What stories, puzzles, games, paradoxes, toys, etc from everyday life are better understood after learning homology theory? To be more precise, I am teaching a short course on homology, from ...
I'm teaching an elementary class about fundamental groups and covering spaces. It was very useful to use "fool's covering spaces" of a space $X$, defined as functors $\Pi_1(X)\to Sets$, where ...
I'm helping to teach an undergraduate algebraic geometry course (out of Hatcher's textbook). We have recently defined the degree of a map of spheres using homology, and the professor and I thought it ...
Background and motivation: I am teaching the "covering space" section in an introductory algebraic topology course. I thought that, in the last five minutes of my last lecture, I might briefly sketch ...
A first course in algebraic topology, at least the ones I'm familiar with, generally gets students to a point where they can calculate homology right away. Building the theory behind it is generally ...