It’s about time we got back to computational topology. Previously in this series we endured a lightning tour of the fundamental group and homology, then we saw how to compute the homology of a simplicial complex using linear algebra. What we really want to do is talk about the inherent shape of data. Homology allows us to compute some qualitative features of a given shape, i.e., find and count the number of connected components or a given shape, or the number of “2-dimensional holes” it has....