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| Detailed information |
| Original study plan |
Bachelor's programme Technical Mathematics 2025W |
| Learning Outcomes |
Competences |
| Students are familiar with various types of fractals and can apply methods of analysis and probability theory to them.
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| Skills |
Knowledge |
- Define iterated function systems and determine their Hausdorff dimension
- Calculate and manage conditional expectations
- Know and apply general properties of Brownian motion
- Know and apply ergodic theorems (to fractals)
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Iterated function systems, Hausdorff measure, Hausdorff dimension, self-similar sets, Markov chains, ergodic theorems, normal numbers, Brownian motion, Julia sets, Mandelbrot set
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| Criteria for evaluation |
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| Language |
English and French |
| Study material |
(*)- Die Bücher 'The geometry of fractal sets', 'Fractal geometry' und 'Techniques in fractal geometry' von Kenneth Falconer.
- Das Paper 'An ergodic theorem for iterated maps' von John H. Elton
- Das Buch 'Fractals everywhere' von Michael Barnsley
- Das Buch 'Fraktale und Julia-Mengen' von Dufner, Roser, Unseld
- Das Paper 'Fractals and self-similarity' von John Hutchinson
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| Changing subject? |
No |
| Further information |
The lecture can be held in English if desired. But the lecture notes are in German.
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| Earlier variants |
They also cover the requirements of the curriculum (from - to)
TM1WAVOFRAK: VO Fractals (1991S-2024S)
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