Long in the making, the online course on expanders starts today.

In the first week of class: what are the topics of the course, and how to prove that the eigenvalues of the adjacency matrix of a regular graph tell you how many connected components there are in the graph.

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I’m curious what the Stanford math department thinks of MOOCs? Looking at e.g. Coursera, there’s a ton of CS material there, but almost a total vacuum of math. The only exception is Rob Ghrist’s class, but that’s only an intro calculus class.

Top math programs in the country e.g. teach the same year-long graduate courses in analysis, algebra and geometry year after year. The professors I’ve talked to seem to not care about MOOCs at all. It’s sort of strange, since our department has both good and, unfortunately, bad teachers. Every year one specific professor has taught algebraic topology, a large chunk of the incoming Ph.D. class has decided to choose that as a research field, so having a good class in a subject makes a world of difference.

Video lectures would seem to provide a great way to provide visualizations of things that are very hard to do on the black board. Of course, it probably means enlisting a students that can do all the animations for the professor, but it would seem to be a much better way to teach people how to think about e.g. topology and geometry in terms of pictures.

I’m really looking forward to seeing how this medium works for a research-level class. I’ve looked at a few MOOCs and some of them, e.g. Dan Boneh’s crypto, was really well done and really made use of the new medium.

Thanks for the thoughtful comments.