Fractal Geometry - Mathematical Foundations and Applications

1. Mathematical background
2. Hausdorff measure and dimension
3. Alternative definitions of dimension
4. Techniques for calculating dimensions
5. Local structure of fractals
6. Projections of fractals
7. Products of fractals
8. Intersections of fractals
9. Fractals defined by transformations - self similar and self-affine sets
10. Examples from number theory
11. Graphs of functions
12. Examples from pure mathematics
13. Dynamical systems
14. Iteration of complex functions - Julia sets
15. Random fractals
16. Brownian motion and Brownian surfaces
17. Multifractal measures
18. Physical applications