Mathematics - 2014-12-17 (page 1 of 5)

Khallil Benyattou

00:01

Hey all! Can somebody drop me a hint for this question?
I'm unsure of where to even begin.
"Show that if $x$ and $y$ are non-zero integers and $x^2 =y^3$ then $x=a^3$ and $y=b^2$ for some integers $a$ and $b$."

Pedro Tamaroff

@KhallilBenyattou Note that any prime factor of $y$ is a prime factor of $x$ and vice versa.

Now consider prime factorizations.

One can do this nicely like this. Fix a prime number $p$, and let $\nu_p(x)$ denote the unique integer $n$ such that $p^n\mid x$ but $p^{n+1}\nmid x$.

Khallil Benyattou

May I ask which notation you use for writing out prime factorisations, @Pedro?

Pedro Tamaroff

@KhallilBenyattou Any understandable notation works =)

One checks that $\nu_p(x^m)=m\nu_p(x)$ for any integer $m\geqslant 0$.

Applying $\nu_p$ to your equation gives $2\nu_p(x)=3\nu_p(y)$. Since $\gcd(2,3)=1$, this gives that $3\mid \nu_p(x)$ and $2\mid \nu_p(y)$.

Say $\nu_p(x)=3k, \nu_p(y)=2j$. Then one gets $2\nu_p(x)=6j\implies \nu_p(x)=3j$ so $x$ is a cube, and similarily $\nu_p(y)=2k$, so $y$ is a square.

Khallil Benyattou

I've never seen a method like that!

Pedro Tamaroff

Valuations are good!

Khallil Benyattou

00:13

Is that what they are called?

Pedro Tamaroff

@KhallilBenyattou Yes. In this case, to each rational number $r$ we may assign a (possibly negative!) integer $n$ such that $r=p^n r'$, and $r'$ is a rational where $p$ "doesn't appear".

Basically, write you rational number as a product of integer powers of primes, and take the integer this prime is risen to.

In this case I considered the valuation on the integers only.

Khallil Benyattou

I don't quite understand the second part. Why must we check the property that $v_p \left( x^m \right) = mv_p (x)$ for any integer $m \geqslant 0$?

Pedro Tamaroff

@KhallilBenyattou Because it is the useful part of the argument.

Applying $\nu_p$ to $x^2=y^3$ gives $\nu_p(x^2)=\nu_p(y^3)$.

Then I want to get the powers down.

$\nu_p$ satisfies $\nu_p(xy)=\nu_p(x)+\nu_p(y)$, so you can prove the above by induction.

Khallil Benyattou

For the last part, if $v_p(x)$ denotes the unique integer $n$ s.t. $p^n \mid x$ but $p^{n+1} \nmid x$ and $v_p(y)$ denotes the unique integer $m$ s.t. $p^m \mid y$ but $p^{m+1} \nmid y$, then we can conclude that $p^{n+m} \mid xy$, so $v_p(xy)$ denotes the unique integer $n+m$ s.t. $p^{n+m} \mid xy$, right @Pedro?

Pedro Tamaroff

@KhallilBenyattou Well, you need to show that $p^{n+m+1}\nmid xy$.

Hint If $n+m+1\mid xy$, then either $p$ has $n+1$ factors in $x$ or $m+1$ factors in $y$. Why?

(This is the pigeonhole principle!)

Khallil Benyattou

00:28

May I ask why it's $-1$ in the exponent?

Pedro Tamaroff

That was a typo.

Khallil Benyattou

Also, do you mean $p^{n+m+1}$ instead of $n+m+1$ in the second line, @Pedro?

Pedro Tamaroff

@KhallilBenyattou Yes.

Ted Shifrin

@Pedro: You wanted to discuss thingies?

Pedro Tamaroff

@TedShifrin Yes.

Khallil Benyattou

00:34

Is that because we've already established that $p^n \mid x$ and $p^{n+1} \nmid x$, then it's left that $p^{m+1} \mid y$ if $p^{n+m+1}$ indeed divides $xy$ (and the other argument is the same by interchanging $m$ and $n$), @Pedro?

Pedro Tamaroff

@KhallilBenyattou We already know that $n,m$ are respectively the largest integers $k$ such that $p^k$ divides $x,y$ respectively.

We want to see that $n+m$ is the largest integer $k$ such that $p^k$ divides $xy$.

It is clear $p^{n+m}\mid xy$. We want to see $p^{n+m-1}\nmid xy$.

Now if $p^{n+m+1}$ divides $xy$, consider two boxes, one for $x$ and one for $y$.

Khallil Benyattou

I thought that's what I was getting at with the contradiction that $p^{m+1} \mid y$ because by original definition for $v_p(y)$, $p^{m+1} \nmid y$, @Pedro.

Pedro Tamaroff

@KhallilBenyattou That's the point yes.

Ted Shifrin

@Pedro, so? :)

Pedro Tamaroff

If we distribute the $n+m+1$ factors, either $x$ receives $n+1$ factors or $y$ receives $m+1$ factors: if $x$ receives at most $n$ and $y$ receives at most $m$, we would account only for $n+m<n+m+1$ factors, @KhallilBenyattou

@TedShifrin I wanted to discuss the last exercise in your final.

How to show there are infinitely many roots.

Ted Shifrin

00:39

Yes, so I presumed.

You need to learn what order of an entire function is, and decide what order that function has.

Khallil Benyattou

Ah, I kinda see what you mean. Thank you, @Pedro! I'll try and write up a solution to it. ^_^

Ted Shifrin

have fun @Khallil

Pedro Tamaroff

@KhallilBenyattou No problem.

@TedShifrin I've just read what the order of an entire function is. So that function has order... $1/2$?

Wait.

Ted Shifrin

Yup (make sure you prove it) :)

Pedro Tamaroff

OK, good.

I am guessing functions with order $<1$ have infinitely many zeros?

Ted Shifrin

00:43

Functions with non-integer order have infinitely many zeroes (indeed, take on every value infinitely often).

Pedro Tamaroff

Oh, cool.

Ted Shifrin

I'll let you figure that out?

Pedro Tamaroff

=O

Ted Shifrin

There is a real theorem here ...

Mathy Person

01:33

does anyone here have any experience with basic graph theory (simple graphs only)?

r9m

@robjohn sensei can you check my answer to my own question here when you have time ? :-) I didn't receive any satisfactory answer of it for a long time !

Mike Miller

01:57

Hm... hell of a nap

Mathy Person

this chat is barely active currently

Studentmath

@Mathy ask (quickly), I'm after work so I am extremely exhausted but I probably can still think if it's simple enough

Mike Miller

Hi, @Ted

Ted Shifrin

@Mike ... @Studentmath: It's way past your bedtime!

Studentmath

4 am..

I should find more reasonable works

Ted Shifrin

02:01

More reasonable hours!

Studentmath

That too

user130018

Hi guys

Ted Shifrin

hi mr eyeglasses

Mike Miller

@TedShifrin So, got time to decode comments?

Studentmath

Well @Mathy, I am off to bed. Ping me and I will check if I can help tomorrow if you didn't get it yet.

G'night @Ted @Mike Eyeglasses

Ted Shifrin

02:03

oh, I've been grading finals most of the day, so not sure I have mental strength, @Mike

night @Studentmath

Mike Miller

Oh, @Ted :(

Alright.

Ted Shifrin

You're doing topology stuff I don't know, @Mike

Soon you'll hate me just like Balarka does, @Mike :D

Mike Miller

@TedShifrin The question is simpler than that. Qiaochu said something to the effect of "Pick a homeomorphism which swaps the smooth structures". I interpreted this to be a homeomorphism that pulls back one to the other. He claimed that these exist by definition of a top. manifold supporting more than one smooth structure; but I seem to have written down an (almost tautological) proof that if $\eta = f \circ \nu$, then $f$ is a diffeomorphism...

Ted Shifrin

Whatever that meant ...

usukidoll

@MikeMiller where you get that hat?

Mike Miller

02:07

@TedShifrin But it's about smooth structures. :(

That's, like, your jam. Your bread and butter.

Your peanut butter and jelly.

Ted Shifrin

Can't we make this quite simple? Take $f(x)=x^3$ mapping $\Bbb R$ to $\Bbb R$. It's not a diffeomorphism in the usual structure. But it will be in the atlas in which $x^{1/3}$ is a chart. So, setting this up the right way should do what Qiaochu meant.

No, I don't think about smooth structures particularly.

Mike Miller

Yes, but I'm talking about exotic structures - structures that aren't diffeomorphic.

Ted Shifrin

But even if they are, this sort of thing gives a homeomorphism that isn't a diffeomorphism.

Worse if the structures aren't diffeomorphic, eh?

Mike Miller

It'll give a homeomorphism that's not a diffeomorphism, but I don't think it'll give a homeomorphism that pulls back the smooth structure you wrote down, @Ted.

(Which is how I interpreted 'swap the smooth structures')

Ted Shifrin

It should if you do it in the right direction :)

Mike Miller

02:12

hm

then the proof I wrote down must be wrong, at least, so maybe his comment makes sense to me.

Thanks a bunch @Ted

Behaviour

@MikeMiller What was your 26th hat?

Mike Miller

@Behaviour Finally got Breaking Bad after a user edited in their ideas post-closing.

Alan

On the plus side, just made 2k rep. On the minus side, I really need to be studying for this stupid algebra qualifier. Grr :)

Mike Miller

I actually can get the treasure hunter hat on MSE (I was resigned to only getting it on Academia) - I just need to review 20 close votes per day until the end of Bash. And that I was going to do already.

Behaviour

@Alan 2K? Go edit all the misformatted questions, forget the qual.

Alan

02:26

grins I haven't done algebra in a full semester. Completely forgot just about all my Galois theory. Though I did approve my first edit!

Behaviour

@MikeMiller Sadly, I reviewed 2300+ close votes already, so no new badge coming from that direction. And LQ too. The other queues are usually empty.

Mike Miller

And upvoting, of course, isn't an option for you.

4

Behaviour

@MikeMiller Got those. Hats are awarded quickly enough so there's time to retract.

Mike Miller

@Behaviour I was thinking of the gold badge for having 600 upvotes.

Behaviour

There isn't such a thing. Electorate does not distinguish by direction, up or down. And I got it long time ago.

Mike Miller

02:30

Oh, I see.

Different set of distinguishing factors.

I should start answering questions by 1-rep users to maximize probability of getting Naruto. I figure a decent soft question or reference request might get 30 minutes or less. I'm only going to take one shot at that, though, not spam the site with soft questions.

Alan

skims the chat Does anyone have a good book suggestion for multivariable analysis? We used Munkres's Multivariable book in my class, and I got completely lost in notation.

What does Naruto take?

Mike Miller

Accepted answer that's not voted on for 12 hours. In particular, the OP can't vote on it.

I don't have any particular suggestions, @Alan, but that particular question has surely shown up on the main site before.

Alan

Yeah, I should skim it at some point, was more a question of opportunity since that seemed to be the topic. Right now I really need to force myself to study Algebra. sigh. I like analysis.

Kaj Hansen

Hey guys

Mike Miller

Hey Kaj. I see you stopped badmouthing hats.

Kaj Hansen

02:35

I got 2 secret hats without even trying @MikeMiller ;)

For all I know they're pretty common though, so...

Holy shit, is this your site @MikeMiller? http://www.math.ucla.edu/~smmiller/90s.html
I'm laughing so hard right now.

Mike Miller

If that's actually the first result for my site on google, I'm in trouble. I should probably get rid of it.

This is my site. Click ctrl+A.

Kaj Hansen

hahahaha, that's so much more boring though

Alan

Boring is another semester of teaching Methods of Calc to a classroom where half of the students don't know algebra. sigh.

Mike Miller

@Behaviour Can you make a script that shows questions posted by new users (users with rep 1), sorted by activity, not hiding questions with many downvotes?

Kaj Hansen

@Alan, would you rather teach precalculus? Serious question.

Alan

02:45

At my school? Yes, only because of the role the two courses hold. Precalculus is only taught for students who want an extra prep course for calculus. Methods is the 'end' course for business majors and soft sciences (psychology, etc.).

Plus, I'm at a 'nontraditional' school, so you get a lot of people who haven't even looked at algebra in 3+ years and are now trying to learn calculus....

Behaviour

@MikeMiller My Review+Edit extension does something like this: looks at the 100 newest questions, takes those by 1-rep users, as well as those with downvotes and closevotes (regardless of rep).

I can write another script like that but I don't quite understand the use case.

Alan

Add to that the joys of our initial math placement test, which is taken online, from home, with no proctoring. The math dept.'s been trying to get that fixed for years.

Kaj Hansen

I'd prefer precalculus too @Alan. I do a lot of tutoring here at my school, and its more difficult to help people with calculus since that usually entails also reviewing a lot of the pre-req material.

Oh man. At least the placement test here is on-site and proctored! :O

Mike Miller

Naruto requires that the OP not upvote your post, which usually only happens with users of rep below 15, @Behaviour; restricting to 1 makes it more unlikely they'll reach 15 with upvotes. Those with downvotes help find posts suitable for Red Baron.

Alan

@KajHansen nod I need to run a correlation between people's day 1 quiz scores (which measures their prereq knowledge) and their final grades, but I highly suspect it's highly correlated

Mike Miller

02:49

Your extension sounds more actively useful for my purposes (as well as in general).

Alan

We have retakes of the test on-site and proctored, but the first time...yeah. It's ugly.

Mike Miller

It seems like it's only accessible via 10k tools, @Behaviour.

Alan

This is my second semester teaching it (and in general), so...we'll see. Finishing up my 2nd year of grad school

Mike Miller

Alan has Naruto already. Showoff.

Kaj Hansen

Agreed @Alan. I have a general rule that when people say they're struggling with calculus, they're actually struggling with the pre-reqs. This is, of course, for the typical calculus sequence and not the theory courses that are taught out of Spivak, e.g., and are actually pretty difficult.

Alan

02:50

laugh Without even trying. Woops

I really enjoyed Spivak's Calculus, but of course that was for my 4000 level undergrad analysis class. We use Stewart here for the calc 1/2/3 sequencee

Kaj Hansen

They have a special 2000-level sequence taught out of Spivak here. I never got to take it though because I tested out with AP Calculus exams :/

I had a rigorous Calc 3 course though. I've never worked so hard to pass in my life :L

Behaviour

@MikeMiller "only accessible via 10k tools"? It's supposed to rewrite the /review page. And I use it on SO where I am under 250 rep and don't have access to the actual reviews, just by navigating to site/review

Alan

Yeah, my calc 3 teacher was awesome/rigirous. I'm getting to take him for a 6000 level set theory class this semester, I expect it to be awesome and incredibly hard :)

Kaj Hansen

That's awesome! What textbook are you guys going to use?

Mike Miller

Oh, I see. I saw the Tools descriptor and was a bit confused.

Alan

02:55

I had a very, very odd math background....summer school of 5th grade through 9th grade I was learning out of MIT's elements of mathematics curriclum, set theory/abstract algebra/etc. 10th grade calc 1, 11th grade calc 2/3. 12th grade, elective credits: Algebra 2, treig/geometry :)

Not sure yet, I need to email the teacher. Been slacking post finals.

Kaj Hansen

Holy crap! I actually had no idea what math was about, or even that deeper math existed beyond calculus until 2 years ago.

Alan

Now, if I'm really, really lucky, we'll scrape together enough students for the department to scrape together enough money for us to offer Algebraic topology in the summer. The joys of going to a small department.

Kaj Hansen

Wrote my first proof in the first week of that calc 3 course as a freshman, haha

Alan

grin Yeah. And then I didn't actually finish my bachelors until age 35. And it was only a B.A. :)

Have you read Godel, Escher, Bach: An Eternal Golden Braid?

Kaj Hansen

I haven't, but I do own the book. And I have free time over the next few weeks ;)

Alan

02:58

It's worth the time. Among other things, it walks you through Godel's proof, informally :)

Behaviour

@MikeMiller This SEDE query picks unanswered questions by users with rep<15.

Kaj Hansen

That's pretty cool. I know absolutely nothing about mathematical logic, so maybe that'll be a good place to wet my appetite.

Alan

It's written for a general audience, but goes into a lot of deep things. Very much a good place.

A classmate of mine gave a talk on a historical paradox, since resolved, whose name I can't remember offhand....was really neat though. In effect, there exists a countable model of set theory that exhibits an uncountable set inside of it :).

Mike Miller

How do you determine titles that are potentially bad, @Behaviour?

Kaj Hansen

If only I knew what that meant :) I'll check that book out though! I'm also planning on brushing up my abstract algebra by going through a new textbook of mine and also start skimming over next semester's point-set book over the break.

Alan

03:04

yeah, I'm trying out a new (for me) algebra text now (Dummit & foote)

Mike Miller

I think D&F talk too much. But their exercises are good.

Kaj Hansen

I really like D&F. I haven't gone through anywhere near the whole thing, but I've revisited the sections on field extensions and Galois theory for something I needed recently, and it was pretty lucid. I couldn't say the same if it was my first time learning the material though.

r9m

My roomie calls D&F The dictionary :-)

Alan

We used Hernstein in my Abstract Algebra classes, which seemed to cover a LOT less material.

Mike Miller

It's not intended to cover as much material.

Alan

03:06

The GTA who was teaching our qual prep course learned out of D&F and was shocked that we hadn't learned some things, like the orbit stabilizer theorem

Kaj Hansen

Which Herstein? There's a "baby" version, and then there's "Topics".

Alan

Baby for the 4000, the topics for the grad one

So I own two of his bloody books, one of which is completely subsumed in the other :)

Kaj Hansen

LOL, yep :)

Alan

Meanwhile, I'm still irked that I didn't get one question in my analysis qual that I would have gotten had we taken it 3 weeks later :). (It didn't matter, I passed anyways), but stilL!

Turned out it was a special case of gromwell's inquality, which I learned (and learned how to prove) in my ODE course

Kaj Hansen

That's a summary of my undergraduate experiences :P

Analysis is a weak point for me. I feel like I don't know much.

Alan

03:10

I'm the opposite. And so I'm terrified about this algebra qual. Bleh. I have one B, the rest As, passeed anaylsis first shot, and still scared about continuing in the program because I haven't done any algebra in a semester.

BTW, if you are planning on taking an analysis qual, I highly recommend learning gromwell's inequality and how to prove it. According to my ODE profgessor, he's seen a bunch of qual questions which can be solved by it (And I have firsthand experience :))

Behaviour

@MikeMiller The title filter is based on this answer, with minor later additions.

Kaj Hansen

That's a few years away, but I'll keep that in mind @Alan

Alan

Well, off to study in the bathtub :)

Kaj Hansen

That sounds relaxing. Good luck with things!

daOnlyBG

03:36

hello everyone

Mike Miller

@robjohn I posted a question that's gotten a fair number of upvotes, but someone pointed out in the comments it's been answered completely elsewhere. Should I close mine as a duplicate of where it's been answered, or ask that author to put his answer on my question?

Pedro Tamaroff

@MikeMiller Why not both?

robjohn

@MikeMiller if it's a duplicate, then it will probably be closed by others, unless your question is somehow better than the other question.

@MikeMiller is the other question the same as yours?

daOnlyBG

I agree with Pedro, if you couldn't find the question when you initially asked it, then why would others have an easier time finding the question? If it's asked in a completely different part of Math.SE, I'd say keep yours

Mike Miller

@robjohn A question was posted that had multiple sub-questions. An answer was accepted and the question on it I was most interested in wasn't touched upon; it seemed like interest was dwindling. I posted that subquestion as its own question. Five days after my posting, it was apparently answered on the other question.

robjohn

03:43

@MikeMiller you can comment on that answer and ask him to have a look at your question.

Mike Miller

thanks.

Alan

Hmm. Is it wrong that I saw the phrase "learning to contain herself" and immediately my brain went to set theory and topology?

Pedro Tamaroff

@Alan Yes. You need to get yourself checked immediately.

user130018

04:11

I find it kind of weird you can downvote in an election lol

skullpatrol

Ya me too. It's sort of like a test with negative marks :P

Now if actual elections had down-votes that would be weird.

Behaviour

@user130018 In the final round, you cannot.

skullpatrol

Why not? It should be consistent.

Statistically speaking of course.

Why change the rules halfway through the game?

Mike Miller

Because the primary and the election itself serve different purposes.

It's not a strict upvote system in the final election.

skullpatrol

chat.stackexchange.com/rooms/19520/winter-bash-secrets

3

Mike Miller

04:25

This question has the potential to award JimmyK4542 with the Red Baron.

Semiclassical

04:36

@MikeMiller: you might've been notified, but I went ahead and gave the bounty to Travis's answer

Mike Miller

I wasn't; glad you did.

Semiclassical

Kind've an odd scenario to end up with, but the results are fine

Mathy Person

@studentmath: Is there any formula to find the minimum value of edges that GUARANTEES that a graph (let's call it "B") is connected? Simple graphs only, and the number of vertices is given.

Ilmari Karonen

@MathyPerson Start with the complete graph of k nodes, and see how many edges you need to remove to split it into two components?

Which, if I'm not totally confused, is k-1.

Ahaan S. Rungta

04:58

@JasperLoy I know -- I meant he could message me on Facebook.

@Venus Still unsure about what you mean by "you should know about that case."

Toxicz

Hello

Could somebody have a look at my answer and tell me why it is incorrect, it concerns the differentiation of a function at a point?

3

A: Differentiablility of a function

$F(x)$ is differentiable at $0$ if and only if $$ \lim_{x \to 0} \frac{F(x) - F(0)}{x-0} =\lim_{x \to 0} \frac{F(x)}{x} \stackrel{\mathcal{L}}{=} \lim_{x \to 0} F^\prime (x) = \lim_{x \to 0} f(x) $$ exists. Now, the real question is whether or not $$ \lim_{x \to 0} \cos(1 / x)$$ exists. I wil...

user128043

Hi xDDD

user128043

wuts up

Bungo

@GabrielH: Andres Caicedo's comment seems to explain why it is incorrect.

Mathy Person

@IlmariKaronen I did try that, but I was actually given two questions. The answer that has k-1 is for the first question (If "B" is connected, what is the minimum possible number of edges?), but for the second question, it asks for the minimum number of edges that GUARANTEES that "B" is connected, so I guess it is sort of different..?

Ilmari Karonen

05:09

@MathyPerson A complete graph of k nodes has (k^2 - k) / 2 edges. If you remove k - 1 of those, how many are left? (That's the maximum number of edges in an unconnected graph. If you want the minimum number to guarantee connectedness, add one...)

Mathy Person

so if there are 40 nodes, then there will be 1560/2 = 780. Remove 39 of those. 780-39 = 741. Add 1 to get 742? @IlmariKaronen

Jorge Fernández

@MathyPerson your answer is equal to the maximum number of edges a disconnected graph on $n$ vertices can have plus one.

Whichis the disconnected graph with $n$ vertices that has the most edges?

How many connected components does it have?

oh yeah, Ilmari Karonen's comments make sense.

Although he didn't tell you how to prove it's the best method.

I mean the most number of edges.

Singh

05:30

See this

anybody interested?

Mike Miller

What's wrong with vadim123's answer?

Singh

@MikeMiller Now please see the comment under the answer of vadim123.

Mike Miller

It's the bottom paragraph that you're looking for.

Singh

Sir that statement is also available in other answers, but I'm not looking for that.

If I'm missing something then please tell me.

r9m

06:16

Android hat !!!! I need that :D

Pirate Ho !! :D

graph

06:54

Hello, I have a problem.

Balarka Sen

@KajHansen D&Fs exercises are classic.

Mike Miller

07:21

Looks like you're on your way to Naruto, @Behaviour.

Balarka Sen

Did you get Naruto on Hippa's question last night? @Mike

Mike Miller

No.

Balarka Sen

Did some idiot upvote it again?

Mike Miller

Yes.

Flag this as spam.

Balarka Sen

Done.

Behaviour

07:24

gone

Balarka Sen

Good question with not so relevant answer

Dessins are nit really meant for realizing graphs as Riemann surfaces. It's just a preimage of an interval under the branched cover.

Behaviour

BTW I disagree with Rec.Deletion on answers that only point to scholarly resources such as journal papers, ArXiv, or OEIS. These are not some random links that will break leaving the answer useless. Like this one

I'll say this is some weird paper, though. :)

But everything involving quantum physics looks like insanity to me.

Mike Miller

You're right, the correct action there was to edit. Thanks for doing so and for calling me out.

Balarka Sen

Did you see the new question on groups that asks for classification of the groups such that inclusion is a proper order on the set of subgroups @MikeMiller?

Mike Miller

No.

Balarka Sen

07:29

It's a pretty interesting question. Not sure how to deal with it for uncountable groups, say.

Mike Miller

I doubt it's true for any uncountable groups.

Balarka Sen

Presumably. I am not sure, maybe we can construct some kind of direct limit of groups to construct an ad hoc example.

Mike Miller

Anyway, I'm busy looking at mediocre questions, not good questions.

Balarka Sen

You're still up for the Naruto hat aren't you? :P

Also good question : the puny bounty was worth setting

Heya @KajHansen

Kaj Hansen

hey

Balarka Sen

07:33

Haha the hat looks good on you

Kaj Hansen

hahaha

Mike Miller

@BalarkaSen Suggested close reason for this?

graph

In how many ways can 12 students take Physics, Mathematics and Chemistry if 4 students are to take each subject? Please explain the problem.

Kaj Hansen

@MikeMiller, stop sweeping your knowledge under the rug!

Mike Miller

If you posted that on the main site it would be closed because you didn't show any work. We're not going to do any different.

Behaviour

07:36

@MikeMiller Duplicate of some 0/0 post.

Balarka Sen

I have commented on it at least @Mike

Mike Miller

Maybe Anixx is going for 30 minutes or less.

Balarka Sen

heh.

Kaj Hansen

It's motivated by hats.

Hats are evil.

Mike Miller

I actually doubt that. I was not serious.

Kaj Hansen

07:39

Yeah

Balarka Sen

I am thinking whether I should post an answer here, now that I know a bit about what's happening in there.

Mike Miller

07:53

Someone kill this off.

Kaj Hansen

"The title is inflammatory and oxymoronic, and you're talking to people who are talking nonsense." LOL

Mike Miller

Kevin's a good guy.

@Behaviour I think you should change Review+ so that you can still go to the review tasks on the RHS even if none are available; in particular, so you can look at the history (which I find is better presented in the review tasks than on your profile.)

Behaviour

@MikeMiller Good idea. Will do tomorrow.

Mike Miller

Thanks.

Anonymous

@KajHansen bbc.co.uk/programmes/b00srz5b/episodes/guide

Balarka Sen

08:03

Hmm.

Kaj Hansen

Interesting. Too bad they aren't free, lol

Anonymous

LOL they are!

Balarka Sen

Is $Gal(\overline{Frac \Bbb Q[[T]]}/Frac \Bbb Q[[T]])$ prosolvable?

Anonymous

You can download them all!

Kaj Hansen

Oh I guess they are.

I just saw the "Buy CD" button lol

Balarka Sen

08:04

In other words, is every Galois extension over $\Bbb Q((T))$ solvable?

Anonymous

Play the audio and then right click and press save as.

Mike Miller

@Behaviour I think it's now a fair assumption that deleted answers don't count.

(It might also be that the answers need to be upvoted.)

Chris's sis

08:26

Greetings

skullpatrol

Greetings
(removed)
(removed)

^removed greetings?

Anonymous

I GTG.Cya!

skullpatrol

Later pal

Balarka Sen

09:01

@MikeMiller Re : This. Doesn't R^2\{x} deformation retract onto V\{x}?

So from the fact above, the nonsimple connectedness of V\{x} should be obvious

Mike Miller

Uh. What do you think $V$ is?

Balarka Sen

Open set in R^2.

Mike Miller

You think $V \setminus \{x\}$ is homotopy equivalent to $\Bbb R^2\setminus \{x\}$ for an arbitrary open set $V$?

Balarka Sen

That's not true I guess.

No that's never true.

Mike Miller

Well, not never. But pretty rarely. :P

Balarka Sen

09:04

Take V to be an open annulus.

Mike Miller

Considering there are lots of very different open sets.

Yeah.

Balarka Sen

My geometric intuition is slow, @Mike. A result of doing mathematics while keeping eyes closed (algebra) :P

Mike Miller

Geometry should be done with your eyes closed, where visuals are unrestrained by the world around you.

Balarka Sen

Fair enough.

Venus

09:49

@AhaanS.Rungta I was talking about Walter Lewin's case. See 2nd paragraph, it's mentioned there, "The woman was taking one of Lewin’s classes on edX, the online learning platform started by Harvard and MIT." Are you a mod at edX, right?

So, I believe you know about this case.

Anonymous

@Venus How will a mod at edX know all these personal things?

Anonymous

@KajHansen I will be taking a break for a short time.Good luck!

Venus

10:05

@Ashwin So the online class in edX is personal or private? #Surprised

Jasper Loy

2 candidates have withdrawn.

N3buchadnezzar

@JasperLoy Epic mod battle of history

Butin the long run, why does it matter, why should we care. The eternal wheel of time will keep turning needless of whom is elected.

Jasper Loy

I think I will change my votes.

I will vote for Thomas, Pedro and Daniel, just because that is the order of the number of helpful flags.

Chris's sis

10:21

@r9m did you manage to see an elementary solution to that question of mine?

@JasperLoy I'd only vote @r9m ... (unfortunately, I don't have this possibility)

Jasper Loy

@Chris'ssis Oh? Why is that so?

Chris's sis

@JasperLoy He makes me laugh often :-)))

Jasper Loy

@Chris'ssis Luckily I did not contest, or I would not be able to delete my account!

Chris's sis

@JasperLoy Oh, da*n, I missed you!:-) I'd also upvote you as a moderator!!! :-)))))

Jasper Loy

@Chris'ssis I think you are better off doing Ramanujan style math than being a mod!

Venus

10:26

The race for rank 9-11 is really tight

Chris's sis

@JasperLoy I'd never accept to do this job for free. Just think about it: I invest my time in accounting, tutoring and research. What about the time spent as a moderator? During that time I might discover another amazing integrals from my books.

Jasper Loy

@Chris'ssis Yes. You should really spend time on getting a math degree and then a PhD after this.

Venus

What would happen if the candidates rank 9-11 have the same votes? Who will go to next phase?

N3buchadnezzar

@Venus I have an even better question. Who cares? =D

Chris's sis

@JasperLoy Yeah, I'm thinking of doing a career in math, but at the moment I'm very entangled and I need other things before. Where I live now I don't have great opportunities ... (I need to be patient)

N3buchadnezzar

10:30

@Chris'ssis Entangled in what? =)

Venus

@N3buchadnezzar I'm curious to know

Chris's sis

@N3buchadnezzar I live in a small village at the moment, away from the city. So, first I have to move on the city soon. For doing that, I need to get a very good job there (and it's not easy to live in the city).

It's not impossible, but, well, I cannot do things faster. So, I need to be patient.

N3buchadnezzar

10:44

@Chris'ssis You need to be healthy, not patient (thats a pun)

Jasper Loy

@N3buchadnezzar That's very true. My mental illness has debilitated me for so long. If not, I might have won the Fields medal by now.

Integrator

@Venus The one who nominated themselves first.

Chris's sis

@JasperLoy Why don't you consider your illness as another challenge? All good things happen in mind first (well, some might not agree with that)

@JasperLoy Change the way you look at things. Make fun of your disease for instance.

Venus

@Integrator Why so?

Integrator

@Venus No Idea. but wait...

6

A: What math decides who is eliminated during election primaries?

I have no idea where to find the official answer, but based on what happened on ServerFault last year (where I had +22/-12 and the other guy had +27/-17), in the case of a tie in the primary, the person who was nominated first goes on to the final Election. I don't know if this is still the case...

@Venus I don't have any idea.

Venus

10:54

Ask for help to mark this problem of mine as favorite. I need 3 more for the sake of hat

@Integrator Thanks

Wrong link! I meant this one. Haha

Transcript for

$Mathematics$ Mathematics