406-3461-AAL Functional Analysis I
| Semester | Autumn Semester 2018 |
| Lecturers | M. Einsiedler |
| Periodicity | every semester recurring course |
| Language of instruction | English |
| Comment | Enrolment ONLY for MSc students with a decree declaring this course unit as an additional admission requirement. Any other students (e.g. incoming exchange students, doctoral students) CANNOT enrol for this course unit. |
Courses
| Number | Title | Hours | Lecturers | |
|---|---|---|---|---|
| 406-3461-AA R | Functional Analysis I Self-study course. No presence required. | 300s hrs | M. Einsiedler |
Catalogue data
| Abstract | Baire category; Banach and Hilbert spaces, bounded linear operators; basic principles: Uniform boundedness, open mapping/closed graph theorem, Hahn-Banach; convexity; dual spaces; weak and weak* topologies; Banach-Alaoglu; reflexive spaces; compact operators and Fredholm theory; closed range theorem; spectral theory of self-adjoint operators in Hilbert spaces; Fourier transform and applications. |
| Learning objective | Acquire a good degree of fluency with the fundamental concepts and tools belonging to the realm of linear Functional Analysis, with special emphasis on the geometric structure of Banach and Hilbert spaces, and on the basic properties of linear maps. |
| Literature | We will be using the book Functional Analysis, Spectral Theory, and Applications by Manfred Einsiedler and Thomas Ward and available by SpringerLink. Other useful, and recommended references include the following: Lecture Notes on "Funktionalanalysis I" by Michael Struwe Haim Brezis. Functional analysis, Sobolev spaces and partial differential equations. Universitext. Springer, New York, 2011. Elias M. Stein and Rami Shakarchi. Functional analysis (volume 4 of Princeton Lectures in Analysis). Princeton University Press, Princeton, NJ, 2011. Peter D. Lax. Functional analysis. Pure and Applied Mathematics (New York). Wiley-Interscience [John Wiley & Sons], New York, 2002. Walter Rudin. Functional analysis. International Series in Pure and Applied Mathematics. McGraw-Hill, Inc., New York, second edition, 1991. |
Performance assessment
| Performance assessment information (valid until the course unit is held again) | |
Performance assessment as a semester course | |
| ECTS credits | 10 credits |
| Examiners | M. Einsiedler |
| Type | session examination |
| Language of examination | English |
| Repetition | The performance assessment is offered every session. Repetition possible without re-enrolling for the course unit. |
| Mode of examination | written 180 minutes |
| Additional information on mode of examination | Students are allowed to participate in the exercise class for the course unit 401-3461-00L and transfer the bonus *) to the course unit 406-3461-AAL. *) The active participation in the exercise class via presentations as a voluntary learning task will be graded and can improve the total course unit grade by up to 0.25 grade points. Students can still achieve the maximum grade of 6 in the course unit even if they only sit the final examination. |
| Written aids | None |
| This information can be updated until the beginning of the semester; information on the examination timetable is binding. | |
Learning materials
| Recording | lecture homepage |
| Literature | Book for Course |
| Only public learning materials are listed. | |
Groups
| No information on groups available. |
Restrictions
| There are no additional restrictions for the registration. |
Offered in
| Programme | Section | Type | |
|---|---|---|---|
| Mathematics Master | Course Units for Additional Admission Requirements | E- |  |