The Wheel Turns
Sep. 7th, 2012 01:10 pm![[personal profile]](https://www.dreamwidth.org/img/silk/identity/user.png){kind=small}
stoutfellowIt seems as though I will have another Senior Project student this year.
Every fall, the department offers Math 498, basically a seminar in writing and presenting a paper. At the beginning of the semester, whoever's teaching it sends around a request to the other faculty, asking for a list of SP topics they would be willing to direct projects on. This year, as usual, I submitted a couple of broad geometric possibilities, but added, as an afterthought, number theory. So, yesterday, a student dropped by to discuss a project in that area. After some discussion of her interests and background, I introduced her to the notion of convolution (as applied to number-theoretic functions), showed her how it tied together various important functions - number of divisors, sum of divisors, and the totient function, for example - and told her about the Moebius Inversion Formula. (This is a distant cousin of the Fourier Transform; the setup seems very different, but the same sorts of things turn out to be true.) She seemed excited by this family of ideas, but wanted to do some poking around on her own before she decided to commit.
We'll talk again, either about these ideas or, if she decides otherwise, about something else. I kind of hope she goes with it; I've been aware of these matters for quite a while, but I've never dug in and studied them myself, and it'd be interesting to see where she goes with it.
Every fall, the department offers Math 498, basically a seminar in writing and presenting a paper. At the beginning of the semester, whoever's teaching it sends around a request to the other faculty, asking for a list of SP topics they would be willing to direct projects on. This year, as usual, I submitted a couple of broad geometric possibilities, but added, as an afterthought, number theory. So, yesterday, a student dropped by to discuss a project in that area. After some discussion of her interests and background, I introduced her to the notion of convolution (as applied to number-theoretic functions), showed her how it tied together various important functions - number of divisors, sum of divisors, and the totient function, for example - and told her about the Moebius Inversion Formula. (This is a distant cousin of the Fourier Transform; the setup seems very different, but the same sorts of things turn out to be true.) She seemed excited by this family of ideas, but wanted to do some poking around on her own before she decided to commit.
We'll talk again, either about these ideas or, if she decides otherwise, about something else. I kind of hope she goes with it; I've been aware of these matters for quite a while, but I've never dug in and studied them myself, and it'd be interesting to see where she goes with it.
