Part 1: “Homology” without Pre-requisites, except “Function” (he un-rigourously interchanges with “Mapping”, although Function is stricter with 1-and-only-1 Image) .

Part 2: Simplex (单纯形)

Topology History : Euler Characteristic eg. (V – E + R = 2) ,
Poincaré invention

This video uses Algebra of point, line, triangle… to explain a Simplex (plural: Simplices) in R^{n} Space, that is organizing the n-Dimensional “Big Data” data points into Simplices, then (future Part 3, 4…) compute the “holes” (or pattern called Persistent Homology).

Part 3: Boundary

Part 3 justifies why triangles (formed by any 3 data points) called “Simplex” 单纯形(plural: Simplices) are best to fill any Big Data Space.

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