Auditing a Fourier course
Looks like I’m going to be auditing a Fourier course offered by Dr. Dinesh Singh this summer. It looks like a lot of what we’re going to be doing in there was covered in the Signal Processing course with Dr. Papadakis earlier, but more in-depth. I.e., in the first course, Dr. Papadakis said we could assume the completeness of the complex exponentials, but in Dr. Singh’s course, we’re expected to be able to prove it ourselves.
I missed the first couple of days, but I can get the notes from someone, and catch up. It looks like it’ll be great fun, and we might even get to wavelets. The only thing I don’t feel well about is the fact that I don’t know Lebesgue integration theory— he said this won’t be an issue, but apparently knowing it helps you to understand what’s going on at a deeper level, as well as with handling the technical minutaie.
Incidents like this are making me wonder: next semester I signed up for the grad complex analysis sequence, mainly because the one course I had on complex analysis didn’t even cover contour integrals, and partly because I took my undergrad real analysis sequence with the prof, and said that since I understood the real analysis, I should understand the complex analysis class without further prereqs. But now I’m thinking maybe I should take the grad real analysis sequence so I’ll have a background in lesbesgue integration before grad school. It comes down to this: which is more important to know prior to grad school: lesbesgue integration, or complex analytic techniques?
Possibly relevant posts:
- Bolzano-Weierstrass theorem (2/6/2005)
- Notes for Complex Analysis, Moore’s style (1/19/2005)
- studying scheme (5/9/2005)
It depends on where you go for grad school.. Some places like NYU expect a strong complex background, others like Penn expect a strong analysis background.
wish I could be of more help.
m
Comment by Marc — 6/11/2005 @ 1:59 pm
I think it is easier to pick up contour integration on your own by reading a book, than to learn Lebesgue integration from Royden. So I would attend classes in Real analysis although I personally prefer complex analysis.
Comment by tpc — 6/12/2005 @ 7:45 am
thanks for the advice. I’m really going to attempt to persuade the undergraduate advisor to let me take both. Unfortunately, I have to go through the engineering department to ask permission to take the 3 extra credit hours above our top (19), even though they aren’t engineering courses. And since I’m already taking 6 hours of grad courses (3 an engineering stochastic processes class, and 3 complex variables I already signed up for), I don’t know how accepting they’ll be— they tend to assume the students don’t know how much they can handle.
Comment by Alex — 6/13/2005 @ 2:53 pm