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263-4510-00L 8 Credits BSC , MSC , WBZ D-ITET , D-INFK , D-MATH
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Introduction to Topological Data Analysis

Lecturers & Examiners: Dr. Patrick Schnider
VVZ CR n/a

Last Updated: 2026-02-05 16:38:53

Abstract

Topological Data Analysis (TDA) is a relatively new subfield of computer sciences, which uses techniques from algebraic topology and computational geometry and topology to analyze and quantify the shape of data. This course will introduce the theoretical foundations of TDA.

Objective

The goal is to make students familiar with the fundamental concepts, techniques and results in TDA. At the end of the course, students should be able to read and understand current research papers and have the necessary background knowledge to apply methods from TDA to other projects.

Content

Mathematical background (Topology, Simplicial complexes, Homology), Persistent Homology, Complexes on point clouds (Čech complexes, Vietoris-Rips complexes, Delaunay complexes, Witness complexes), the TDA pipeline, Reeb Graphs, Mapper

Resources

Literature

Main reference: Tamal K. Dey, Yusu Wang: Computational Topology for Data Analysis, 2021 https://www.cs.purdue.edu/homes/tamaldey/book/CTDAbook/CTDAbook.html Other references: Herbert Edelsbrunner, John Harer: Computational Topology: An Introduction, American Mathematical Society, 2010 https://bookstore.ams.org/mbk-69 Gunnar Carlsson, Mikael Vejdemo-Johansson: Topological Data Analysis with Applications, Cambridge University Press, 2021 Link Robert Ghrist: Elementary Applied Topology, 2014 https://www2.math.upenn.edu/~ghrist/notes.html Allen Hatcher: Algebraic Topology, Cambridge University Press, 2002 https://pi.math.cornell.edu/~hatcher/AT/ATpage.html

Learning Materials (Links)

General Information

Language
English
Levels
BSC , MSC , WBZ
Frequency
Yearly recurring

Examination

Type
session examination
Mode
oral 30 minutes
60% final oral exam: 30 minutes oral exam with 30 minutes preparation time (no material allowed) plus two graded homework (20% each). The two mandatory graded homework (compulsory continuous performance assessments) will be released throughout the semester, at specific dates that will be announced. Each graded homework will have a deadline two weeks after the release.The solutions must be typeset in LaTeX (or similar).

Course Components

Type Title Time & Place Hours
lecture Introduction to Topological Data Analysis
  • Thu 13:15-14:00 (CAB G 51)
  • Fri 12:15-14:00 (CAB G 61)
3 h weekly
exercise Introduction to Topological Data Analysis
  • Wed 10:15-12:00 (CHN F 46)
2 h weekly
independent project Introduction to Topological Data Analysis No time listed 2 h weekly

Offered In