modules

Fractal geometry is the study of certain irregular sets (called fractals), which arise naturally in many branches of mathematics such as Dynamical Systems and Ergodic Theory, Diophantine Approximation, and Analysis, and which are used to model natural phenomena in the natural sciences. The importance and ubiquity of these irregular sets is a significant realization of modern mathematics. Unlike the more familiar sets from classical geometry, these irregular sets are not, in general, amenable to the techniques of classical calculus. Instead, new ideas, especially from measure theory, are required to understand their properties.

This module aims to give an introduction to fractals, to develop basic tools for their study, especially various notions of dimension, and to give applications to other fields of mathematics, especially Diophantine approximation, and Dynamical Systems and Ergodic Theory. The basic notions of measure, box dimension, Hausdorff dimension, etc., will be introduced and developed. Important examples of fractals will be introduced and studied. In every section covered in this module, we will start by studying the definitions and then we will present examples and some basic properties. Some important theorems will be stated and proved. With this module you will have the opportunity to further refine your skills in problem-solving, axiomatic reasoning and the formulation of mathematical proofs.

Pre-requisite Module: MTH2001 or MTH2008  

_{Please note that all modules are subject to change, please get in touch if you have any questions about this module.}