In this we examine the concept of the dimension of fractals, extending the idea of integer dimension to fractals, which we define and investigate here in. Moving on we consider the Minkowski dimension, sometimes referred to as the "box dimension", of a fractal. We then continue to define and examine another type of dimension; the Hausdorff dimension. We then investigate under what conditions these are equal finally moving on to prove Hutchinsons Theorem,
This project introduces the idea of recursive sequences. Students then prove that a given recursive sequence converges and find its limit. The final portion of the project is a derivation and investigation of the Fibonacci Sequence and the Golden Ratio.
A thesis template using the memoir class, which is mainly based on book class, but it's intended to look fancier and, above all, to get more control on environments as Figures, Tables, etc.. The template was designed to follow the University of Bristol thesis guidelines.
This template can be used for typesetting solutions to homework assignments.
We define a document class that includes a number of useful packages, defines shorthand macros for commonly used constructs and makes it easy to typeset answers to exercises. The template default content demonstrates how various tasks can be achieved in LaTeX as well: mathematical notation and many symbols, typesetting a table, including a figure, et cetera.