Playlist: https://www.youtube.com/playlist?list=PLOROtRhtegr7DmeMyFxfKxsljAVsAn_X4
We introduce the notion of the degree of a map from S^n to S^n. As a nice application, we use degree to prove the Hairy Ball Theorem. Then we develop cellular homology, another homology theory equivalent to simplicial and singular homology. We show how to calculate the cellular homology of the torus and Klein bottle.
Presented by Anthony Bosman, PhD.
Learn more about math at Andrews University: https://www.andrews.edu/cas/math/
In this course we are following Hatcher, Algebraic Topology: https://pi.math.cornell.edu/~hatcher/AT/AT.pdf