Mathematics - 2015-05-09 (page 3 of 4)

pjs36

13:02

Yes that's all true, Mary. $f(a) = f(a + 2\pi k)$ for all integer $k$, as well as $f'(a) = f'(a + 2\pi k)$

Mary Star

Ok... Thank you!! :-) @pjs36

pjs36

Yep! The latter (about derivatives) is true if you think in terms of the definition of a derivative: $f(a + 2\pi k + h) = f(a + h)$

Mary Star

I see...

Ted Shifrin

boo @Pedro

Pedro Tamaroff

Morning!

Ted Shifrin

13:14

Well, I'm done. What are you up to?

pjs36

Ooh, are we booing Pedro? How ghastly

Ted Shifrin

No, ghostly.

Pedro Tamaroff

@TedShifrin Thinking about taking a nap. =)

pjs36

I'm using English modulo vowels.

Balarka Sen

hey @Ted

hello @Pedro.

Pedro Tamaroff

13:25

Hello.

Balarka Sen

sanity check : if (X, A) is htpy equiv to (X, B), then is X/A htpy equiv to X/B or do we need homotopy extension property?

Mary Star

Could someone take a look at the second edit and tell me if it is correct?

2

Q: Find the Fourier series of the function

I want to find the Fourier series of the following function : $$g: [-\pi, \pi]\rightarrow \mathbb{R} \\ g(x)=\left\{\begin{matrix} -\frac{\pi+x}{2} & , -\pi \leq x \leq 0\\ \frac{\pi-x}{2} & , 0<x\leq \pi \end{matrix}\right.$$ $$$$ I have done the following: $$g \sim \frac{a_0}{2}+\sum_...

Balarka Sen

i guess i probably need HEP

Clarinetist

Hello MathSErs. :) Really excited to put in my 2 weeks on Monday! :D :D

user147690

Still at uni >.<

evinda

13:30

@AlexClark On Saturday?

user147690

@evinda Saturday - 11:31PM

evinda

11:31 PM? In which country are you? @AlexClark

user147690

The best one ;)

evinda

@AlexClark Which is the best country? ;)

user147690

Straya' m8

evinda

13:32

What do you mean? @AlexClark

user147690

@evinda Australia, mate

Clarinetist

Australia?

Woo I was right! :)

user147690

xD

evinda

@AlexClark Nice :) How is the weather there?

user147690

Cold atm, but not cold like most of the world knows it probably

user147690

13:34

55 degrees F or 13 C right now

evinda

Aha... @AlexClark

user147690

Is that cold to you @evinda?

evinda

@AlexClark Yes, a little..

Clarinetist

Two winters ago, I went through -30 degrees F weather

user147690

Wow

user147690

13:36

That's insane

Clarinetist

(so what is that,... -34.44 C)

user147690

First time I have heard someone experience colder celcius than F

Clarinetist

And that was NOT taking into account the wind chill

user147690

Coldest I have ever felt is like 5c ish

Clarinetist

With the wind chill, I think it was -70 degrees F

Mary Star

13:37

@pjs36 Are you familiar with Fourier series?

evinda

user147690

Never seen snow in person, never had ice

Clarinetist

(so -56.67C)

user147690

We get 42C summer, is that atleast hot for where you are in summer?

Clarinetist

Heh, I would not recommend Minnesota or Wisconsin for you, lol @AlexClark

pjs36

13:38

@MaryStar Probably not familiar enough to be helpful, unfortunately

Mary Star

Ok...

user147690

I am wearing shorts and a teeshirt all year though, since I am an aussie

user147690

middle of winter to middle of summer :)

Clarinetist

Yes, that would be very hot. We're usually around 70-90F (21.1-32.2C) @AlexClark

user147690

@Clarinetist oh that makes me feel less like a little girl ahaha

Clarinetist

13:39

I remember I had to walk outside that day when it was -30F

It was AWFUL

user147690

I was cold as heck outside before at 13C

user147690

admittedly I am always cold when I haven't eaten in ages, and we are going on 10 hours or so

Clarinetist

The closest thing I can relate it to is having needles try to stab your face.

user147690

That sounds un-fun

pjs36

Can you believe this is an actual attempted edit?

Ted Shifrin

13:41

@Pedro: Napping first thing in the morning is discouraged.

Clarinetist

@pjs36 That happens more frequently than I would like :/

Ted Shifrin

Hi @Balarka

Pedro Tamaroff

@Clarinetist Really?

pjs36

That's insane.

Clarinetist

@PedroTamaroff Of course, I'm not on often

so I might be looking at a relatively small sample size

Balarka Sen

13:42

@TedShifrin How's your day?

Ted Shifrin

Quiet so far @Balarka ... Done flunking students.

Clarinetist

@TedShifrin Happy retirement :)

user147690

@TedShifrin Now to start teaching us :)

Balarka Sen

@TedShifrin aw, you're gonna miss that moment.

Ted Shifrin

Some things are hopeless, @AlexC :)

Clarinetist

13:44

One of my math profs who got her degrees from MIT and UCSD, I suppose, has been asking on FB for other job options she could consider

Ted Shifrin

happy return to school, @Clarinet

not getting tenure?

Clarinetist

@TedShifrin Hehe, I'm more excited than I should be to pay $2000-2300 per month to go back to school :P

@TedShifrin She has tenure

user147690

@TedShifrin Too true :)

Ted Shifrin

ah ... Not happy?

Clarinetist

@TedShifrin Remember, this is WI we're talking about

Ted Shifrin

13:45

ah ...

Clarinetist

Yep, @TedShifrin

I don't think merit raises have happened at my alma mater since 2000, from what I gather

Balarka Sen

$2000-2300 per month? yeesh.

Ted Shifrin

our anti-intellectual society will pay for this ....

Clarinetist

OOPS @BalarkaSen, should be per SEMESTER

LOL

Balarka Sen

oh, lol

Clarinetist

13:47

But there is no way you could've told me a year ago that I would've been excited to see matrices again. Lol.

Ted Shifrin

start saving your rupees, @Balarka :)

Balarka Sen

i'm not going anywhere if i don't get a good scholarship. too poor.

Clarinetist

Looks like I will need to do some linear algebra review and learn some stuff about matrix/vector differentiation and pseudoinverses

Ted Shifrin

All quite learnable, @Clarinetist

Balarka Sen

ps : i think we don't need HEP, but i am not sure. plus, too lazy to work out the details.

Clarinetist

13:49

I am HOPING that the material will come back easily. My impression is that not everyone gets into a M.S. statistics program having already taken 2 semesters of analysis

Ted Shifrin

I think you'll do fine, @Balarka

Balarka Sen

Not sure what you are referring to. The problem?

Clarinetist

But anyway, I am ECSTATIC to be leaving actuarial science and to not learn about life insurance regulations!!!!!!!!!!!!

Ted Shifrin

No, scholarship. If you already have a homotopy, how can you need HEP?

pjs36

@Clarinetist You have my condolences, knowing you even had to think about life insurance regulations

Balarka Sen

13:52

oh, that.

@TedShifrin yeah, it was a silly sanity check. never mind.

robjohn

@MaryStar having a period of $2\pi$ not only means that $f(0)=f(2\pi)$, it means that $f(x)=f(x+2\pi)$. Thus, $$\frac{f(x+h)-f(x)}{h} =\frac{f(x+2\pi+h)-f(x+2\pi)}{h}$$ take limits, and what do you get?

Balarka Sen

i'm just too worried about pathological spaces to say "it's ok" outright.

Ted Shifrin

Maybe you'r right. Write it down.

Balarka Sen

okay. let me see.

Ted Shifrin

Maybe you need some hypothesis on the subspaces to induce a continuous map.

Clarinetist

13:58

Random rant:

I have never had to burn more bridges than I have in the two actuarial positions I have been in

With this current position, a project that I am apparently supposed to work on until 2017 (because of awful data structures) will likely be terminated and I will be leaving the day before the new supervisor comes in. If I were to stay past memorial day, I will have had 3 supervisors in 9 months of working here.

Ted Shifrin

Not a great business model.

Huy

@TedShifrin: Got any cool applications for finite-dimensional eigenvalue problems apart from Google PR algorithm (for my high schoolers)? Most things I can think of require diagonalisation, which they have not seen yet, or infinite dimensions.

Clarinetist

The turnover is insane in the subdepartment of the actuarial department I work in. I also found out that my first manager here had only been a manager for a month (after some investigation).

Ted Shifrin

How can you talk eigenvectors w/o diagonalizarion?

Clarinetist

I am assuming that it is to my benefit to put in my two weeks so that I leave before the new supervisor comes in, so that I am doing.

Ted Shifrin

14:02

There are some projective geometry/computer graphics apps, I guess.

Huy

@TedShifrin: I started with eigenvalues and how to find them (and eigenvectors) first and was going to do diagonalisation afterwards, but it'd be nice to do a few simple applications where just finding eigenvectors & eigenvalues suffices (like google pr).

Ted Shifrin

My idea is too much of a side trip.

Balarka Sen

The most fun bit of eigenstuff is about doing fixed-point theory with Grassmannians, 'course.

Ted Shifrin

Steady state of a Markov process?

Clarinetist

And the last position I had been in was awful. It was with a well-known actuarial education company, but really, none of them know how to write mathematics. A lot of my conflicts with them consisted of them using a bunch of loose wording in their publications, and me telling them to avoid doing so. For example, if $\Omega$ is your sample space, they defined for $A \subset \Omega$, $\mathbb{P}\left(A\right) = \dfrac{\#A}{\#\Omega}$, which is NOT RIGHT for a general definition.

Mary Star

14:04

$$f'(x)=\lim_{h\rightarrow 0} \frac{f(x+h)-f(x)}{h} =\lim_{h\rightarrow 0}\frac{f(x+2\pi+h)-f(x+2\pi)}{h}=f'(x+2\pi)$$

right? @robjohn

Ted Shifrin

Ah, Frobenius Thm on eigenvector of positive matrices, @Huy

Huy

@TedShifrin: I only did one example of a Markov chain in my linear algebra course, and I think that required diagonalisation. Is it different for steady states?

Clarinetist

I am waiting for Ph.D. mathematicians and statisticians to take over actuarial science so that people can realize how archaic actuaries' methods are for analysis and can at least revamp their so-called "education" system.

Ted Shifrin

You find steady state as 1-eigenspace. You don't need diag other than to prove theirems.

It's all moved toward the business side, Clarinet, so I dunno.

Clarinetist

@TedShifrin - Quite serious here - if you are a Ph.D. in math or statistics and you sell actuarial study materials, you will make money, guaranteed. Ph.D.s are so, so rare in this field.

There are two people that I know of that are doing that

The sheer irony is that actuaries are intimidated by Ph.D.s, so they don't support anyone's pursuits of any sort of graduate work (M.S. or Ph.D.).

Anyway, I am going to start packing! :)

Ted Shifrin

14:14

Come pack for me too :)

Clarinetist

Lol :)

I wonder if I should hire a contractor for moving...

robjohn

@MaryStar yes. Then you can plug in $x=0$ to get $f'(0)=f'(2\pi)$

Balarka Sen

14:43

hi @iwriteonbananas

Mary Star

15:07

Ok... Thanks!! :-) @robjohn

Could you take a look at the second edit of my question and tell me if it is correct?

2

Q: Find the Fourier series of the function

I want to find the Fourier series of the following function : $$g: [-\pi, \pi]\rightarrow \mathbb{R} \\ g(x)=\left\{\begin{matrix} -\frac{\pi+x}{2} & , -\pi \leq x \leq 0\\ \frac{\pi-x}{2} & , 0<x\leq \pi \end{matrix}\right.$$ $$$$ I have done the following: $$g \sim \frac{a_0}{2}+\sum_...

real-analysis definite-integrals fourier-series

@robjohn

N3buchadnezzar

15:34

Why arent jokes in base 9 funny? Because 7 8 10...

Chris's sis

Greetings

@robjohn I managed to create a very nice solution to the Hadjicostas (integrals) formula, and besides that I also solved the variant in 3 dimensions.

mathworld.wolfram.com/HadjicostassFormula.html

I wonder if someone else solved before the variant in 3 dimensions (or in more dimensions).

pjs36

15:49

@N3buchadnezzar, I think you just blew my mind with that one :)

Mike Miller

morning

N3buchadnezzar

@pjs36 ^^ Hopefully someone will get it

ADG

16:09

hello

Clarinetist

Anyone want to help me with basic trigonometry?

"To find a distance $AB$ across a river, a distance $BC = 627$ cm is laid off on one side of the river. It is found that $B = 113.8$ degrees and $C = 17.3$ degrees. Find $AB$ to the nearest meter."

So I have drawn a "river," left side of the river has a point $A$ and right side of the river has a point $B$, connected the line through them, and I'm not sure at all how to draw $BC$.

[I haven't used trig seriously in 7 years.]

Or do I assume that $ABC$ is a triangle?

and then maybe do some law of cosines/sines work to it?

pjs36

16:28

I believe the set-up is something like... Hmm, well, I apparently can't upload a picture

But yeah, I'd assume $ABC$ is a triangle, then use law of cosines, then law of sines

And basically side AB directly crosses the river, side BC is entirely on one side of the river

Nickolas

16:54

Hey everyone! Can articles (eg an article on evaluating difficult integrals) be published on arxiv or does it have to be a research paper?

banach-c

hi

evinda

Hello :)

banach-c

2

Q: move a cuboid from start to destination

Consider the field with infinitely many boxes, "S" means start, "D" destination, and I already found a way to move a $1\times 2\times 4$-cuboid (as you can see on the right at this picture) from the start position to destination trough tilting this cuboid. My question: If I choose an arbitrary...

geometry game-theory

Remember me

Hi!!!!@evinda

evinda

How is it going on? @Nickolas

@Rememberme What's up?

banach-c

16:59

i need help to understand the answer; I don't understand why it is always possible

but I understand the elementary moves

Nickolas

17:11

@evinda hey

@evinda everything's fine

evinda

@Nickolas Nice :)

Nickolas

@evinda at the end of the month we held the panhellenic conference on geometry here at the department

evinda

@Nickolas Did you take part at it? In Anogeia, there was also a two-day conference about Euclidean Geometry..

Nickolas

@evinda yes I will, it will cover many topics from geometry

evinda

Will you present a specific topic? @Nickolas

Remember me

17:26

Whats the definition of an algebraic number??

iwriteonbananas

@BalarkaSen hey balarka, what are you studying these days?

Remember me

hi@iwriteonbananas

iwriteonbananas

hi

Nickolas

@evinda no, some of my profs will though

@Rememberme a number is algebraic if it is root of a polynomial with integer terms

for example pi is not algebraic

evinda

I see... @Nickolas

Remember me

17:32

@Nickolas So if i take for example the fermats last theorem and plug in algebraic powers will the same conjecture hold true??

Is there any algebraic number between 1 and 2

Nickolas

@Rememberme yes, Square root of 2

@Rememberme an algebraic number can be real. If a number is not algebraic it is said to be transcendental.

Remember me

Ha!!! does that mean fermats last theorem works for $\sqrt2$??@Nickolas

Nickolas

@Rememberme take a look at wolfram mathworld.wolfram.com/AlgebraicNumber.html for a table of some common algebraic numbers

Remember me

$a^{\sqrt2}+b^{\sqrt2}=c^{\sqrt2}$ for some a,b,c this is true right @Nickolas

Nickolas

@Rememberme are you applying Fermat's last theorem?

Remember me

17:40

No its just a wild thought

Nickolas

@Rememberme $a^n + b^n = c^n$, n has to be an integer

Remember me

it is not mentioned

Nickolas

@Rememberme though I'm not a fan of algebra I remember n is an integer.

Remember me

Yes Yes integers that dosent make me happy though...

But lets say i do happen to state it will it hold true for any algebraic number @Nickolas

Nickolas

@Rememberme state what

Remember me

17:45

I state that $a^n + b^n = c^n$ holds true for an algebraic number n where a,b,c are integers..

Nickolas

@Rememberme that won't work Im afraid

Remember me

Hmmm why a proof?

Nickolas

Wait

Remember me

Fine. $waits$

pjs36

Well, we can certainly find algebraic triples $(a, b, c)$ for which $a^n + b^n = c^n$

Nickolas

17:48

@Rememberme let me take that back and guess it would work.

Since we can't find integers, we can find algebraic numbers a,b,c

@pjs36 corrected me first :)

Remember me

Hmm everything algebraic it seems

Hi @TedShifrin how was your day??

Ted Shifrin

Hi @Rememberme ... Still in the middle. You?

Remember me

Stuck with meds...suffering from anemia.. :( @Ted

@pjs36 You have some kind of a proof for it that it works for all algebraic....

Ted Shifrin

oh dear ... I had that when I was in bad shape with cancer ... Get better soon!

Remember me

Yes trying to as quickly as possible....

Nickolas

17:51

@TedShifrin hey

Remember me

Lets see everything algebraic.... I cant think of a proof...

Ted Shifrin

Hi @Nickolas

Nickolas

@Rememberme suppose there are no algebraic numbers but there are integers, impossible from fermat's last theorem.

Remember me

I didnt get you?@Nickolas

Mike Miller

what's the question

Remember me

17:59

@MikeMiller you are asking me?

pjs36

I guess what I mean to say is that, given any integers $a$ and $b$, then if $a^n + b^n = c^n$, it seems that $c$ must be algebraic. It's in fact a solution to the equation $x^n - (a^2 + b^2) = 0$ :)

Remember me

@MikeMiller If you are asking me then i want to know that will fermats last theorem work if everything in it that (a,b,c, and the power n) are algebraic?

$a^n+b^n=c^n$ where a,b,c,n are algebraic

Mike Miller

Why would you expect that to be true? Let $n$ be some positive rational, $c$ be some positive algebraic number, and let $a = b = \sqrt[n]{c/2}$.

Remember me

Hmm...So we just cant say anything about it or can we@MikeMiller

pjs36

Actually, it's just a theorem that the algebraic numbers are a subfield of the real numbers, from which we conclude that $a^n + b^n$ is algebraic if $a$ and $b$ are. So if $a^n + b^n = D$, then $D^{1/n} = c$ is algebraic (as the $n$th root of an algebraic number), and $a^n + b^n = c^n$, with $a, b, c$ algebraic.

Remember me

18:07

oh...that way.....

Mike Miller

There's no reason you should be able to say anything interesting about it. If you want to generalize FLT, the interesting path is to consider $x^a+y^b=z^c$, for fixed exponents $(a,b,c)$ and $1/a+1/b+1/c < 1$.

Remember me

Looks nice

Mike Miller

You assume $gcd(x,y,z)=1$ so that there aren't stupid solutions for every exponent. Then the suspicion is, discarding trivial solutions with $xyz=0$, that there are only finitely many sextuples $(x,y,z,a,b,c)$ that solve this.

Remember me

Also does this imply that we also cant say anything about the transcendental numbers in FLT@MikeMiller

Mike Miller

Not all that much is known about this. It's an absolutely absurdly difficult problem, given that FLT was already absurdly difficult. Some partial results are known for specific exponents; e.g. we know all the solutions to $x^2+y^3=z^7$.

Remember me

18:10

we know.....Pretty nice....

Mike Miller

Of course you can't say anything about transcendental numbers. If you include transcendental numbers then $x^n+y^n=z^n$ is just a curve in the plane, with the uncountably many solutions that entails.

This is not an interesting way to generalize these ideas.

Remember me

Thanks @MikeMiller for the answer i will keep on thinking about FLT ...

Mike Miller

If you want.

pjs36

So, any classes you'll be taking in the future, @MikeMiller ?

Remember me

Hi!!@TobiasKildetoft

Tobias Kildetoft

18:17

@Rememberme Hi

Mike Miller

Nothing scheduled. I'm doing a reading course with my advisor now; at some point I'll be directed towards the literature on a problem I want to work on, and after that I'll get to work, I suppose.

pjs36

Not bad, not bad at all!

Tobias Kildetoft

@MikeMiller Just started a PhD?

Mike Miller

@DanielFischer: God damnit.

Daniel Fischer

@MikeMiller You overlooked the absolute value, I guess?

Mike Miller

18:20

Of course I did. In retrospect, what you wrote down is obviously what's desired...

I was thinking of cutting at one irrational, and flipping one side, rather than at two.

And read your answer in kind. I'm not nearly careful enough lately, I've been making lots of stupid mistakes in the last couple days.

@TobiasKildetoft: Yes.

Tobias Kildetoft

@MikeMiller Nice. Where, and what general topic?

Mike Miller

UCLA, low-dimensional topology.

Ted Shifrin

Goodnight, Mike.

Tobias Kildetoft

@MikeMiller Cool

Daniel Fischer

Evening @Ted.

Mike Miller

18:23

I deleted the comment, @DanielF.

Morning @Ted.

Joe Stavitsky

as x goes to infinity, limit (9+9/x) goes to 9, right?

Mike Miller

@TobiasKildetoft Google says you're a group theorist; enjoying it?

Tobias Kildetoft

@MikeMiller Yes, though I am more of a representation theorist now

Ted Shifrin

Ah, Tobias found character :)

Tobias Kildetoft

I switched from finite groups to algebraic groups when I switched from masters to PhD, and I am now also doing some $2$-representation theory

@TedShifrin Good one

Ted Shifrin

18:26

Schur thing! shutting up

Mike Miller

yeah, I opened your latest arXiv preprint and was met with "let G be a group scheme..."

Tobias Kildetoft

@MikeMiller That doesn't sound like a precise quote. Probably more like "a reductive algebraic group"

(though that does of course mean a group scheme)

Mike Miller

It wasn't a particularly accurate quote. I missed about five adjectives.

Tobias Kildetoft

Yeah, probably half of them can be ignored, but they make things easier (then if anyone needs to do without them, you let them do the argumentation for why they can be left out)

Mike Miller

what sort of problems do 2-representation theorists care about?

Tobias Kildetoft

18:28

@MikeMiller representations of $2$-categories

so generally the idea of categorification

Mike Miller

I mean, what's an actual problem you care about?

Tobias Kildetoft

For example Khovanov homology is an example you might have seen as a topologst (though not originally phrased in terms of $2$-categories)

Mike Miller

Sure.

Tobias Kildetoft

@MikeMiller Recently I have been working with my mentor on proving that projective functors on the principal block of category $\mathcal{O}$ for a simple Lie algebra of type $A$ remain indecomposable when restricted to a parabolic subcategory (when non-zero)

which is not directly about categorification, but the proof we have uses a lot of results from that area

Mike Miller

OK, that's the sort of thing I was looking for, thanks. :)

pjs36

18:33

@DanielFischer Is there anything to do about spam but flag it? That is, there's someone spamming in real time :)

Tobias Kildetoft

It has taken me quite a while to get used to the ideas of categorification

Daniel Fischer

@pjs36 Just flag as spam, but if you can grab a moderator in chat directly, doing so leads to speedier destruction of the account. That one is history.

pjs36

@DanielFischer Thank you, good to know. Mark me down for an "assist" then :P

Daniel Fischer

@pjs36 You, and some others.

Remember me

@JoeStavitsky yes its right

Karim Mansour

18:52

hi guys

Remember me

[email protected] are you??

Ted Shifrin

19:32

Hopes not to be eradicated by @DanielF

Daniel Fischer

@TedShifrin As long as you don't start spamming, you should be safe.

Ted Shifrin

Isn't some people's pork some people's spam?

Remember me

@TedShifrin your and my handwriting is quite the same.. :)

Ted Shifrin

@Rememberme Oh?

Daniel Fischer

@TedShifrin Spam in that sense is merely off topic. If you start posting "Packers and Movers San Luis Obispo" every day, then you'll be in trouble.

Remember me

19:37

Yes it is ... :)

Ted Shifrin

Oh, I could use a good mover! :)

Balarka Sen

@iwriteonbananas mostly linear algebra.

Ted Shifrin

Hi, bananas and Balarka.

Balarka Sen

@Rememberme You shouldn't, believe me.

hello, @Ted

Remember me

Hi!!!!!@BalarkaSen i mean that there is a theorem in hoffman kunze which says that $T(T(\alpha))=0 \iff T(\alpha)=0$

why??

Balarka Sen

19:44

Well, if there is a theorem, then you should be able to prove it.

Remember me

Yes i am

why did you say i shouldnt think about FLT

Balarka Sen

Because it's absurdly hard.

Ted Shifrin

I hope that theorem has some hypotheses and $\alpha$ means something.

Remember me

I know it is super damn hard but it is the source of something super interesting isnt it

Oh sorry @Ted i forgot to mention the details about the vector space and t being a linear operator and all

Ted Shifrin

No, you need lots more ...

Remember me

19:47

yes the field , etc....

Balarka Sen

@Rememberme Yes, but I don't think you'd be able to understand what that stuff is even when you go to, say, grad school.

I don't think I'd be either.

So it's better not to set "I'd like to understand the proof of FLT" as a goal.

Remember me

Yes i know that i am very well aware of that ..... that why i like it....air of mystery... :p

Ted Shifrin

no, no. It's something special about the linear map.

Remember me

its from V to V,....ha the range and the null space are disjoint

@Balarka you understand the proof of FLT?

Balarka Sen

no, I don't expect to

not even in far future.

Ted Shifrin

19:50

Very few professional mathematicians do, Sayan.

Remember me

Few?? very weird

Tobias Kildetoft

@TedShifrin Depends on how many it takes to be "few"

Balarka Sen

I don't think it's weird.

hello @Tobias

Tobias Kildetoft

@BalarkaSen Hi

Remember me

Ya it is difficult but lets see do you understand the proof of Poincare conjecture @Balarka

Balarka Sen

19:52

no, absolutely not.

Remember me

Thats more weird

Balarka Sen

Why is that weird?

Remember me

Because i thought you are the master of altop

Balarka Sen

The amount of math involved has almost about the same complexity as the proof of FLT.

Ted Shifrin

Remember the majority of mathematicians are not at the top few universities.

Balarka Sen

19:53

@Remember you are mistaken if you think Poincare conjecture is algebraic topology :P

besides, I am just learning algebraic topology.

Mike Miller

@TedShifrin My impression is that this is only true in the sense that there are very few arithmetic geometers; but that in the field, and especially among those who do Diophantine geometry, knowing how to do Taniyama-Shimura is absolutely essential. One of the professors here teaches a class on it once every few years.

Ted Shifrin

Indeed.

Remember me

Ha now i fall into a pit again ...

Ted Shifrin

Sure, @Mike ... Still way under 1% of math professors everywhere.

Mike Miller

OK, agreed.

There's a fairly common meme that only 5 people understand it, which isn't true. It's very few people to be sure, though.

Remember me

19:54

Poincare conjecture is not from altop.......??!!

Balarka Sen

The precise statement of Poincare conjecture is of course algebro-topological, @Remember, but the proof involved very hard differential geometry/topology stuff.

Ted Shifrin

Analysis too!

Mike Miller

@Rememberme Why did you post this question when I told you this was false?

Balarka Sen

blah, @Ted, yes.

Remember me

You said this is not well know i thought that sorry@Mike

Mike Miller

19:56

That is absolutely not what I said.

Remember me

I might have misinterpreted you...

So FLT is damn hard and anything on it is more harder .....conclusion

Balarka Sen

@TedShifrin interesting fact I got to know : Perelman was a 3rd year grad student when my prof went into grad school in Berkeley.

if I recall correctly.

Remember me

@MikeMiller You were talking about the 4th dimension....why is it so complicated....isnt it supposed to be less complicated because we have gone till n dimensions right?

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