Module 1 (8 hours) Review of basic metric spaces, Hausdorff metric, Transformation on metric spaces, Contraction mapping, The contraction mapping theorem, The space of fractals, Classical fractals.
Module 2 (10 hours) Iterated function system, Attractor, Construction of fractals, Collage theorem, Self-similarity.
Introduction to dynamical systems, The address of points on fractals, Equivalent dynamical systems, Chaotic dynamics on fractals, Code space.
Module 3 (10 hours) Fractal dimension, Hausdorff Measure, Properties of box and Hausdorff dimension, Dimension of self-similar fractals, measure on fractals.
Module 4 (8 hours) Construction of fractal interpolation functions, Fractal dimension of fractal interpolation functions, Fractal splines, Fractal Surfaces.

To give a better perspective and understanding of the general area of fractal geometry and its relationship to other aspects of analysis, geometry and dynamical systems

To study the properties of several fractal dimensions

To develop skills and techniques that will allow them to study many areas where Fractal Geometry plays a role, including analytic number theory, engineering, and ergodic theory

To introduce the construction of fractals, fractal functions, surfaces and dynamics on fractals

CO1: Students will be familiar with the different constructions of fractal sets, including several explicit constructions, and the different notions of dimension available to describe them.
CO2: Students will learn to construct fractals and the chaotic dynamics of fractals.
CO3: Students will learn several fractal dimension techniques.
CO4: Students will learn to construct fractal functions and their dimensions.
CO5: They will be able to approximate irregular structures and non-smooth functions.

Michael F. Barnsley, Fractals Everywhere, Academic Press , 1988

K. Falconer, , Fractal geometry: mathematical foundations and applications, Wiley , 2003

Gerald A. Edger, Measure Topology, and Fractal Geometry, Springer-Verlag , 1990

. Heinz O. Peitgen, Hartmut Jürgens, Dietmar Saupe, Chaos and Fractals, New Frontiers of Science, Springer , 2004