Visualization in Mathematics (Summer 2019)

This course is a BMS advanced course and the lectures will be in English. Please feel free to ask any questions in English or German.

News

• For the tutorial a laptop is required. To speed things up it is recommended to install (or at least download) the Houdini apprentice version before the first tutorial.

Contents

We will learn how to set up mathematical experiments and visualizations, taking examples from the theory of smooth and discrete surfaces. Some knowledge of Geometry or Differential Geometry would be helpful, but it also could be acquired in the course of the class. The tutorials will be based on the free version of Houdini (SideFX), which is the leading modeling and rendering software for motion pictures. If needed, this class can also be taken as Geometrie III or Differentialgeometrie III.

A free version of Houdini can be downloaded from here. The programming languages we use will be python and VEX.

Material

There is a course blog where also tutorials and homework exercises will be published.

For questions on Houdini and programming vex see the Houdini Tech Blog (an extended version of the DDG2016 blog). Other useful blogs are the following:

• Visualization in mathematics - TU Berlin Summer 2018
• Discrete Differential Geometry - Carnegie Mellon Spring 2016
• Mathematische Visualisierung - TU Berlin im Sommer 2013
• Discrete Differential Geometry - Caltech im Herbst 2011
• Mathematische Visualisierung - TU Berlin im Winter 2010

• Seifert, Threlfall: Lehrbuch der Topologie, Teubner 1934. [pdf]
• J. R. Munkres: Elements of Algebraic Topology, Perseus Books 1984.

Homework policy

There will be small programming projects every week. Depending on the number of students they should be turned in by groups of two students.