Course Category：Professional Basic Course
Prerequisites：Elementary of functions of real variables, Probability theory.
Aims & Requirements：
This course is concerned with the general theory of fractals and their geometry.
Mathematical background: Basic set theory; Functions and limits; Measures and mass; Box-counting dimensions, Hausdorff measures and dimension, Iterated function systems, Graphs of functions, Dynamical systems: Repellers and iterated function systems, The logistic map; Iteration of complex functions: Sketch of general theory of Julia sets.
Fractal Geometry: Mathematical Foundations and applications, K.Falconer, translated by Wenqu Zeng, Posts and Telecom Press, 2007.
 Fractal theory and its application, Xia Sun, Ziqin Wu and Yun Huang, China Science and Technology University Press, 2003.
Author：Junxiao Zhao (School of Mathematical Sciences, GUCAS)