Course: Applied Algebraic Topology
Times and place
Spring quarter 2012: April 2–June 6
Tuesday, Thursday 12:50–2:05pm in 200-303 (Lane History Corner)
Topology has in recent years spread out from its roots in pure mathematics and provided key ideas to a new discipline at the intersection with computer sciences and applied statistics. All these fields work together to create new methods that can be applied to understand data in life sciences, chemistry and elsewhere.
Starting with minimal prerequisites, this course will teach the main concepts in Applied Algebraic Topology. This comprises in particular persistent homology as the most prominent tool for data analysis with topological methods. Compared to a standard first course in topology, we will trade some of the breadth and maximal generality for a more selective path through the subject to reach the main goal of this course: understanding the theory of persistent homology and gaining practical skills to analyze and describe the shape of concrete data sets.
Linear Algebra. Topology is not required, as all necessary concepts are developed in the course. Students with prior knowledge of topology and higher algebra are equally welcome, as they will be able to appreciate some concepts in greater generality and enjoy connections from a higher point of view.
The following textbook is recommended for reference:
- Herbert Edelsbrunner, John L. Harer
Computational Topology: An Introduction
- Problem set 1, due May 1
- Problem set 2, due May 15
- Problem set 3, due May 22
- Problem set 4, due May 29
April 17: Suggestions for mini-projects are out
April 10: we have a mailing list which is updated daily and automatically with all students who have registered for the course: firstname.lastname@example.org.
Links to resources
- Computational Topology group at Stanford: http://comptop.stanford.edu (Broken link as of May 2015!)
- Unix computing at Stanford: http://farmshare.stanford.edu
- MATLAB help: try the “Getting Started” section in the MATLAB documentation or the PDF user's guide available at MathWorks' MATLAB Tutorials and Learning Resources
- Persistent homology computations: javaPlex
- Memory problems with javaPlex? Increase the Java VM heap space!
Daniel Müllner, office 382V, e-mail:
Office hours: Thursday 2:05–4pm.