Mathematics - 2020-05-29 (page 2 of 2)

Leaky Nun

19:03

@TedShifrin wow that was huge

Ted Shifrin

Huh? @Leaky

Leaky Nun

did you listen to Trump's speech

just now

Ted Shifrin

no

Leaky Nun

he said that China is violating Hong Kong's freedom and it has now become one country one system instead of one country two system

he said he will do something meaningful and powerful

and he will sanction Chinese officials

Ted Shifrin

oh, and he's threatening to have the military kill off American citizens, too. He's a little boy gone mad.

Leaky Nun

19:08

and something about tariffs with Hong Kong

robjohn

19:30

@Yuvraj I have tried to post my work here, but it really needs the functionality of the main site. Can you pose your question there?

Ted Shifrin

Goodness griefousness.

robjohn

@TedShifrin Did that cause a problem?

Ted Shifrin

LOL ... it was overwhelming :P

That looked like a lot of work, but I didn't pay attention to the mathematics.

robjohn

@TedShifrin there was an image, but it would not go as desired into the answer. The links also failed to appear as usual.

Ted Shifrin

Right, I clicked and saw the image.

You have to upload the image separately and then it will be fine.

robjohn

19:36

@TedShifrin Ah, so it was a bit useful

@TedShifrin It is uploaded, but it has a higher resolution version when you click on the lower resolution image in the post.

higher resolution image

Ted Shifrin

Salut, @Astyx.

Greetings, twin of A.

a perspicaciously curious mind

hello professor

Ted Shifrin

LOL, now triplets.

robjohn

That's about as well as I can do in chat

a perspicaciously curious mind

we're growing exponentially!

Arnold Fernández

19:43

If x = [2;3>
(x^3+4)/(2x-1)=?

robjohn

@TedShifrin yeah, but clicking on the image just brings that image up. The other link is there so that the higher resolution image does not take up so much screen real estate.

Ted Shifrin

Gotcha, @robjohn.

@Arnold: I don't know what your question is. You can do long division and get a quadratic plus a remainder term.

robjohn

on the main site, it can be set up so that clicking on the low res image brings up a high res image.

a perspicaciously curious mind

( (2.3)^3 + 4 ) / ( 2*(2.3) - 1 ) @ArnoldFernández

user462942

Hi @TedShifrin

Ted Shifrin

19:48

@a, what does $x=[2;3>$ mean?

hi @Joanna

Arnold Fernández

See-> x=[2 ; 3>

Nota x=2.3

Ted Shifrin

We do not know what that means, @Arnold. You have to explain.

a perspicaciously curious mind

4.4908333... @ArnoldFernández

user462942

@TedShifrin Your Lie brackets answer was cool -- though difficult for me to understand. Once, I got a Lie brackets project in Applied Math, with applications to robotics. Something about computing all the different ways an object can move to in its configuration space, subject to constraints (parallel parking was the simplest example to learn of, I think). I kinda regret not taking that project.

Ted Shifrin

Yes, the Lie bracket application to parking cars is a classic and quite fun. I've included it in homework for graduate differential geometry several times.

user462942

19:54

@TedShifrin I see -- interesting.

Arnold Fernández

What it's the solution for 3a^2+1/a if 3<a<19

Ted Shifrin

That question does not make sense to me, I'm sorry.

Do you mean what values do you get for that function on that interval?

Arnold Fernández

What's the interval for 3a^2+1/a if 3<a<19

Ted Shifrin

Do you know calculus?

Arnold Fernández

The idea is not to use advanced mathematics

a perspicaciously curious mind

19:58

Then sub in the values.

Ted Shifrin

That only works if you know the function is increasing or decreasing.

It is, but how do we check without calculus?

I guess there is tedious algebra, which I am not going to even think about.

genescuba

Lets say I have two people whom I trust equally and one tells me that an event occurs with $a$ probability and the other tells me an event occurs with $b$ probability. I want two average these two probabilities together. I should be taking the harmonic mean of a and b right rather than doing (a+b) / 2

Arnold Fernández

It's a math problem for high school students

a perspicaciously curious mind

ask them to sub in 3, 4, 5, ... ,18, 19

and graph the solutions

Arnold Fernández

Mmm, whit graphs is easy

I know

The text is to find the most ingenious way.

Ted Shifrin

20:04

Prove that the function is increasing on that interval.

user462942

20:18

@TedShifrin do you think the research in the mathematics of data science is here to stay, or do you think it will fizzle out in a few years?

genescuba

Anybody have any idea? I think arithmetic mean may be ok here

Ted Shifrin

@Joanna I don't know enough to respond.

user462942

@TedShifrin ok, no worries

user462942

@TedShifrin How could I find a nice problem to work on, like an application of Lie brackets, that might result in a good paper? A mathematics professor at our dept. said to read papers and then find unfinished aspects of those papers, as a start. What do you think?

Ted Shifrin

Yes, reading papers is where you start. Lie bracket is just a tool, like a derivative.

user462942

20:35

@TedShifrin I see; but how does one know that if they follow up on some unfinished aspect of a paper, that that project is worth the effort and valued by the community? It seems that one must run the problem by a more senior academic in order to know.

user462942

Sorry, annoying question.

Ted Shifrin

Yes, that's why advisers are important.

user462942

Yeah ...

user462942

Thanks @TedShifrin :)

Ted Shifrin

Sorry I don't have a magic wand for you.

user462942

20:38

@TedShifrin I know :(

user462942

@TedShifrin Did you always have more ideas / problems to work on than time?

Ted Shifrin

Well, no, because I was more a teacher and book writer than researcher. But I did my share of the latter.

user462942

I see

user462942

@TedShifrin I met someone who went to UGA and they said the college town there is pretty unreal, with tons of parties. Do you participate in the lifestyle? I'll be at a school that's located in what's often considered the top college town in the U.S. I wonder what life will be like for me. I'm not an undergrad, so I wonder whether I would even participate in the social scene that I'll be surrounded by. I am guessing I wouldn't really have the time to do so.

Ted Shifrin

LOL, not in that lifestyle, I didn't. Other than Boston/Cambridge, I have no intelligent guess for the "top college town."

Balarka Sen

20:50

There's sure as hell not going to be serious parties until a year or two anywhere in the world, much less in the US

Ted Shifrin

Yeah, I doubt there will be classes in buildings.

Just parties in Tromp hotels.

user462942

haha I see :)

Balarka Sen

Hi @Ted, by the way

Ted Shifrin

Hi, a A Balarka.

Balarka Sen

Nice.

Alessandro Codenotti

20:57

I wouldn't even be surprised by Americans organizing big "end of the lockdown" parties

user462942

@AlessandroCodenotti Yeah ...

Leaky Nun

it isn't even halfway through 2020

Stan Shunpike

21:20

@TedShifrin hey ted!

Ted Shifrin

Hi Stan.

user462942

@LeakyNun Yeah, seriously -- I work at a cafe to make ends meet. And, I've been staying at home (with pay) for almost 2.5 months, though it feels like forever now that I haven't worked.

a perspicaciously curious mind

that parenthetical remark is a huge plus

Stan Shunpike

@TedShifrin you were right about explaining the concept. We had a follow up problem and I didn't understand it as well as I would expect given the grade i got

so perhaps a lesson for the future is i should be able to clearly articulate why i got something right and, if i cant, more learning to do

Ted Shifrin

Fair enough.

user462942

21:32

@aperspicaciouslycuriousmind Yeah ... I'm very grateful. Maybe you could even guess which cafe it is. It might be the only one that offers pay during a catastrophe. The work is grueling, but the benefits turned out to be top of the line, compared to the industry standards.

Balarka Sen

Here's a nice lemma which literature attributes to Borel (something more general is true, but let's leave it): Suppose $f_0, f_1, f_2, \cdots : \Bbb R \to \Bbb R$ are smooth functions. There is a smooth function $F : \Bbb R \times \Bbb R \to \Bbb R$, $(x, t)\mapsto F(x, t)$ such that $\partial^i F(x, 0)/\partial t^i = f_i(x)$ for $i = 0, 1, 2, \cdots$.

user462942

Pizza time, bye everyone :)

Balarka Sen

That is to say, it is possible to find a deformation of $f_0$ which follows $f_1$ upto order $1$, follows $f_2$ upto order $2$, ...

a perspicaciously curious mind

cya

Starbucks?

Balarka Sen

I misspoke; $F$ is only defined in a neighborhood of the origin in $\Bbb R \times \Bbb R$

Shing

21:45

hey

guys

I have a question: can all matrix be expressed as outer product of two vectors?

Thorgott

can you express the identity matrix as outer product of two vectors?

Balarka Sen

No, because those are always rank <= 1

Thorgott

yeah, that's an iff even

good exercise

Leaky Nun

rank <= 1

Balarka Sen

Indeed.

Thanks for correction, @Leaky :P

Thorgott

21:48

the degenerate cases have been excluded wlog

Leaky Nun

@BalarkaSen it's ok, we all know you meant the 1st stratum of the decomposition of Hom(R^n, R^n) as vector bundles over the point according to rank

Balarka Sen

insert crying laughing emoji

That's what I will be famous for, reinterpreting all of mathematics using stratified spaces.

Univalent foundations

Thorgott

but it's bad when someone does the same with higher toposes

hypocrisy smh

Shing

I see, thanks guys!

Alessandro Codenotti

@BalarkaSen Stratified identity types

Leaky Nun

21:54

if you think about it, a stratification is just a continuous map into $\Bbb N$ equipped with the upper order topology

so we can generalize this to arbitrary posets

in particular you can stratify types by their cardinality

Balarka Sen

22:09

Messed up sleep schedule again

Gonna knock myself out

See ya

Ted Shifrin

22:23

I wonder if all three Balarkas went to sleep.

Arnold Fernández

How would you factor x^3-2bx+5?

Ted Shifrin

What makes you think it factors?

It has a real root, but who knows what it is.

Thorgott

I'd let my computer do it

Cause this is a degree 3 polynomial, I know that my computer will be able to pull it off, so no worries

Arnold Fernández

In the real body

Ted Shifrin

It seems Arnold has a collection of crazy high school math questions he just posts without showing effort here.

Arnold Fernández

22:39

I have solved several questions, those are the most interesting I found

Without using advanced mathematics they become more interesting

robjohn

23:11

@Yuvraj I posted an answer here. It should be easy to see how to apply that to the case of complex points in $\mathbb{C}$.

@TedShifrin: I posted the answer on an older question.

No cluttering up the chatroom

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$Mathematics$ Mathematics