12:01 AM
Maybe the system in India is different. As an example, american students get into doing research much earlier than e.g. german students

what's an research??

Even though german students learn real analysis etc from the start, instead of first doing calc I-III and discrete maths/intro logic classes
But both seems to work out fine in the end

Well, most of the undergraduate research is pretty routine. But some of it ends up being super impressive.
The English is horrible and full of errors, but the math seems a bit more advanced in that one. I'd have to look more carefully than I want to now.

Oi, they cite both perelman and the longer version of geometrization by cao and zhu

Pretty sure they haven't read a lot of it :)

12:05 AM
Uh
I looked for footnote [4] and there is none what

amazing

@JackZimmerman I just write shitty metal on guitar pro and upload it in the hope that I might some day record them properly rofl

By now I'm pretty sure I'll only understand linear algebra after doing a lot of functional analysis

Stupid question: the finite* extension of a local field is always a local field right ?

no
e.g. an extension with infinite residue field

12:12 AM
Right, I meant "finite extension"

err then I think so

who even understands linear algebra

not I !

@EdwardEvans pretend that you don't know what a finite*-extension is
is there an involution involved??

lmao

12:15 AM
@Astyx consider a finite extension of a local field as a f.d. vector space over your field and show the topology generated by the unique extension of the absolute value to your extension is locally compact

no, it's the weak*-topology on the extension

sorry ard

and the right answer to this question is a rhetorical question: is a convolution convolved?
@Thorgott bigthink

ard?

rofl I defined that yesterday or smth

12:18 AM
did anyone already try flagging the pinned post that we shouldn't flag so much

it's pretty offensive tbf
Hey I got a job interview at a nice company btw
congratulate me so I feel good

Cool!

gratz! that was quick

nice!

12:19 AM
yeah I'm gonna mention how number theorists are rare creatures and they'll probs employ me based on that alone

you may have our approval now, but you don't yet have Wiles' approval

some bank told a friend of mine that they don't care at all about what she studied

alas, Wiles will have to wait
This company just want you to have studied IT, Physics, or Mathematics

@EdwardEvans but will Wiles wait?

Wil-e wait
I'll read his proof of the main conjecture in the meantime

12:21 AM
'e won't

in the end, people always choose dollar stacks over algebraic stacks

@EdwardEvans do you know the norf fc memes

@Thorgott coulda gone for "people always pursue dollar ..."
still funny though

@user2103480 I absolutely do

What's interesting with tame/wild/ferocious ramification? why is there such a distinction?

12:28 AM
@EdwardEvans I crack up everytime I see them they're great

Ich rauch Pfeifentabak aus einem Apfel, weil ich keine Zigaretten habe und ab 20 Uhr nicht rausdarf
@Astyx something to do with wild ramification being a big problem

tame ramification is somehow easy to understand but wild ramification and the inertia part of infinite extensions is for some reason super hard
but I have no reason to know or believe this
just Kevin Buzzard talking shit

@EdwardEvans miese zeiten, gibt es keinen kippenautomaten in der nähe??

His lectures are on my to-watch list

12:29 AM
Man kann sich ja bestimmt kurz rausschleichen

Doch aber ich hab erstens kein Geld und zweitens eine Ausgangssperre zu berücksichtigen

also yeah Buzzard is great
very

"I need a job so that I can buy tobacco"

English
literally

12:30 AM
the distinction exists solely because algebraists wanted to claim some funny terminology for themselves

@Thorgott since there isn't already enough of that?

Eierlegende Wollmilchsau
I'ma go play D3

What class do you play?

Necromancer atm rofl

not enough

12:33 AM
cool, have fun!

one of my favorites still is
cylinder object
*good* cylinder object
**very good** cylinder object

@EdwardEvans have fun
@Thorgott sehr gutes zylinderobjekt
ooff that's a very german translation

also, buy yourself some rolling tobacco smh

12:35 AM
lol
ugh I have infinity-category ptsd
small object argument
"Kleines-Objekt-Argument"
sounds cute in german
that is quite an ambitious syllabus for people that haven't seen the stuff before
Although it is remarkable how few prerequisites are strictly needed for such a course
Also, I love that people get hit with regular cardinals out of nowhere, to make the small object argument work
(it's just a transfinite induction though, nothing special)

transfinite induction is a very natural process, should be taught more often

1:11 AM
indeed
sounds crazier than it is
to logicians it's no difference to induction over any well-founded relation anyways
okay, there's a well-order instead of just well-foundedness, but that just reduces the base cases
en.wikipedia.org/wiki/Mostowski_collapse_lemma one of the very beautiful basic set theory results
@Thor are you in frankfurt
if yes, and if next semester is still online, you could consider doing the modal logics course in darmstadt

right now? no
but i do go to uni there

absolute FYRE choon

their logic group is great, and with an algebraic/categorical leaning since streicher teaches there
streicher is such a great name, if I were him I'd put on an aragorn costume every carnival
@EdwardEvans gtfo it's friday night

yeah, I know some people who commuted to Darmstadt (this was before covid) just to attend a logic lecture there since we don't have any

ooi

1:25 AM
was always funny to get a "if you wanna know more about this, attend a logic lecture... except we don't offer any" in the first semesters

hahaha there's rarely any logic department around though
some philosophy and CS departments grant asylum to logicians
darmstadt is possibly the best logic department in germany, if one views logic as being separate from pure set and model theory
@EdwardEvans one of me favourits

CAM ON INGERLAAAND

simple as
@EdwardEvans I'm dying hahaha
SCOAR SUM FACKIN GOALS

Oi loike me footie, me pork pies, an me beer, dont lyk it u can fak orf, simples

Brits just cant resist the pub
My super leftist friends dragged me into a wetherspoons
betrayed all their values for a pint

1:35 AM
Wetherspoons is worth it tbf
Doombar and ale pie with a pint of piss, lavly

my favourite was the pub that charged 2 pound 20 for a pint

were you in the north?

we sang hey jude there and one old man held his ears shut
yup manchester

Lmao I was in Manchester for 2 weeks at a summer school and was astounded at the cost of pints

the bartender called our performance "bloody marvellous" though
@EdwardEvans cheap as hell. the german equivalent of the saarland probably
uh british equivalent
breaking news: manchester now part of germany, britain gets the saarland in exchange

1:44 AM
rofl
who would miss the Saarland

everybody that drives through germany
dab

wot

ugh that's ambiguous. Of course I mean that no one goes there

ohhh okay then it's funny

I'll watch some bioshock 1 walkthrough now, good night

1:49 AM
the dream
cyuh

are there simply connected manifolds that don't cover a compact manifold?
apparently CP^2 is a counter-example, so let me change the question to whether every open simply connected manifold covers a closed manifold

2 hours later…
4:12 AM
Hello dear people of math chat.
can someone take a look into this question which has ID 3987120 ? Although a nice person showed up and gave some hint, and while I commend his effort. It doesnt address the problem as the intended method. Perhaps someone out there with some experience could help me with ideas on how to solve it using euclidean geometry?

@user2103480 he used to wait for lunch...

@ChrisSteinbeckBell Better to give the actual link. The ID# is not something we find easily.
Actually, your hinter is one of our chat regulars, so be nice.

4:29 AM
@Thorgott wat CP^2 covers itself. There should be many examples, like the Whitehead manifold
It seems annoying to prove, but something like the following: The Whitehead manifold is contractible, so if it covers a compact manifold $M$, $M = K(\pi_1(M), 1)$. Finite dimensionality implies $\pi_1(M)$ is torsion-free; in particular it must contain a copy of $\Bbb Z$
Pick the generator, this guy is a self-homeomorphism of the Whitehead manifold which pushes everything to infinity eventually (by proper discontinuity). This should mean the Whitehead manifold is simply connected at infinity.
The point is universal covers of compact manifolds cannot have complicated space of ends; they have periodic tilings
@EdwardEvans Thanks, gonna listen. Glad you liked Nachtterror btw

5:34 AM
Q46..A step by step guidance is most welcome...

6:24 AM
@user586228 The answer is d. No step-by-step guidance provided. You should get III immediately.

Hi @Ted

Boo.

hides

Hiding is good.

Is this hide-and-seek?

6:28 AM
Hide the seeker, rather

Well, now that you’re helping Socks, I don't have to hide as much.

Karl immediately hides himself away

Oh :(

It's midday and 60F with chilling breezes
Going to be rough tonight

It was over 80F here today. Crazy.

6:31 AM
Absolutely nothing wrong with the climate. Nope. Just the way it ever was.
- a geocentric flat earther

Where's the center if the earth is flat?

I expect the earth is a disk with a complete Riemannian metric

@TedShifrin I am not being able to calculate and justify 1
I do not understand how do I use the values that are provided

You need to repeat Columbus's voyage.
What is the probability of passing exactly 3? 2? 1? 0?

I can figure out only exactly 2...

6:47 AM
I don't believe that.
If that’s true, then quit math.

I mean atleast 1 and atleast 2 is ok
But how do I figure out the exact values

You think.

give me some clue

What does at least 2 mean?

Passed in 0, passed in 1 ,passed in 2
That is it

6:50 AM
Huh?
No, that's at most.
English is a prerequisite.

I cannot think anything else
What else do I express this as
I do not really understand how to use the values

Do you even understand what I just said? Do you speak English?

Yes I do

Look up “at least.”

@user586228 atleast 2 means that the student passes in a minimum of two subjects. I.e passes in 2, or passes in 3, 4 ..etc.
@user586228 this is atmost 2.

6:59 AM
ohh sorry sorry
Yes
@TedShifrin sorry
So He is supposed to pass in 2 or 3
Atleast one means 1,2,3
Now whaat next

OK, now figure out what I asked.

How do I do that...I drew a Venn diagram
@TedShifrin

You have to understand the sentences. That's it. But I will not be helping any more.

@Ted: You might be intrigued by this problem.

@satan29 Can u help me out?

7:35 AM
@copper.hat I am having a tough time with this problem can you help me out..

8:10 AM
Hi
I am having confusion in function . Pls check this
So here , x = 5 , why is y = 0? For the 1st one

8:22 AM
it doesn't say f(5)=0 anywhere in there
it says that f(x) gets smaller and smaller if we keep increasing x, which is true

0.03125 < 0.05 Good enough for me

@BalarkaSen i'm intrigued by the last name. Apparently Larry Guth is the son of Alan Guth, who i recognize as one of the people who came up with the idea of cosmic inflation
(which is something so far out of my expertise that i can't even pretend to talk about it)

@user586228 i can help for 5 mins, no more.
but you need to respond before i finish my night cap, which is $<=5$ mins.

nice

8:45 AM
@user586228 you are given the numbers for $>=1$, $=2$, $>=2$ passes. from this you can figure out the numbers for $=0$, $=1$, $=2$, $=3$. assuming independence, you can get that $pmc$ is the same as $=3$. this cuts out two options. now you need to compute $p+m+c$. draw a venn diagram with 3 circles corresponding to $p,m,c$. you want to add the 'areas' of $p,m,c$. note that the area is one times the chances of $=1$ plus two times the chances of $=2$ plus threes times the chances of $=3$.
good luck & good night!

9:06 AM
Ok.Thanks all I got it
i have another question
For Q3
is it all values of x except -7/3

Why do you say that?

Denominator shouldn’t be 0 @user85795

Ok, but why can you not divide by 0?

Then g(x) would be infinity right

Right, "infinity" is not a number

9:11 AM
it's not that g(x) would be infinity if you tried to compute h(-7/3)
it's that you'd be trying to evaluate g(x) where x isn't a number

No.just find domain of h(x)
Should I write x = 2x+3/3x+7 instead then

what do you know about g(x), thoguh
no, that'd be improper
better to write f(x)=(2x+3)/(3x+7)
so that you have h(x)=g(f(x))
but this isn't a question you can answer without knowing the domain of g to start with
as an example: is 0 in the domain of h(x)? well, f(0)=3/7, so you'd be computing g(3/7). so if 3/7 is in the domain of g, then that's fine.
but if it's not, then 0 won't be in the domain of h(x)
so you really can't know the domain of h without knowing the domain of g

Ok.
sorry had gone for a min @Semiclassical

The question is cut-off on the right hand side where it says "is ..." In the photo @user102532?

it also seems like the previous question is asking about the domain of g(x)

9:17 AM
There is nothing written there
typo in question
@Semiclassical then how do you find g(x)

Domain
But in the textbook answer is there
@Semiclassical

is the textbook answer "everything but -7/3 is fine"

No.That was my assumption
in book , it has different amswer

okay. then my guess would be that they want you to use the same g(x) in Q4 as in Q3
so, what did you get for the domain of g in Q3?

9:23 AM
I think he left, again.

shrug

“Spoon feeding in the long run teaches us nothing but the shape of the spoon.”
― E.M. Forster
2

Sorry. Battery low
answer is 5 U 9 given
U is union

so only g(5) and g(9) are defined?

9:28 AM
Yes,That is what it says.This book has lot of wrong answers also.

well. assuming it's correct, then h(x)=g((2x+3)/(3x+7) only makes sense when (2x+3)/(3x+7) equals either 5 or 9
so that tells you what the domain of h is

So , is it right

is what right

5 or 9

you haven't told me what g(x) is, so how would I know?

9:31 AM
ok.

Directional derivative of a function $f$ along a curve $\Gamma$ at a point $\mathbf x$ do not necessarily equal to the directional derivative of $f$ along the tangent vector of $\Gamma$ at the point $\mathbf x$. This statement is correct, right?

9:52 AM
@copper.hat Could anyone tell me two things...(1) Why are we assuming independence?(2)Why is pcm=p3(3) Why does it cut down two options?4)Why is the last line holding true,""note that area is one times the....".
Anybody can explain this to me whoever knows..

2 hours later…
11:47 AM
@BalarkaSen ah, that sounds reasonable, thanks

12:33 PM
In the proof of weierstrass preparation, we have that $f(z_1,0,\cdots,0) \neq 0$. This gives us an $\epsilon_1$ sized disc around $z_1$ in $\Bbb{C}$ where $f(z_1,0,\cdots,0)$ is nonzero. Then we go on to let $a_1(z_2,\cdots,z_n),\cdots,a_d(z_2,\cdots,z_n)$ denote the zeroes of $f(z_1,z_2,\cdots,z_n)$ inside the $\epsilon_1$ sized disc. Why should this zero set be finite?
finite for fixed $(z_2,\cdots,z_n)$

$f$ is analytic?

Yeah
You can have analytic functions which have infinitely many zeroes inside $\Bbb{D}$ right

so if you fix $(z_2,...,z_n)$, that's an analytic function of one variable and those have discrete zero sets, so if you pass to a slightly smaller closed disc, it will be finite
analytic functions of more than one variable can have infinitely many zeroes, but those of one variable can't (in a disk, that is)

$\sin(\frac{1}{1+z})$ ?
That is an example of a one variable function with infinitely many zeroes inside $\Bbb{D}$ isn't it.
Or am I missing something

0

I'm reading through a proof on the uniqueness theorem of Laurent series in my lecture notes and came across this sentence: The point $c$ ($\in \mathbb{C})$ is a limit point of zero points of the (analytic) function $f$ and therefore there exists a circle $K$ around $c$ where $f=0$. Under wh...

12:44 PM
no, you're right, I misspoke in the last message
but "pass to a slightly smaller closed disc" still works

Right that is a good point, the zeroes are discrete

You don't even have to pass to a smaller disc since the function is analytic on $\Bbb C$

also true

Oh right damn it, how did I miss that

1:03 PM
When do I assume two events to be independant
Unless given do I take it for granted?
Also tell me something for this curve
Is the first derivative also zero
Btw I know that this is a point of inflection

1:32 PM
Depends it looks like it
as long as at that point slope is horizontal
I'm wondering for RHS, the outer sup is really interchangeable with max right?
S, T are bounded nonempty sets in R

Yes, the sup of a finite set is its max

aight thx

finite non-empty set, to be pedantic

Empty sets works as well if you wanna go there

So how does having $k$ perfect and $f''(x) = 0$ (possibly not necessary condition for this question) imply that $f'(x) = \Sigma_{i \textit{ } even, 0 \leq i \leq s -1} a_{i+1} x^i$ when $f(x) = \Sigma_{i = 0}^s a_i x^i$?

1:38 PM
it's $-\infty$ either way

well, it's a definitional matter, I guess, but to me the maximum of a set should be an element of it and the empty set simply doesn't have a max

it all comes down to the eternal debate whether 0 is an integer

scholar of the empty set

@BigSocks Are you in char 2 ?

oh dang, maybe that's it
the previous example was in char 2...
I didn't think that assumption carried over but it makes a lot of sense if it does
yeah no, looking ahead this was just a split up claim within the same example. Thanks. should've been tipped off by the $even$

1:43 PM
And the fact that $f'(x) = \sum i a_i x^{i-1}$, hence you're asking that $i a_i x^{i-1}$ is zero whenever i is even, and i =1 whenever i is odd

yeah, lots of now apparent ways it could be seen

@Thorgott $-\infty$!!!

I disagree

Only because you never had to work with this

$-\infty$ factorial factorial factorial ?

1:55 PM
For stopping times this is super intuitive. Define a random time as the infimum of some random set, for example this first time that a random walk hits 0
Doesn't happen? => value is inf

What can I do about titles when I can't write my question in the title, since my title would be 240 characters? math.stackexchange.com/questions/3987557/…
The title is now ambiguous, or is there something I can edit it to which would be less ambiguous?

So that for all t smaller than the stopping time, the process does not hit the intended set

yeah, cause that's an infimum
I do agree the infimum of the empty set is infty

... take a process indexed by negative numbers, do the same as before with sup?

He disagrees with max and min
Not inf and sup

1:59 PM
Hey some guy just removed one of my tags (propositional calculus)? Why is that?

I don't see the difference, max is the sup of a finite set and the empty set is finite