MATH149
Course: Applied Algebraic Topology

General information

Times and place

Spring quarter 2012: April 2–June 6
Tuesday, Thursday 12:50–2:05pm in 200-303 (Lane History Corner)

Course announcement

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.

Prerequisites

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.

Textbook

The following textbook is recommended for reference:

Homework

Notes

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: math149-spr1112-all@lists.stanford.edu.

Links to resources

Course staff

Daniel Müllner, office 382V, e-mail: 
Office hours: Thursday 2:05–4pm.

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