Teaching mathematical logic
I taught two courses this year that I haven't taught before. One of them was our 4th-year undergraduate course on mathematical logic, "Logic, Computability, and Incompleteness". As usual, I ended up writing my own textbook. Here it is as PDF and here as HTML.
Why yet another textbook? Two reasons mainly. One is that many existing textbooks are addressed at maths students. This shows up not only in the examples and illustrations, but also in the fact that comparatively little time is spent motivating, explaining, and discussing definitions, proof ideas, or results. I wanted more of that.
Second, and relatedly, I wanted to cover more than what's covered in most existing textbooks. Many of my students have never heard of compactness, ZFC, ordinals, or the arithmetical hierarchy. But these are interesting and important topics. I obviously couldn't cover all of them in depth, but I think it's useful to have at least heard of them.
The course was reasonably well received, especially given that it was a first run and scheduled at 9 am. Nonetheless, I feel ambivalent about it. The topic is fascinating and rewarding. But it's also, in many ways, settled. The central results were established in the 1930s, almost a century ago. There are hardly any accessible open questions. This is in strong contrast to, for example, the decision theory course that I often teach for 4th-year students. That course also has a formal character, but it constantly touches on issues that are under debate: almost every week I can tell my students a few questions that would make good PhD projects. (And postgraduate research is naturally on many minds in the final undergrad year.) I couldn't do this in the logic course. But I might try again.