Mathematics

Ted Shifrin

12:05 AM

How'd your talk go, @Fargle?

Leaky Nun

ok I finished my second lecture... 2 down 4 to go

Ted Shifrin

re everyone else

Leaky Nun

but it's 12AM now

Fargle

Apparently there was a competitive aspect to it, @Ted. I got third place (out of about 8-10 speakers in the math part of the day).

Ted Shifrin

Was it like an MAA meeting, @Fargle? I've judged student talks at those before.

Congratulations! That's great.

Fargle

12:07 AM

It was similar, although maybe slightly less demanding. Strictly speaking it was an annual meeting of a science society, so math wasn't the focus, but yeah, something like that.

Ted Shifrin

Well, that's still nice. Well done.

Fargle

Thank you. I'm rather happy to have done so well (and also to be finished, for now, with numerical things...)

Ted Shifrin

You can even mention the talk and the prize in your list of achievements when you apply to grad school.

Fargle

Indeed!

Ted Shifrin

Right. Now back to my number theory question and all our diff top and diff geo. watches Fargle flee like the wind

or maybe it's flea ...

Fargle

12:10 AM

Nah, now I can dive headlong (in between my extracurricular fun-and-games nonsense). Though that number theory question's still stumping me, I'll be honest.

Mostly because I haven't done the due diligence of doing it.

Leaky Nun

@TedShifrin is this what typical US food looks like?

Ted Shifrin

The key idea is quadratic reciprocity, as you mentioned, although I don't know that stuff. I just know from group theory that if $a$ is not a square mod $p$ and $b$ is not a square mod $p$, then $ab$ must be a square.

MatheinBoulomenos

what is the number theory question?

Ted Shifrin

No, that's gluttonous barbecue American food. Far from universal.

Showing that $x^4-10x^2+1$ is reducible mod every $p$, @Mathein. And don't give any more away.

Demonark already gave one slick solution ages ago.

MatheinBoulomenos

okay, I won't say anything

Fargle

12:13 AM

To be fair, I don't know it either. I hope to know it by the time this number theory course finishes.

Ted Shifrin

Your assignment, @Mathein, is to prove that "almost every" $f(x)\in \Bbb Z[x]$ is irreducible over $\Bbb Q$ and reducible mod every $p$.

Leaky Nun

@TedShifrin a typical meal outside is at least 10 pounds... but cooking by myself takes a lot of time

Ted Shifrin

I doubt it, @Fargle. But I phrased it in terms of group theory so you can prove it with the algebra you know.

Leaky Nun

I'm starting to not like London :P

Ted Shifrin

@Leaky: Don't you have friends you can share cooking/eating with?

You can't afford to eat out all the time as a college student.

Leaky Nun

12:14 AM

I don't

Ted Shifrin

Well, make some friends!

This is why dormitories are good.

Leaky Nun

I share a flat with 2 other people

their eating schedules are... conflicting

they never cook, at least

Ted Shifrin

Ah.

Leaky Nun

one of them buys those ready meals every night

where you just put it to the microwave

and then you're done

yeah, no

Ted Shifrin

Yes, not my style of cooking, but it has become more universal.

Leaky Nun

12:17 AM

I mean, in Hong Kong you can at least find cheap restaurants and you can choose

Fargle

@Ted, I think I see. Odd plus odd is even, and if something isn't a square, it's an odd power of whatever generator you're considering for $\Bbb Z/p\Bbb Z^\times$.

Ted Shifrin

I'm sure there are cheap Asian and Indian places in London, Leaky, perhaps not near you.

Leaky Nun

yeah no

I live in London London

Ted Shifrin

Oh, you don't even need to know that group is cyclic, @Fargle. That's overkill. But OK.

Leaky Nun

so hard luck

Ted Shifrin

12:18 AM

I'm sorta surprised, Leaky, but I haven't been in London in a long time.

Leaky Nun

by "London London" I mean central London

Ted Shifrin

You've done a serious google search?

Leaky Nun

yes

I even walked like 20 blocks down a street

you can only get food less than 5 pounds in mcdonalds

and that's like 20 blocks away and super unhealthy

Ted Shifrin

no, don't eat that crap.

Leaky Nun

sure

Ted Shifrin

12:21 AM

googling indian restaurants in central London I found a few that aren't super expensive.

Leaky Nun

where?

Ted Shifrin

Try this.

Leaky Nun

central londond is big

and it's hardly worth it to go out of walking distance

Ted Shifrin

there are tube and buses ...

Leaky Nun

they're expensive

and it takes me 20 minutes to go to the nearest tube station

it would take me less time to cook

and less money

Ted Shifrin

12:23 AM

There's nothing wrong with cooking. Make food that'll last 3 or 4 meals.

That's what I usually did in school.

Fargle

@TedShifrin That's overkill? Huh. I'll try to see if I can see that another way.

Leaky Nun

hmm

that's a good idea

so reheat it with microwave each time?

man I've never thought of that

stupid me

Ted Shifrin

Sure. Most stuff will do fine if you're smart about it.

I do that with Chinese stir fries every time I make 'em.

Leaky Nun

my rice cooker is small though

Ted Shifrin

well, it's easy enough to make more rice. I'm talking about the other stuff.

Fargle

12:25 AM

I'm not exactly sure yet how to relate this to the problem entirely, though. I think I need to just work on it again for a while.

Leaky Nun

@TedShifrin man I feel so stupid now

Ted Shifrin

Yup @Fargle. I gave you hints about different ways of factoring ...

@Leaky: I serve a purpose here.

Leaky Nun

ok I'd need to buy those thin plastic things that keep things from spoiling

those things made of ethylene and what not

Ted Shifrin

plastic containers? yeah ... they're cheap

Fargle

Yeah, I remember the hint and I remember some of my factorizations. As I recall, my problem was that I couldn't systematize that.

Leaky Nun

12:26 AM

what do you call them?

no, those flexible ones

Ted Shifrin

storage containers

Leaky Nun

where you cover it on top of the food

Ted Shifrin

oh, plastic wrap

Leaky Nun

aha

Ted Shifrin

I put stuff in containers. Better seal.

Leaky Nun

12:27 AM

alright

ok I now feel like an entire idiot

Ted Shifrin

Someone should star that :P

Leaky Nun

you should

I mean, I'm an idiot that is defined everywhere and complex differentiable everywhere

Ted Shifrin

I did not star it.

Leaky Nun

but I still need to wash the dishes...

Ted Shifrin

Yes, cooking takes some effort. So does eating.

Leaky Nun

12:29 AM

but I can do maths while eating

I can't do maths while washing the dishes

Ted Shifrin

Sure you can ...

Leaky Nun

...

@MatheinBoulomenos kannst du?

Ted Shifrin

Oh oh, it's Semiclassic.

More Anonymous

1:32 AM

help anyone?

1

Q: Non unique decomposition of series in a "particular way"?

Introduction I recently was playing around with some series and a natural question came to mind how many ways can a series be decomposed "a certain way" to a sequence? Background I believe for if the below holds for all $n$ holds then: $$ \sum_{r=1}^n\frac{a_r}{r} = \frac{1}{n}\sum_{r=1}^n b_...

Julius

2:29 AM

Hi. I got $n$ equations $p_i^2 \sum_{j=1}^n(d_j + p_j^2) = (d_i + p_i^2)^2$ for $i=1,\dots,n$, where $d_i$ are known nonnegative integers and I wish to solve the system for $p_i\in [0,1]$. Any hopes for a closed form solution?

Whiteclaws

3:50 AM

Hello, if i have y = f(x), x = e^t, why is it that when i differentiate dy/dx with respect to x, I get d^2y/dx^2 * dx/dt

Henias

4:30 AM

Whiteclaws chain rule isnt it

More Anonymous

4:42 AM

Also the question I mentioned above ... is it me or can some sort of group theory be used?

Balarka Sen

6:03 AM

@LeakyNun If it isn't immediate you should stop learning about schemes and revisit basic topology dude

vzn

holy @#%& hes ALIVE! o_O

in The h Bar, Nov 13 at 19:51, by Blue

hBar has gotten boring without 0celo and Balarka

↑ lol 4 stars! go star it yourself man! :P

Secret

6:19 AM

15 hours ago, by Leaky Nun

Consider $\Bbb R$ but for every rational number we add one copy, so for $q \in \Bbb Q$ we have $q^-$ and $q^+$

Balarka, what's your take on this?

N. Maneesh

I got ontoness, How do I complete the proof of continuity and homeomorphism?

2

Q: Prove that the Cantor set is homeomorphic to $(X,\mathscr T)$.

For each $n\in \mathbb N$, let $X_n=\{0,2\}$ and let $\mathscr T_n $ be the discrete topology on $X_n$. Let $X=\prod_{n=1}^\infty X_n,$ and $\mathscr T$ be the product topology on $X$. Prove that the Cantor set is homeomorphic to $(X,\mathscr T)$. Proof. Let $C$ be the Cantor set, Let $(C,\math...

general-topology alternative-proof cantor-set

Akiva Weinberger

7:06 AM

@Secret @LeakyNun Oh wait this is just the Cantor set

Secret

cantor???

But cantor does not have the property $q_- < q_+$ for its order topology?

Buddhini Angelika

7:23 AM

A graph admits an embedding in projective plane means the graph is projective planar right? The graph has a projective arrangement right?

N. Maneesh

@Secret Cantor set seen as the subspace topology of $\mathbb R$

Secret

hmm...

Ok so that means since it is isomorphic to the cantor set, it is nowhere dense

N. Maneesh

Let $(a_1,a_2,...,a_n,...)\in B=B_1\times B_2 \times B_3...\times B_N \times B_{N+1}...$. I can choose $N\in \mathbb N$: $B_n=X_n, \forall n\ge N$. Let $x\in C$: $x=\sum \frac{a_i}{3^i}$

Geometrically I could prove that \psi((x-\frac{1}{3^{N+2},x+\frac{1}{3^{N+2})\subset B $

How do I prove abstractly?

Alessandro Codenotti

Cantor set without endpoints @Akiva but you're probably right

Is this order the Dedekind completion of an order of type $2\cdot\eta$ where $\eta$ is the order type of the rationals? If this is true (and it looks true) you're right

N. Maneesh

7:38 AM

@AlessandroCodenotti I took end points with second representation with ternaries 0 and 2 s.

Alessandro Codenotti

Oh, we're talking about another problem also (maybe) involving a Cantor set, sorry

N. Maneesh

okay

Akiva Weinberger

10:38 AM

@AlessandroCodenotti Ah, true

I recant

(pun)

@Secret Look at the points on the "boundary"

(boundaries of the deleted intervals)

Those give you pairs of points with nothing in between

Shobhit

11:08 AM

Hello

I am studying probability, there's a question : given pdf of random variable $X$, find pdf of $Y=sinX$. I have studied a theorem that helps solve these type of problems, it says that the pdf of $y=g(X)$ is given by $f(g^{-1}(y)) |(g^{-1}(y))'|$, given that $g'(x) >$ or $< 0$ for all $x$, but here, $g'(x) = cosx$ and for the given pdf of $X$ this function is not $>$ or $< 0$ for all $x$. what to do now?

Takashi

11:27 AM

Does anyone know if there is any result that says "if two minimal surfaces equal to neighborhood then they are equal"?

Liad

12:09 PM

@Astyx hi. not sure hwy showing $span(\{f_x\})$ is dense is enough (we dont need its closure). i want to show that Parseval's equality holds for each $f\in L_2(0,1)$

Mats Granvik

12:30 PM

$$f(t)=\frac{\text{sgn}
(Z(t))\left|\sum\limits_{n=1}^{n=k} \frac{1}{n} \zeta(1/2+i \cdot t)\sum\limits_{d|n}\frac{\mu(d)}{d^{(1/2+i \cdot t-1)}}\right|}{\frac{\partial \vartheta (t)}{\partial t}+H_{\text{k}}}$$

Artificial Stupidity

12:55 PM

Hi folks, I have a mathematical puzzle for you. :-) Here it is:

0

Q: Just a simple puzzle on calculus

Don't down vote unless you know that you are actually wrong. $$ f(x)= \begin{cases} \frac{x^2+2kx+\mathrm{l}}{x+1} & x<-1\\ x^2+2 & x\geq -1 \end{cases} $$ Find $k$ such that $f(x)$ is continuous at $x=-1$.

mathematics

Mary Star

1:44 PM

Does someone of you have an idea about my question: math.stackexchange.com/questions/3003026/… ?

user193319

When does first countable imply second countable?

Akiva Weinberger

2:04 PM

Remember about a week ago when I said I had an idea to attack the Collatz conjecture?

Well, I procrastinated too much on writing it down, and now I can't remember what it was

Leaky Nun

@AkivaWeinberger it probably won't succeed anyway :P

Akiva Weinberger

True

But we'll never know for sure, now, will we? :P

r9m

Is it a well known fact that $\displaystyle \frac{\sin |\xi|}{|\xi|}$ is not in range of fourier transform on $L^1(\mathbb{R}^n)$ for $n \ge 3$?

@Blue cool profile pic! :) Itachi ..

Anonymous

@r9m Heh, thanks ;)

Astyx

2:31 PM

@Liad If the span is dense, you can find a sequence of elements $(f_n)$ converging to any $f$. Then you have $\left\langle f, f_n\right\rangle = \sum_k \langle f_n, v_k\rangle\langle f, v_k\rangle$ (because $f_n = \sum_k \langle f_n, v_k\rangle v_k$)

Left term converges to $||f||^2$

Right one to $\sum_k \langle f, v_k\rangle^2$ (there's probably some work to do here)

Akiva Weinberger

Fun fact: if the sun spun once every 15 seconds it would break the speed of light

'cause its circumference is 14.5 lightseconds long or something

Astyx

Around itself ?

Akiva Weinberger

Yeah

Astyx

I sure am glad it doesn't spin that fast then

Imagine if light was broken !

Akiva Weinberger

Oh, also, since it's about 4 lightseconds wide, that means the bits of the sun on the edge of the half we can see are 2 lightseconds further away than the bit of the sun in the middle of the half we can see

Astyx

2:35 PM

That's cool

Akiva Weinberger

so if we look at the sun, there's a sort of relative lag

It's distorted

Astyx

So if the sun were to go out, we would see the center go out before the edges

Akiva Weinberger

Yeah I guess

Well, there's still the bits we can't see, that are further away

We would slowly see the sun erode over the span of four seconds

And it would be eight minutes after it actually happened

I'm trying to think if we would see the core of the sun when we're two seconds in

Anonymous

@Astyx We'd be too dead and cold to see that :P

Akiva Weinberger

We wouldn't die immediately

Sun goes out, we have eight minutes of ignorant bliss, four seconds of "What the hell is happening," and an indeterminate amount of panic

and then we die

Anonymous

2:40 PM

@AkivaWeinberger If we've no gravity to hold the planet, we'd float out in space as a projectile. And that would happen immediately

Astyx

If we really tried I guess we could make a small portion of the population live for a while longer

Akiva Weinberger

Yeah but we're already floating in space

It would just change from moving in a circle to moving in a line

That said, I'm starting to think that this is a bad idea, and that maybe we shouldn't destroy the sun

@Astyx Geothermal-iness

Astyx

Instead of going around and around in circles we would be going somewhere

Akiva Weinberger

@Astyx Oh so maybe it is a good idea

Let's do it

Anonymous

@AkivaWeinberger Yes, I do agree we wouldn't die immediately. But we'd get pretty cold within those 8 minutes. I need to look up the exact figures though

Anonymous

2:44 PM

Maybe you're right. It might not be that cold either. The atmosphere does retain heat

Anonymous

And a considerable amount of it

Akiva Weinberger

We wouldn't get cold within the 8 minutes. The eight minutes are the amount of time it would take for the information to get to us.

During those eight minutes we're still getting the final rays

We wouldn't know anything was wrong

Anonymous

@AkivaWeinberger A force suddenly vanishes. No acceleration?

Akiva Weinberger

There's a lightspeed delay if the force source is sufficiently far away

Gravity travels at the speed of light

We're not attracted to the sun, we're attracted to where the sun was eight minutes ago, I think

@Semiclassical Is that right?^

Liad

@Astyx yea, it's exactly what i got that is left to prove ^^

Akiva Weinberger

2:49 PM

As stated, that would depend on the reference frame, so it's probably wrong

Astyx

@Liad So you're good ?

Anonymous

@AkivaWeinberger Okay, if we regard GR as partly true you're correct. :P

Akiva Weinberger

We're probably attracted to where the sun was going eight minutes ago (i.e. where it would be if it didn't accelerate in the last eight minutes)

Anonymous

But the sun vanishing instantaneously in itself violates GR

Anonymous

So not much use of talking about it

Akiva Weinberger

2:52 PM

Hm, true

The worst case scenario is for the sun to just go out, but the mass would still be there

Anonymous

What do you mean by "go out"?

Akiva Weinberger

Turn off

Go dark

Anonymous

ehhh

Liad

@Astyx working on it

Anonymous

22 mins ago, by Blue

@Astyx We'd be too dead and cold to see that :P

Anonymous

3:00 PM

In any case, my this claim was wrong ^

Anonymous

8+ mins of no sun isn't enough to kill us ;) (mainly because we have a great atmosphere due to earth's size)

Anonymous

11

A: If only the sun's light went out, how long would it take for all living things to die out?

How fast will the Earth cool down? This is going to be the dominant factor. If it takes too long to cool down, then maybe all the plants will die without sunlight and creatures will starve to death. But if it cools down fast enough, everyone will freeze. We can apply the Stefan-Boltzman law to ...

Shaun

3:28 PM

in Group Theory, 44 secs ago, by Shaun

Quick question:

Let $\phi: G\to H$ be a surjective homomorphism. Suppose that $H$ is virtually solvable. Is $G$ then virtually solvable?

Shaun

3:56 PM

Well, if $G$ has a free, non-abelian subgroup, then $G$ cannot be virtually solvable, but $G$ is homomorphic to the trivial group, which is virtually solvable.

Richard

can someone help with a projection quesiton ?

Transcript for

$Mathematics$ Mathematics