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.
5 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 expand and deepen their mathematical knowledge and skills in the field of Analysis and can apply them in yet another current research context.
Course type Lecture with tutorials:
The students master the basic contents and methods of a special subject area of Analysis, in particular they can independently carry out complex proofs in this area requiring a high level of mathematical expertise.
Furthermore, students recognise further-reaching connections to previously acquired mathematical facts. They can transfer and apply the knowledge and methods they have learnt so far to other, deeper mathematical problem areas. Students also expand their mathematical intuition through further and more intensive study.
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.
Course type Seminar:
Students are able to give a specialised mathematical presentation independently. They can independently develop a mathematical problem from Analysis, prepare it for a presentation and present it in an understandable way in the presentation and prepare a technically correct elaboration on the contents of the presentation. They will be able to independently fill any gaps, e.g. missing proofs/proof steps or missing illustrative examples.
With the seminar presentation and the preparation of the presentation, students develop both their ability to discuss and write mathematical texts. This prepares them further for the requirements of the Master's module, in particular the writing of the Master's thesis, the Master's seminar presentation including scientfic discussions and the defence of their Master's thesis.
Course type Project:
Students are able to plan, carry out and evaluate a specialised mathematical project (e.g. mathematical modelling of a concrete application situation, creation of a mathematical simulation, programming or software project, development of a mathematical treatise/mathematical materials as part of a reading course) in the field of Analysis, independently. In particular, they will have mastered the scientific content and methods required for the project, especially the independent proving of mathematical theorems.
The courses in this module lead to current research questions in the field of Analysis in terms of method and content. Possible contents include:
Depending on the chosen subject, the requirements will be specified in the course announcement.
—
In the module, students either attend a lecture with a tutorial or a seminar or carry out a project.
Module structure: 1 SL, 1 bPr 1
| Allocated examiner | Workload | LP2 |
|---|---|---|
|
Teaching staff of the course
Project Selected Topics in Analysis
(project)
Regular exchange and scientific discussion on the project, for example in the form of short reports on the project status and questions on further project design |
see above |
see above
|
|
Teaching staff of the course
Seminar Selected Topics in Analysis
(seminar)
Regular contributions to the scientific discussion in the seminar, for example in the form of comments and questions on the seminar presentations. |
see above |
see above
|
|
Teaching staff of the course
Tutorials Selected Topics in 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
|
(electronic) written examination in presence of usually 90 minutes, oral examination in presence or remote of usually 30 minutes, A remote electronic written examination is not permitted.
A corresponding product is created as part of the project ending date (e.g. mathematical model. simulation software, computer programme, treatise/materials). The project includes the planning, implementation and analysis of the project idea on a mathematical topic, the technically correct and comprehensible written description and evaluation (analysis) of the project, including essential mathematical contexts for the genesis and use of the product. The project must be 5-10 pages in length.
Correct and comprehensible presentation of a mathematical topic including essential steps of proof in a presentation, usually 90 minutes in length including a technical discussion.
Technically correct and comprehensible written elaboration of the presentation including essential proof steps, 5-10 pages in length.
If the module is taken together with module 24-M-AN-ST5a, the competences must have been acquired in different courses.
| 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.