis.
Requirements for attendance (informal)
- [MAT-12-23-K-3] Introduction to Functional Analysis (2V+1U, 4.5 LP)
- [MAT-12-28-K-3] Measure and Integration Theory (2V+1U, 4.5 LP)
Requirements for attendance (formal)
References to Module / Module Number [MAT-70-11-M-4]
|Course of Study||Section||Choice/Obligation|
|[MAT-88.B84-SG] M.Sc. Actuarial and Financial Mathematics||Statistics and Computational Methods||[WP] Compulsory Elective|
|[MAT-88.105-SG] M.Sc. Mathematics||Pure Mathematics||[WP] Compulsory Elective|
|[MAT-88.105-SG] M.Sc. Mathematics||Applied Mathematics||[WP] Compulsory Elective|
|[MAT-88.706-SG] M.Sc. Mathematics International||Pure Mathematics||[WP] Compulsory Elective|
|[MAT-88.706-SG] M.Sc. Mathematics International||Applied Mathematics||[WP] Compulsory Elective|
|[MAT-88.118-SG] M.Sc. Industrial Mathematics||General Mathematics||[WP] Compulsory Elective|
|[MAT-88.276-SG] M.Sc. Business Mathematics||General Mathematics||[WP] Compulsory Elective|