Dieses Modul ist Teil einer langfristigen Gesamtlehrplanung für das Masterprogramm, die sicherstellt, dass in allen fünf Gebieten jedes Jahr jeweils mindestens Module im Umfang von 20 LP angeboten werden. Im Rahmen dieser Gesamtlehrplanung wird das Modul in unregelmäßigen Abständen angeboten.
10 Credit points
For information on the duration of the modul, refer to the courses of study in which the module is used.
Non-official translation of the module descriptions. Only the German version is legally binding.
Students master advanced content and methods of Harmonic Analysis, in particular they can independently carry out very complex proofs in this area requiring a high level of mathematical expertise.
The students are introduced to fine properties of real-variable functions. They are able to recognise fundamental operators in real analysis such as the maximal functions, the Fourier transform, and integral operators arising as fundamental solutions of PDEs. They are able to prove boundedness of such operators, and to employ methods of Fourier analysis which is important for the in-depth analysis of partial differential equations.
Students will be introduced to current research questions in the area of Harmonic Analysis. They are able to recognise and assess further development opportunities and research goals.
Furthermounregelmäßigre, students recognise further-reaching connections to mathematical issues that have already been worked out. They can transfer and apply the knowledge and methods they have learnt so far to deeper mathematical problem areas. Students also expand their mathematical intuition as a result of more intensive study.
In combination with other in-depth modules, they will be able to write their own research papers, e.g. a master's thesis in the field of Harmonic Analysis.
In the tutorials, students develop their ability to discuss mathematical topics and thus further prepare themselves for the requirements of the Master's module, in particular for the scientific discussion within the Master's seminar presentation and the defence of their Master's thesis.
The following advanced content of teaching from the field of Harmonic Analysis is compulsory:
Interpolation, maximal functions, tempered distributions, Fourier analysis, oscillatory integrals and the method of stationary phase, Calderon-Zygmund theory of singular integrals, Fourier multipliers, Littlewood-Paley theory, introduction to pseudodifferential operators
In addition, the following content of teaching can be covered, for example:
Fourier restriction or Strichartz estimates, Infinitely divisible distributions and Levy-Khintchine formula
This module prepares the content of a master's thesis.
Real Analysis, Measure and Integration Theory, Lebesgue spaces, basics knowledge of Elliptic Partial Differential Equations
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Module structure: 1 SL, 1 bPr 1
| Allocated examiner | Workload | LP2 |
|---|---|---|
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Teaching staff of the course
Tutorials Harmonic Analysis
(exercise)
Regular completion of the exercises, each with a recognisable solution approach, as well as participation in the exercise groups for the module's lecture. As a rule, participation in the exercise group includes presenting solutions to exercises twice after being asked to do so as well as regular contributions to the scientific discussion in the exercise group, for example in the form of comments and questions on the proposed solutions presented. The organiser may replace some of the exercises with face-to-face exercises. |
see above |
see above
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(electronic) written examination in presence of usually 120 minutes, oral examination in presence or remote of usually 40 minutes, A remote electronic written examination is not permitted.
| Degree programme | Profile | Recommended start 3 | Duration | Mandatory option 4 |
|---|---|---|---|---|
| Mathematical Economics / Master of Science [FsB vom 28.02.2025] | Mathematics | 1. o. 2. o. 3. | one semester | Compulsory optional subject |
| Mathematical Economics / Master of Science [FsB vom 28.02.2025] | Economics | 1. o. 2. o. 3. | one semester | Compulsory optional subject |
| Mathematics / Master of Science [FsB vom 28.02.2025] | 1. o. 2. o. 3. | one semester | Compulsory optional subject |
The system can perform an automatic check for completeness for this module.