Video of the lecture.

Started with a computer illustration of how persistent homology can be used to place some topological structure on a data set which might help an expert in the application domain interpret the data.

Then gave the precise definition of persistent homology and persistent Betti numbers.

Finished by stating that the computation of persistent Betti numbers boils down to nothing more than column reduction of a matrix to semi-echelon form.

Warning: I think I kept saying "row reduction" and "row echelon form" at the end of the lecture where I meant to say "column reduction" and "column echelon form". Apologies for that!