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YouTube

Applied Topology - Introduction to Topological Data Analysis - 2020

Applied Algebraic Topology Network via YouTube

Overview

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Learn topological data analysis through this comprehensive video lecture series designed for undergraduate mathematics students with a linear algebra background. Explore fundamental concepts including simplicial and cubical complexes, filtrations, homology computation, and persistence diagrams through whiteboard-style presentations. Master the bottleneck distance metric and its triangle inequality property, then delve into the stability theorem that underpins topological data analysis. Discover the intersection of topology and statistics across three dedicated sessions that demonstrate practical applications. Access accompanying PDF materials of the whiteboard content to reinforce your understanding of these advanced mathematical concepts used in data analysis and computational topology.

Syllabus

Quick Review Part A Complexes and Filtrations - Damiano - 2020
Quick Review Part B Simplicial Complexes - Damiano - 2020
Quick Review Part C Computing Homology - Damiano - 2020
Intuitive Persistence - Damiano - 2020
Persistence Diagrams - Damiano - 2020
Bottleneck Distance - Damiano - 2020
Bottleneck Distance Triangle Inequality - Damiano - 2020
Stability Theorem - Damiano - 2020
TDA and Statistics I - Damiano - 2020
TDA and Statistics II - Damiano - 2020
TDA and Statistics III - Damiano - 2020
Introduction to Cubical Complexes and Persistence - Damiano - 2020

Taught by

Applied Algebraic Topology Network

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