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Topics in Mathematics, III
We will mainly use the following book:
Fractal Geometry: Mathematical Foundations and Applications, Second Edition. Author: Kennet Falconer. Edited by: John Wiley & Sons, 2004.
You will have four homework during the semester.
The plan is to cover the following topics:
-Introduction to Fractal. Examples will be given.
-Basic set theory, Functions and limits, Measures and mass distributions.
-Box-counting dimensions, Properties of box-counting dimensions.
-Hausdorff measure, Hausdorff dimension, Calculation of Hausdorff dimension, Basic methods of calculating dimensions.
-Iterated function systems, Dimensions of self-similar sets, Some variations, Continued fraction examples.
-Graphs of Dimensions of graphs, the Weierstrass function and self-affine graphs.
-Repellers and iterated function systems, The logistic map.
-Sketch of general theory of Julia sets, The Mandelbrot set,Julia sets of quadratic functions.
The plan might change during the semester due to time restrictions or guided by your specific interests.
The first lecture will be next Tuesday, January 18 at 3PM. Here is the link to the full schedule
TimeEdit Kungliga Tekniska högskolan - SF2723-1 (VT22), Topics in Mathematics I...
You will have four homework during the semester, aiming le understanding of the course.
Schedule of the homework:
1st homework: given 1/2, deadline 8/2
2nd homework: given 22/2, deadline 1/3
3rd homework: given 29/3, deadline 5/4
4th homework: given 26/4, deadline 3/5
Problem Classes
The lectures on 4/3 and 6/5 will be partially devoted to solve exercises.