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12:00
how many solutions does $\pi^x=-2x^2+6x-9$ have?
@BalarkaSen eh, sometimes I touch the touchpad and accidentally select some text which then gets overwritten. :(
Also $T_x={Y\subset X| X\setminus Y \text{is finite}, Y =\emptyset}$ so $X\setminus U_1$ cannot be finite and since it is there in the topology it will be empty and similarly $U_2$ the other and hence there wont exist any separation and thus it will be connected @Soham
Is it fine ?
Huy
Huy
@SohamChowdhury: Use a real mouse.
why can't $X-U_1$ be finite? you want to say either $X - U_1$ is finite, or $X - U_2$ is finite.
But not both.
Yes yes ...
12:02
@Huy yeah.
@Soham watccha been up to?
oh, physics.
well, mechanics is easy stuff.
Huy
Huy
@SohamChowdhury: you think?
12:03
in 11th grade, yes.
Yes it is super easy.. :)
Balarka wrinkles noses
@Soham Doing torque .....
You did torque?
it's in the class 10 syllabus.
12:04
No In 11..... mine
use three dots, not four.
Are you ICSE or CBSE?
Ellipsis (plural ellipses; from the Ancient Greek: ἔλλειψις, élleipsis, "omission" or "falling short") is a series of dots that usually indicates an intentional omission of a word, sentence, or whole section from a text without altering its original meaning. Depending on their context and placement in a sentence, ellipses can also indicate an unfinished thought, a leading statement, a slight pause, a mysterious, echoing voice, or a nervous or awkward silence. Aposiopesis is the use of an ellipsis to trail off into silence—for example: "But I thought he was . . ." When placed at the beginning or...
@Rememberme ISC
Hmm... Me CBSE .. so we are well behind you guys
do you have some kind of paperweight on your full stop button?
12:06
No i dont ... :p
or is your apostrophe key another full stop button?
that seems plausible too.
anyway.
Currently I am watching insidious 3 . Seems scary @Soham
drats. I need an algebraist right now, but everyone seems out. I can just go and ask in the homotopy theory chat, but I am afraid I will get to know more than I want to.
Is there any problem if you get to know more @Balarka
yes, there is.
12:10
oh.. I wont ask more
I suspect all of what I want to do has been done by Grothendieck, so knowing more might solve all of my problem :(
Tell me, Balarka, just as an, uh, academic curiosity: does algebraic geometry have any prerequisites besides heaps and heaps of algebra?
Don't skin me.
@Soham have your teachers ever told you " dont do what you are doing , just study school maths"?
official prereq is nothing other than algebra. but knowing a fair amount of topology and differential geometry is useful.
12:13
algebraic geometry is all about taking topological concepts and analogizing it in algebra. but it's not reasonable to wait until you have learned everything in top. and diff. geo. to start algebraic geometry -- that'll take a few years.
Munkres does too much general topology. I'm not sure I'll ever finish the first four chapters.
I am in the third chapter...
tietze, uryshon, tychonoff are necessary to start alg. top. or whatever you want to. and it's not reasonable to expect that you'll finish all of topology in a month
Though there are few nice chapter like:
Quotient spaces , Imbedding of manifolds ,
etc
12:14
yes, those are nice.
@BalarkaSen that reminds me of what you said just now.
where is that snapshot taken from?
Preface i guess
Hartshorne?
12:15
Dhur.
Vakil's notes. I downloaded them a looong time back (~9 months, I guess). They scared me. :P
oh, ok.
"French literature"
actually useful.
for EGA and whatnot.
yes, lol.
why and how?
EGA, SGA, GAGA, . . .
12:17
there is no translation of EGA/SGA/FGA available.
all those Bibles.
French literature and topology .. seems poles apart
@Soham GAGA is a theorem. duh.
Though I dont have any sense of humor.... Is this humor
It's a paper, Google says. But what do I know, lol.
12:18
oh, didin't know.
@Rememberme no, it's not humor.
It is.
(IMO)
if you want to read algebraic geometry, you have to go through Grothendieck's works.
and to do that, you have to know some french.
Wha??????
agreed, French "literature" is a bit too much
@Rememberme yes.
12:19
No translation?
6
Q: Is an English translation of Grothendieck's EGA available?

Amitesh DattaI have always wondered whether there is an English translation of Grothendieck's EGA (Elements de Geometrie Algebrique) available. Does anyone know whether there is and if so where I can find it? If not, are there English texts that cover similar material to the EGA that you would recommend? (My ...

nope, none
(iirc)
the guy who asked it was 15 then, btw.
@Soham funny. prof linked that to me a couple months back when I was complaining about studying French.
My god .. I left french in 6 standard, Huge mistake
12:20
you are studying French?
nope, I am not.
will, the next year.
I will do French for dummies
I think that will take me to the shore...
you don't have to study French if you don't want to do algebraic geometry
Academic question part 2: if I wanted to study AG, what should I study apart from algebra?
Again, don't skin me. I'm just keeping tabs on all the options.
literally nothing apart from algebra is required
loads, loads of algebra
12:22
yeah. like AM and everything?
Huy
Huy
40
Q: The importance of EGA and SGA for "students of today"

user1161That fact that EGA and SGA have played mayor roles is uncontroversial. But they contain many volumes/chapters and going through them would take a lot of time, especially if you do not speak French. This raises the question if a student, like me, should even bother reading EGA. There must nowada...

just A-M won't do.
I will study A-M and only read the first chapter of Hartshorne. At least, that's the plan for next year.
Lot more is needed to really study algebraic geometry.
ah.
I dunno, I'm fast getting tired of Munkres' inordinate nonsense about $S_\Omega$ and stuff, that's why I was asking.
(although, as you say, it might be useful later)
recommend you eject that tiredness.
Who gets tired of Munkres.....
Its the best book after Spivak I encountered
12:24
it'll spread and will make you tired of mathematics in general
Huy
Huy
I didn't like it either.
(speaking out of sheer experience)
what made you tired?
Same question here
algebra.
12:25
what, specifically?
group theory.
You studied advanced group theory?
Like all that geometric / hyperbolic stuff?
Same here ......
(out of few days experience)
that's geometric group theory.
sylow theory was tiresome at first. i even stopped doing math for a month.
but when i got back, it was amazing
I love algebra. Absolutely, totally love algebra. (at least, what I've encountered till date, which is hardly a drop in the ocean)
But analysis-ish arguments . . . euuuughhh
12:27
I was similarly ignorant towards analysis.
Huy
Huy
I remember.
However, I feel I'd do better if I knew more calculus. Could have done diff. top.
I was ignorant towards commutative algebra too. Now I feel bad about that - knowing more of it would have got me ahead and I'd have been able to do alg. geo. sooner.
Feeling ignorant about math will only land you into trouble (i.e., pull you back from studying what you'd like to study)
2
Your real analysis course will help you , Ted once told to me
@Huy indeed you do :P
Nevertheless, I'll do algebra for a while now, at least I visit SB again and ask him where to go from here.
It's easier to focus on one thing with the limited time I have.
12:33
I emailed this IISc guy and he never replied....
But I don't require anyone since I have good people like you @Balarka for advice @TedShifrin and @MikeMiller if he ever starts to talk with me) and many more people :)
you have a lot of time, @Soham.
11th grade means "loads of free time".
if you ever want a letter of recommendation, you'll need a real-life mentor.
sounds bad, but that's the way the world works. nobody's going to trust you if you talk about Galois theory with teary eyes. :(
No @Balarka .....
@BalarkaSen not in my world.
I have exams in a month.
KVPY as well, in October.
I have exams in August
Huy
Huy
12:34
@BalarkaSen: Aren't you in 11th grade or so too?
@Huy he's in 10.
I wouldn't care about my exams in 11th grade if I were you.
Even you giving KVPY @Soham?
Huy
Huy
:P
My mom dad do.. So i got to do them
nicely
12:35
I mean, who does? Spend time on more useful things.
@SohamChowdhury So do you know anyone who can be my mentor?
Even w/o thinking about time, Munkres just makes me angry (although I will try to reduce that)
Because I have no one
@Rememberme nah
Huy
Huy
You mean like sports, @BalarkaSen? :)
12:36
@Huy what are those?
@Huy nah. I will spend time on math.
@SohamChowdhury you said you like topology, and now you don't :P
Same here ... @Huy But i cannot do coz of my parents
that's what I meant when I said "passing fancy"
I like cooking, not cutting the heads off chickens, as I like to say.
Whats the problem in topology @Soham ?
12:38
or, if it's about the book, try Simmons
SB's orders :(
orders?
you were violating his orders from the beginning
/partially violating
It totally is about the book. I like Lee a lot.
@BalarkaSen eh, he told me to study Artin. I do. ;)
no, you want to jump to algebraic topology
well, use Simmons along with Munkres
12:39
Then do what you like ....
Balarka always says that
@BalarkaSen Yes, I do.
Simmons is good, in my opinion.
Very nice for intro @Soham
I did half of topology from there
@SohamChowdhury you'd get bored with algebraic topology too :P
it's not just about fancy pictures either
And then suddenly if you get a craze of functional analysis ... Simmons can be again a good intro @Soham
12:40
@BalarkaSen I don't think so, not at all.
There's a ton of algebra in there as well.
you didn't think that when you studied topology either
no, there's not a ton of algebra.
I never liked point-set. You know it.
can't do alg. top. without point-set. you'll have to do rigorous arguments in alg. top. too.
And the other thing is that you can go for days without proving anything interesting. (except, say, Heine-Borel)
Its good that its not me (who always is) whom balarka is pointing out mistakes of :p
12:41
the very defn of fundamental groups uses pasting lemma (it's in Munkres)
Ahh...
great one liner proof
I can prove the gluing lemma.
(I learned it in Armstrong)
I know you do, I just gave an example that you need point-set things in alg. top.
Lower limit topology?
$S_\Omega$?
how can you assign algebraic invariants to your spaces without knowing topological spaces, man?
12:43
Yes, but not all of what Munkres does is required, right?
well, knowing pathological topological spaces helps
That's my point.
Urysohn, Tietze, Tychonoff, fine.
at some point of time, you'll need all of what is in Munkres
But he does a lot of unnecessary stuff.
No everything is required (except Baire spaces and dimenison theory also a nowhere differentiable function )@Soham
12:44
@BalarkaSen I can learn those things as I go, can't I?
@SohamChowdhury pfs of all those theorems need previous stuff
throws up hands in exasperation
so you mean Lee or Armstrong won't do?
I want to learn the bare minimum I need to get started on AT, not everything up to French literature, man. :P
Again do what you like @Soham But do everything
@SohamChowdhury how can you say something is unnecessary without knowing where it's used??
So he does nothing unnecessary? If then, I apologize, I didn't know.
12:47
@SohamChowdhury you'll get stuck that way. people who use Lee/Armstrong get rigorous point-set courses before in their undegrad.
@SohamChowdhury nope, none. but to actually study algebraic topology, you need some selected chapters and all of what's in there.
how much of Munkres' part I did you do?
@BalarkaSen which?
1-4?
@SohamChowdhury 1-5.
all the separation axioms?!
12:49
also, he does space-filling curves in 7 or 8, I think. those are important too.
I've done those from Armstrong.
(there's a bit on them, not much)
Yes Space filling curves .. amazing stuff
there's a lot more to space-filling curves than you think.
2
Oh topology is so damn nice!!
I don't recall how much Armstrong does
@SohamChowdhury remembering the separation axioms is not needed. I recommend 4 because of Uryshon and Tietze theorem.
12:51
and 5 is?
Tychonoff, I think
What about Baire spaces @Balarka Aren't they important?
very well then. I'll get there slowly.
Dimension theory ?
dimension theory is good.
I never needed Baire spaces
@Soham also, he does stone-cech cptication in ch. 5. i never cared about it, but since you're a category theory lover :
12:52
Okay ... Dimension theory is nice
@BalarkaSen the Wikipedia diagram?
stone cech cptification $X \mapsto \beta X$ defines a functor from $\mathsf{Top}$ to the catgeory of compact hausdorff spaces
yes, I learned that yesterday.
$\sf CHaus$, yes.
do you know what stone-cech cptification is?
not really, not yet.
I saw a Wiki link in the chat.
12:54
then what's the point of knowing that it's a functor lol. but in a more serious note, that's the point : cool things are all over in Munkres
you just have to translate Munkres's boring monotonous way to state those into your language
Cool things are not over...
Topologists sine curve....
well, then. I'll do 2 and 3, 4 with an emphasis on Urysohn and Tietze, and Tychonoff from 5. (slowly)
Is that enough?
Imbedding of manifolds
@SohamChowdhury yep.
almost.
Nothing is ever enough
12:55
@BalarkaSen what else, in the way of general top?
There always exists something that will stump you
@SohamChowdhury what d'you mean?
@Soham So you want to reach altop quickly ?
nothing more than that is needed to do alg. top. but there are a lot of cool things
@BalarkaSen okay. I can always learn stuff as I go.
12:56
for example, Mike told me about the Nagata-Smirnov metrization theorem.
it's in ch. 6, I think, something I never did
Its there in Munkres !!
it's very cool
Also the Kuratowski set thingy
I really liked it
So many things can be thought and deduced from it
It's really just computing the order of a monoid with a given presentation. :P
I figured.
12:58
That was for him, not you.
no, I mean, I figured it was a combinatorial problem.
But still figuring that doesn't mean the end of the story ...
I haven't really given it a though.
That one question kept me busy for 2 weeks
It really felt i was doing research :p
13:00
anyway, guys, I should go.
thanks, @Balarka.
me too.
I'll make a checklist and cross stuff off. :P
gotta study and prepare for tomorrow.
sure @Soham.
@SohamChowdhury ?
13:00
ISI?
Balarka you in ISI?
gotta print out what I have latexed up
and think more about the problems I haven't figured
 
1 hour later…
14:06
Is there a way to get a definition of $P_d(k,n)$ knowing a definition of $H_d(n)$ and the following fact ? $$H_d(n)=\sum_{k=1}^n k! P_d(k,n)$$
Huy
Huy
Yes.
@Huy Do you have a hint to give me ? :)
Huy
Huy
@iluso: You could try to define $P_d$ as the numbers that satisfy your given equation, if it's well-defined, you have your desired definition. If that doesn't work, maybe using Möbius inversion?
@Huy Thanks, I'll look into that ! $H_d$ is already ugly, it will be fun
@Huy Thanks a lot
14:48
@Rememberme baire spaces occur in functional analysis.
15:26
Oh.. @BenDover
Huy
Huy
BCT is actually really cool.
One of my favourite parts of functional analysis.
15:41
@Huy can I get help from you ?
Huy
Huy
Depends on what kind of help you need.
Topology
@Huy lets say X is a connected space and Y is a connected space and A a d B are proper subsets of X and Y respectively .
How do I prove that (X*Y)-(A*B) is connected where "-" denotes the set minus
Huy
Huy
Use the definition?
I don't think we can....
Lets say we have a separation for (XY)-(AB) then the separation will belong to (XY) and not to (AB) . But since we know that (XY) is connected so that separation cannot be for (XY) . Now after this what should I do @Huy
The Dirichlet energy funtional describes the variability of a function over some region.
Are there other examples of functionals that describe interesting properties of a function over some region as well?
15:58
@Huy any ideas?

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