Mathematics - 2014-08-16 (page 1 of 2)

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12:01 AM

What's funny about that? @Khallil :D

Thanks for sharing.

12:57 AM

News on arXiv.org: Over the weekend researchers used representation theory to discover the meaning of life.

6

3 hours later…

4:01 AM

Sometimes I feel like picking up and shaking the chatroom... WAKE UP!!

4:17 AM

meh

5:06 AM

@robjohn Here I come!

@anon That sounds like bullshit.

3 hours later…

7:52 AM

WAKE UP!!

8:35 AM

@BalarkaSen For some reason Autocorrect decided that the world would be a better place if your name got changed when I was typing.

@BalarkaSen I thought about it's existence and I came to the conclusion that it must exist. I constructed auts such that they formed cyclic groups and they had properties which allowed all extensions to be real. The explicit construction of such a polynomial is way beyond my knowledge however it is described here

my proof/evidence is nowhere near formal

all I could come up with on a plane

9:17 AM

This is a lot quieter now term time is over.

9:38 AM

@skullpatrol His reactions to the 'define ...' questions are hilarious "There's a perfectly good definition with dictionaries over there". I also particularly enjoyed the ending with the star sign comment. I wholeheartedly thought the interviewer was serious until he, himself, started laughing!

9:53 AM

@AlecTeal Indeed.

10:32 AM

Greetings

@r9m Brilliant! :-)

@Khallil Hey.

@Chris'ssis ^_^ .. does that mean the outline of our methods are similar ? :D

@r9m No ... (it's hard to get something better)

@r9m It might be. :-)

<- (makes a guts pose :-)

@r9m :D

10:37 AM

@r9m Hey hot tempered.

@Sawarnik hi :)

@r9m Do you have to study something called operation theory in course?

@Sawarnik its an optional course .. but I'm not taking it :) (not in our core courses)

Ok :)

@r9m And are you in Maths & CompSci or Maths & Physics?

@Sawarnik Maths & CompSci

10:41 AM

:O And you told you are poor in programming...

I'm far worse in physics :|

:P

hee .. same with me ... and i see you have to study languages as well :O : O :?

that was in the first semester :P ..

@r9m There was a time when I used to spend an important amount of money on books, and neglected other very important priorities. I made many sacrifices to learn. :-)

MSE was a blessing when I firstly saw it.

My audit was really strange. "The answer to your question is a mathematical penis boomerang described in this paper #link#".

10:45 AM

@Alizter Which audit?

For reviewing low quality posts

@r9m :D Why is there no BSc purely for maths? :O :'(

@Chris'ssis agreed its a blessing :)

Hey, @Sawarnik.

@Alizter :O

@Khallil Hey.

10:48 AM

@Sawarnik That's what I'll be doing!

@Khallil Its not there in r9m's institute. :O

@Sawarnik there are no heavy comp sc courses (heavy stuff are always optional)

phew...

@Chris'ssis I know little about sacrifices :( ... but I know a bit about gambling with life and situations a bit :D

@r9m Interesting. Maybe you like the dangerous situations ... :D

:17180569 Are you a professor? Just asking ... :-)

10:56 AM

@Chris'ssis lol!

What was the deleted message? :O

@Sawarnik Why "lol"? :-)

@Chris'ssis Maybe r9m will answer better :D

@Chris'ssis I'm 20 .. come on :P .. i'm a ug student

@r9m Do you know personally, you and Sawarnik? :-)

Anyway.

@Chris'ssis No :|

10:59 AM

@Chris'ssis no I don't know him personally .. and I intend to keep it that way for the forseeable future :P

@Sawarnik Well, I think @r9m has answers much cleverer than many professors I met so far. So, it's natural to think of that. He has the mind of a mathematician.

@r9m Hmm, why? Theimpdemandsareply!

@Chris'ssis Oh, but his childish also... don't you think? :P

@Sawarnik 'coz u are an imp :P

@r9m Oww, then I will come to you one fine day....

@Sawarnik oy .. who u call childish .. ? >8(

@Sawarnik delete that

@Chris'ssis :O .. I only wish that was true :)

11:06 AM

@r9m Well, follow your dreams, I'm sure you can get there where you want to. :-)

What's this about, guys?

10 hours ago, by anon

News on arXiv.org: Over the weekend researchers used representation theory to discover the meaning of life.

@Chris'ssis ^_^

@Khallil it's a very sophisticated joke

@blue Ah. The only part I got was $i\infty$. That's complex infinity, isn't it?

usually, but not in this case

actually I'm not sure

2 hours later…

1:30 PM

@r9m Do you think we can possibly evaluate this one in a nice way? math.stackexchange.com/questions/464769/…

It looks like all solutions provided both there and in other parts were pretty ugly.

My inner voice tells me "we can do it".

@blue: I assume you got my message yesterday afternoon?

Hello @TedShifrin

g'day @Alec

@Chris'ssis the comment section makes me worry a lot .. :O !!

looks totally non-trivial

@r9m :-)))))

@r9m don't worry about that. It's just an appearance. :-)

1:42 PM

@r9m "Standard computation time exceeded..." - Hahahahahaha!

@Chris'ssis if you say so .. ^^

@Khallil I haven't checked W|A yet :P

@r9m Maybe you think that the one that has a nice way there shoud be called the mother of the integration gurus on earth? :-)))

@Chris'ssis Are you still at college/university, or have you already graduated?

@Khallil I graduated from financial accounting.

@Chris'ssis Awesome! Was it a really math heavy course?

1:44 PM

@Khallil No. I'm self-educated. Usually I corrected the test questions in my uni. It wasn't a good uni as expected. They couldn't have taught me what I learned on my own so far.

@Chris'ssis Oh, I see!

@Chris'ssis :o who ?

@r9m just hypothetically speaking ... :-)

@Chris'ssis okay ! .. seems you are pretty excited :) .. did you do it in a simpler way ? :D

@r9m I have some ideas. :-)

1:51 PM

@Chris'ssis :D .. okay !!

Hey guys, could you help me see why the following equality is true:

$\lim_{n \to \infty} ( 1/(n+1) + 1/(n+2) + ... + 1/2n ) = lim_{n \to \infty} 1/n \sum_{k=1}^{n} 1/(1+k/n) = \int_{0}^{1} dx/(1+x)$

Why is that sum equal to that integral? :)

(also: can I make what I just wrote appear in LaTeX?)

@rehband math.ucla.edu/~robjohn/math/mathjax.html

@r9m Thx :)

@rehband There you have a Riemann sum. It's a candy.

@rehband that is an expression for reimann sum $\displaystyle \lim_{n \to \infty}\frac{1}{n}\sum_{k=1}^n f(k/n) = \int_0^1 f(x)\,dx$, here $f(x) = \frac{1}{1+x}$ .. are you looking for a proof of reimann sum ?

2:03 PM

@r9m Thank you Chris and r9m. Yes please, r9m

@rehband this 1 and this 2

@r9m Oh yeah, thanks! I know what's meant now :)

@rehband okay :)

bbl

1 hour later…

3:24 PM

@Balarka: Hey, I was talking about Srinivasa Ramanujam(n). Okay..

Mathematician171

Hi

3:40 PM

Dang, main is in read only again

@Mathematician171: Oy

4:05 PM

I'd love to bump this math.stackexchange.com/questions/899005/… please don't DV because it's a weirdly phrased question, I'm genuinely trying to understand

4:21 PM

hello everyone

4:33 PM

@Alizter Yes, it's described there, but it'd have been much fun if you tried to work that out by yourself.

@BalarkaSen No I did. I came to the conclusion that such a polynomial would exist. Then I looked for an example.

How did you derive it's existence?

4:56 PM

@BalarkaSen its

right.

@BalarkaSen =D

hah, i always confuse that.

gah, a crank is claiming that -1/12 crap again.

typing furiously

@Chris'ssis Did you ever feel annoyed about the divergent-series-being-convergent posts?

@BalarkaSen hmm, do you have an example on MSE now? :-)

@Chris'ssis nope, i am on another forum.

5:05 PM

@BalarkaSen Ah.

@BalarkaSen Where?

not in MSE

@BalarkaSen This is only because some people miss the point with the validity of Riemann zeta function ...

The real part of $s$ is greater than $1$ ...

@Chris'ssis yeah. they just don't realize that analytic continuation never claims that $\zeta(-1) \neq 1 + 2 + 3 + \cdots$

I'd blame the professors that do not clearly explain this point ... I also saw many students being very confuse about this point.

5:08 PM

yes, the theory of analytic continuation is very delicate.

it's considerably less work to point out the flaws in rearrangements however. there is always the riemann's trap

@BalarkaSen Yeah, this is a big trap too.

what always seemed amusing is the connection with physics. heavens knows why such stuff pops up in there.

Hmm I got a downvote

I'm not sure I'll ever get an answer.

@BalarkaSen it's is the contraction of it is or it has, and its denotes some form of possession.

@Khallil i know.

5:18 PM

@BalarkaSen I was mainly writing that to remind myself, haha!

it's just a typo which i make too often.

I've not written in continuous prose for a long time.

@BalarkaSen it's? =P Just messin'!

no wonder you had a row with thomas.

@BalarkaSen Can you still call it a row if only one person argues?

sure. it's a one-rowed matrix.

5:24 PM

user image

mangas. pfft.

Today I was thinking of the fact that it's terribly hard to attend mathematics art. Just think about it: anyone can solve a problem, but to bring all to the level of an art, it's something spectacular and a lot of effort is required.

@Chris'ssis Unless you're a genius, in which case, hardly any effort is required.

I still don't know what you mean by mathematics art.

@Chris'ssis anyone can solve a problem Really?

But I like to do things like that. The fulfillment you get after finishing your work is great. :-)

@BalarkaSen well, hypothetically speaking ... :-)

(I'd better have used there "might")

5:30 PM

@Khallil Me neither.

@BalarkaSen It might be something you look at and say "Unbelievable, I've never seen such an awesome approach, too nice to be real!".

The art of connections.

Ah, so you are talking of approach.

Indeed, the main attraction of mathematics comes from the approaches you take.

Yeap.

@Chris'ssis I guess it only seems too nice to be real if you've not seen it before.

@Khallil $i$ is neither nice nor real.

5:36 PM

What somebody might do in 2 lines, you do in 7.

This world is not real. After all, what is an atom?

What you might do in 1 line, someone else might do in 10.

the length of the proof doesn't really matter.

@BalarkaSen I know.

The main point is that we're all different.

A longer proof might be more natural than a shorter one.

5:37 PM

indeed, @JasperLoy

@r9m i summon thee

I like the one line proof of Cauchy-Schwarz inequality.

It's also perhaps more important to not get too preoccupied by the 'art' which someone else produces.

My prof once said it was not natural, but I disagree.

The one line proof is much more natural than the stupid discriminant proof.

I've never seen the inequality before, what does it look like @Jasper?

@BalarkaSen we haven't signed the binding contract .. :P

5:39 PM

@r9m Kuchiyose no jutsu!

@Khallil hehe lol :P

Cauchy–Schwarz inequality

In mathematics, the Cauchy–Schwarz inequality is a useful inequality encountered in many different settings, such as linear algebra, analysis, probability theory, and other areas. It is considered to be one of the most important inequalities in all of mathematics. It has a number of generalizations, among them Hölder's inequality. The inequality for sums was published by Augustin-Louis Cauchy (1821), while the corresponding inequality for integrals was first proved by Viktor Bunyakovsky (1859). The modern proof of the integral inequality was given by Hermann Amandus Schwarz (1888). == Statement... ==

Thanks.

The internet has everything.

It is considered to be one of the most important inequalities in all of mathematics.

How have I not seen this before!! :O

5:40 PM

@r9m Have you seen my approach to that Olympiad problem?

It's much nicer than Jumping.

@BalarkaSen okay .. that $ = 3$ one ?

@BalarkaSen What does jumping mean in a mathematical context?

@Khallil Google [Vieta Jumping]

@r9m yeah

the one i approached with Pell

@BalarkaSen I haven't seen your approach

Life would be only half as good without Google and Wikipedia.

5:43 PM

I was watching monty python and holy grail :P

I have run out of things to watch.

@JasperLoy, try the filmography of Michael Haneke!

OK.

@r9m

Sometimes, I just feel very sad when I think about everything I have lost in life.

5:48 PM

@BalarkaSen hmm .. okay !! not bad :D

@nullgeppetto I guess you are a girl, lol.

@JasperLoy, hmm, so you find Haneke's movies ..what? For girls? If so, I'm impressed!

@nullgeppetto No, because of the heart in your avatar.

@JasperLoy -_-

@JasperLoy, ah ok! Impressed again!

5:50 PM

@nullgeppetto So am I correct?

@r9m at least now I can peacefully think of applying the Hardy-Williams conditions to that Pell-like species.

@JasperLoy, no, you aren't, but it's really weird you came up to this conclusion...\

@Khallil it takes some years to understand the beauty of mathematics.

@BalarkaSen okay .. do you have a link explaining the Hardy-Williams condition ?

@JasperLoy, I enjoy tempting homophobic people! I often write with a pink pen in the office... Not saying you are homophobic of course!

5:55 PM

@nullgeppetto Oh so you are gay? Good, good. I like gay people.

@JasperLoy, no I'm not. But it's really irrelevant to anything...

@r9m Throw a search at google scholar -- you'll find the paper.

@BalarkaSen okay ,. i'll look into it later :) .. lemme finish the movie first (i blv this will take some attention .. i'm distracted atm :) )

movies. pfft.

Wiley books are too expensive.

I feel like writing to that company and complaining.

Some of their hardcovers cost over 200 USD.

The hardcover of Rudin's Functional Analysis seems to be out of print. You can still get copies from amazon though.

The softcover international edition is still in print it seems.

@nullgeppetto Many people think I am gay, lol.

@BalarkaSen Have you decided which universities to apply to? I think you will make a great mathematician.

Wow, I am the only person talking in here, lol.

6:16 PM

@JasperLoy It is polite the others listen to you (and not talk at the same time). :-)

@Chris'ssis Do you wear glasses? I imagine you don't.

@JasperLoy No, I don't wear glasses.

I like to wear my Superman glasses. Black and thick, lol.

:-)

There is a person with my same name and in my country who also wears such glasses. Do not confuse me with him!

6:33 PM

@BalarkaSen Can the same be said for all albelian finite simple groups?

or if that can't be said. What is the smallest group that can't be isomorphic to the galois group of a real extension over Q?

7:00 PM

@Chris'ssis That's incorrect.

On second thought, it'd be better to say that it's way too general a statement to make.

7:13 PM

@Khallil I entered one of the universities I applied for in the past with 200 points out of 200 points. The point is this: at that moment, although I was the only one with a perfect score, I didn't perceive the beauty of mathematics, I was only solving things. It took me some years to perceive the beauty of mathematics.

@Chris'ssis The point is anecdotal. It's not general. Just because you had a perfect score, you can't be the point of reference for others. At least, I think that's the point you're making.

This means that you need to spend a lot of time, doing a lot of practice, no matter that you're a genius or not. There is no way to avoid a huge amount of work, and this requires a lot of time because out there is a lot of stuff .

(What did you get a perfect score in out of interest?)

@Chris'ssis When I disagreed, you assumed that I was correlating genius with appreciating the beauty of maths. Somebody with little knowledge of an object can appreciate it more than somebody with a plethora of knowledge on the object.

@Khallil I didn't assume anything.

I completely understand that hard work is necessary to understand math, but it's not entirely necessary to appreciate the beauty of a concept. The Pythagorean theory is pretty beautiful, and is something that you learn in high school.

@Chris'ssis Lets agree to disagree.

7:20 PM

@Khallil Maybe for you the beauty of mathematics gets reduced to the Pythagorean theory. I tell you there is much more than this ...

@Chris'ssis What are you trying to imply?/What do you mean? I didn't quite understand that statement.

Beauty is in the eye of the beholder. Using the word 'reduced' means that you probably don't think that the Pythagorean theory is the most beautiful thing in math. Others might disagree. That's entirely subjective and unique to the individual. What you've done, is assume the generality of such a statement when it might only be 'true' for yourself.

@Khallil Are you 10 years old? If yes, then I understand you since the Mathematics you have learned doesn't contain too much stuff. If you tell me you graduated from high school and then say that the beauty of matehmatics gets reduced to the Pythagorean theory, I don't believe this.

@Chris'ssis Yes. Why do you ask?

@Chris'ssis I didn't say that it is reduced to the Pythagorean theory. Please read that comment again.

I was around 10 years old when I learned the Pythagorean theorem.

Ok ...

7:39 PM

what the hell do you mean by pythagorean theory in any case?

@JasperLoy nah.

@BalarkaSen $a^2 + b^2 = c^2$

that's not a theory.

it's a theorem as a matter of fact.

@BalarkaSen Another typo. I'm sure you can appreciate that.

I also used the wrong term (I was lazy and copied the words from Khallil), but finally replaced it.

=P

7:44 PM

user image

typos are viral

@Khallil seems like that look will haunt me to death.

@Chris'ssis I think @Khallil is trying to say that it's not necessary to learn a lot of stuffs to appreciate the beauty of mathematics. I somewhat agree with him.

@BalarkaSen That's the main message I was trying to, albeit not very successfully, get across.

But simultaneously it's also true that more you learn the more beautiful it seems.

Jorge Fernández

do reference request questions automatically get no reputation?

@BalarkaSen It doesn't seem, it is. :-)

7:53 PM

@Chris'ssis of course "seems" is the right word here, as it's completely subjective. there are people who just take math as a boring or stupid subject.

@BalarkaSen but you said "more you learn the more beautiful ... ". I supposed that "learning" means "learning". :-)

@Chris'ssis yes, so?

i don't get your point.

by "you" of course i wasn't directing the statement towards you =P

@BalarkaSen I thought you referred to those people interested in mathematics, because you then referred to "there are people who just take math as a boring or stupid subject".

yes, i was.

@Chris'ssis There's still a load of variation in those that take interest in math.

7:57 PM

@BalarkaSen That "more you learn the more beautiful ..." makes me think that some people there hardly work on mathematics.

Jorge Fernández

why did I not get rreputation from the upvotes to my question?

@Chris'ssis i don't think i implied any meaning like that.

@JorgeFernández It's because you have enough (11,767) reputation! =P I kid, I have no idea why.

@BalarkaSen In general, I work hard where I need to work, but this is not a general rule. I think Mathematics needs a hard work though.

@JorgeFernández Four upvotes, +20, according to your profile. The Top-bar is once again borked after the failover, so you don't get notification. Should work again tomorrow going by past experience.

Jorge Fernández

8:00 PM

@DanielFischer oh ok, thank you Daniel.

@Chris'ssis i never said anything about hardworking.

you misunderstood.

@BalarkaSen I don't think so.

@Chris'ssis I do.

@DanielFischer You're free to think anything you want to. I don't care too much. Actually I don't care at all.

I was talking to @BalarkaSen.

Interrupting the conversation midway : $$\int_0^{\pi/2} x^2\log^2(2\cos x)\,dx$$ Elementarily .. if one can !!! :D

8:08 PM

Well, @Chris'ssis, you don't need to care, but you should occasionally ponder the possibility that you in fact misunderstood the other person when he/she says you did.

@r9m elementarily? :-)

@Chris'ssis I added 'if one can' in the end .. :P

How to appreciate the beauty of mathematics without learning a lot of stuff? This discussion didn't take place at kindergarten, but on a very serious site.

@Chris'ssis By appreciating the beauty of the little one knows/studied.

Nobody knows a lot of stuffs, in any case.

@Chris'ssis When I "clicked" I did not know that much. It was plotting equations on a computer that made me appreciate.

8:19 PM

@Chris'ssis math.stackexchange.com/questions/330057 absolutely stunning solution by @robjohn !! :O

2

@r9m Cracking solution! You can tell a lot of thought went into that one.

@r9m Fantastic!

@r9m Did integration by parts do anything? Also, have you tried substituting $u = \frac{\pi}{2} - x$? Those are the only things that come to mind. Also, have you tried to break up the logarithm using $\log (ab) = \log (a) + \log (b)$?

Hey maths geeks . . I need your ideas -> How to find out a^b^c . . . % m , when a is not coprime to m .

@monsterspy By '%' you mean mod, right?

8:26 PM

@Khallil I haven't tried it yet :)

yups % == mod . .

Use Euler's theorem.

$a^{b^c} \bmod n = a^{b^c \bmod \phi(n)} \bmod n$.

@r9m Good luck with it! I'm more into basic set theory right now. I love the box analogy. $\{ \varnothing \}$ is like a box with an empty box inside of it.

Okay but I think we can use Euler's totient function when a is coprime to m , but I don't know what we so if a is not coprime to m . @BalarkaSen

Bro my ques. is a^b^c^d^ . . . .mod m .

@monsterspy You can apply that repeatedly. But in any case, I didn't note that you said (a, n) != 1

8:29 PM

@Khallil We have a course on logic this sem .. we will be doing some set theory too :)

@Chris'ssis $$\int_0^1 \left\{ \frac{\{1-x^2\}}{\{1+x^2\}}\right\}\mathrm dx$$

Okay . . @BalarkaSen

@Chris'ssis @Khallil here is a solution .. I was thinking maybe we can do sth more simpler than that :)

@r9m I looked at the first part, but now I regret looking at it. It looked good.

@Alizter This one is for kids ... :-)

8:34 PM

@monsterspy I've honestly no idea what happens when $(a, m) \neq 1$. Maybe a bit of manipulation through exponentiation is involved, but other than that, I dunno.

same here !!!!!!! :-( @BalarkaSen

@r9m don't you like cody's solution?

@Chris'ssis that is nice too :) .. I want real methods ya know ;)

@monsterspy Let $d = (a, m)$. How about reducing $a^{b^c}$ modulo $m/d$ and solving the system with $a^{b^c} = 0 \bmod d$?

That should do it.

The former is easy with the Euler's theorem process, as $(a, m/d) = 1$.

thanks for your idea . Now i move forward to learn some more concepts . One of my friend suggest me to learn Chinese Remainder Theorem to solve this. @BalarkaSen

8:46 PM

@monsterspy yeah, CRT is precisely what you need.

Okay then If you know some good source to learn CRT , then please suggest ! @BalarkaSen

@monsterspy you should find it in any standard elementary number theory text.

@r9m do you have an elementary way? (I won't ask you to show it :-))

my favorite is Niven-Zuckerman-Montgomery, so try it if you want.

@Chris'ssis I haven't tried it yet :) .. robjohn's solution was so striking awesome for the other one .. that made me wonder if we can do this the same way :)

8:48 PM

Okay thanks alot . . @BalarkaSen

@r9m I think robjohn's way is a natural way to go.

@Chris'ssis :) okay !! :) I don't have much experience with integrals so I can't tell which is more natural :-)

@r9m There is something even more interesting ... Just look at the integral sos didn't compute there.

@Chris'ssis I saw that too :D

:D

8:58 PM

@skullpatrol I didn't get the joke.

no joke, just having fun pal

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