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I am a graduate student in mathematics interested in Persistent Homology.

Can anyone recommend any good books / resources to self study Persistent Homology?

I am taking a course in Algebraic Topology, studying the book by Hatcher.

Thanks a lot for any help. (Persistent Homology is quite a new subject hence there is not much literature on it)

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    $\begingroup$ I'm no expert in the subject, but this is a fantastic video explaining the gist of it. $\endgroup$ – Mnifldz Oct 12 '15 at 3:30
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    $\begingroup$ Aside from the important articles in that Video's description. You might like to begin with "Topology for Computer", Zomorodian. Although slightly outdated, it is very accessible! $\endgroup$ – Weaam Oct 12 '15 at 4:21
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    $\begingroup$ Oops, I meant Topology for Computing, Afra J. Zomorodian. Sorry! $\endgroup$ – Weaam Oct 12 '15 at 5:57
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    $\begingroup$ I'm not an expert, but I would expect that a solid background in algebraic topology would be more than helpful before attacking persistent homology. $\endgroup$ – Najib Idrissi Oct 12 '15 at 11:01
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For a quick introduction, you can read this AMS survey.

http://www.ams.org/notices/201101/rtx110100036p.pdf

A basic notion in persistent homology is a barcode. The following article gives an introduction to the subject with an emphasis on shape recognition, and tells you what a barcode its.

https://www.math.upenn.edu/~ghrist/preprints/barcodes.pdf

Here is another introductory survey article giving you more background material about the theory and implementation of persistent homology. This one also talks about some heavier stuff from algebraic topology, like spectral sequences.

http://pub.ist.ac.at/~edels/Papers/2008-B-02-PersistentHomology.pdf

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