Topological Data Analysis

On this page I have a number of items to get the interested reader started with persistent homology and topological data analysis. If you know linear algebra you are ready to start!

Introduction to Topological Data Analysis and Persistent Homology

Topological Data Analysis with R

If you want to get started doing topological data analysis.

Topological Data Analysis and Persistent Homology

Here are three recent introductory articles. If you want to learn more about the subject I would recommend starting here. The first two are mathematical, the third emphasizes connections to data science, and the fourth is more statistical.

There is a Wikipedia page.

The following slightly older introductory articles provide background, some mathematical details and a few applications.

The following are more technical summaries of some of the main results in the field.

For a serious introduction, I highly recommend the following new book. It is an excellent resource for mathematics graduate students wanting to learn the subject.