Mathematics - 2015-08-01 (page 2 of 2)

Tobias Kildetoft

7:04 PM

The more precise goals of homological algebra then depends on what sort of objects one is interested in

Remember me

Can we study topological objects in it (like surfaces,manifolds)?

Tobias Kildetoft

@Rememberme It is inherently the study of chain complexes of modules, so we need to somehow attach these to the objects we want to study. This can be done in various ways

Remember me

Ahh I see

Tobias Kildetoft

For my purposes, they generally come from non-exact functors, via a projective or injective resolution

Remember me

I have no idea what functors are actually

Tobias Kildetoft

7:12 PM

well, homology is itself a functor

Remember me

I didnt know that (since I dont know what a functor is)

Tobias Kildetoft

@Rememberme loosely speaking, it is a "function" that takes objects of some types to objects of some (possibly other) type, and such that it also takes morphisms between those objects to morphisms between the other objects (in a compatible way)

Remember me

Oh. Well thanks for the intro to the subject @Tobias It has made me more excited about it. And for all the terms like homology ,chain complexes it would be better off if I wait for a month or so

Balarka Sen

7:32 PM

@MikeMiller thanks. it surprises me that you can define what a vector bundle is sensibly for alg varieties with Zariski topology. I thought it's useless, and apparently I am wrong,

Remember me

Night @Balarka

Balarka Sen

bye.

heya @TobiasKildetoft.

Tobias Kildetoft

@BalarkaSen Hi

Balarka Sen

How goes writing the project for the grant?

Tobias Kildetoft

@BalarkaSen I have been on vacation for the past 2 weeks, so haven't done much. I do have a few ideas though that I will now need to take a closer look at

Balarka Sen

7:38 PM

ah. well, I do hope that you come up with something interesting!

Tobias Kildetoft

@BalarkaSen So do I (or I won't have much of a chance to get the grant)

Mike Miller

7:52 PM

@Balarka: Why would the Zariski topology be useless...?

Balarka Sen

I can't do much topology with it. Algebraic varieties behave pretty badly when given the Zariski topology.

Tobias Kildetoft

@BalarkaSen What other topology would you give a variety?

Balarka Sen

At least, this was what I used to think, and I don't know much algebraic geometry,.

Tobias Kildetoft

anyway, one needs to remember to replace all "continuous" by "rational" to make it nice

Balarka Sen

Dunno, @Tobias. I don't think giving varities a topology is very nice to do mathematics with them.

Hearing of Grothendieck topologies (and knowing about 0% about them), they sound interesting.

Mike Miller

7:58 PM

Yeah, man, I'm sure that Zariski idiot had no idea what he was doing.

Balarka Sen

a bit embarrassed

Guess who it is.

8:22 PM

@Mike, :D

Mats Granvik

haxiomic.github.io/GPU-Fluid-Experiments/html5

Pure mathematics, Navier-Stokes I guess

Guess who it is.

That is beautiful, @Mats.

Mats Granvik

@Guesswhoitis. It has been created by this guy: twitter.com/Haxiomic

Mike Miller

8:46 PM

@PVAL: A compact group $G$ that acts transitively and effectively on a manifold $M^n$ has dimension at most $n(n+1)/2$. Do you know what we can say if $G$ is noncompact?

PVAL

@MikeMiller I do not.

Karl Kronenfeld

@Guesswhoitis. Guess who I am :P

Guess who it is.

@Karl, very unfortunately, I have a crappy memory. Did we ever talk before my hiatus?

pjs36

@Mats That lead to some interesting in general, @Mats, thanks for sharing!

Karl Kronenfeld

@Guesswhoitis. Joking. Though we did correspond once in passing in the chat and once in email.

oops, scratch the email part. we chatted once here though

Mike Miller

9:02 PM

@Karl: I just checked your email, and you hadn't.

Karl Kronenfeld

lol

Guess who it is.

I had to ask, since a number of people on math.SE I once talked to have moved on to new pseudonyms… :)

In short, not much of this site looks like when I last left it.

Karl Kronenfeld

@MikeMiller how many unread emails do I have?

Mike Miller

A few too many.

Guess who it is.

If it's spam, then no worries…

Karl Kronenfeld

9:07 PM

yeah, also he checked the wrong email

I might have been user1 at the time @Guesswhoitis.

Guess who it is.

Tch, still not ringing bells. Sorry… 2013 really was a long time ago.

Chris's sis the artist

@robjohn I wonder what can be in the mind of someone that downvotes such a question.

17

Q: About the integral $\int_{-1}^1 \frac{1}{\pi^2+(2 \operatorname{arctanh}(x))^2} \, dx=\frac{1}{6} $

Here is a question that naturally arose in the study of some specific integrals. I'm curious if for such integrals are known nice real analysis tools for calculating them (including here all possible sources in literature that are publicaly available). At some point I'll add my real analysis so...

I bet only one thing: they most probably know nothing about such questions, tackling. attacking ways.

Look, if I see I'm not good at something I don't blame anything related to that something, I look at myself first. If I wanna improve that, then I work da*n hard, I don't have time to downvote or criticize life.

Study, learn, do research, study, learn do research and so on, crawl and suffer, there is nothing for free, easily obtained. No one ever obtained amazing results staying confortable and clicking a mouse only.

Should my integrals smile to anyone? NO.

Guess who it is.

Repeat after me: "votes are arbitrary and capricious".

2

Karl Kronenfeld

I just don't get why people downvote my answer. It must be people who do not appreciate the techniques of infinite summation when simplifying expressions.

Dave

can some one explain something. I just watched a video on geometric sequences and in the video it had the expression for it as: a1(1 - r^n)/(1-r) where r was less than 1.

And they said that you can add up all the numbers to infinity and thus r^n becomes zero.

But surely it never truly reaches zero it just infinitely gets closer to zero. So why do they then say it can therefore be written as simply (a1/1-r) if in reality it never is actually zero?

Guess who it is.

9:18 PM

@Karl, okay, I remember that. Hilarious!

The "becomes zero" is wrong, yes.

Chris's sis the artist

@KarlKronenfeld That is a nice answer. It's weird on that page the arrows disapparead. It's only a problem to me?

Cristopher

I have been downvoted too, I don't think it's a big deal. There are just internet points after all. Some people downvote for no good reason. It's been like that, and it always will. You have 17 upvotes, it means the community thinks it's a great question, and that's the thing, personally, I would focus on.

Dave

@Cristopher if down votes were not anonymous and a simple reason was given it might reduce people doing it for no reason.

Guess who it is.

@Chris, it's a locked thread.

Karl Kronenfeld

@Chris'ssistheartist They disappeared for me, must be related to the question being locked

Chris's sis the artist

9:21 PM

@Guesswhoitis. @KarlKronenfeld ah, I see.

robjohn

@Chris'ssistheartist Well, there are people who will downvote any question that doesn't show appropriate context.

Dave

@Guesswhoitis. so even though it never fully reaches zero is it still common practice to cancel out that part of the expression for the sum of infinity ?

Chris's sis the artist

@robjohn Is my post that bad? After all I asked for more information about that kind of integrals, less about full solutions.

"It's a question for the informative purpose rather than finding solutions, the solution is optional."

robjohn

@Chris'ssistheartist I upvoted it and wrote an answer, so I don't think it is bad, but I don't really think that context is necessary for all questions. I think it was originally required so that there would be a reason to get rid of homework questions that showed no work without arguing about whether they were homework questions.

Chris's sis the artist

I also added the tag reference-request.

Karl Kronenfeld

9:27 PM

@Dave You're entering the 0.999... = 1 waters, which people seem to struggle with upon first learning infinite summation.

Cristopher

I agree with you, Dave.

robjohn

@KarlKronenfeld Hey, they don't even look the same...

Dave

well it just feels uncomfortable to cancel it out

Mike Miller