The n-Category Café

You’re absolutely right; I shouldn’t have overlooked that factor! Galois theory is such an amazing story.

Thanks!

Here’s the story. I first taught the course in spring 2021, which in Edinburgh was the second fully locked down semester of teaching. What this meant was that by the time I came to design my course, we’d already had plenty of feedback from the students about the challenges of learning in lockdown. One point that came out strongly was that many students found it hard to know whether they were making adequate progress. I guess attending class in person and being around your classmates gives you reassurance that you’re doing OK, and the absence of that was leading to insecurity.

To try to do something about this problem, I came up with the idea of a random multiple choice quiz that you could take any time, with ten random questions each time you took it. It was called the “How am I doing?” quiz. The “I” refers to the student, not me — it’s not like “How’s my driving?” :-)

As for how I had the energy to write 477, they just came pouring out. Most of them are true/false statements, which are easy enough to come up with. With ten weeks in the semester, that’s only 40–50 per week. I didn’t set myself a goal of how many to write, and there was only one section of the class. That was just how many I thought of. I found it quite pleasant, and infinitely less work than writing the notes or recording the videos.

Thanks! Glad to have piqued your interest.

Right, agreed! See my reply to Asvin above. Galois theory is a hugely appealing subject.

Personally, as an undergraduate I loved linear algebra. Well, I didn’t much like the first-year course on it (a mishmash of matrix methods and linear transformations), but the second-year course on the abstract theory of finite-dimensional vector spaces lit up my world. We were lucky enough to have a lecturer who didn’t hold back from letting the abstract beauty shine through. For example, he went carefully through the theory of dual vector spaces, and even now I can’t put into words how supremely satisfying I found it.

The lecturer in question was the analytic number theorist Roger Heath-Brown, and I guess analytic number theorists aren’t particularly renowned for being attuned to the beauty of abstract algebraic structures, but that course was pure joy.