Canonicity

[sniffnoy]

Yesterday was the first day of Algebra with May, where we did, surprise, a bunch of category theory stuff.

Today was the first day of manifolds with Nori. (Peter and Youlian are in this also.) While in class today he just reviewed basic multivariable calculus and then gave a non-usual proof of the inverse function theorem (my guess is that the first part is to make sure everyone's on the same page, and the second part is because he didn't know what else to do but he'd found this cool proof of the inverse function theorem...) After class, however, he sent out an email containing his current idea for an outline of how the class will go.

It begins as follows:

first week:
[basically the stuff we just did, which I've omitted for space.]
second week: Presheaf, stalks, complete presheaf.
Definition of a C^∞ manifold via sheaves.
comparison with dfn in Warner.

Peter and Nic show this to Lucas. Lucas's remark: "I see he's being very canonical..."

(It occurs to me that remark wouldn't make sense if you had no idea what any of the above meant, because it's certainly *not* the usual way of doing things at first!)

Also today was first day of Operating Systems, which was, uh... soporific. Youlian is also in the class and he concurred. Partly that it's an hour and a half long and we didn't really do very much today, partly the hot room, and probably also partly that manifolds is at 9 AM...

-Harry

Comments

[sivakrytos.livejournal.com]

also implicit function theorem is very important for manifolds
further something Nic noticed: Nori abbreviated "Inverse function theorem" as IVT

[sniffnoy.livejournal.com]

Yeah, but this is Nori, not May.

[sniffnoy.livejournal.com]

That's exactly what he said he's going to do...

[sniffnoy.livejournal.com]

Uh, well, I took the class, but Broaddus was teaching it, and I think I've written about what an absolutely shitty teacher he is; of course I've meant to go back and learn some algebraic topology on my own, but I've never gotten around to doing so so far. :P And this is a grad class, so I doubt May is off-base in assuming most people in it know their basic algebraic topology. So yeah, should probably sit down and review all that...

[sniffnoy.livejournal.com]

No, but it is 3rd quarter, and, you know, the actual grad students in it will have been taking the grad topology class this whole time...

I mean the very first problem set assumes you know your covering space stuff, as an illustration of an equivalence of categories.

But "algebraic topology is usually a first-year grad class"? Really? I thought you couldn't do much topology at all without algebraic stuff...