Functional Analysis

Module MA3001

This Module is offered by TUM Department of Mathematics.

This module handbook serves to describe contents, learning outcome, methods and examination type as well as linking to current dates for courses and module examination in the respective sections.

Basic Information

MA3001 is a semester module in English language at Master’s level which is offered in winter semester.

This Module is included in the following catalogues within the study programs in physics.

  • Catalogue of non-physics elective courses
Total workloadContact hoursCredits (ECTS)
270 h 90 h 9 CP

Content, Learning Outcome and Preconditions


Banach and Hilbert spaces; bounded linear operators, open mapping theorem; spectral theory for compact selfadjoint operators; duality, Hahn-Banach theorems; weak and weak* convergence; brief introduction to unbounded operators

Learning Outcome

After successful completion of the module students are able to understand and apply basic theoretical techniques to analyze linear functionals and operators on Banach and Hilbert spaces.


MA1001 Analysis 1, MA1002 Analysis 2, MA1101 Lineare Algebra 1, MA1102 Lineare Algebra 2

Courses, Learning and Teaching Methods and Literature

Courses and Schedule

VO 4 Functional Analysis [MA3001] Filbir, F.
Leitung/Koordination: Krause-Solberg, S.
Dienstag, 14:00–16:00
Freitag, 14:00–16:00
sowie einzelne oder verschobene Termine
UE 2 Exercises for Functional Analysis [MA3001] Filbir, F. Krause-Solberg, S. Termine in Gruppen

Learning and Teaching Methods

lecture, exercise module, assignments




W. Rudin, Functional Analysis, McGraw Hill, 1991. M. Reed/B. Simon, Functional Analysis, Academic Press, 1972. D. Werner: Funktionalanalysis, Springer, 2007. F. Hirzebruch, W. Scharlau: Einführung in die Funktionalanalysis, BI-Hochschulbücher, 1991.

Module Exam

Description of exams and course work

written exam

Exam Repetition

There is a possibility to take the exam at the end of the semester.

Current exam dates

Currently TUMonline lists the following exam dates. In addition to the general information above please refer to the current information given during the course.

Mi, 19.4.2017, 11:00 bis 12:30 MW: 1801
bis 3.4.2017 (Abmeldung bis 12.4.2017)
Fr, 3.3.2017, 16:00 bis 17:30 MW: 2001
bis 15.1.2017 (Abmeldung bis 24.2.2017)

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A journey of discovery to understanding our world at the subatomic scale, from the nuclei inside atoms down to the most elementary building blocks of matter. Are you ready for the adventure?


Biological systems, from proteins to living cells and organisms, obey physical principles. Our research groups in biophysics shape one of Germany's largest scientific clusters in this area.