Mathematics - 2015-05-26 (page 3 of 4)

Remember me

6:00 AM

You are writing anything new now for your blog@Paul

Paul Plummer

@SohamChowdhury Yes

Soham Chowdhury

@PaulPlummer I didn't really understand that (sorry). In any case, I've seen that as soon as I ask a question here, things magically start to make sense. :)

Paul Plummer

@Rememberme Have you even read the first(and only) post? :P I do have a couple things planned, but I have not started writing them yet, partly because the ones that I was planning to do first, I am pretty sure will be pretty long again, so I instead I am figuring out if I can make a couple shorter posts instead (which I have a couple ideas for that too)

@SohamChowdhury Well what was confusing you?

Remember me

I am reading slowly

Every day

Soham Chowdhury

@PaulPlummer Mostly how he pulled $H^{\oplus A}$ out of thin air (that's what it seemed like to me at first)

Paul Plummer

6:07 AM

The idea is that the $A$ should generate the group, but in your group you can only ever have finite combinations of elements (with out introducing extra structure), if $A$ is suppose to generate the then you only need to look at finite combinations, and that is what the "$ \alpha (a) \neq e_H$ for only finitely many elements of $a \in A$ means, and since this is abelian groups we don't have to keep track of how elements combine, so it is okay to only look at coordinates individually...

that is you don't have to keep track of strings

Soham Chowdhury

Yeah, I think I'm getting you.

The idea of the "general case" was just to define $Z^{\oplus A}$, right?

Paul Plummer

so each of these functions is basically a "sum" of elements from $A$, but only finitely many, and if $A$ is infinite then there are infinitelly many $0$'s in the sum

Soham Chowdhury

So that we could then do $Z^{\oplus n} \cong Z^{\oplus A}$,and then show that $Z^{\oplus n}$ satisfies the universal.

Paul Plummer

Basically, yes, since they are both useful concepts, and it is not any more difficult

Soham Chowdhury

Yes, but it helps to understand the motivation for introducing something (ie what part of a proof it helps with).

Anyhow, I got it. Thanks.

Paul Plummer

6:11 AM

@BalarkaSen Hello

Remember me

hello@Balarka

Soham Chowdhury

@Paul, have you done the entire book?

Hey @BalarkaSen

Paul Plummer

Lol, no, I am not so organized, and focused, I do bits and pieces here and there @SohamChowdhury

Soham Chowdhury

Actually, I believe the reason I was confused is that for a large part of the section he continually assumes that $A = \{1,\cdots,n\}$.

Then $\forall A\in {\sf Obj(Set)}: F^{\text{ab}}(A) \cong \mathbb{Z}^{\oplus A}$ is a jump from there.

^ (I wanted to do that.)

Paul Plummer

@BalarkaSen So the marked group topology probably won't be the next post, I was thinking about , and even before research, that it was going to be long, and it sort of looks like I would have to learn some French to do it right :D

user147690

6:16 AM

@PaulPlummer So it is going to be my pick :)?

Sawarnik

@Paul Why ignore Alex? :D

Paul Plummer

Well it does say "for every set $A$ $F^{ab}(A) \cong Z^{\oplus A}$" @SohamChowdhury

user147690

@Sawarnik He doesn't, he loves me too much

Paul Plummer

Did you read it? @Sawarnik

user147690

(and I know where he lives, his phone number and his social security)

Paul Plummer

6:17 AM

Lol

Sawarnik

@PaulPlummer I read the starred thing :D

@AlexClark haha ... to confirm, what is his social security?

Paul Plummer

Well you also got to read a bit before to see what happened

Soham Chowdhury

Dunno why I got confused, @Paul. I suppose everything is easy after you understand it.

Thanks.

Hey @AlexClark

user147690

Hey @Soham

Soham Chowdhury

Still having fun with DF?

Paul Plummer

6:18 AM

@AlexClark You wanted ping-pong or the free product thing with an extra relation?

user147690

Working on Artin atm actually @Soham

Soham Chowdhury

I finally finished the free abelian groups bit. It took me a whole day for a page-and-a-half's worth of stuff.

Sad.

user147690

@PaulPlummer Yeah the latter sounded cool, I have forgotten what the ping pong thing was now, but from wiki it was cool

Soham Chowdhury

Onward to subgroups, quotients and all. I'm familiar with those (because when I got into solving the Rubik's cube, I learned a little group theory then), so you'll have even more catching up to do in a while :)

How's Artin?

Paul Plummer

I actually asked a question relating to the ping pong lemma fairly recently @AlexClark

Sawarnik

6:20 AM

@SohamChowdhury You are preparing for CMI/ISI?

user147690

@SohamChowdhury Artin is good. He explains much of the things I didn't know from D&F, so I really did it in the wrong order

Soham Chowdhury

@Sawarnik Not yet, I expect I shall.

Sawarnik

Aha. Not JEE?

Soham Chowdhury

Don't want to, seeing as I won't study in an IIT even if I got in somehow.

Paul Plummer

@AlexClark here, although I don't really explain it, only talk a bit about the application and my hopes that a "ping-pong" proof exists

user147690

6:22 AM

@PaulPlummer I was just reading it now actually

Remember me

Lets do munkres!!

Paul Plummer

I might do the free product thing, although I have two other things that might end up being shorter and easier to do (that I did not mention to you guys)

user147690

@PaulPlummer Hmmm my energy levels are too low to dig into it

Paul Plummer

so I might do those things first

Soham Chowdhury

@Rememberme I started semi-seriously looking at Munkres yesterday.

user147690

6:24 AM

I have worked out how to categorise my energy levels into 3 decent sections.
1) Enough energy I can focus on reading while listening to music
2) Enough energy I can focus on reading while not listening to music(not enough while)
3) Enough energy I can focus for short periods while it is essentially silent

Remember me

A set of limit points X of a set E will be closed right because since $E\cup X$ will be closed.

user147690

@Rememberme What is the definition of being closed?

Remember me

I know.. All the limit points of the set have to be in the set

user147690

Is an open ball a set of limit points?

Remember me

But my proof just seems rounded logic to me sometimes

What i didnt get you

user147690

6:27 AM

Well I am not totally sure what you are asking to be honest

user147690

But an open ball is a set only containing limit points and is it is not closed

Remember me

I am asking that how should i prove that the set X of all limit points of a set E is closed

user147690

What is the notation for the set of all limit points of $E$ I have forgotten, is it $E'$?

Remember me

$E^{\bar}$

user147690

I thought $\overline{E} = E'\cup E$?

user147690

6:30 AM

E.g. the closure of $E=\overline E=E'\cup E'$

Remember me

$E'$ i remember is the complement of E

user147690

@Rememberme Isn't that $E^c$

Remember me

Ya its the closure

Well i think it is E'

Forget it

user147690

Anyway I will use my notation above

Remember me

Lets make new notations

user147690

6:31 AM

So you want to show that $X=E'$ is closed

Remember me

Yup

For it to be closed all the limit points of it have to be in the set

Paul Plummer

@Rememberme I think this makes you my most loyal reader :D

Remember me

lol@Paul

user147690

@PaulPlummer If I had more time I would move up the rankings :P

Remember me

But this set is itself the set of limit points

Balarka Sen

6:32 AM

Hello @Paul, @Remember, @Soham

user147690

Wow^

Paul Plummer

And with the topology you have been learning you will soon be able to understand most of it (maybe all of it) @Rememberme

Haha

Balarka Sen

?

Paul Plummer

@AlexClark You did not say high to him though

user147690

Hey @balarka

Balarka Sen

6:34 AM

Why would Alex say "high" to me?

user147690

Paul does that a heap haha

Balarka Sen

:P

Remember me

Since it is the set of all limit points its limit points have to be in the set hence it is closed(I think) @AlexC

Paul Plummer

Haha

Because he wants to corrupt the youth

Remember me

Its the first time i have seen @balarka ping everyone like that :D

user147690

6:35 AM

@Rememberme 'everyone'

user147690

:'(

Balarka Sen

I was merely answering the highs above, @Remember

:P

Paul Plummer

3 hours ago, by Paul Plummer

$\square \!\!\!\! \checkmark$ Make @AlexClark realize everybody ignores him, by letting him do something, which everybody ignores, then I do the same exact thing, which everybody thinks is the best thing since sliced bread.

Remember me

Poor @AlexC

user147690

Noone better star that...

Balarka Sen

6:36 AM

hahaha

user147690

You and them damn tick boxes @Paul

user147690

tick check whatever

Paul Plummer

They are "tick you off boxes"

user147690

I know where you live @Paul

Paul Plummer

I know where you live @AlexClark

and it would be a pain in the ass for you to come to where I live, and expensive too, for a poor soul such as your self

Balarka Sen

6:38 AM

munches popcorn

user147690

@PaulPlummer Hahahaha too true

Remember me

Okay @alexC what do you think about the proof

Paul Plummer

@BalarkaSen got the munchies? I knew @AlexClark was corrupting the youth

user147690

I'll wait until you go to university of O

user147690

@Rememberme I am unconvinced as the devils advocate

Remember me

6:39 AM

Even i am unconvinced

user147690

Try again

Remember me

Thats why i am asking you

user147690

If you keep getting hints, you won't improve

Remember me

I know :(

user147690

Gotta take a break and try again, and you'll get it

Paul Plummer

6:40 AM

8 mins ago, by Alex Clark

@PaulPlummer If I had more time I would move up the rankings :P

looks at chat graph of @AlexClark

Balarka Sen

OK, enough fun.

I am gonna go do some math.

Remember me

Shhh... Balarka is back to normal

user147690

@PaulPlummer Yes, but I study in bursts and my brain dies each time

Paul Plummer

I know just teasing you

user147690

@PaulPlummer My brain is pretty dead now and my chat will drop off when I lose motivation

user147690

6:42 AM

Actually damnit, I have class in 15 min wtf

Soham Chowdhury

@Rememberme I spent a whole day on two pages :)

@BalarkaSen What? Moar alg-top?

Oh, you're doing calculus, forgot

Balarka Sen

@AlexClark Let me know when you finally study the definition of solenoids. I have lots of open problems to share, maybe you'll be able to get them :)

nah, @Soham. I am gonna do calc, but not right now. Have to think about a topology problem.

Remember me

Solenoids.... In altop?

user147690

@BalarkaSen That would be nice xD(both you sharing them and me magically solving them)

Paul Plummer

Oh I was going to ask you if you knew of any papers of "groups acting on solenoids" similiar to Groups acting on the circle by Ghys @BalarkaSen

Balarka Sen

6:45 AM

Well, not open problems. Much like a "program".

No, I am not familiar. p-adic solenoids are well-understood objects, I think.

Mike Miller

Have you read that paper, @Paul? Great article.

Balarka Sen

it's a fact that a $p$-adic solenoid is isomorphic to $\Bbb R \times_{\Bbb Z} \mathbf{Z}_p$, in $\mathsf{TpGrp}$.

Soham Chowdhury

:P

@BalarkaSen So we're going to have a Sen program now?

Like Erlangen?

Balarka Sen

I think this program existed long before I started thinking about it.

Paul Plummer

Very little of it, I have read a couple pieces of it. What do you like about it? @MikeMiller

Balarka Sen

6:48 AM

And probably people have some very cool results too. I just want to think about it independently.

Mike Miller

It's just a good introduction to the subject, @Paul. Very clear and lots of good examples.

Paul Plummer

Will be reading more of it very soon though, (that is why the solenoid was on my mind)

And some "ping-pong" stuff I have been thinking about

Balarka Sen

what's it about, @Mike?

Remember me

Well If the union of two sets is closed and one of the sets is open does that imply the other one has to be closed?

Mike Miller

Groups that act on the circle.

Paul Plummer

6:50 AM

Lol

Balarka Sen

blah

N3buchadnezzar

Still no @DanielFischer?

Paul Plummer

Actually I think I am going to start reading it now for a bit before I go to bed, maybe I will chat with you about it in the near future @MikeMiller

Balarka Sen

I dunno why should I care about $\text{Diff}(S^1)$.

Paul Plummer

Why shouldn't you care?

Balarka Sen

6:54 AM

Not being sure of why I should care doesn't mean I don't care.

Mike Miller

Sure, @Paul.

Balarka Sen

oh? $\text{hom}(\pi_1(M), \text{homeo}_{+}(S^1))$ classifies $S^1$-bundles over $M$?

Remember me

7:24 AM

@BalarkaSen can you check a proof of mine?

@Paul are you free??

Vrouvrou

@robjohn is here ?

Paul Plummer

Just ask, not ask to ask, I am reading at the moment and will be going to bed soon. So probably wont help much. @Rememberme

Remember me

Just check a proof

No questions

Soham Chowdhury

Put it here.

Remember me

I have to prove that the set of all limit points E' of a set E is closed
My proof:
Let p be a limit point of E' so this means that every neighborhood of p will have a point q such that $q\neq p$ and $q\in E'$ we can see from here that every neighborhood of q will contain a point z such that $z\in E$ that means every neighborhood of x contains a point z such that $z\in E$ that implies x is a limit point of E and implies x is in E' and hence E' is closed
@Paul

Anyone here to check my proof

Fargle

7:43 AM

@Rememberme Is x supposed to be p?

Paul Plummer

What is $x$ (I am guessing $x=p$)? Could you explain why you have a neighbourhood around $q$, if you have a neighbourhood around $p$? It looks like all the key ideas are there, and it looks like you know what your are doing. @Rememberme

(I am mostly asking why you have a neigh around $q$ to make sure you know why, it looks like a good proof though)

Remember me

Ya ya sorry

We can have a neighbourhood around a point

Paul Plummer

Well I am going to bed

Remember me

Okay night

Vrouvrou

Please someone has an idea: math.stackexchange.com/questions/1298594/…

have you an sequence bounded in W^{1,p}_0

but all its subsequenses are unbounded in $L^{p^*}_1$

@PaulPlummer ?

Daniel Fischer

8:43 AM

@N3buchadnezzar Hi. What is it about?

fubal

9:15 AM

A point on the boundary of $\Omega$ is called regular, when you can construct a barrier in it. A barrier in $x$ is a function $w$, with $w(x) = 0$ and $w$ superharmonic in $\Omega$. Now $|x|exp^{-|x|}$ is $0$ at $0 \in R^n$

and it is superharmonic everywhere else. Now I can just move that function to any boundary point of any set $\Omega$ (define $|x - a|exp^{-|x - a|}$ for $a \in \del \Omega$). why isn't every point now regular? what am I missing?

a I missed the barrier has to be strictly greater 0. but my example still works

@DanielFischer you are into pde as I understood it?

Daniel Fischer

@fubal No, I avoid PDEs whenever possible. Too much of a hodge-podge with gazillions of conditions to remember for when what applies.

fubal

@DanielFischer ah ok then I got the wrong impression

that is btw the problem I have with algebra. For analysis stuff it somehow works out for me

in algebra I just can't remember all of the millions of defintions and what applies to which under which circumstances etc

Daniel Fischer

Yeah, when you go beyond the fundamentals, algebra also has that problem.

fubal

9:41 AM

ok problem solved, I miscalculated the laplacian, $|x|exp^{-|x|}$ isn't superharmonic

Remember me

9:53 AM

Hello@Robjohn

robjohn

@Rememberme hi there

Remember me

What have you been thinking lately?@robjohn

robjohn

@Rememberme what do you mean?

Remember me

I mean what kind of mathstuff are you working on in the past few days?@robjohn

Remember me

10:17 AM

Hey @Balarka I have this question which i want to get clarified about?Are you free

go on.

hi balarka

hello bananas

We know that a linear transformation is said to be into if and only if its kernel is 0 Is the inverse also true?

Balarka Sen

What do you mean by "inverse"? You have just said "if and only if".

Remember me

10:18 AM

Yes okay thanks

iwriteonbananas

that's a weird question

but the following is true: a linear transformation is injective iff it has trivial kernel

Remember me

I mean that its kernel will be 0 when T is injective

Balarka Sen

well, yes, then, it is also true that T is injective => ker T = 0

robjohn

@Rememberme I have been away at a conference over the weekend, so not much, really.

Balarka Sen

@iwriteonbananas so, did you figure out that problem?

iwriteonbananas

10:21 AM

yeah

Balarka Sen

that's nice :)

iwriteonbananas

but i didnt figure out what space we get if we take two solid tori and identify boundaries via $x\mapsto -x$

Balarka Sen

i haven't tried to visualize it. the gluing map pastes each nullhomologous circle in one copy to the nullhomologous circle in the other copy after rotating 180 degrees, yeah?

iwriteonbananas

yeah

Balarka Sen

ok, then i am not sure how that's any different from $S^2 \times S^1$. i guess it's not what i say it is.

first we have to understand what $-x$ means :P

iwriteonbananas

10:25 AM

:D

that's what ted meant when he said boundary homomorphism that reverses orientation, right?

Balarka Sen

no idea. probably not.

iwriteonbananas

ok

nevermind then

Remember me

Well @Balarka I have a topology proof to show you.... Mind having a look?

iwriteonbananas

i'm now gonna try to do the general problem that ted proposed yesterday

where the boundary tori are identified via any linear map

we have the same short exact sequence: $$0\to H_2(X) \to H_1(U\cap V) \to H_1(U) \oplus H_1(V) \to H_1(X) \to 0$$

and $H_2(X) \approx \text{ker "third map"}$

@Rememberme what is it?

Remember me

chat.stackexchange.com/transcript/message/21834702#21834702 this one @iwrite

iwriteonbananas

10:34 AM

@Rememberme write it down again, i think you got some letters mixed up

Remember me

Ya ya that x is p

Otherwise everything else is fine @iwrite

iwriteonbananas

"we can see from here that every neighborhood of q will contain a point z such that..." is a bit sketchy, you should write it out in more detail

Remember me

As in (detail what should i include)

Soham Chowdhury

hi guys

iwriteonbananas

why does that follow?

Remember me

10:39 AM

Oh okay thanks will come back

Gato

@robjohn Can you help with the following problem ? I need to prove that $$ \forall A \in M_n (\mathbb{R}), \int_{\left\|X\right\| \leqslant 1} \left\langle AX,X \right\rangle \, \mathrm dx_1 ... \text{d}x_n = c_n \text{tr}(A)$$

My problem is that here, $A\in M_n(\Bbb{R})$ I cannot diagonalize this matrix (not symmetric, and not triangularizable ). So how can I compute this ?

Ramanewbie

Hi @gato

Remember me

Hello@Raman

Gato

@Ramanewbie Hi, how are you ?

Ramanewbie

Hi @Rememberme

@gato Fine what about you ?

Gato

10:47 AM

Pretty good today. I am on holidays :p.

Ramanewbie

@Gaot What ? WHy ??

robjohn

@Gato Have you tried simply writing $$\langle AX,X\rangle=\sum_{j,k=1}^na_{j,k}x_jx_k$$ and integrating?

I think that makes it pretty simple

user147690

I seem to have fallen behind in Algebra. My class mates know tonnes more than me, don't know what I am doing wrong :\

Soham Chowdhury

@AlexClark You need competition, child.

user147690

This hasn't happened to me before

Gato

10:50 AM

@Ramanewbie la fac, la fac :p.

Soham Chowdhury

I was away for most of the day. Free now?

Gato

@robjohn Ah right, forgot this. Thanks

user147690

Somewhat free beyond feeling depressed

Soham Chowdhury

I'm casually chewing on a chilli right now lol

Ramanewbie

@gato You're in fac ? What level / subjects

Remember me

10:50 AM

Chilly @Soham

Soham Chowdhury

I am depressed, @AlexC. Got time for Aluffi?

@Rememberme Completely kosher variant spelling.

user147690

@SohamChowdhury Dunno. I am apparently doing terrible in Algebra now, so maybe not

Gato

@Ramanewbie Licence 3 mathématiques, I was in physics last years but I was not "happy" so I decided to change, but it's a bit difficult to catch up L1,L2..

Soham Chowdhury

@AlexClark Maybe you need a new viewpoint?

Remember me

@AlexC You finished DF?

user147690

10:52 AM

@SohamChowdhury Dunno, they were talking about shit, and I didn't even understand

Soham Chowdhury

Like?

user147690

Shit about ideals

Soham Chowdhury

Did you miss classes?

user147690

I did miss classes, but I have covered all the missed content

user147690

Only missed 2 and I have read the notes

Soham Chowdhury

10:53 AM

Apparently you haven't, or there's some conspiracy going on

user147690

I dunno man, feels bad

Soham Chowdhury

I know that feel, man. commiserating pat on the back

Remember me

@AlexC I felt that when i wasnt getting even a single proof in topology

Soham Chowdhury

@Rememberme How far are you through Munkres?

Remember me

Second chapter first topic

Balarka Sen

10:56 AM

@iwriteonbananas right

Soham Chowdhury

@BalarkaSen is the accepted answer here accurate in your opinion?

As a list of prereqs?

I plan to follow those after learning some algebra properly.

Balarka Sen

yeah, yeah, Amitesh's answer is good.

Soham Chowdhury

Aaaaaand Balarka is offline again.

user147690

what^

Balarka Sen

but why are you guys obsessed with studying algebraic topology? :P there is more to math than that.

Soham Chowdhury

11:01 AM

Lag, man.

@BalarkaSen I want to know what a fundamental group is. Reason enough.

@BalarkaSen who else is?

user147690

@BalarkaSen Balarka what does your study look like? Do you study when you aren't in chat, with zero distractions?

iwriteonbananas

@BalarkaSen $U\cap V$ need not be a torus anymore, right?

Soham Chowdhury

@AlexClark Right now, you're probably like "everyone is real focused, unlike me, that's why I got pwned today", I guess.

Keep calm and read DF, man. This sorta stuff happens.

@BalarkaSen I'm curious too, though. How do you study?

Ramanewbie

@gato What didn't you like with physics, was it the way it was teached in your fac ?

iwriteonbananas

actually, i guess it still is a torus.

Remember me

11:09 AM

@SohamChowdhury I am

Soham Chowdhury

Oh.

Balarka Sen

"how do you study" is rather broad.

huh, @iwriteonbananas? why wouldn't it be a torus?

iwriteonbananas

we're making some identifications right?

Balarka Sen

yes.

@Rememberme @SohamChowdhury algebraic topology is not the end of math. I highly recommend you to study what you'd like to study, not study something because it sounds cool.

try doing algebra very thoroughly, and study some algebraic number theory say. learn some class field theory and come back and let me know about it. i don't know anything about those.

iwriteonbananas

i dont find it obvious that $U\cap V$ should still be a torus under identifications via some linear map

Soham Chowdhury

11:14 AM

I am going to do algebra very thoroughly.

Balarka Sen

just doing the first few fundamental chapters and jumping into topology/algebraic topology wouldn't do. do everything Aluffi talks about/you'd like to learn about.

don't study algebra because you'd want to understand algebraic topology.

Soham Chowdhury

I'm going to finish Aluffi and then learn some homological algebra.

Balarka Sen

it's a subject in it's own.

Soham Chowdhury

My main motivation was to learn some Galois theory.

For Abel-Ruffini.

Balarka Sen

you'll find Galois theory more interesting than you think it is.

class field thoery is all about galois theory of cyclotomic extensions, for one.

Soham Chowdhury

11:17 AM

Chill, I know what I'm doing, @Balarka. I'm not going to jump from one thing to another with half-baked ideas in my head. I've learned not to do that the hard way.

@BalarkaSen Yes, wiki tells me as much.

Balarka Sen

I know you're not jumping from one thing to another, just make sure you learn everything for it's own sake, not as a tool for understanding something which sounds cool.

Soham Chowdhury

But algebra all day is sort of tiring after a while, so I'm going through a bit of Munkres these days. Because I do want to learn topology, after all those cup-donut gifs and Aluffi teasing me about fundamental groups of the figure-eight.

And it seems quite fun.

Isn't that the main requisite?

Balarka Sen

sigh ok, do whatever you want.

Soham Chowdhury

C'mon. I can't really study class field theory right now.

Balarka Sen

i wouldn't call anything fun unless i have motivation to study something. to be frank, i am studying algebraic topology because i want to study arithmetic geometry (which is algebra).

Soham Chowdhury

11:21 AM

what's that now?

"studying schemes over Spec(Z)"?

"A vaguely defined branch of mathematics dealing with varieties, the Mordell conjecture, Arakelov theory, and elliptic curves."?

Balarka Sen

@SohamChowdhury well, why not? it's fun stuff.

Soham Chowdhury

"vaguely defined" makes it sound bad

Balarka Sen

if you do first few chapters of Aluffi and some algebraic number theory, you'd be just fine with class field theory

@Soham i don't know anything about arithmetic geometry, so i am not gonna talk.

Soham Chowdhury

how do you know it's fun then?

@BalarkaSen what does it do?

Balarka Sen

it's not vaguely defined, last time i heard. Grothendieck was not munching grass all through his life :P

Soham Chowdhury

11:23 AM

"Its primary motivation is the study of classical Diophantine problems from the modern perspective of algebraic geometry."

iwriteonbananas

didnt you also want to learn differential geometry, balarka?

Soham Chowdhury

Now that's cool.

I want to learn about manifolds, too.

Balarka Sen

@SohamChowdhury 'cause it answers a question i want to be answered.

Soham Chowdhury

Manifolds are another reason why I want to learn algebraic topology.

Aren't those related?

Manifolds, because physics.

iwriteonbananas

you'll learn about manifolds way before you learn about algebraic topology

Soham Chowdhury

11:25 AM

@iwriteonbananas really?

Balarka Sen

@iwriteonbananas differential topology, yes.

that's because i want to understand cohomology really well

iwriteonbananas

yeah, once you've learned some point set topology stuff, you can define manifolds

Balarka Sen

manifolds have nothing whatsoever to do with learning algebraic topology

Soham Chowdhury

I think, before choosing what I want to do after Aluffi, I'll just finish it (and get familiar with a little point-set) and then think.

That seems like the best thing to do.

Balarka Sen

good idea.

Soham Chowdhury

11:26 AM

Achha, when you "gotta run", I assume you go off to study?

(mostly)

Balarka Sen

yes.

but not always.

iwriteonbananas

@BalarkaSen have you studied cohomology yet?

Balarka Sen

bits.

Soham Chowdhury

@BalarkaSen study math?

Balarka Sen

i have skipped singular cohomology : i want to know de Rham cohomology first

Soham Chowdhury

11:27 AM

don't you get distracted at all?

Balarka Sen

i am doing some homotopy theory alongside multivariable analysis right now

iwriteonbananas

ok

Balarka Sen

@Soham often i do. and no, i don't study math 24/7. i have exams to take care of.

Soham Chowdhury

@BalarkaSen we all do have exams.

LeGrandDODOM

11:51 AM

@r9m can you help me with math.stackexchange.com/questions/1299378/… ?

user147690

The sad thing is finding out I seem far behind has decreased my motivation substantially

Soham Chowdhury

@AlexClark Aw, c'mon, it's just two classes, and you can make up for it.

user147690

@SohamChowdhury I don't know why it has gotten to me haha

Soham Chowdhury

You were on page 5, which is a problem. You need to be on 6.

Go.

user147690

But that's aluffi and I should be doing D&F haha (although I am on page 7 now :))

Soham Chowdhury

11:57 AM

Do DF, then.

Aluffi might help you because of the different kind of treatment. Usain Bolt plays basketball, as I like saying.

user147690

I didn't know that

Soham Chowdhury

And all your Aussie cricketers play football or tennis. It's called cross-training.

user147690

How do you study? Do you sit there in silence or talk to yourself or what?

Soham Chowdhury

I just stare at pages until things click. Sometimes I explain stuff to imaginary students.

I often write things down. (I love drawing commutative diagrams <3)

user147690

Explaining stuff to imaginary students is by far the best technique I have, but I can't do it at uni

Soham Chowdhury

12:01 PM

You can write stuff down / take notes.

I do that when stuff gets hard.

user147690

I think I'll just go attack it all on my whiteboard for awhile, see if just going at it for an hour will help. Talk later

Soham Chowdhury

It will, good luck!

:)

Soham Chowdhury

12:17 PM

@BalarkaSen: the fact that $H$ is a subgroup of $G$ iff $\forall a, b \in H: ab^{-1} \in H$ (and how this implies all the other requirements) reminds me of the Wolfram axiom.

And I'm warming to the idea of studying a little number theory properly, too.

Soham Chowdhury

12:54 PM

Hey, @AlexClark, did it help?

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$Mathematics$ Mathematics