Edit resource "Homology Theory — A Primer" Accepted
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Update Homology Theory — A Primer
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 Homology Theory — A Primer
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 Homology Theory — A Primer
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 Web
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 Web
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 20130404
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 20130404
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 This series on topology has been long and hard, but we’re are quickly approaching the topics where we can actually write programs. For this and the next post on homology, the most important background we will need is a solid foundation in linear algebra, specifically in rowreducing matrices (and the interpretation of rowreduction as a change of basis of a linear operator). Last time we engaged in a whirlwind tour of the fundamental group and homotopy theory. And we mean “whirlwind” as it sounds; it was all over the place in terms of organization. The most important fact that one should take away from that discussion is the idea that we can compute, algebraically, some qualitative features about a topological space related to “ndimensional holes.”
 At edit time
 This series on topology has been long and hard, but we’re are quickly approaching the topics where we can actually write programs. For this and the next post on homology, the most important background we will need is a solid foundation in linear algebra, specifically in rowreducing matrices (and the interpretation of rowreduction as a change of basis of a linear operator). Last time we engaged in a whirlwind tour of the fundamental group and homotopy theory. And we mean “whirlwind” as it sounds; it was all over the place in terms of organization. The most important fact that one should take away from that discussion is the idea that we can compute, algebraically, some qualitative features about a topological space related to “ndimensional holes.”
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 https://jeremykun.com/2013/04/03/homologytheoryaprimer/
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 https://jeremykun.com/2013/04/03/homologytheoryaprimer/
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Add Topological Data Analysis
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 Topological Data Analysis
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 Introductory Topological Data Analysis (TDA) course that includes notes and class videos as well as practice assignments.
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 https://www.enseignement.polytechnique.fr/informatique/INF556/index.html
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 INF556
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Add Topology
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 Topology
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 In mathematics, topology (from the Greek words τόπος, 'place, location', and λόγος, 'study') is concerned with the properties of a geometric object that are preserved under continuous deformations, such as stretching, twisting, crumpling and bending, but not tearing or gluing. A topological space is a set endowed with a structure, called a topology, which allows defining continuous deformation of subspaces, and, more generally, all kinds of continuity. Euclidean spaces, and, more generally, metric spaces are examples of a topological space, as any distance or metric defines a topology. The deformations that are considered in topology are homeomorphisms and homotopies. A property that is invariant under such deformations is a topological property.
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 https://en.wikipedia.org/?curid=29954
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Add Topological data analysis
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 Topological data analysis
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 Topological data analysis (TDA)
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 In applied mathematics, topological data analysis (TDA) is an approach to the analysis of datasets using techniques from topology. Extraction of information from datasets that are highdimensional, incomplete and noisy is generally challenging. TDA provides a general framework to analyze such data in a manner that is insensitive to the particular metric chosen and provides dimensionality reduction and robustness to noise. Beyond this, it inherits functoriality, a fundamental concept of modern mathematics, from its topological nature, which allows it to adapt to new mathematical tools. The initial motivation is to study the shape of data. TDA has combined algebraic topology and other tools from pure mathematics to allow mathematically rigorous study of "shape". The main tool is persistent homology, an adaptation of homology to point cloud data. Persistent homology has been applied to many types of data across many fields.
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 https://en.wikipedia.org/?curid=17740009
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Add Homology is treated in Homology Theory — A Primer
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Add Topological data analysis is treated in Topological Data Analysis
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Add Topology relates to Homology
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Add Topology a tool for Topological data analysis
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