In the first week of January I’ve taught an intensive course on Number Theory in Prague. Here’s a bit about how it went (well, of course! :) ).

I got the idea at the beginning of the Fall semester. During my undergraduate and Master’s studies I have already done quite a lot of teaching, so I knew it would be fun – and an excellent opportunity to learn the topic thoroughly. The only problem was that I’m studying in the US and after all, it is somewhat impractical to commute over the ocean every week. However, after talking with some of my friends and students at the Charles University, I figured out that they’d indeed be interested in such a course, and that a good format would be to cover the material during two intensive weeks. And thus I’ve arranged everything with my “home” Department of Algebra, even got some travel money from my Fulbright grant, and all was ready to begin.

The first week was at the beginning of January. There were 2 90-minute lectures in the morning and a recitation in the evening every day. I’ve really enjoyed the week, and the students (there were 12 of them) seemed to have liked it as well.We’ve covered quite a lot of material (for mathematicians – the basic facts about number fields, their primes, ramification, units, etc., and valuations and completions; more or less the material mentioned in this article at Wikipedia), and had quite a few interesting discussions mostly about the mathematical content, but about linguistics as well:

Naturally, I’ve taught the course in Czech, which posted quite a few problems about the translating the notions I knew mostly in English. I hope I’ve managed to find the right and used Czech translations, but it wasn’t always easy. For example, it seems there is no good way of saying “prime” in Czech – whereas we do have words for “prime number” or “prime ideal”, it’s sometimes useful just to say “prime” without specifying which of these you mean. It’s of course possible to extract the part “prime” from these words (“prvo” in Czech), but that sounds unnatural and not very melodious. Although we came up with a few possibilities (prvok meaning protozoon, prvověc = prime thing, or prvák = freshman), but in the end didn’t start using any of them.

It was of course quite tiring for me, especially since I had to prepare some of the classes and recitations during the afternoons. But although I had to spend almost all my time on it, I’ve liked it. And there were a few special joys to keep me going – for example erasing the blackboard. To clean the blackboard well, it is of course much better to wash it with a wet sponge. But then you are faced with the problem of having a wet blackboard on which you can’t write. In elementary school we sometimes tried to solve it by quickly moving the blackboard so that the resulting wind hastens the drying. As you can expect, it didn’t work very well. The mathematicians in Prague have a much better solution – just use a squeegee!

The second week will take place in June, we’ll continue by doing Class Field Theory – and I hope it will be even more interesting!

Thanks to everyone, especially to the students for coming to the classes in a busy part of the semester, and to the people from the Department of Algebra and the Institute for International Education for their help!