Mathematics - 2015-06-07 (page 5 of 9)

Paul Plummer

15:06

What are you doing up @AlexClark

user147690

@PaulPlummer Playing tetris no doubt

Paul Plummer

Oh is this your study method, instead of play 15-30 minutes, you play tetris all night?

Remember me

@r9m have you send the email?

Oh I also love playing in between

user147690

@PaulPlummer Yep :)

user147690

@PaulPlummer Nah I play tetris battle of facebook, they give you one game every 25 min lmao

Paul Plummer

15:09

Haha

user147690

(and it stores up to 6 games if you leave it for the 150min)

Balarka Sen

damn it, I am seeing sheaves everywhere

Paul Plummer

Here is what happened to the lastest complaints about downvoting: meta.math.stackexchange.com/questions/20707/…

Balarka Sen

although I wouldn't pretend that I know what sheaves are.

Paul Plummer

You need to get your eyes checked, and maybe head too @BalarkaSen

user147690

15:13

@PaulPlummer Love it

Soham Chowdhury

$\def\{{3}$$\def\}{4}$

user147690

@BalarkaSen Someone was asking for a calculus level explanation of pre sheaves

Remember me

What are sheaves?

user147690

There would be no point for you to learn this in all honesty. Do you know any topology, category theory or understand morphisms? — Alex Clark 11 hours ago

Balarka Sen

glares hard at @Remember

Remember me

15:18

Gone

Bye...

Balarka Sen

@AlexClark well, I am not the right person. ask Ted, he says the the origin of sheaves is really complex analysis.

The Artist

I got some great advice from someone today :P

he Told me " never get emoticional with two things, girlfriend and car...those are two things that never stay with you"

Remember me

@TheArtist was it from @Chris'ssistheartist :P

Paul Plummer

Here is another piece of advice, if you get downvoted please don't go to meta and complain about it.

Remember me

Best piece of advice I heard

user147690

15:21

@BalarkaSen Sorry I meant for you to click the 11 hours and go to the linked question

Paul Plummer

Damn someone has to say never listen to @BalarkaSen to nullify that statement

The Artist

@Rememberme no :) she has given me advice, but not this one as you can see :)

user147690

0

Q: Can someone explain presheaf to a calculus student?

From reading some stuff online, there is the claim that continuous functions are presheafs, so that the toy functions I play with in class such as $f(x) = x^2$ can also be thought of as presheafs. Can someone better illustrate this idea so that a student of introductory calculus can understand?

Remember me

Which paul @Balarka :p

Balarka Sen

yes, saw it.

no, I don't want that to be starred.

user147690

15:22

Ahaha

The Artist

@PaulPlummer yes! those people have no life.....to cry over down votes (50% of which they deserve)

Soham Chowdhury

Your gravatar looks similar to presheaves kid's, @Alex.

Remember me

If you really want to disturb someone upvote him :P

Soham Chowdhury

mwahahahaha

Paul Plummer

Haha

r9m

15:23

@Rememberme sent

Remember me

Thanks a lot

Soham Chowdhury

I guess learning point-set is teaching me to follow "analysis"-ish proofs. :)

(Oh, @Balarka, no longer using Bredon, per wise advice.)

user147690

Do you guys ever do math, hmmmp -balarka

Soham Chowdhury

?

Balarka Sen

I am doing math right at this moment :P

Soham Chowdhury

15:25

so am I.

but it's just math.

not Math.

user147690

Me 2 amirite, geometry(tetris)

Soham Chowdhury

urnt

Remember me

Even me... Halo, Topological spaces,@paulp's blog, and ofcourse @r9m paper

user147690

2200 elo :'))

Agawa001

elementary algebra is accidentally gouped with maths

Soham Chowdhury

15:26

@AlexClark who?

Paul Plummer

I am making pancakes

8

user147690

@SohamChowdhury Me in Tetris battles(2mil players)

Remember me

Hello@Mats

Soham Chowdhury

Elo is mathematically sort-of-interesting.

Agawa001

seems that many people like pancakes

user147690

15:28

@SohamChowdhury Indeed, it's pretty decent.

Remember me

@Soham Are you ignoring me??

user147690

Back to study after I get some tuna + crackers

Soham Chowdhury

@PaulPlummer "Small Fermentation Theory". for your beer.

2

user147690

@Rememberme Why do you think that?

Soham Chowdhury

@Rememberme no.

why?

Remember me

15:29

I was having this weird feel

Balarka Sen

btdubs, @AlexClark, what happened to your inverse limit of rings presentation?

Remember me

Never mind

user147690

@BalarkaSen :'(. I backed out like a pansy to get my functional analysis 10% in

Balarka Sen

:(

user147690

Lost .5% of algebra, but probably got 5% extra on functional overall so worth

user147690

15:30

@BalarkaSen Maybe I can give it for fun next semester :P. We are encouraged to give 10 min talks whenever we can(allowed to do it every week once)

Remember me

Isnt it tiring to do so much stuff @AlexC

Balarka Sen

@AlexClark that's cool

user147690

@Rememberme It is when you have non-math stuff bringing you down

Remember me

Nice point

Balarka Sen

10 minutes sound much more decent.

Soham Chowdhury

15:31

a-hole real life. always butting in.

Balarka, are you working?

Balarka Sen

yes, I am.

user147690

@BalarkaSen It does, and 1) I won't be graded for it, 2) people that turn up are actually interested, 3) I will be the only one giving it

Remember me

@Soham For me physics and chemistry butting in

Soham Chowdhury

@BalarkaSen oh.

user147690

@SohamChowdhury Indeed.

Soham Chowdhury

15:32

and my world-saving environmental science project

@AlexClark accidental pun, too

Balarka Sen

I am pretty sure there's some theoretically interesting thing going on with directional derivatives. I am trying to get that right.

Remember me

My assignments havent yet started ... What on earth will I do then

Balarka Sen

@AlexClark nice.

Karim Mansour

hi guys

user147690

@SohamChowdhury True :P

Remember me

15:33

Hello@Karim

user147690

Hey @Karim

Balarka Sen

for a 10min talk, probably you could also give some interesting examples of inverse limit of rings/groups

a better idea is to do inverse limit of groups, really

lots of interesting ones there. the solenoid, $\mathsf{Gal}(\bar {\Bbb Q}/\Bbb Q)$

user147690

Well that will be easier to talk about when I am doing Advanced algebra as well

Balarka Sen

right

user147690

Since I don't yet know what that even means

Balarka Sen

15:36

the group of field automorphisms of the field of algebraic numbers

it's so interesting that probably you could just forget about all other inverse limits and talk about just Gal(\bar Q/Q) itself.

:P

Remember me

Okay lets play some games and then switch to maths again

user147690

@BalarkaSen Hahaha

Balarka Sen

no, really. there's a famous quote of Tate that number theory is all about the study of Gal(\bar Q/Q)

user147690

Are these things named and given notations in honour of galois, or he really did do all of this?

Remember me

Sorry to but in..
Gal means Galois representation right @Balarka

Balarka Sen

15:38

it just means galois group.

@AlexClark No, I don't think Galois did a lot of infinite Galois theory.

Remember me

And how is number theory study of that ... Isnt number theory about positive integers??

Soham Chowdhury

"the shortest path through two points in the real plane . . . "

Balarka Sen

number theory over $\Bbb Z$ is not often hard. however, for some purposes (proof of FLT, say), doing number theory over integral closures of algebraic number fields become necessary, and therein lies the difficulty.

but I don't think you can make sense of all of that unless you study some algebra, @Remember

Agawa001

@SohamChowdhury a line ?

Soham Chowdhury

a quote.

Agawa001

15:43

euclidean distance

Semiclassical

just because one is trying to prove things about positive integers doesn't preclude the tools you use for that being far more sophisticated

Mats Granvik

@Rememberme Hi! Do you know about eigenvalues?

Soham Chowdhury

@Semiclassical that is a beautifully constructed sentence

Semiclassical

@MatsGranvik: i saw your question earlier. in what sense did you mean invariant?

Balarka Sen

Number theory over integral closures of algebraic number fields is wacky, because primes to crazy things.

Soham Chowdhury

15:44

is wacky.

Mats Granvik

I will give an example: @Rememberme

Semiclassical

(warning: i'm more versed in sparse matrices than in random matrices)

Soham Chowdhury

@Balarka, are you familiar with Gamelin-Greene?

Balarka Sen

algebraic number theory is a beautiful branch, @Remember. why don't you study that instead of algebraic topology? :)

Mats Granvik

I meant @Semiclassical

Balarka Sen

15:44

no, what the hell is that, @Soham?

Semiclassical

kk

Soham Chowdhury

@BalarkaSen never mind. a book I'm using instead of Bredon. It's working really well.

Remember me

Why do you want me not to study altop @Balarka:p

Soham Chowdhury

@BalarkaSen one wishes one could study everything.

I like NT too (a ton)

@Rememberme he thinks you(and I)'re fixating on it

Remember me

@Soham Even I like number theory but geometry has got its own beauty

Agawa001

15:46

@PaulPlummer now everyone knows u make pancakes , i can esteem ur pancakes are that good as your maths ?

Balarka Sen

@Rememberme I am not stopping you to study algebraic topology. I just want to let you know that there is far more mathematics out there than that.

hello @Ted

Ted Shifrin

hello @Balarka

Soham Chowdhury

hey, @Ted

Ted Shifrin

hi Soham

Balarka Sen

I'm obsessing over directional derivatives.

Semiclassical

15:46

@balarkasen: out of curiousity, what would be a very basic example of a result in algebraic number theory?

Remember me

Heya @Ted

Ted Shifrin

Glad to hear it, @Balarka.

Did you settle my $\alpha,\beta,\gamma,\delta$ question? :D

hi Remember

Soham Chowdhury

$\def\alpha{\beta}$@Rem, there?

Balarka Sen

@Semiclassical depends on what you mean by "basic"

Semiclassical

(one consequence of playing a fantasy MUD in which british spelling is taken as valid IC: my use of color/colour etc. is pretty much a coin flip)

something i'd be likely to actually grasp :P

Mats Granvik

15:48

@Semiclassical
I am saying that these two matrices have the same eigenvalues even if both are multiplied elementwise with the same random matrix.

$$\left(
\begin{array}{ccccccc}
1 & \frac{1}{2} & \frac{1}{3} & \frac{1}{4} & \frac{1}{5} & \frac{1}{6} & \frac{1}{7} \\
2 & 1 & \frac{2}{3} & \frac{1}{2} & \frac{2}{5} & \frac{1}{3} & \frac{2}{7} \\
3 & \frac{3}{2} & 1 & \frac{3}{4} & \frac{3}{5} & \frac{1}{2} & \frac{3}{7} \\
4 & 2 & \frac{4}{3} & 1 & \frac{4}{5} & \frac{2}{3} & \frac{4}{7} \\
5 & \frac{5}{2} & \frac{5}{3} & \frac{5}{4} & 1 & \frac{5}{6} & \frac{5}{7} \\

Balarka Sen

There's Kummer's proof of a toy-version of FLT that exploits the structure of ideals. It's actually the very beginning of algebraic number theory.

Ted Shifrin

toy version meaning $n=3$ and $4$?

Balarka Sen

no, no.

for regular primes, I mean

Semiclassical

think i've heard of that, or at least of Kummer initially thinking he had a proof of the general FLT that way

Paul Plummer

@Agawa001 They are pretty good, not sure how good my math is though

Ted Shifrin

15:50

sorry to have tweaked you, @PaulP, but it wasn't meant for your eyes :P

Balarka Sen

yeah, it doesn't work for general FLT because of that damn class number thing.

Paul Plummer

Haha, You may want to advert your eyes if this blog post gets put on the math.se blog (it has infinite games) @TedShifrin

Ted Shifrin

Axiom of choice has never been relevant to me in any of my research, @PaulP, and it doesn't bother me to make choices :)

Mathematical foundations have never been particularly interesting to me.

Semiclassical

@MatsGranvik hmm.

Soham Chowdhury

I'm afraid of turning into a foundations guy and then becoming like Wildberger or Zeilberger.

Ted Shifrin

15:52

I think you young'uns are way too young to turn into anyone.

Soham Chowdhury

We won't stay young'uns forever. :)

@BalarkaSen do you always study one subject at a time?

Balarka Sen

yes

Ted Shifrin

No, Soham, eventually you'll be old and dead like me :D

Semiclassical

@TedShifrin math is a big tent, thank goodness

Balarka Sen

two things at a time would result in studying nothing

Karim Mansour

15:53

@Ted you know what I like though I always like to dig deeper and understand the everything that makes the system be that math or cs or physics

Ted Shifrin

@BalarkaSen Really?

Soham Chowdhury

@BalarkaSen how does uni work, then?

Semiclassical

it's hard to be a true universalist these days, though

Karim Mansour

@TedShifrin that is why I like foundation of math

Balarka Sen

@TedShifrin well, I didn't used to, but now I do.

Paul Plummer

15:54

Maybe he is saying it doesn't work @SohamChowdhury

Soham Chowdhury

ah.

Karim Mansour

what is universalist @Semiclassical

Semiclassical

being an expert/contributing to all areas of mathematics

Ted Shifrin

I was very proud of being more broadly well-rounded than most of my friends in grad school, @Semiclassical, but many of them turned out far more accomplished researchers ... Partly my fault for making teaching my priority.

I chose a research area which was part of three or four fields.

Semiclassical

eh, research as a discipline is a strange beast

Karim Mansour

15:55

no I think it is possible as long you dedicate enough time to be well-rounded in most subjects @Semiclassical

it is also easy right now with internet and easy access to knowledge

Agawa001

@PaulPlummer i mean that , from a pilote to a bar keeper , if someone is good mather , he can do everything perfectly :D

Karim Mansour

I mean it easier to do it now since easier access to knowledge is possible to be polymath

Fargle

I've tried to keep my education as rounded as possible as I go up. That will eventually become untenable, but I just really really like the subject.

Ted Shifrin

heya @Fargle ... haven't seen you since you've been hiding from me :D

Shin Kim

Hey guys, anybody wants to study undergraduate-math with me? I'm searching for a colleague.

Fargle

15:57

@TedShifrin Haha, I haven't been hiding! I've just been looking for work.

@ShinKim Sure.

Ted Shifrin

Actually, I wasn't around much the last few weeks :) Did you find a job?

Soham Chowdhury

Is "adherent" used much in topology?

Ted Shifrin

It may be an old term, @Soham. What is the context?

Fargle

@TedShifrin I think maybe. Thank goodness for friends working at places.

Balarka Sen

OK, @Ted : Let $\vec{f} : \Bbb R^n \to \Bbb R^n$ be a $\mathfrak{C}^1$ function. $D_{\vec{v}} \vec{f}(a)$ be the directional derivative at direction $\vec{v}$ at $a$. This is a linear function of $\vec{v}$ (a proof can be found in [Shifrin] :P). Call the linear function $T_a\vec{f}(-) : \Bbb R^n \to \Bbb R$ to be $D_{(-)}\vec{f}(a)$. I'll also forget about $a$ by saying $\phi \vec{f} : \Bbb R^n \to \text{hom}(\Bbb R^n, \Bbb R)$ given by $a \mapsto T_a\vec{f}$.

Ted Shifrin

15:58

Well, @Fargle, congrats. Let me know how the diff geo is going :)

Semiclassical

@KarimMansour eh, i don't really agree with that attitude. it's like a physicist saying that knowing everything about the basic interactions of the fundamental particles (something that would encompass and surpass the standard model) is what's necessary to be able to answer all physical questions

Fargle

@TedShifrin Slowly. I'm not as strong on my fundamentals as I thought, I guess. Out of practice.

Ted Shifrin

Call it $D\vec f$, @Balarka; most people do.

Karim Mansour

@Semiclassical are you mathematician or a physicist ?

Semiclassical

woops, wrong reply

Ted Shifrin

15:59

Well, the point of learning math is to go back and solidify things that have come before, @Fargle. Don't be discouraged.

Semiclassical

physicist, though a very mathematical one

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$Mathematics$ Mathematics