Mathematics - 2022-05-21 (page 1 of 2)

we almost bought a house right on the beach. we had an offer accepted subject to conditions that ended up not being met. it probably had 10 more years of being on the beach.

Fargle

Prepositions are important. You don't want to buy property in the beach.

leslie townes

we didn't want to buy a starter kit for a coral reef and scuba wildlife sanctuary.

well, i guess we did, in that we did put in an offer. it would have been a good, beachy 10 years.

we live on a hill high enough that i think it will not be submerged in my lifetime, although i haven't researched whether it might become an island

Ted Shifrin

5:55 AM

We've seen just a few days ago the news stories of a newly purchased beach home washed away on the NC shore.

leslie townes

oh yeah, the outer banks. that stuff is sea level already.

Ted Shifrin

@Fargle: I forget if I told you or not. But Ken is now a daddy.

leslie townes

my late uncle used to vacation there and the place he vacationed is, i think, no longer reliably above sea level all year.

Ted Shifrin

I have been lots of places on the east coast, but never to the NC seashore, let alone the outer banks.

leslie townes

it's alarmingly flat and only inches above sea level.

it would surprise me if you could get homeowners insurance for a place there these days

Koro

6:00 AM

@CalvinKhor Actually today would be the first time I'd learn Jensen's inequality for integrals.

leslie townes

markets already know what the politicians don't. try to get a loan to develop a ski lodge in a currently snowy area that is not really up in the clouds and find out.

Koro

I never noticed this inequality before. Thanks a lot.

leslie townes

koro: hadn't we talked about this? wasn't it on your sheet?

Calvin Khor

@Koro I take it you solved it, glad to help!

leslie townes

almost all of that contest crap on that formula sheet generalizes to integrals. it's the integral stuff applied to counting measure.

this is a weakness of wikipedia, i think. the standard format for a page on an inequality is five or six cases of something discrete, with applications and maybe proofs, and then something at the end maybe about integrals.

Koro

6:03 AM

Leslie: for integrals? I think it wasn't there in this form: if $\phi$ is convex then $\phi (\int f)\le \int \phi(f)$.

leslie townes

there's some normalizing there. that's f on a space of measure 1, i think.

it probably wasn't on the formula sheet, but, i would have thought we'd talked about it. maybe not. i could be blending this memory with something else.

copper.hat

If it is a probability measure

leslie townes

the discrete stuff can be used to prove the integral stuff, so it's not like you need special technology to get from one to the other.

but, hrm. i wonder who i was talking to.

Koro

@leslietownes I understand that. Holder for discrete for e.g. transforms nicely to integral form too.

(●'◡'●)

Calvin Khor

@Koro if you know holder inequality in the form $\|fg\|_p \le \|f\|_q \|g\|_r$ holds when $\frac1p = \frac1q + \frac1r$ then the proof is one line

just from $\frac1n=\frac1{n+1} + \frac1{n(n+1)}$, $\|f\cdot 1\|_n \le \| f \|_{n+1} \|1\|_{n(n+1)} = \|f\|_{n+1}$

leslie townes

6:22 AM

figures that mr. convex would come in for jensen's inequality

Calvin Khor

chinese word for convex is literally 凸

leslie townes

an extended middle finger to those who would have thought it would have been convex

Calvin Khor

lmao

concave is 凹

leslie townes

that's awesome

Calvin Khor

Let $K$ be a closed set, and let $K^凸$ be its convex hull....

I suppose 凸 could also be copper.hat's hat

$\overset{凸}{\text{copper}}$

leslie townes

6:29 AM

it looks a bit like a devo energy dome

Calvin Khor

hahahaha

Koro

6:49 AM

clicking links in internet explorer is opening them in edge browser.

Calvin Khor

you have both IE and edge installed?

Koro

@CalvinKhor I wasn't familiar with that until now. I know the inequality when $1/p+1/q=1$

@CalvinKhor in my office laptop, they have kept both.

some intranet sites here don't open except in ie.

Calvin Khor

@Koro Step one: for any $a,b<\infty$, $f\ge0$, $ \|f^a\|_{b} = \|f\|_{ab}^a$

step two: if $\frac1p = \frac1q + \frac1r$ then $1 = \frac1{q/p} + \frac1{r/p}$.

oh i remembered it slightly off. but anyway

Koro

yeah, I'll try that. Thanks :)

Calvin Khor

oh no its fine

leslie townes

6:53 AM

no microsoft, i don't need to install windows 11, this year is already going badly enough

Calvin Khor

Step 3: $\|fg\|^p_p = \|f^pg^p\|_1 \le \|f^p \|_{q/p} \|g^p\|_{r/p} = \|f\|^p_q \|g\|^p_r $

dangit no preview

phew fixed it under 2m

DiagramChasingBlues

I think I've got the twin prime conjecture now

@Koro

Calvin Khor

DiagramChasingBlues

Annals, how inappropriate for this site :P

Calvin Khor

why inappropriate lol

DiagramChasingBlues

7:04 AM

Why not call it Rosebuds of Mathematics

Sounds much nicer than what they have put

Calvin Khor

idk

DiagramChasingBlues

Oh, shit, I'm a bad speller lol

I would definitely just arxiv my crap, instead of going annal with it

Calvin Khor

its not one or the other

DiagramChasingBlues

DUDE

I'm joking, lol

Calvin Khor

:)

same m8

DiagramChasingBlues

7:09 AM

Do you like twin primes?

Calvin Khor

not as much as you for sure, i work in analysis

DiagramChasingBlues

LOL!

Now that one is spelled with one n

Calvin Khor

lol

bumblebee

Hey Calvin I need your feedback.

I want the question on MSE to be reopened.

DiagramChasingBlues

Sure link us

we'll reopen that chit, pending we agree

and we're not being too anal-retentive

bumblebee

7:12 AM

The problem is that their justification for closing the question is not applicable to my case.

DiagramChasingBlues

What was the reason?

bumblebee

Here is the question:

2

Q: What are some nice topics in undergraduate mathematics to write about?

As a high school student, I will soon be going on to do the IB(college equivalent). As part of the IB curriculum we are expected to write an Extended Essay(EE) that counts towards our grade. For the EE we are expected to motive a question on a subject, or particular topic, and write a paper answe...

Questions about choosing a course, academic program, career path, etc. are off-topic. Such questions should be directed to those employed by the institution in question, or other qualified individuals who know your specific circumstances.

DiagramChasingBlues

Yes, I agree with you

I voted

leslie townes

i'm not sure that the quoted reason (if that's what it is) fully makes sense, but questions that are "too" open-ended do get closed with regularity.

Calvin Khor

hm. this is definitely on the border

bumblebee

7:14 AM

leslie townes

questions that fundamentally ask "hey, what do you think" get closed, and i understand why.

DiagramChasingBlues

I think the site should allow us to ask the difficult questions

bumblebee

But i'm not asking for an opinion.

surely topic ideas are not opinions

leslie townes

"nice topics" is definitely asking for an opinion. i understand the purpose of the question.

DiagramChasingBlues

Oh yes, don't think, don't get creative, just follow instructions from the textbook, thx

leslie townes

7:15 AM

it's a great question, but i also see why it got closed.

for the record, i did not vote to close.

bumblebee

Any recommendations for what I should to get it reopened?

Removing the nice part is definitely one.

leslie townes

maybe narrow it down to a topic that you have specific interest in. remove inherently qualitative adjectives like "reasonable" and "interesting".

if someone were to write an undergrad-level intro to topic X, what resources would assist them to do it, i am aware of X,Y,Z but want more on W.

DiagramChasingBlues

Can we talk about Prime Twins for a minute?

leslie townes

i have no control over the harpies who vote to close, but, focus is always better. very cabined value judgments are less likely to attract the harpies than something open-ended.

DiagramChasingBlues

I think all posts of this site should be deleted, they're all pretty bad

leslie townes

7:20 AM

to be fair, closure isn't deletion. closure means, this is in the realm of the site, but let there be no more answers to this until there is something fixed with the question. deletion is more for stuff that just doesn't belong.

DiagramChasingBlues

I think you should get some leeway

Calvin Khor

did the comment about being confused if its highschool or ug level come before or after you explained that you are highschool but looking for higher level stuff?

DiagramChasingBlues

maybe a "off-topic post allowance" that recharges when you ask or answer some good questions

leslie townes

the main response to any closed question is: focus, focus, focus.

bumblebee

It came before Calvin.

Fargle

7:22 AM

@TedShifrin I believe you did mention that! I'm quite happy for him.

DiagramChasingBlues

THat's what she said

Calvin Khor

OK then I would say you have already addressed that point

bumblebee

But I made sure to make it more clear by responding directly and editing the post/

Calvin Khor

@leslietownes closure is a prerequisite for deletion though, right? (if score>0 or something i cant recall)

leslie townes

ask a moderator. i don't know why i've gone out on a limb here opining about closure and deletion. i have no idea what mods do.

i'm just yelling into the chasm, same as the rest of us.

bumblebee

7:25 AM

I changed the first point to "Are there some resources that would be useful in explaining the topic like youtube videos, papers, journals et cetera?"

I removed the "as a note to the first point" part.

I think that should be quite obvious.

DiagramChasingBlues

The moderators are just telling you to go study math and come back and ask about solutions to an equation, don't get social with us

bumblebee

@DiagramChasingBlues do you need more pot?

DiagramChasingBlues

Don't get smaht

bumblebee

Then what are you doing?

Calvin Khor

I voted to reopen because I don't think its as broad as it ostensibly seems. Sure you could write an essay on e.g. wiles' proof of fermats last theorem but no one in the intended audience is going to learn anything. There are only so many hallmark results that are in reaching grasp of a highschool student. And if you know of a obscure result that is also interesting but not too technical, I would love to read about it.

DiagramChasingBlues

7:31 AM

Okay, let me run this by you guys. Define $M = \{(x,y,z) : x - y - z = 0; x,y,z\in \Bbb{Z}\}$ clearly a $\Bbb{Z}$-submod of $\Bbb{Z}^3$. Follow me so far?

bumblebee

what does submod even mean?

Calvin Khor

submodule

yes i guess so

DiagramChasingBlues

duh

Calvin Khor

lol 'duh' he's a highschool student

DiagramChasingBlues

DUH

:D

bumblebee

7:34 AM

Don't worry, in 2 years i'll be in uni.

DiagramChasingBlues

Okay, anyway. Can't we endow $M$ with a ring structure?

$M = \{(x,y,x-y) : x,y \in \Bbb{Z}\}$.

is another way of writing it

Define $(x,y,x-y)\cdot(a,b, a-b) = (xa + yb, xb + ya, xa + yb - (xb + ya))$

Do we need well-definedness here?

*I mean do we need to show it

I don't think we do

Anyway, is it clear to you that $\cdot$ is both associative and distributive over $+$ of $M$?

Fargle

Well, how could it fail to be well-defined? You don't have anything here that's some sort of a representative of a class, so...

Calvin Khor

no, i would need some paper

DiagramChasingBlues

Okay, cool, I will prove it in my post. They done donvoted my first sketch write

Calvin Khor

i dont like the minus sign, i'm guessing distributive might fail

DiagramChasingBlues

7:39 AM

It's all linear though...

Okay, perhaps that's where the flaw was

I will check it on paper

SymPy would actually work for this too

Calvin Khor

well i had to take 5 seconds to remember what distributive even meant, so don't trust me

Fargle

Distributivity seems to work. I suppose what I'd question here is: what, really, is the point of having it be $\{(x, y, x - y)\} \subset \Bbb Z^3$? Seems like this would wind up just being ring-isomorphic to $\{(x, y)\} \subset \Bbb Z^2$ with the appropriate multiplication.

Calvin Khor

yeah ok i was being silly. i think it distributes

bumblebee

Oh btw @CalvinKhor the final version of my EE will be read by a math professor somewhere in the world. So you are right, the intended audience will not learn anything from my EE.

Calvin Khor

Is that the grader?

bumblebee

7:47 AM

Unless I write about some super shady thing no-one knows about.

Yeah, they are the grader.

Calvin Khor

the grader is not supposed to be the audience, they are supposed to grade according to the rules

Fargle

Indeed, this just looks like the split-complex integers $\{m + nj\;|\;m,n \in \Bbb Z;\;j^2 = 1\}$.

bumblebee

@CalvinKhor then are criteria, rules?

Calvin Khor

if you wanted to write to teach a math prof something maybe tell him how to do his taxes or something not math

bumblebee

But I don't know how much the tax bracket is.

I don't even know them

They won't even know me

Calvin Khor

7:50 AM

in Ajay personal room, 6 hours ago, by bumblebee

It must be written so that fellow students can understand

Fargle

@DiagramChasingBlues So, in short, the answer is yes, and in fact it's an already-known ring structure, just with some extra baggage in that third coordinate.

Calvin Khor

I read this to mean that your fellow students are the target audience

DiagramChasingBlues

The "extra baggage" can be simplified using the first form of $M$

bumblebee

They are test subjects to see if your work has been communicated well

i.e. Math HL students.

DiagramChasingBlues

it's then just $czw$ instead of the sum thing

bumblebee

7:51 AM

I also forgot to mention that math teachers will be checking.

Calvin Khor

well i disagree, I do not want high school students to help me check what to read. But I only have my opinion. I would say check with a teacher

bumblebee

I agree.

Calvin Khor

and my opinion should not be very important, because I dont know anything about IB or the IB EE

Fargle

@DiagramChasingBlues Well, what I mean is, because of how you've defined the submodule, you don't actually need that third coordinate, which can be seen because it's isomorphic to the split-complex integers (as a ring structure on $\Bbb Z^2$), and indeed simply by the projection map $(x, y, z) \mapsto (x, y)$.

bumblebee

Though, I do have a friend who has some insane math roots. Her grandfather(When alive) and father write research papers heavily concentrated with math.

Michael Tsetlin

Michael Lvovitch Tsetlin (the surname is also written Cetlin, Tzetlin, Zeitlin, Zetlin; cyrillic: Михаил Львович Цетлин) (22 September 1924 – 30 May 1966) was a Soviet mathematician and physicist who worked on cybernetics. He introduced the Gelfand–Tsetlin basis for finite-dimensional representations of classical groups. He was the founder of the learning automaton approach to machine learning. == See also == Gelfand–Tsetlin integrable system Boolean differential calculus Learning automaton Tsetlin machine == Collection of the publications == Tsetlin M.L. Automation theory and modeling ...

I wonder if I can get her dad to check 😏

Calvin Khor

7:56 AM

What I mean is, check with a teacher who the "intended audience" should be

Like, if my teacher says, write an essay for 5 year olds to read, a 5 year old is not going to be the person marking the work

....sorry for typo

@bumblebee co-author with gelfand is the hugest casual name drop ive seen in a while

bumblebee

i don't know who Gelfand is.

leslie townes

hahaha

weird flex but OK

google him

bumblebee

I get chess master

Calvin Khor

@leslietownes im dying lol

leslie townes

en.wikipedia.org/wiki/Israel_Gelfand this one

good lord

bumblebee

8:02 AM

Yeah i got the point, he's amazing...

leslie townes

the tsetlin stuff is even on his main page, i'd never heard of that

he's maybe one of the best mathematicians of the 20th century

i never met him

met a few of his students

bumblebee

Anyways, I need to study for my econs exam. Bye-Bye!

Calvin Khor

:) glhf

bumblebee

I leave with you a brat. Take care of him.

Calvin Khor

i refuse to sign

leslie townes

8:06 AM

that's a great costume

looks like the kid, like my daughter, has not had a haircut since covid-19

Calvin Khor

hahahaaha

leslie townes

its 1 in the morning, my cat just got up from her bed downstairs, came upstairs, meowed at me, rubbed my leg, and then went back downstairs

cats are inscrutable

Calvin Khor

needed to check if food bowl will be refilled tomorrow

leslie townes

my wife does the morning bowl

she [the cat] flips out when i'm on conference calls because she can't tell who i'm talking to

Calvin Khor

whats the solution lol or do you just let everyone hear the meows

or scratching etc

leslie townes

8:14 AM

the latter

and god help me if it's zoom

Calvin Khor

hahaha

leslie townes

some of my teams know her they say "hi olivia" and i'm like DON'T ENCOURAGE THIS

Calvin Khor

she aint need no encouragement, its for the love of flipping out

leslie townes

i've had a few meetings where she's right in front of the camera so if you do gallery view it's like a cat is having a conference with three other people

Calvin Khor

lol there was a person who turned on some cat filter right

and couldnt turn it off

leslie townes

8:17 AM

yes at a court hearing

"i'm not a cat"

Calvin Khor

hahahaha

leslie townes

i felt for that guy

i was once on a phone teleconference with a judge and the guy who was doing the talking turned to me and hit a button on the phone that should have been 'mute' but was, in fact, 'hang up'

Calvin Khor

first hit on youtube for im not a cat hahahaha

leslie townes

and we looked at each other and were like "uh oh"

Calvin Khor

ahh so good to laugh at others' misfortune (sorry everyone)

technical errors must be all over the place still

leslie townes

8:22 AM

the worst thing about eating shit as a lawyer is there is a court reporter literally writing all of it down

and transcripts are publicly available

Calvin Khor

ooh thats double bad

leslie townes

one time i had to appear at a hearing that we knew we were going to lose, and lost, and in the time it took me to drive back to the office they had received the transcript

Calvin Khor

have they been writing every single word tho. like even at the start of the call, can you hear me etc

leslie townes

so i just said "yup" and went back to my office

reporters do put a lot of that preliminary stuff in, which is why i don't say any preliminary stuff

Calvin Khor

i expected them to start when the judge gives a signal or smth

leslie townes

8:25 AM

you see this even at the US supreme court, sometimes the official transcript includes stuff 20-30 seconds before the actual argument begins

Calvin Khor

has it ever helped or hurt a case? to your knowledge

leslie townes

no it makes no difference to the case, it's just lulz for people who know that it's there if it's funny

Calvin Khor

haha ok

i guess i could forsee especially with zoom that someone doesnt mute at the start and says something they shouldnt say which then goes into record

leslie townes

in the transcript of the last decision i lost, which was four years ago, we knew we were going to lose and were going to appeal so i told the judge at the outset, we'll go on the briefs, and there was argument from opposing counsel guided by the judge, leading to the judge saying something, and the judge asked me what i had to say in response, and i said "we disagree with absolutely everything you just said"

and he kindly told me to f off and we had a nice transcript at that point

cool way to make a living

we settled before the appeal so everybody won

math.stackexchange.com/questions/4455409/… is probably a dupe but a good exercise in group theory

Calvin Khor

looool

$|G| \mid |H|$ is technically correct typesetting but I hate it

linear_combinatori_probabi

9:02 AM

hola chat

Calvin Khor

hålo

linear_combinatori_probabi

A quick sharing: I'm happy

when learning linear algebra

Calvin Khor

good for u m8

linear_combinatori_probabi

thank you :) Calvin

Calvin Khor

linear algebra is cool

linear_combinatori_probabi

9:05 AM

3blue1brown makes it accessible to normal people like me

Calvin Khor

haha

before there was 3b1b there was Halmos

imo a sicc book

linear_combinatori_probabi

Guess what, I have a (privated?!) pdf lol

did try to read it before, but it's still too hard for me

ohhhh

i meant pirated

Calvin Khor

oh lol

linear_combinatori_probabi

I'm private pirate living in a ... TBD

Calvin Khor

shh theres a lawyer literally right there

linear_combinatori_probabi

9:08 AM

Never mind, it has already been deleted since I cannot understand it, lol

I was too poor to buy a new book when I was a student

so I can only searched around free books online (and I never further shared it to any others)

I recommend watching this one, my hero: youtu.be/R6S-b_k-ZKY

Calvin Khor

k looks fun will watch when i cant be bothered to compute more integrals

linear_combinatori_probabi

integrals are like girls, at first look they're beautiful

At second look, it's complicated and (fill in your answer here)

Calvin Khor

be careful not to get cancelled

linear_combinatori_probabi

lol

thank you Calvin, you saved my afternoon, I'm leaving

Calvin Khor

9:30 AM

how did i do that

you're welcome tho

Koro

9:57 AM

@DiagramChasingBlues :-)

linear_combinatori_probabi

11:08 AM

hola chat

waiting for my pizza now

Saturday, pizza day

bumblebee

hello

@linear_combinatori_probabi do you speak fluent Spanish?

Leaky Nun

@bumblebee I do, how can I help you

bumblebee

I have my Spanish exam soon, could you help me practice.

?

Calvin Khor

they teach you spanish in singapore? thats sick

bumblebee

International school tho

Calvin Khor

11:24 AM

yeah duh ofc gelfand's friend's granddaughter goes to an international school

bumblebee

I have this question: Escribe entre 60-75 palabras sobre qué tiempo hace hoy donde vives y qué tiempo te gusta o detestas. Debes utilizar estes palabras: 1. Me encanta 2. El mal tiempo 3. Prefiero 4. El paraguas.

This is my translation: Write between 60-75 words about the time where you live and the time that you like or hate. Use the words: 1. I love 2. A bad time 3. I prefer 4. The umbrella.

Is this correct?

@CalvinKhor U went to an international school urself.

Calvin Khor

:) ill leave you to your spanish. gl m8

bumblebee

So @LeakyNun is it good?

Leaky Nun

@bumblebee (hace) tiempo = weather

bumblebee

Thanks

That was a test to see if you actually knew Spanish. Sorry, i've been trolled too many times.

Now let me type out my real question

Calvin Khor

11:29 AM

lmao

bumblebee

Could you check that I conjugated everything correctly.

and written the correct words for the things in bold @LeakyNun

Gotta eat dinner now

¡Hasta luego!

Leaky Nun

@bumblebee e and f should be past tense, h should be past tense (not past participle)

bumblebee

12:10 PM

Thanks Leaky

bumblebee

12:39 PM

Jeez, some people on mathstack are just not it. My post is getting downvotes. Now people are upvoting the comments saying the question is confusing even after I clarified the commenters doubt. I ask users on CURED to help me reopen the question. They call it "such an off-topic question". But when I ask for reason and justification they ignore. Honestly, i'm thinking of leaving mse, this site is so biased and some people here are just not it.

Calvin Khor

12:51 PM

lol

Prithu biswas leftmse

1:08 PM

@bumblebee Write "bumblebee left mse" in your username and we can be best friends :D

Calvin Khor

1:19 PM

when did desmos turn blue?

one potato two potato

How can I show $so(3)$ and $sl_2(\Bbb R)$ are not isomorphic as $\Bbb R$ Lie algebra?

Using generator is nasty. Is there any better way?

Koro

someone downvoted a post of mine without giving any reason whatsoever.

bumblebee

1:46 PM

@Prithubiswasleftmse I haven't reached that point yet.

But I am close.

Prithu biswas leftmse

@bumblebee you will get there eventually.

Soon we will have an entire army of "left mse".

bumblebee

I have my pride. I'm not gonna waste my precious time on people like them.

yay another downvote for no reason! im loving it!

Mad Spaces

Hello, i am trying to prove the grassman identity using the language of vector analysis and differential forms ( IE No BAC CAB no vectors and diffs etc, just translating the vector fields into one forms and then working it out) however i am not sure how you would understand the laplacian of a vector field in this language?

Transcript for

$Mathematics$ Mathematics