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 concepts, results and methods of Stochastic Dynamics, i.e.: They can independently carry out very complex proofs in this area requiring a high level of mathematical expertise. They are able to derive large deviation principles . They can analyse the long-time behaviour and exit probabilities of diffusions and students are able to qualify and to quantify the effect of small random perturbations on time-continuous dynamical systems
Students will be introduced to research questions of current interest in the area of Stochastic Dynamics. They are able to recognise opportunities to further develop the theory and to assess research goals.
Furthermore, students recognise deeper connections to the mathematical knowledge they aquired earlier in their studies. They can transfer and apply the knowledge and methods they have learnt so far to more complex mathematical problems. Students also deepen their mathematical intuition as a result of more intensive study.
In combination with other in-depth modules, they will obtain the necessary skills to write their own research papers, e.g. a master's thesis in the field of Stochastic Dynamics.
In the tutorials, students further develop their ability to discuss mathematical topics and thus 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 topics from the field of Stochastic Dynamics are compulsory:
In addition, for example the following topics can be covered:
This module provides the required scientific knowledge for the preparation of a master's thesis.
The competences from 24-M-PT-PT2 are expected.
Basic knowledge of deterministic dynamical systems is recommended.
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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 Stochastic Dynamics
(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 | 2. o. 3. | one semester | Compulsory optional subject |
| Mathematical Economics / Master of Science [FsB vom 28.02.2025] | Economics | 2. o. 3. | one semester | Compulsory optional subject |
| Mathematics / Master of Science [FsB vom 28.02.2025] | 2. o. 3. | one semester | Compulsory optional subject |
The system can perform an automatic check for completeness for this module.