Ups and Downs
May. 18th, 2011 05:42 pm![[personal profile]](https://www.dreamwidth.org/img/silk/identity/user.png){kind=small}
stoutfellowYesterday was a good day.
I took a course in modern differential geometry in the fall of 1978. (It was one of the required courses in the first stage of the U of Chicago doctoral program.) In the not-quite-33 years since, I really haven't thought about it much. It's true that I teach a course in differential geometry, but we cover strictly 19th-century stuff there; the crown of the course is the proof of a theorem discovered by Gauss.
This spring, the best of my students in that class was F. F is an engineer; I think he's actually a bit older than I am. In any case, he's been doing what amounts to differential geometry from the practical side for about twenty-five years, and wants to learn the theory. At the end of the semester, he asked if I would be willing to guide him in a readings course of the modern stuff. I was a little hesitant, but agreed to do so. W is also sitting in, to back me up.
Yesterday was our first meeting. Let me tell you, it is a joy to have a student who has the breadth of vision that F has. For example: he pointed to the definition of a manifold, which describes it as a topological space having three properties. "Okay: what do we gain by assuming property one? Why is it there?" He understood the definition perfectly well, and wanted to know why the definition was what it was. This, again, is one of my pet points in History of Math - the extent to which mathematics is an artifact. We define things the way we do, because they make it easier to think about the questions we're interested in; and F recognizes that (though he never took my history class) and its implications. I wish I had had that perspective back when I was learning this stuff! (There was another point where the author of the textbook used a certain word in a significantly different way than usual, and F picked up on and questioned that as well.)
Today was less good, on the teaching front. There are always students who complain about their grades, but today I'm having to deal with a particularly egregious case. I'm not going to go into details, but this student has me thoroughly ticked.
Oh, well. Can't win them all.
I took a course in modern differential geometry in the fall of 1978. (It was one of the required courses in the first stage of the U of Chicago doctoral program.) In the not-quite-33 years since, I really haven't thought about it much. It's true that I teach a course in differential geometry, but we cover strictly 19th-century stuff there; the crown of the course is the proof of a theorem discovered by Gauss.
This spring, the best of my students in that class was F. F is an engineer; I think he's actually a bit older than I am. In any case, he's been doing what amounts to differential geometry from the practical side for about twenty-five years, and wants to learn the theory. At the end of the semester, he asked if I would be willing to guide him in a readings course of the modern stuff. I was a little hesitant, but agreed to do so. W is also sitting in, to back me up.
Yesterday was our first meeting. Let me tell you, it is a joy to have a student who has the breadth of vision that F has. For example: he pointed to the definition of a manifold, which describes it as a topological space having three properties. "Okay: what do we gain by assuming property one? Why is it there?" He understood the definition perfectly well, and wanted to know why the definition was what it was. This, again, is one of my pet points in History of Math - the extent to which mathematics is an artifact. We define things the way we do, because they make it easier to think about the questions we're interested in; and F recognizes that (though he never took my history class) and its implications. I wish I had had that perspective back when I was learning this stuff! (There was another point where the author of the textbook used a certain word in a significantly different way than usual, and F picked up on and questioned that as well.)
Today was less good, on the teaching front. There are always students who complain about their grades, but today I'm having to deal with a particularly egregious case. I'm not going to go into details, but this student has me thoroughly ticked.
Oh, well. Can't win them all.
