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In fact I was in a situation which sounds similar to yours: I am by training an arithmetic geometer (which is a kind of algebraist, I think) and as a postdoc less than two years out of my PhD I taught a second semester undergraduate analysis class. The big difference between my story and yours is that I wasn't required to do this -- on the contrary I campaigned quite actively (even a bit pushily, because it seemed necessary) to be able to teach an advanced class in any discipline, rather than the multivariable calculus / linear algebra that it seemed like I would otherwise get stuck with. I also had plenty of time to prepare for the course in advance, so I went to the library and thumbed through many different texts to get an idea of what the possibilities were. I had a fantastic time teaching the course, and my understanding of real analysis is much stronger now than it was before. (This was also the first course for which I typed up rather extensive lecture notes: scroll down to Real Analysis II on http://www.math.uga.edu/~pete/expositions.html to see them.)

In fact I was in a situation which sounds similar to yours: I am by training an arithmetic geometer (which is a kind of algebraist, I think) and as a postdoc less than two years out of my PhD I taught a second semester undergraduate analysis class. The big difference between my story and yours is that I wasn't required to do this -- on the contrary I campaigned quite actively (even a bit pushily, because it seemed necessary) to be able to teach an advanced class in any discipline, rather than the multivariable calculus / linear algebra that it seemed like I would otherwise get stuck with. I also had plenty of time to prepare for the course in advance, so I went to the library and thumbed through many different texts to get an idea of what the possibilities were. I had a fantastic time teaching the course, and my understanding of real analysis is much stronger now than it was before. (This was also the first course for which I typed up rather extensive lecture notes: scroll down to Real Analysis II on http://alpha.math.uga.edu/~pete/expositions.html to see them.)

If you think about it, getting asked a question that you don't know the answer to immediately (and if you don't know it immediately, there's no shame in not giving the answer in that class period -- how much time are you willing to spare standing silently and thinking before you give up at least temporarily? not very much time at all, I hope -- any question which has given you such pause is well over the heads of the majority of the class, who are just waiting for you to get on with it) is just about the most positive experience you can have in a classroom. One of the reasons that I can't get excited about teaching freshman calculus is that I know from long experience that anything that I find remotely interesting is going to be difficult (and worse, boring) for 95% of the students. The number of interesting questions that I get when teaching calculus is, very sadly, about one every two or three courses. By the way, I don't recall ever getting stumped in that real analysis class that I taught. I sincerely wish I had been -- it would have meant that the students were engaging with the material at a much higher level). By way of contrast, for each of the three days of the course I am currently teaching I have received at least one question that really caused me to think and in my answers say things that I thought were true but wasn't completely sure. (Sample question: let $p$ and $p'$ be distinct prime numbers. Are the rational numbers equipped with the $p$-adic topology and the rational numbers equipped with the $p'$-adic topology homeomorphic? Probably, right? But I wasn't and still am not completely sure.) This is awesome -- I can't wait for tomorrow. By the way, the title of this course is (graduate) Number Theory II, i.e., I am supposed to be an expert in this.

If you think about it, getting asked a question that you don't know the answer to immediately (and if you don't know it immediately, there's no shame in not giving the answer in that class period -- how much time are you willing to spare standing silently and thinking before you give up at least temporarily? not very much time at all, I hope -- any question which has given you such pause is well over the heads of the majority of the class, who are just waiting for you to get on with it) is just about the most positive experience you can have in a classroom. One of the reasons that I can't get excited about teaching freshman calculus is that I know from long experience that anything that I find remotely interesting is going to be difficult (and worse, boring) for 95% of the students. The number of interesting questions that I get when teaching calculus is, very sadly, about one every two or three courses. By the way, I don't recall ever getting stumped in that real analysis class that I taught. I sincerely wish I had been -- it would have meant that the students were engaging with the material at a much higher level. By way of contrast, for each of the three days of the course I am currently teaching I have received at least one question that really caused me to think and in my answers say things that I thought were true but wasn't completely sure. (Sample question: let $p$ and $p'$ be distinct prime numbers. Are the rational numbers equipped with the $p$-adic topology and the rational numbers equipped with the $p'$-adic topology homeomorphic? Probably, right? But I wasn't and still am not completely sure.) This is fantastic -- I can't wait for tomorrow. By the way, the title of this course is (graduate) Number Theory II, i.e., I am supposed to be an expert on this.

First, it's a little unfortunate that you "have to teach" somewhat advanced courses in a discipline that you feel is far away from your training and current interests. Are there not other faculty who are more qualified to teach analysis courses than a young, inexperienced algebraist? Notice that if the answer is no, then that's no fault of yours, and it is somewhat valiant of you to be willing to pitch in outside of your core expertise.

First, it's a little unfortunate that you "have to teach" somewhat advanced courses in a discipline that you feel is far away from your training and current interests. Are there not other faculty who are more qualified to teach analysis courses than a young, inexperienced algebraist? If the answer is no, then that's no fault of yours, and it is somewhat valiant of you to be willing to pitch in outside of your core expertise.