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Modul
Fractal Geometry [M-MATH-105649]
Credits
6Recurrence
UnregelmäßigDuration
1 SemesterLanguage
German/EnglishLevel
4Version
2Responsible
Organisation
- KIT-Fakultät für Mathematik
Part of
Bricks
Identifier | Name | LP |
---|---|---|
T-MATH-111296 | Fractal Geometry | 6 |
Competence Certificate
The module will be completed with an oral exam (20 - 30 min).
Competence Goal
Students
- can name and explain important terms and concepts of fractal geometry;
- know important results of dimension theory and can apply them to examples;
- have the ability to use specific methods for the analysis of fractal structures;
- are able to construct fractals and random fractals with certain prescribed properties;
- master important proof techniques in fractal geometry and are able to at least sketch the more difficult proofs;
- are able to work self-organized and in a reflective manner;
- are prepared, to write a thesis in the field of fractal geometry.
Prerequisites
None
Content
- iterated function systems and self-similar sets
- chaos game algorithm
- random fractals
- fractal dimension theory
- Hausdorff measure and dimension
- packing measure and dimension
- Minkowski contents
- methods of computing dimension
- self-similar measures and multifractals
- dimension of measures
Recommendation
The contents of the courses Analysis 3 (measure theory) and Probability theory are recommended.
Workload
Total workload: 180 hours
Attendance: 60 h
- lectures, problem classes and examination
Self studies: 120 h
- follow-up and deepening of the course content,
- work on problem sheets,
- literature study and internet research on the course content,
- preparation for the module examination