An audio version of the slides is available <a href="uploads/lecture2.mkv">here</a>.
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Introduced, in an informal way, the notion of persistence of 1-dimensional holes in a data set, and explained how this persistence can be represented using barcodes.

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Ended up with the definition of the degree n homology vector space H<sub>n</sub>(K) of a simplicial complex K. For finite K this vector space has finite dimension equal to the Betti number &beta;<sub>n</sub>(K).