Mathematics

Mike Miller

8:00 PM

Good, @BalarkaSen.

ᴇʏᴇs

Because none of my algebras are particularly strong

Julian Rachman

OOOOOOOO..... Topology discussion

David Wheeler

A lot of "examples" in topology come from $\Bbb R^n$, and this is an inner product space-which induces a norm, which induces a metric.

A Beautiful Mind

@JulianRachman I don't think every discussion here is beneficial.

Julian Rachman

No. It definitely think that this discussion will not help me at all. But I just heard topology and see if I could help or do something

:)

@ABeautifulMind

David Wheeler

8:01 PM

So one can gain a "concrete" example of how "nearness" is related to our ordinary notion of "close together in physical space"

A Beautiful Mind

Yeah, sometimes people listen to some discussion and get all the wrong ideas about something.

Balarka Sen

@MikeMiller My prof recommended Hoffman-Kunze for LA and Spivak (calculus on manifolds) for mult. calc. D'you think they are good?

teadawg1337

FINALLY, I FINISHED THE PROOF!!!!!!!!! This took me one month, I can't describe how relieving it is to not have it hanging over me anymore :D

Balarka Sen

Hi @Julian

David Wheeler

Hoffman-Kunze is good. The typography is terribad, but the presentation is nice, idea-wise.

Julian Rachman

8:03 PM

@Balarka Hello

Balarka Sen

Thanks, @David. I'll try it out then.

teadawg1337

Spivak is a must-have

Mike Miller

I think Spivak's calculus on manifolds is awful.

teadawg1337

Oh, on manifolds? Nope, nope nope nope nope

Mike Miller

I don't really know linear algebra books.

Julian Rachman

8:04 PM

@Balarka WHat you up to?

David Wheeler

Spivak's "calc on manif" is like a reader's digest version-it's not terribly in-depth.

Mike Miller

@teadawg1337 It's just a multivariable calculus book. There's not really any manifolds. I still think it's bad.

Balarka Sen

Hmm, OK. What would you recommend for a thorough study of mult calc/diff geo, @Mike?

teadawg1337

Stewart's Calc ET (7E) is pretty decent for multivar up to the chapter on vector calc

David Wheeler

"Big" Spivak (the 3-volume set) is generally recognized as far better

ᴇʏᴇs

8:06 PM

@Bal Someone gave me Hubbard's Vector Calculus, Linear Algebra, and Differential Forms and told me it was good

Balarka Sen

I am familiar with basic calculus. I just need something that'll guide me through prereqs and basics of diff geo.

Mike Miller

That assumes you know multivariable calculus, @DavidWheeler.

Lee's smooth manifolds book is good. You mainly need to learn the implicit and inverse function theorems. It wouldn't hurt to see a discussion of div-grad-curl to prepare you for what comes later, but it's not really a big deal.

A Beautiful Mind

@DavidWheeler What is big Spivak?

Mike Miller

If you don't want a huge tract, and mostly want to learn some topology, then get Guillemin-Pollack's book, "Differential topology".

Still need to know the inverse/implicit function theorems, and it won't tell you everything you need to know about smooth manifolds, but it's more in line with what you've been doing.

Ask Ted where to learn multivariable.

Balarka Sen

I am not sure if I care about just topology. More to the point, I want to understand forms.

OK.

David Wheeler

8:08 PM

@ABeautifulMind amazon.com/… is volume 1

A Beautiful Mind

@DavidWheeler That is 5 volumes.

teadawg1337

Ted says Spivak is really good

Mike Miller