Iteration and Visualization
Contents
In this course we will learn how to use techniques from algebra, geometry and analysis to visualize mathematical concepts. The course is built around three themes that each take 1 week to complete. For each of these themes, a number of topics are discussed about which a lesson in mathematical theory is given and a lesson on how to implement this mathematical technique on the computer. Each lesson the students work through a worksheet on each topic in Jupyter and make an image, which they collect in a portfolio. In the penultimate week they choose a topic that belongs to one of the themes and they make a poster about it in groups in the last week.
Topics
 Python Imaging Library
 Affine Transformations
 Tilings of the plane
 Ray tracing
 Moebius Transformations
 Tikz
 IFSfractals
 Julia and Mandelbrot sets
 Random Surfaces
 Fourier transforms
 Fast Fourier transform
 Convolution filters
 Harmonic Functions
Study Material

Notebooks
A zipfile with all jupyter notebooks is available 
honours version
The honours version contains a more in depth treatment of the topics
Learning goals
 recognize transformations of the plane, implement them in python and use them to generate symmetric patterns.
 make a projection of a threedimensional geometric object from different orientations.
 generate an IFS fractal and determine its Hausdorff dimension.
 Julia, Mandelbrot and NewtonRaphson generate fractals and illustrate the relationships between them.
 describe and approximate a curve and surfaces in polar and spherical coordinates using Fourier transforms.
 implement and use the FFT algorithm to manipulate images
 Apply graphical techniques in python and use new libraries.
 Create a poster that explains a mathematical idea clearly and visually.