Mathematics - 2014-06-22 (page 2 of 5)

N3buchadnezzar

1:00 PM

@Chris'ssis Here is another document I have written folk.ntnu.no/oistes/Eksamen%20-%20VGS/Diverse/R2-V13.pdf

It is an exam for highschoolers

Parth Kohli

@Sawarnik :)

MrWho

@N3buchadnezzar Our final exam question ! WT...!

Chris's sis

@N3buchadnezzar you're a little master at using latex. :D

N3buchadnezzar

=D

Alizter

@Chris'ssis I have personally found latex to be very "sticky". As in when I learn new things I usually don't have trouble recalling them. The syntax is nice and make sense if you know what I mean?

Chris's sis

1:04 PM

@Alizter That's true!

N3buchadnezzar

Deppends how deep you go into things, I quite often need to look up things. But I know where to find them

Chris's sis

I hope no one wrongly judges me, but I've never seen results as the ones I found in the last 2 weeks (say). I definitely need to write a book ...

N3buchadnezzar

I never remember how to use SIunitx in tables for an example. I think it is something like *{}S[tabel space = 3.4]

Alizter

@Chris'ssis Do you have a scanner?

Chris's sis

@Alizter No :-))))

N3buchadnezzar

1:07 PM

@Alizter What is that good for ?

Alizter

@Chris'ssis I know Ethan has an online collection of his scanned works maybe it would be a good idea. I know you write alot down on paper!

Chris's sis

@Alizter That's true!

Alizter

@Chris'ssis I'm sure you can get some quite cheap dedicated scanners

Chris's sis

@Alizter :D

@N3buchadnezzar Did you think to publish that book in your country?

N3buchadnezzar

dunno

need atleast 2 more years with this speed

MrWho

1:14 PM

@N3buchadnezzar Write it in English!

N3buchadnezzar

Working, studying and having friends take an insane amount of time , and is exhausting. I only work on it when I feel motivated

Chris's sis

@N3buchadnezzar How many problems would you like to publish in your first volume? By the way, what is the price of a good math book there?

MrWho

@Alizter You undergrad?

@Alizter I found a way to make intuition for $n^2$ sums!

N3buchadnezzar

@Chris'ssis Dunno, I only add problems I love. So it as many as I discover / find

The document has a small section on basic techniques for solving integrals, and then a bunch of cool problems that is built upon the theory.

Chris's sis

@N3buchadnezzar Since I have thousands of questions ... hmmm ... I'm not sure yet what is the best number of problems I should publish at first.

Alizter

1:18 PM

@MrWho Go on

N3buchadnezzar

Just start with the best of the best

Alizter

@MrWho No.

@Chris'ssis Number then use this

Chris's sis

@Alizter :-))))

@Alizter $1429$ :-)))))))

Alizter

@Chris'ssis Find it and tell us!!

or publish

N3buchadnezzar

@Chris'ssis Better to have fewer problems with more solutions / clearer solutions ;)

Alizter

1:20 PM

@Chris'ssis Or you could spend time creating families and classifying them

MrWho

is there any way to go to next line in the chat text box?

Alizter

@MrWho Shift enter

MrWho

Okay

Chris's sis

@Alizter It takes some times. One of my dreams is also to publish a book with limits that can be computed by geometrical means. (I have some thoughts, amazing solutions here)

For this one I still have to work incredibly hard, but yeah, I'll do it.

Alizter

@Chris'ssis If you scan the paper (or photo or somtething) we can help you with the writing

Coeditors :)

Chris's sis

1:24 PM

@Alizter :-)))

MrWho

1+4+9+16+25+36+49 = $\sum_{i=1}^{7} i^2$
_____________________________________________

1+1+1+1+1+1+1 = 1.7
3+3+3+3+3+3 = 3.6
5+5+5+5+5 = 7.4
9+9+9 = 9.3
11+11 = 11.2
13 = 13.1

@Alizter ^

Alizter

@Chris'ssis Maybe this will help

MrWho

@Alizter Did you see the intuition? :)

Chris's sis

@Alizter Ooo, nice! Thanks! :-)

Alizter

@Chris'ssis It is free ... the pro features are not needed that much

@MrWho I am trying

@Chris'ssis If you create an account then a test paper then we can have a go at online collaborative editing.

Chris's sis

1:31 PM

@Alizter OK ;)

Alizter

@Chris'ssis You just need to give me the link for the paper

in the share option

Chris's sis

@Alizter :-)))

Sawarnik

@ParthKohli Are you happy at that?

MrWho

@Alizter What's up you inductionist ! :P

Alizter

@Chris'ssis Why do your smiley faces have so many chins? They should exercise.

Chris's sis

1:33 PM

By the way, how do I skip a certain page and begin to write from the next one?

\newpage

:)

@Alizter OK

@Chris'ssis It starts it as a new paragraph just to let you know! :)

@MrWho I give up. You will find something one day that will need induction... ;)

MrWho

One of my friends has gone to MIT, now he thinks he has won a Nobel prize! =))

N3buchadnezzar

1:34 PM

@Alizter NO

@Chris'ssis Why do you want to skip a page?

folk.ntnu.no/oistes/Diverse/Integral

Alizter

@N3buchadnezzar I knew there was a better way

MrWho

@Alizter No need to give up, I'm not fighting or something :-)
BTW, I accept that sometimes we're forced to use induction, and I didn't claim that induction has no use, I only say it's a little bit far from intuition!
You math major?

Chris's sis

@N3buchadnezzar I want to let a blank one.

N3buchadnezzar

Stuff like \phantom{mess} \medskip \\ \newline \linebreak should be avoided as much as possible. Latex should not by any means be micromanaged by the user

Alizter

\clearpage?

N3buchadnezzar

1:36 PM

@Chris'ssis Use the book class

G.T.R

@MrWho we throw a ball, why does it fall ?

Alizter

@G.T.R Because it has a monoid structure. Somewhere.

MrWho

@G.T.R That's my biography, I'm looking for the answer dude :)

N3buchadnezzar

Then instead edit the preamble with styles and alike to finetune the look.

Chris's sis

@N3buchadnezzar I'll check that now.

N3buchadnezzar

1:38 PM

@Chris'ssis After a proof, after your name, starting a new section on a new page, after an image?

MrWho

@G.T.R You got an answer for it?

Chris's sis

@N3buchadnezzar aha

MrWho

Believe me no one has a clear answer !

G.T.R

it does not need an answer

MrWho

@G.T.R Why's that?

Chris's sis

1:40 PM

hehe, all works fine!

MrWho

This has got me stumped for a while : $\int\frac{4x^5-1}{(x^5+x+1)^2}dx$

Alizter

@MrWho It would be nicer if it was definite. Anti derivatives are not that exciting.

MrWho

@Alizter What's the difference?calculate the anti-derivative first then think about the boundaries.

Alizter

@MrWho The anitderivative is a definite integral

with an unknown in the limit

MrWho

@Alizter The anti-derivative is indefinite integral(an integral without having boundaries) :)

Alizter

1:48 PM

@MrWho No. The anti-derivative/indefinite integral is a definite integral with an unknown in the boundry

MrWho

@Alizter Oh, by without having boundaries I meant unknown boundaries.

Ted Shifrin

@GTR: I assume the concert stopped by midnight or so? :) Did you solve your linear algebra conundrum?

N3buchadnezzar

@MrWho :p

t's a nice one

Ted Shifrin

Heya @N3

N3buchadnezzar

I guess $x/(x^5+x+1)$

Alex

1:57 PM

Hello everyone

Ted Shifrin

Hello, someone.

Alex

What's the point of doing maths Ted?

G.T.R

@Ted nah it stopped at 1 AM :( I'm considering some block diagonal matrix with blocks ${\begin{array}{cc}
0 & 2k\pi \\
-2k\pi & 0 \\
\end{array} }$

Alex

Spending your life doing maths...

Ted Shifrin

1 AM isn't that bad, @GTR :) OK, that's a good start on the linear algebra, @GTR.

Is this a rhetorical question, @Alex?

Alex

2:00 PM

@Ted No not at all...

Ted Shifrin

Most of us who do it do it because it brings us pleasure and intellectual satisfaction. And I've done it because I'm dedicated to teaching students.

Alex

Is anyone familiar with the result: Let K be compact and convex and let F:K -> (R^n)* (the dual) F: K -> (R^n)* be continuous. Then there is an x in K such that <F(x), y-x> >= 0 for all y in K?

G.T.R

@Ted but showing these are the only ones is out of my league

Ted Shifrin

They're not, @GTR. Take $PAP^{-1}$ any invertible $P$.

Alex

@Ted Are you a smoker?

Ted Shifrin

2:03 PM

Hell no @Alex. Where did that come from?

MrWho

@TedShifrin What shall people who love math but hate teaching do?

robjohn

@N3buchadnezzar how does it know what package is needed?

Ted Shifrin

Many of them teach at research universities, @MrWho :D Most get jobs doing research in real-world jobs. There are some ...

G.T.R

@Ted of course you're right

Ted Shifrin

But, @GTR, that's where you need to use Jordan canonical form, to give a proof.

Alex

2:04 PM

@Ted I don't know...imagine you as an old guy with a pipe...

Ted Shifrin

Well, you have the old guy part right, @Alex.

Although I was not always one.

MrWho

@TedShifrin That's really unfair, we do math, we spend our life time, but our life passes hardly compared to a singer !

Alex

@Ted I feel like an old guy sometimes...

Ted Shifrin

Huh? @MrWho

why is that, @Alex?

MrWho

@TedShifrin I mean our outcome would be less than a singer!

@TedShifrin Of course I don't do math because of money, but hey , why should a mathematician have lots of financial problems than other people!

Ted Shifrin

2:07 PM

Well, most people who work in the arts don't get noticed. Why should we be different?

Alex

@Ted Because life passes so quickly...you wake up one day and realize you are almost 30...

N3buchadnezzar

@robjohn ? If you miss a package it just installs it, if I type \usepackage{microtype} and it is not installed it checks a libary online and downloads if it is found

Ted Shifrin

Where are you, @MrWho?

Alex

@Ted Did you march against the Vietnam war?

Ted Shifrin

Yes, actually.

MrWho

2:08 PM

@TedShifrin Somewhere in which mathematics and physics are considered a waste of time than anything else!

Ted Shifrin

Heya @Studentmath

G.T.R

@Ted or maybe some dunford will do

Ted Shifrin

Well, in the US, athletes and entertainers make the most money, @MrWho.

Studentmath

Prof. @Ted, really?

MrWho

@Alex How old are you?

Alex

2:08 PM

@MrWho I agree somewhat...Since I don't have money for medical costs as a student but I would still prefer spending my time doing maths that working somewhere doing something I hate making lots of money.

Ted Shifrin

Comment? @GTR

Studentmath

I think it's so everywhere. Perhaps after some really succesfull businessmen

Alex

@MrWho 26

Ted Shifrin

Right, of course, I'm not mentioning Donald Trump et al.

Studentmath

@Alex I doubt anyone can make tons of money doing something he truly hates - he just wouldn't be good at it if it was so.

G.T.R

2:10 PM

@ted fr.wikipedia.org/wiki/D%C3%A9composition_de_Dunford

Studentmath

But maybe I am naive

Ted Shifrin

There are plenty of people in business who do that, @Studentmath.

Alex

@Ted What song do associate most with Vietnam...Can I guess "For what it's worth" by Buffalo Springfield?

MrWho

@Alex I agree with you on that.Sometimes, even if you hate to do something else instead of math, you're obliged to work and do the tedious job!

G.T.R

The English counterpart should be Jordan–Chevalley

Ted Shifrin

2:11 PM

That's basically Jordan form, @GTR, yes.

Studentmath

@Ted really, truly hate their job? It sounds just wrong..

Ted Shifrin

Buffalo Springfield? Huh?

Alex

@Studentmat you underestimate people's desire for money...most people work jobs they hate for money...

Ted Shifrin

Yup, I concur with @Alex.

MrWho

@Alex I acknowledge it.

Ted Shifrin

2:12 PM

I think most academics take their lower pay because they love their jobs.

Alex

@Ted "Stop children what's that sound..." no?

MrWho

@TedShifrin My problem is I hate teaching and love math.

Ted Shifrin

Oh, Crosby, Nash, Stills, and Young ... didn't know the name.

MrWho

Am I convicted to live as a poor person? :)

Ted Shifrin

Are you interested in applications of math, or just abstract math, @MrWho?

MrWho

2:13 PM

@TedShifrin I'm interested in mathematical physics and mostly application.

Ted Shifrin

There are plenty of Wall Street businesses, consulting companies (Mckenzie), National Security Agency ... who hire Ph.D. mathematicians.

Get a job in biotech, @MrWho.

Alex

@Ted How were the 60s? Did you take any psychedelics?

MrWho

@TedShifrin I don't like to be considered a Rocket Scientist !

Ted Shifrin

LOL, no, @Alex. I've never even smoked pot. I hate it.

I'm not talking rockets, @MrWho. I'm talking things like CT Scan ... all sorts of fascinating math in there ... and jobs.

Alex

@Ted I have smoke a fair bit of weed...and I can say it's not good for maths...

Ted Shifrin

2:15 PM

Yeah, it's hard enough doing math with a clear head ... a foggy one probably isn't good :P

MrWho

@TedShifrin Is the outcome good enough to live a life with? how's biotech about?

Alex

@Ted But you should try shrooms...I did it only once and it's quite an experience...I think I will do it again after my masters...

MrWho

@TedShifrin Any chance of getting somewhere in physics?

Ted Shifrin

yes, @MrWho ... more like engineering ... Physics leads a lot to biophysics and biotech, too.

Alex

@Ted It's really not good...I learnt that the hard way by wasting a year at university...

Ted Shifrin

2:16 PM

Do some research into it, @MrWho.

Most students waste a lot more than a year being ineffective or not sufficiently dedicated.

Alex

@Ted it was my first year out of high school and I had an idea that I was good enough to pass without working hard...

MrWho

@TedShifrin So tell me, what should I do? I hear research, research , .... !

@Alex Don't smoke! It leads nowhere!

Ted Shifrin

Do some web research, @MrWho ... look into engineering firms that work in biotech and look for math/physics hires they want to make.

I gather you're not interested in the business-world consulting. A lot of my super-talented math students end up doing that.

Alex

Okay have a good day everyone going to do some maths, today it will be for the love money...c yer

MrWho

@TedShifrin Sorry, I ask lots of questions, but could you please give me a general picture of the job I'm supposed to do?

Ted Shifrin

2:19 PM

Bubye, @Alex.

No, @MrWho ...

MrWho

?

Why?

Ted Shifrin

I'm telling you to do some research on the web and look into it.

MrWho

Aha

:)

@TedShifrin I will do that.I thought you've got real world experience, consulting business stuff?why should a super talented math student go in such field?

Mike Miller

@TedShifrin I'm going back to bed, but: I think Bredon is a fantastic (second) text. I keep learning new things while going through it (and filling in the details he leaves behind solidifies my understanding); in a section on explicitly computing some de Rham cohomology, he (without using the phrase) told me a little about spectral sequences.

OK, night.

Ted Shifrin

No, I do not have real world experience. I advise hundreds of students, so I try to know something to direct them. You also need to like using computers, @MrWho. The day of ignoring computers is long gone.

Studentmath

2:22 PM

Noooooooo

Ted Shifrin

Night? @Mike ... It's time to be doing morning.

Did someone step on your tail, @Studentmath?

Studentmath

But yeah, they force you to take computer courses and study a bit of coding pretty much everywhere.

Computers did.

Mike Miller

@Ted I went to bed way past my bedtime... :)

Studentmath

I have to constantly lie that I love it to advance in places..

MrWho

@TedShifrin I like programming, I've got a disease too, I must get things as clear as crystal to go further and that's why my math knowledge is still not enough!

Ted Shifrin

2:23 PM

You're young, @Mike.

OK, @MrWho ... Look into the math of things like tomography (Radon transform), CT scans, etc.

You don't have to love it, @Studentmath. You just have to know how to use it to solve problems.

MrWho

@TedShifrin Okay, as a side note, I'm interested in physics too, is it any of help?

Ted Shifrin

In the end, its brains and problem-solving skills that make math people stand apart.

Yes, sure, @MrWho. There's lots of physics needed in designing the actual machinery!!

And I'm sure there are dozens of other similar things that a physicist could tell you about ...

Mike Miller

@Ted Anyway, it was cute. He computed a way of passing from $H^2(\mathbb{CP}^2)$ to $H^1(S^1)$ from a diagram involving the fibration... and my understanding is that such information/homomorphisms "come" from the Serre spectral sequence.

So it wasn't too hard to see how it might generalize.

OK, now I am going back to bed.

Studentmath

True, it isn't bad at all actually, can be fun - especially designing it to be effecient and readable and so on.

Ted Shifrin

@Mike: Yup, such things are spectral sequences. Can't get that one out of the coboundary map on sheaf cohomology :P

P.S. @Mike: You want to look at Bott & Tu at some point ... Add that to your list.

Mike Miller

2:32 PM

@Ted I'm still awake. Anyway, that one's on my nightstand too.

Ted Shifrin

Ah, good.

Mike Miller

At this point I think it's too late for sleep. Ah well.

Ted Shifrin

Go for a brisk walk before it gets hot.

Mike Miller

Good suggestion, I think I will.

Ted Shifrin

I've already sweated for 90 minutes playing tennis, even starting at 7:45 am ...

MrWho

2:35 PM

@TedShifrin What about astrophysics?

Ted Shifrin

@MrWho ... Go talk to some of your professors.

MrWho

@TedShifrin My professors don't care about their students future !

@TedShifrin Also she dislikes me due to the fact that I solved a problem the student had given to her but she wasn't able to tackle it.

@TedShifrin My financial situation is under the red line! I'm almost running out money for the next semester, and I'm not allowed to get job outside the campus!

Ted Shifrin

There's only one person in all of math, physics, astronomy you can talk to?

MrWho

@TedShifrin Well, in my Uni the story is different!

Ted Shifrin

Well, this is not fifty years ago. You have all sorts of information available to you on the web.

MrWho

2:44 PM

@TedShifrin Contacting people is the real part of what we're looking for!

eXtremiity

3:23 PM

"For example, if one of them is compact, then the other is as well; if one of them is connected, then the other is as well; if one of them is Hausdorff, then the other is as well; their homotopy & homology groups will coincide. Note however that this does not extend to properties defined via a metric; "

So what exactly are the topological invariants under the metric topology?

user105491

@eXtremiity Where did you quote that from?

eXtremiity

Homeomorphism

In the mathematical field of topology, a homeomorphism or topological isomorphism or bi continuous function is a continuous function between topological spaces that has a continuous inverse function. Homeomorphisms are the isomorphisms in the category of topological spaces—that is, they are the mappings that preserve all the topological properties of a given space. Two spaces with a homeomorphism between them are called homeomorphic, and from a topological viewpoint they are the same. The word homeomorphism comes from the Greek words ' (homoios) = similar and ' (morphē) = shape, f...

user105491

@eXtremiity What do you think the invariants are?

eXtremiity

Compactness is certain. I have learn't that in class. However, my lecturer has not touched on anymore.

Perhaps it is the only one under the metric topology.

What do you think for connectedness?

user105491

@eXtremiity Homeomorphisms preserve connectedness.

eXtremiity

3:31 PM

Great :).

Thanks.

user105491

@eXtremiity Sure!

anorton

4:23 PM

@N3buchadnezzar You might just make me learn German. :) That's incredible.

Hm. I thought it was German; Google translate is saying it's Norwegian.

Bananarama

4:52 PM

@robjohn why do deleted things linger?

Is there a way for me to completely erradicate any traces of a problem or solution I have written?

anorton

@Bananarama See here: meta.stackexchange.com/questions/107985/…

Bananarama

wow,I don't like that

People with 10k or more can see my answers?

anorton

@Bananarama That is my understanding. I'm ~800 rep away, though, so I'll know for sure soon enough. ;)

Ted Shifrin

5:10 PM

Yup. I have X-ray vision. Deleted schmeleted.

Hi @anorton

anorton

Hi!

robjohn

5:25 PM

@Bananarama what deleted things?

@Bananarama no

Bananarama

anything in general, can it be deleted permanently, instead of having it red?

anorton

(A note: in general, nothing on the internet should ever be assumed to be totally deleted.)

2

robjohn

@Bananarama nothing is ever deleted unless your account is destroyed and that only happens when an account is used only to spam.

Bananarama

I see

robjohn

@Bananarama the license agreement to use SE says that SE has a license to use material submitted, so although you own the material, SE has a license to use it. That is why when people delete their post out of spite, we usually restore the post.

Vibhav Pant

5:41 PM

hullo

Daniel Fischer

@Bananarama If there is really confidential information involved, you can ask SE to hard-delete, at least the sensitive parts. It's not a good idea to contact them if you just want your "Uh, I dun goofed" erased, but if you accidentally post your credit card number, that would be a candidate for hard deletion.

@anorton Except if you really need to look at it for some reason. Then it is definitely gone forever without leaving a shadow of a trace.

anorton

@DanielFischer Yep. Funny how that works, isn't it?

Daniel Fischer

Just the normal conspiration of the world against you. It was always so, but it has become more conspicuous with the internet.

Studentmath

sigh two different proofs and I get neither..

Mike Miller

How does one accidentally post their credit card number?

Bananarama

5:48 PM

@DanielFischer haha, nothing serious, thanks

Vibhav Pant

@MikeMiller using a usb card strip reader

@MikeMiller If you are referring to bash.org

Studentmath

@Mike and unto SE, no less

Vibhav Pant

Also, I have this somewhat large question:

anorton

@MikeMiller If you're on one of the other sites (e.g. Finance) and copy some bank information to illustrate a point. Then, you realize, "oops! I forgot to take out my account numbers and passwords!" There's a hypothetical example....

Vibhav Pant

Given a function $g$, continuous everywhere such that $g(1)=$ and $\int^1_0g(t)dt=2$. Let $f(x)= 1/2 \int^x_0 (x-t)^2 g(t) dt$. Prove that $f'(x)=x\int^x_0g(t)dt-\int^x_0 tg(t)dt$

oops, $g(1)=5)

$g(1)=5$

Also, compute $f''(1)$ and $f'''(1)$

robjohn

5:53 PM

@Chris'ssis: I took an integral to a sum, then back to an integral, and finally back to another sum. :-) whee!

there must be an easier way :-)

Vibhav Pant

If I use the first FTC for proving $f'(x)=x\int^x_0g(t)dt-\int^x_0 tg(t)dt$, I get $f'(x)=0$, where am I wrong?

anorton

Did you use a product rule at all?

Vibhav Pant