Mathematics - 2015-01-02 (page 2 of 7)

oh thank you @George whoops hehe. also meta thread i made if someone wants to improve it meta.math.stackexchange.com/questions/19043/…

hey @kaj everyone has started to ignore me, will you be next lol

I would just like to apologize to everyone that has received my hateful comments, particularly you, @beginner.

@don i didn't flag you for the record, why are you apologising??

because I was a jerk

4:12 AM

now that you are being honest(i think) are you a graduate or not @don?

no.

@RajeshD thank you & same to you.

how to get reply notifications of my posts to my email inbox?

thank you @don, I appreciate the apology and now we can be friends

if someone like my pic in fb, then i get notification to my email, so if my answer get upvote, then how to receive the upvote notification to my email.?

thanks @beginner. I appreciate it.

4:25 AM

@don thanks for appreciating my appreciation for your apology

did anybody get my question?

Kaj Hansen

Not sure how to do it @hraishkumar

I did, but I don't think it is possible

@beginner how can you tell?

5:36 AM

@balarka At what age did you become super series and why?

any opinion on my meta thread @behaviour? meta.math.stackexchange.com/questions/19043/…

I imagine you are neutral but I might be wrong

You are against noise for sure so there is that

But you are against homework solutions as well :s

I suppose you are against misuse of the platform, but I might be wrong, so I guess with that you are against it

fredsbend the Grinch

6:29 AM

Someone's way ahead of you: biology.stackexchange.com/users/10450/hraish-kumar

404

6:44 AM

what did don say

@behaviour I would assume you read the above, were you the downvoter of the only answer?

I ask because your opinion is one of the most valuable since you are pretty much a lone wolf in cleaning up the past content

can anyone read this??

dustin

7:06 AM

@beginner can anyone read what?

7:30 AM

@beginner I never became "super series"

I don't even know what that means.

@balarka I meant serious! super serious

I ain't super-serious.

@MikeM Hatcher has nice exercises.

It's a good book.

@balarkaSen when did you start saying stuff like, this silly nonsense is a waste of time. Do math stop this garbage chat stuff

Those are just jokes.

WOAH that blew my mind are you serious??

7:41 AM

I waste a lot of time chatting/doing nonsense.

so your non-joking attitude was a joke...

Off-topic, @beginner : I agree with Ted. You should slow down.

You didn't did you?

I am already very slow.

I'd stick to algebraic topology for a year.

you were doing dummit and foote at 11 weren't you?

7:43 AM

Plus, I haven't studied any analysis.

@beginner No.

no?

I started it when I was 13.

Oh you were saying same age to my fake age that confused me

so I have 2 years to get to dummit and foote

Heh. You're way younger, @beginner.

Just do basic set theory, teensy bit of calculus and whatnots.

Being fast doesn't pay off, @beginner. I have tried doing it, you'll just have to come back to what you skimmed through later.

what made you interested in math?

7:50 AM

i've forgotten

how old are you now? 15?

right

does that mean you have a girlfriend?

nah

isn't that the age 15 thing to do?

7:52 AM

maybe, but i won't.

Too distracting?

perhaps

i just want peace.

Also is it true that for $\Bbb Z / p \Bbb Z$ where $p$ is an odd prime that for $\phi:\Bbb F_p^\times \to \Bbb F_p^\times$ defined by $\phi(x)=x^2$ that $\operatorname{ker}\phi=\{1,p-1\}$? sorry if math didn't render

are there no other elements of the kernel?>

Well, do you know what a kernel of a homomorphism is?

The elements from the domain that map to the identity of the range

So here all the elements mapping to $1$, which seems to be only $1,p-1$ from my trials

7:56 AM

ok, so what should be the kernel of $\phi$?

It looks like $1$ and $p-1$

but it is all the elements that are their own inverse

just write down what is $\ker \phi$.

using set builder notation

$\ker\phi = \{x\in\F_p^\times : x=x^{-1}\}$?

$\ker\phi = \{x\in\F_p^\times : x\equiv x^{-1} \pmod {p}\}$?

yes, but let us just keep everything simple. $\ker \phi = \{x \in \Bbb F_p^\times : x^2 = 1\}$

$x=\pm 1$ oh my god noooo so obvious

8:00 AM

no, @beginner

those are not the only solutions mod p.

you have done the exercise, it's your job to recall it

see, that's what happens when you go fast.

what exercise was it I cant remember nooooo

Actually, @beginner, yes. Forget what I said above.

:P

My bad.

what happened lol

was it $\pm1$ in the end

$x = \pm 1$ are indeed all of the solutions.

yay :)

I failed on algebra lol :(

8:05 AM

You mean your high-school algebra?

I am not in highschool yet, I just meant I failed to do $x^2=1$ ages ago

Now apparently using the first isomorphism theorem I can get that half the elements of the odd prime field to be squares

Ah, yes ;)

You can.

i went to $x=x^{-1}$ and overlooked the easy way

@beginner You are familiar with the first isomorphism theorem? Does that mean you have already done Lagrange?

not familiar with either lol

8:08 AM

Well, you said you're going to use the first isomorphism theorem...

should i just be using it for the group under multiplication?

yeah George v Williams told me to use it

@beginner Not necessarily. It's a theorem that says if $f : G \to H$ is a group homomorphism, then $G/\ker f \cong f(H)$

cool, eh?

awww no you were impressed with me but i got help and now it is gone :(

f(H) meaning surjection?

$f(H)$ is the image of the group $G$ onto $H$ by $f$.

Have you done lattices yet on Dummit-Foote, @beginner?

no i cant get into dummit and foote yet until i download the DJVU opener

8:12 AM

oh

well, if you knew what those are, there was a very visual interpretation of the first isomorphism theorem using quaternions and klein-4 group

let me look through cohn

are you doing that thing you said you don't do lol

throwing names around to scare me away

i pondered the similarity between the lattices of those two for some time which i finally understood after i studied quotient groups

@beginner you don't know what quaternions and klein-4 group are?

isomorphism theorems are page 242 and i cant see lattices :(

if not, throw your copy of cohn on the dustbin.

quaternions are complex plain *4 or *8 or something. wait why am i throwing it out? for not having lattices?

8:15 AM

well, guess you have to download DjVu reader and study D-F.

until then, bubye.

wait why am i throwing it out??

lattices are chapter three of his second book

and isomorphism theorems are chapter 2 of his second book

oh no idea about Cohn

but i'd rather D-F

yikes, i totally gotta go now

so are you leaving or just not helping me until DF?

Oh okay going cya! thanks!

8:32 AM

Upon observation of a modern trend, I deduce that there will be more riddles about integers in the range $\left[2000,2100\right]$ in this century than any other numbers. Thank you new years :)

8:46 AM

What is it with people who try to find meaning in numbers? 7 is lucky. 13 is unlucky. 23 is an enigma. 42 is the answer to life, the universe and everything. And now, the current year must have some interesting mathematical property.

columbus8myhw

What is $1-2+3-4+5-\dotsb$?

I claim that, it some sense, it's $\dfrac14$.

Proof:

Call the sum $s$.

$s=1-2+3-4+5-6+7-\dotsb$

$s=\;\;\;\;\;1−2+3−4+5−6+\dotsb$

$s=\;\;\;\;\;\;\;\;\;\;1−2+3−4+5−\dotsb$

Now, add down the columns:

$4s=1+0+0+0+0+0+0+\dotsb$

This, $s=\dfrac14$.

@columbus8myhw:Alternate method, differentiate $\displaystyle 1 + x + x^2 + x^3 + x^4 + \dots = \dfrac{1}{1-x}$ and stick in $x=-1$. It's much quicker.

columbus8myhw

Too much heavy machinery. This is simpler. (Do you really need differentiation for this?)

Note: The series is not convergent. However, it fits the fact that $\eta(-1)=\dfrac14$.

@columbus8myhw Simple but vague. I don't like that method. Why? Because it is fundamentally unclear to me. I would like to have a discussion about it with someone but no one likes to talk about it. It has something to do with $\aleph_0$ and it seems complicated. I can atleast see the machinery behind my method.

do you like algebra @nick?

Do you know the first isomorphism theorem?

9:00 AM

@beginner No, I hate math. I stick around here because of all the nice people.

@beginner No, you should probably try Wikipedia. I'm just a lazy highschooler.

i assume that is a joke, well @nick i have $\Bbb F_p^\times / \{1,p-1\} \cong \phi(F_p^\times)$ where $\phi:F_p^\times \to F_p^\times$ is defined as $\phi(x)=x^2$

what do you do in highschool?

@beginner That assumption is invalid because I really am just a lazy highschooler. You have to wait until a person who is versed in the subject enters the room (could be a long time because they're probably out attending new-year parties) or you have to ask on the main site.

@beginner I sleep during lectures and hide in the library during the most important classes.

i meant the first line was a joke not the second one sorry

what is highschool math like? i am only in grade 7 starting in 3 months, which is primary school still in my country

Depends on the country.

@columbus8myhw Your silence re-iterates the fact that no one likes to talk about it. The reason your method works is because every time you move a column, you are exploiting the fact that $\infty \pm n \to \infty$. It is an assumption that all of a certain type of terms cancel out. This is where it becomes vague to me. The limitations of your method are clearly demonstrated by this answer

@beginner In my country, under the Central Board, no one learns anything useful until grades 11 and 12. There would be a total of more than 60 chapters per subject in those two years which have to thoroughly learnt in order to get into a good college.

@beginner highschool math is a just a touch of all popular basic branches of math excluding topology and good geometry.

9:22 AM

so what grade is the stuff i am doing above? i think algebra is one of the more enjoyable fields

@GustavoMontano No, it depends on curriculum and teacher quality. I sat in a foreign country for gladly over a decade learning under the same board as in my native country. When I came back for the final years, I realized that the decline in educational quality was directly proportional to the lack of good teachers. My point: You can sit anywhere in the world and recieve the education level of a certain country's standards.

One does not need to get an education from qualified teachers.

I taught myself and relied on university students as my guides.

Too many formulas in the current curriculum.

my teachers are balarka, alec teal, ted, kaj, mike miller, pedro, but four of them are ignoring me now i think

&quid

Australia has it messed up between years 7 -> 10. Years 11 and 12 are much better. Especially the higher levels.

&anon

9:26 AM

I don't think you're going to enjoy high school mathematics beginner

@GustavoMontano You're right but I meant education in a more deeper sense than mere textbook information. Textbooks are a constant parameter under the same board.

really @gust

You're too smart.

thank you hehe, only in math though i think

For your age.

9:27 AM

and physics

which is why @huy is ignoring me

@beginner In my country, you'd be considered doing math associated to the final year learnings of a certain BSc. course.

@beginner maybe i should put you on ignore too

Best thing for you to do is accelerate. Get involved in various competitions.

@balarka whyyy?????

He's just a kid, haha.

9:28 AM

@GustavoMontano i wish I had that advice when I was younger. Hopefully, it's never too late.

Me too, @Nick.

@balarka why do you all ignore me noooooo

Instead of wasting my time playing RuneScape, haha.

@beginner since you're ignoring everyone's advice and jumping around

im going to do spivak calculus and book of proof

and then everyone will take me off ignore

9:29 AM

@beginner Protip: Listen or Pretend to listen. Do not make them think you aren't.

do that. when you finish it, i'll unignore you

@balarka what really that could be two weeks!?

could even be a month. the faster you finish all exercises of book of proof, the better.

ok :(

i don't care about spivak.

9:31 AM

cya in 2weeks to a month

@beginner so bubye.

@beginner one week , if you don't sleep. But you need passion for that, you need the drive and commitment. You need to put in hard work and all that other blah blah that people say success is made of.

@nick i don't think my parents would let me do that lol

@beginner And my my parents wouldn't get me an internet connection. Yet, I'm here.

@kaj @ted @alec @mike @anon @pedro @balarka @quid i am going to go do spivak and book of proof by hammock and ill be back when they are done in 2wk-1month wish me luck! then you can all not ignore me :)

and @ted i will then do your exercises! bye!

9:34 AM

Enough talking, more working.

I am doing bits of altop and bits of comalg at the same time, @GustavoMontano.

@beginner Good luck. Try hard. Don't think about doing it. Just do it!!

How is it? I bought myself Munkres today!

It's an interesting study-technique.

@GustavoMontano Oh cool. Munkres' algebraic topology?

Just Topology.

That's the title: "Topology"

9:35 AM

Yeah, but you're going to altop, right?

There are two parts of that book.

Oh is there? Explain.

Oh, Altop = Algebraic Topology. Sorry :p.

Well at the first part there is just usual point-set topology, a bit about manifold, a bit about dimension theory.

And at the second part you have algebraic topology.

Yes will definitely go into algebraic topology.

It's a must!

my opinion would be to revise 1) Tietze extension theorem 2) Uryshon metrization theorem before getting into algtop, @GustavoMontano

I have not heard of those.

9:38 AM

Those two are the only really nontrivial results in general topology.

I see.

And used quite a lot in altop.

Thanks for the advice!

No problem. My favorite result in general topology is Uryshon lemma, which gives a sufficient condition on a topological space to be metrizable.

Cool, eh?

Oh wow!

9:43 AM

@GustavoMontano When you get into altop, ping me. I have been planning to do Hatcher (I just started) but I'd be glad to restudy from Munkres and fill up the rational holes in my understanding to strengthen up my foundations.

@BalarkaSen. That sounds great! I think after all this topology I'm going to learn General Relativity.

So does one go from Munkres to Hatcher?

Ah, @Huy has been meaning to find someone to study G-R with.

@GustavoMontano I am not sure what you mean. Just study Munkres and then go to Hatcher I guess?

:P

I'm going to post on Physics Stack, asking for a suitable book for G-R. One suitable for a pure mathematician and without dilution.

Haha, yes that's what I was implying :)

Munkres' altop is introductory algebraic topology, while Hatcher also covers homology, cohomology, higher homotopy and all of that.

Little question : Is $\dfrac{d^{n} y}{dx^n}\Big ] _{n = 100}$ valid/correct notation to express the 100th derivative of $y$?

9:47 AM

The good stuf.

Well, @Gustavo, study hard. See you when you get into altop.

@BalarkaSen. You too my friend. C ya!

I have to do a bit of Atiyah-MacDonald now. Hard exercises, but very interesting.

@BalarkaSen Atiyah-MacDonald had a cow. $e$-$i$-$e$-$i$-$\mathcal{O}O()$

Sorry, I couldn't resist.

I couldn't $\frac{V}{I}$ .... gosh, I suck at puns.

Greetings

9:58 AM

@GustavoMontano: Study GR with me!

When the time is right. Have you found a suitable book?

@GustavoMontano: I don't use books very often. Also, I have looked at your website and I'm wondering whether you have any background in physics?

I did physics in high school. I decided to do finance and mathematics in university.

However, for my topology and differential geometry course, I wrote an essay on curvature and general relativity. While the essay was heavily diluted it did spark a great interest.

Knowing the mathematics is a great starting point. I am eager to get to it soon!

@GustavoMontano: And how much of the GR part did you understand? I often find people who have hardly any physical background who would e.g. "like to learn some QFT", and it's not too hard to learn the maths, but it's not very useful if you have no idea what this all means.

@Huy. Hmmm, I thought I understood it quite well. However, I was not very familiar with tensors.

So I was not able to progress from there.

Have you done physics? How much of GR do you understand?

10:08 AM

@beginner Sorry for the late reply, have you already got along with Huy?

@GustavoMontano: I'm probably doing much more physics than most math majors, I only started studying GR a week ago or so.

What do you think?

@Chris'ssis What's up? I'm fine btw

@Huy What happen with you & beginner? Did you get along with him?

@GustavoMontano: What do you mean by what do you think?

@Venus: I decided to ignore him/her.

@Huy What do you currently think about GR given the week that you have spent learning it?

10:13 AM

@Huy Why?

@GustavoMontano: That without any physics background, one would have a rather hard time understanding what it's about and how to use it. And I don't consider physics in high school a background in physics.

@Huy Awake already?

@Venus: Because I had no reason to talk to him/her anymore.

@N3buchadnezzar: It's 11am over here, already.

Well, I covered the intuition between special relativity. That helped a bit :). But you're right.

@Huy 11:15 here :p Well I did fall asleep around 02-03 and was up around 10. Holidays :D

10:15 AM

9:15pm here xD.

@N3buchadnezzar: So we live in the same time zone.

6.15 pm here :P

@Huy Eeek

@Venus Hey, I'm fine thanks. I'm trying to create some nice stuff. :-)

@GustavoMontano: I don't really know what you mean by "I covered the intuition between SR"

10:18 AM

@Chris'ssis As always. Meanwhile, I'm taking a break here.

@Venus I don't remember my last break ... it was long time ago ... I work hard, I wanna publish my book.

Errr, it made sense.

@GustavoMontano: It is a lot easier to read about something and saying "ok, this makes sense" and to do it on your own. I think every maths students finds out the difference at some point. :D

Oh of course!

@Chris'ssis It's holiday here & I spend as much as possible my time with my fam. Good luck for your book. :-)

10:21 AM

To create theorems and abstract concepts is amazing.

@Venus Thanks! Have a nice time then! :-)

For Einstein to "think" about these concepts. It amazes me.

@Chris'ssis I have been trying to see how strange integrals I can solve using series and Rieman sums, it is somewhat fu n:p

@N3buchadnezzar Ooo, there are lots of such integrals! :-)

@Chris'ssis do you know if the following holds?

$$ \int_a^b |f(x)| \mathrm{d}x \leq \int_a^b f(|x|) \,\mathrm{d}x$$

10:29 AM

@N3buchadnezzar I don't think it holds.

@Chris'ssis Same

@N3buchadnezzar $f(x)=-c$

@Chris'ssis :p I came up with $x^3-x-1$ for $0 \leq x \leq 1$. Convoluted but it has a nice graph :p

@N3buchadnezzar hmmm, that makes me think of another problem ...

@Chris'ssis Let $f(a) = \int_a^{ab} e^{-x^2}\,\mathrm{d}x$ find $a$ such that the integral is maximal :p Here $b$ is some non-negative number.

10:37 AM

Hmmm, I am curious. What do people use to generate their latex?

Lyx? Texworks?

@N3buchadnezzar isn't it useful to compute and analyze $f'(a)$?

Yeah. I just think the answer is cool.

@GustavoMontano In my head. Atm I am using Overleaf (google it) I used texmaker. Thinking of switching to emacs or vime, deppending on which is best for general programing.

Oh wow. I have never heard of those!

I just use TeXnicCenter.

Wow! Overleaf looks beautiful!

10:41 AM

@GustavoMontano It has it's restrictions but works fine

Cool!

I think there is a restriction of 30 images (or 60) and a maximum number of files. It is also terrible if you need to compile several files in a single document (it is impossible). But yeah I am using it, so it has to have some nice things to it.

math.stackexchange.com/questions/1088323/… Is there a simple example for such a function?

Hahah :).

I have only used MikTex, and I found it quite nice. Does anyone use a live rendering Tex editor?

10:50 AM

@Committingtoachallenge: Last time I checked, MikTeX wasn't an editor.

@Huy Define 'editor'.

@Committingtoachallenge: Software to create and edit documents.

MikTex does both of these, unless I was using software that utilizes MikTeX, and if so that wouldn't matter, you would find it by the same means.

@Committingtoachallenge: As I said, last time I checked MikTeX wasn't an editor. Maybe that changed. Also, of course it matters. If people are suggesting editors and you're saying you've only been using MikTeX so far, that says nothing about which editor you've been using, because ... MikTeX is not an editor.

Let me reiterate, I downloaded off of the MikTeX website, a piece of software that can write, edit and render Tex.

10:56 AM

@Committingtoachallenge: I'm sure that piece of software has a name.

Yes, I am sure it does.

I am quite sure that name was MikTeX.

What do we call the following identity $$(a\pm b)^{2} = a^{2} \pm 2ab +b^{2}$$?

I do recall it having a name.

How have you been over the last month @Huy?

@GustavoMontano: In German, we call them binomial formulae.

Argh, I recall a different name.

But that sounds fine too.

11:01 AM

@Committingtoachallenge: Pretty good, but I should have studied more.

@Huy I know that feeling. Do you keep track of your time spent studying?

@Committingtoachallenge: No, I have a very good memory and I don't study much. :D

Haha, fair enough. I do keep track but life distractions had almost entirely stopped me from studying for about 15 days

Since when is it possible to remove a question after someone has answered? I thought it was only possible before any answers have been posted.

@Committingtoachallenge: I wasn't distracted too much, just lazy, tbh.

mikeonly

Hi.

I wonder, how can I contact David Zhang, in order to look at his Mathematica code related to this answer? math.stackexchange.com/a/1088258/169859

I do not have enough reputation to comment, unfortunately.

11:06 AM

@Huy Are you on break from university?

@Mikeonly One of us could comment for you I suppose. I will do it.

mikeonly

@Committingtoachallenge Great, thanks!

@Committingtoachallenge: There are currently no lectures being held at my university, if you mean that.

@PedroTamaroff: Has it always been possible to remove a question after someone has answered? I thought it was only possible before any answers have been posted.

@Huy I am not certain, but I think that as long as the answer is not uprooted, the question can be removed. Yes that was what I meant.

Upvoted* Apologies, I am using a phone.

Ah, okay, too bad. I put quite some effort into answering a very elementary question and the author decided to remove it, apparently. :(

@mikeonly I have requested it, but it may not be fulfilled.

@Huy yes that happens from time to time. It is always frustrating. Perhaps search for a duplicate :)?

11:13 AM

@Committingtoachallenge: It was a very specific question to a certain misunderstanding he was having while going through his notes, so I doubt I'd find anything. :(

I wonder who's still serial-downvoting me though, after about 70% of the downvotes were reversed.

@Huy If you remember his question, you could post it up with the answer yourself :P

@Committingtoachallenge: I'm not THAT narcissistic.

xD. If it was long enough, I would probably do it haha

@JyrkiLahtonen: Is it possible for you to find out whether the person who downvoted my answer here was also the one responsible to the serial downvoting that has been reversed twice in the past two days on my profile? math.stackexchange.com/questions/1087332/…

Jyrki Lahtonen

Mods don't have the tools to ID individual votes, but we do keep an eye on things like voting reversals.

Taking a look.

The case is a bit more delicate than I thought. What I can see right away needs further investigations. Also, I'm not sure that I am allowed to tell you everything I can see.

11:26 AM

@JyrkiLahtonen: Of course, I didn't expect that you were allowed to tell me what you can see. But it's good to know that someone's looking into it, other than the system itself. Thanks for your help!

mikeonly

@Committingtoachallenge Everything ok. It's it. Thanks again.

@mike No problem, sounds like very interesting stuff!

@mike He is here now if you had any questions.

Anonymous

12:30 PM

Hello!

I need to explain why $\displaystyle \int_{|z|=1} \frac{1}{z-2} dz = 0$, but without actually calculating it explicitly. But I can't think of which theorem I can appeal to in this situation. Cauchy's integral formula isn't valid in this case, and neither is Cauchy's theorem. What else is there that I could use?

Anonymous

@Committingtoachallenge Where'd you been?:)

12:45 PM

Would I be able to use the integral formula in Taylor's theorem to do this?

@user112495: What is Cauchy's theorem? The fact that the integral is zero follows immediately from Cauchy's theorem, as far as I recall it.

@Huy Let f be holomorphic on $\Omega$. Let $E \subset \Omega$ be a simple region with boundary $\partial E$. If $\gamma$ is a parametrisation of $\partial E$, then $\displaystyle \int_{\gamma} f = 0$

@Huy But f isn't holomorhpic in this case is it?

@user112495: That sounds about right. Why do you think $f$ isn't holomorphic?

Oh wait, it only isn't holomorphic at z=2, but that's outside the region

@user112495: Exactly!