This course is on Mondays 10-11.45, Wednesdays
13.15-15.00, and Thursdays 15.00-16.45.
Location is MVH-12 on Mondays and Thursdays, MVF-21 on
Wednesdays.

The topics are as follows:
1. Algebras, sigma algebras, measures, and outer measures.
2. Completion of a measure, creating a measure from
an outer measure, and pre-measures.
3. Pre-measure extension theorem and metric outer
measures.
4. Metric outer measures.
5. Canonical metric outer measures and Hausdorff
measure.
6. Hausdorff dimension.
7. Self-similarity and Hausdorff dimension.
8. Similitudes, Hausdorff and Lebesgue measures,
and Urysohn's Lemma,
9. Similitudes and iterated function systems.
10. The canonical invariant measure of an IFS
fractal.
11. The Hausdorff dimension of an IFS fractal and an
introduction to complex dynamics. Notes
on the fundamentals of complex analysis (auf Deutsch)
12. Complex dynamics on the disk, plane, and sphere.
13. Fixed points.
14. Conformal conjugation at attracting and
repelling fixed points.
15. Super attracting fixed points, irrationally
neutral fixed points, and rational iteration.
16. The Fatou and Julia sets of rational functions.
17. Julia sets of rational functions:
properties and fractal nature.
18. The Mandelbrot set.

Lecture notes which include an extensive collection of
exercises shall be posted after each lecture.

Examination shall be one of the following (your
choice): (A) Research project and presentation (can
be done in a group or individually), (B) Oral exam, (C)
Written exam.