#serious-discussion

1 messages · Page 259 of 1

timid bronze
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Ugh i have to go back to work now

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Fml

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U like 1D too?

latent edge
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Good luck

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I finished my work today

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I yapped about modular forms with prof chan

livid willow
latent edge
#

or ig advisor chan

livid willow
velvet dagger
cyan goblet
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i've been walking in circles in this empty blackboard room

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reading these notes

latent edge
#

Algebraic geometry?

cyan goblet
#

yeah

timid bronze
livid willow
median knot
timid bronze
latent edge
#

till 9 is okay-ish

livid willow
velvet dagger
#

I guess it depends in part on whether it's "constantly doing things until 9" vs "on the clock until 9 but not necessarily super busy"

livid willow
velvet dagger
#

Either way yeah you're at the home stretch Ally!

livid willow
#

And what are you guys working on?

median knot
#

Trying to sleep 🥲

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But cramps are killn meh

timid bronze
#

im having thi icl this is a good group

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of 20 ppl

velvet dagger
#

Okay that's a plus

livid willow
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😔

median knot
#

😭🫶

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Thank you 😭

velvet dagger
median knot
#

Thank you 😭😭

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Alright imma head to bed

livid willow
#

YES

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Definetly😭

median knot
#

Good night 😄

fresh comet
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🤍

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have a wonderful night! aecatheart

median knot
#

Thank you guys!! You too! 😭🫶

livid willow
#

Good night!🪷💁

timid bronze
#

Omg u math ppl r stinky

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im doing my presentation in the math building actually cuz i was assivned and

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wHY THIS smell LKKe 19 cans of ASS

latent edge
#

Holy yap

timid bronze
#

Ur one of the exceptions dw

timid bronze
old oak
#

Have you considered heeding the advice in your PFP?

velvet dagger
#

Advertising of this form isn't allowed

velvet dagger
latent edge
bitter pier
#

Who knows Gilbert strang?

cyan goblet
#

Like personally?

brittle socket
deep mango
twin flicker
rancid vine
#

My highest was a Rem 😭

ocean harbor
#

lmfao

slender light
#

what is trignometry

ocean harbor
#

google it

agile fiber
#

trigonometry is the study of triangles, except it's secretly the study of circles

zealous garden
#

No comment

bitter pier
timid bronze
twin flicker
twin flicker
#

ally what does your username say

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i cant read it

timid bronze
timid bronze
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Hi omg im free

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Im so tired but

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Idk im feeling kinda down

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Might take a walk in the city

fresh comet
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a walk couldn't hurt c:

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I love night walks to clear my mind EB_EspeonLove

jagged forge
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but u get eaten alive by the mosquitoes

timid bronze
fresh comet
#

night walk photos are always so beautiful aecatheart

velvet dagger
#

Tru

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I'd love to see them as well if you're down!

timid bronze
#

wtf why only 14k i usually get like 10k a day but this is barely above normal for a work day

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I need to get it to 20k

velvet dagger
#

Keep it up! You're on the way!

fresh comet
#

you can do it! happy

jagged forge
timid bronze
#

hopefully no one attacks me in the streets

jagged forge
#

so jealous

timid bronze
velvet dagger
velvet dagger
timid bronze
#

we dont talk about that one day i was in a town at 9 pm in the winter

velvet dagger
#

Uh oh zoomEyes

jagged forge
native latch
#

unrelated but i would like to know if anyone plays deltarune in this server

timid bronze
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15.6k

Time to recircle even though my phone is nearly dead

velvet dagger
zealous garden
velvet dagger
timid bronze
velvet dagger
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Fair enough lmao, you're welcome

timid bronze
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@jagged forge

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why the reaction

jagged forge
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it was funny

timid bronze
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he meant well but thats not an area where i need encouragement because im good with it

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but i could use it in areas like math

velvet dagger
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Guess that's just my default when I see people getting good work done :P but yeah you def got it when the math comes back around

true slate
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(general statement)
Some people really want to dominate everyone or be dominated by anyone (this is for my ex)

velvet dagger
#

I feel like the last parenthetical contradicts the first

Also

What

true slate
#

Its general statement for some people

velvet dagger
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I think "for some people" makes it fairly non-general

true slate
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And my ex come in some people

velvet dagger
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"For all people except the ones for whom for this is false"

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Anyway more crucially than the nature of generality... I just wonder if this really needed to be shared with the class

true slate
#

She really thinks she can dominate everyone
But reality is something else she don't know about this

celest terrace
#

I imagine these results are likely not applicable to all

true slate
#

Sure they aren't applicable to anyone
But if they r applicable to someone that means someone isnt right in mind

velvet dagger
#

Anyway like I said, the generality of this is secondary

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The really important thing is that I question whether mathcord was the ideal place to talk about who dominates whom

jagged forge
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🥀

celest terrace
#

Yeah, not the most ideal place

true slate
#

Im talking this in discussion
And I see everyday people talk some shit
Can't i do today?

velvet dagger
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People talk about a lot of things here, obv this channel isn't math centric

true slate
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Lol just chill

velvet dagger
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And I haven't yet said anything about rules because domination is a bit vague

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I'm just confused

true slate
celest terrace
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I’m three

true slate
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I thought it is good place to talk about this other than other channelz

true slate
tender heron
celest terrace
#

we never converge

true slate
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And there is lot of possibilities

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What can happen

celest terrace
#

something something i genuinely need to start buffing up my analysis now that I think about it

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meh, that’s an August problem lolll

celest terrace
true slate
#

I don't like analysis btw

celest terrace
#

I can think of 1 I saw recently

celest terrace
verbal gazelle
#

Hey chat?

vivid halo
#

daily reminder

celest terrace
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(for now)

true slate
celest terrace
vivid halo
#

-1/12 moment

true slate
celest terrace
#

with minimal effort required other than ur brain

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/pencil

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/paper

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/computer for occasional coding

true slate
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But idk 😐

vivid halo
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nah it's fine

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this is correct

tender heron
true slate
timid bronze
#

everyone has different areas where they need or want encouragement

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i love that of you

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and as for math you help me so much with it

jagged forge
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-1/12 bell curve meme

timid bronze
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so while i may have said that about walking you make me a happier person when you encourage me in math

velvet dagger
velvet dagger
velvet dagger
vivid halo
true slate
velvet dagger
#

Oh oh

vivid halo
#

this is the sort of thing that shows up when computing zeta regularized determinants of Laplace operators or whatever

celest terrace
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oooh sounds interesting

velvet dagger
#

My mind defaulted to thinking Gamma function when I saw a factorial

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But then thought wait that's not...

timid bronze
#

my phone is really dying anyway so ill leave it at 18.8k that makes me mad but wtv dumb phone

vivid halo
#

tfw computing the determinant of an operator on a Hilbert space

velvet dagger
#

Phone battery running low is a pain

fresh comet
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@verbal gazelle welcome to the mathcord! nachoWaves

timid bronze
#

my phone battery is always running low fr

tender heron
timid bronze
#

even my vision is stronger than my phone battery

celest terrace
#

sometimes it does last a little longer if brightness is basically nonexistent

fresh comet
velvet dagger
#

Once I'm working, I'll have a much smaller case I bring around with me which will hold a laptop, laptop charger, phone charger, and that external battery for a phone

fresh comet
verbal gazelle
celest terrace
#

but my iphone has lately had a really shitty battery life—as the Big Apple intended 😔🥀

velvet dagger
#

Just so that I have fewer incidents when I'm at < 10% and panicking

fresh comet
verbal gazelle
timid bronze
fresh comet
#

plenty of people have mistook me for a bot by now

#

I get a new one each day

verbal gazelle
velvet dagger
#

Daily? Dang

fresh comet
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often more than daily

velvet dagger
#

I guess people are just used to welcome messages from bots

fresh comet
#

sometimes several times a day

timid bronze
fresh comet
verbal gazelle
fresh comet
#

no! it's good that you got a good laugh out of it aecatheart

celest terrace
#

your profile star animations are too good to be a bot, i fear

jagged forge
fresh comet
#

my days are better when you're smiling 🤍

verbal gazelle
fresh comet
timid bronze
#

ur so endearing higher u make my day

fresh comet
#

no need to apologize

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I'm not upset at all

verbal gazelle
#

But got ignored by most of em

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Which is blue

fresh comet
#

I just looked at your message history and realized you got ignored for days bearlain

timid bronze
#

r these kids gonna get out the shower or what

well theyre college freshman i shouldnt call them kids but

jagged forge
#

nah

timid bronze
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I do anyway w my co workers

jagged forge
#

they r kids

timid bronze
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What if one of them is 30

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u never know

fresh comet
#

in any case though, we're happy to have you here, and I hope you enjoy your stay aecatheart @verbal gazelle

jagged forge
#

true

timid bronze
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what if one of them is 27

timid bronze
#

like do u admit ur a kid

jagged forge
#

everyone is a kid to someone else

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well

verbal gazelle
#

I run my own server...
And was planning to add some real good professor in it

timid bronze
#

ur a kid to me then

jagged forge
#

maybe not past the age of 40

timid bronze
#

amukh is an adult

celest terrace
timid bronze
#

and ur a kid

jagged forge
#

or 60

velvet dagger
timid bronze
#

they act like kids most of the time anyway

velvet dagger
#

With the way prices are going I could def see working for a while before college so as to minimize loans catching on

velvet dagger
timid bronze
#

oh yeah im so excited to see what trump has done to my financial aid package

jagged forge
#

there was someone in my english class in college who seemed like 40s

timid bronze
#

may dropout frfr

celest terrace
#

It’s actually a nightmare paying for college without any form of external help

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be it financial aid or family support

velvet dagger
#

Or both at this point...

celest terrace
velvet dagger
#

Hopefully the aid will stay intact

timid bronze
#

maybe trump will make it so financial aid only goes to rich people

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more money for the rich

celest terrace
#

I would actually be shocked and intrigued

tender heron
fresh comet
celest terrace
#

at that point he’s doing it for the plot

timid bronze
true slate
velvet dagger
#

He won't directly cut much except for perhaps Pell Grants and federal aid, but because his shenanigans have hurt university funding at large

jagged forge
timid bronze
#

trump won i might as well dropout and work unpaid for him

velvet dagger
#

The worry would be that they will meet a lesser percentage of students' demonstrated needs in order to offset the losses from the federal research cuts

celest terrace
#

I will at least try to enjoy the spot I’ve got now while I still have it

velvet dagger
#

I think that's less likely, their inclination seems to be to cut the funding on the level of research (accept fewer grad students, hiring freezes, cancelling research projects)

timid bronze
#

it was nice knowing you all before trump makes me work all day for free and have no breaks

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See you again maybe never

celest terrace
#

maybe even making “trump scholarships” or smth

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wait is that a thing?

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probably

velvet dagger
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Which makes sense on some level: if they lose the money for a given research grant, they just cut the project that grant funded but keep the educational mission going

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Still obviously sucks but yeah hopefully financial aid won't be affected?

true slate
velvet dagger
celest terrace
#

I’d lowkey be down for that

timid bronze
celest terrace
#

especially cause my bf is an international

timid bronze
#

just deport me out of this shithole

celest terrace
#

so there’s concern there already

jagged forge
fresh comet
celest terrace
#

but make sure my Springer books make it with me!!

velvet dagger
#

Like okay we claim the $1000, go to a different country where we're gonna thrive more, but still have citizenship to come back if things improve

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Win win

jagged forge
fresh comet
celest terrace
true slate
#

What country u want

celest terrace
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/which countries would be open to taking a (potentially) huge influx of Americas

velvet dagger
#

Well, in my case the default is Morocco, but we're not broadcasting this strategy too much

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So we won't be part of a package

timid bronze
#

also im not comfortable with elon musk and trump’s relationship i saw them two making out in public and being so cuddly

pls save that for private like look one of u owns teslas go to ur office or smth and stop burning our eyes

#

oh nvm i forgot theyre fighting rn

jagged forge
#

yeah didn’t you see elon had a black eye

true slate
celest terrace
#

Meanwhile his wife smiles at, barely kisses him, and otherwise seems like she despises being in the vicinity of him

celest terrace
#

culture at its finest

true slate
#

21thh century's most epic relationship

tender heron
timid bronze
#

oh wait the name sorry dami

velvet dagger
# true slate What country u want

In my case my inclinations are gonna be Germany/Austria/Switzerland, Morocco, Malaysia/Singapore, Australia/NZ, Gulf Arabia, or East Asia

velvet dagger
celest terrace
timid bronze
#

i just sent the trump and elon musk couple meme but i deleted it bc the tiktok username (not the image of trump and elon musk) is a bit 18+ inappropriate

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didnt realize

celest terrace
#

but at that point it would be like a preferential-accelerated visa app anyway lol

jagged forge
timid bronze
#

i dint need to apologize to u suremark

jagged forge
#

i what

timid bronze
#

anyways get back go ur furry labor

#

u have 3 furry babies

timid bronze
#

idk ab the other 2

jagged forge
#

unhinged

timid bronze
#

u have triplets

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how fun

velvet dagger
# true slate So many choices

Yeah I mean, in my mind

  • Germany is good from the pov of jobs/economics (Austria seems very nice and is right next door so throwing that in, Switzerland if I have a ton of money)
  • Morocco is my family's original country and is a good place to do business. Maybe not ideal to be an employee
  • Australia/NZ are anglosphere and seem very pleasant
  • Gulf Arabia might be good economically. If I work there it has to be as an American, as a Moroccan I'd get a lot less money (they pay based on nationality) and I think the treatment can be a bit rough, but I'm close enough to Arab that maybe there's some momentum in navigating culture
  • East Asia seems great economically and quality of life, might be a bit of a departure from what I'm used to
  • Malaysia/Singapore seem to have great quality of life (weather might be a bit rough and Singapore is kinda expensive, Malaysia being Muslim might give some inertia with navigating cultural matters)
timid bronze
#

its ok uncle daminark can support u if needed

velvet dagger
#

LMAO

true slate
#

Bro is ready

jagged forge
timid bronze
timid bronze
true slate
timid bronze
#

hell support ur birthing

jagged forge
timid bronze
#

pregnancy is hard suremark

velvet dagger
#

So probably if I move to a place where citizenship requires giving up American, I'll just go for residency

celest terrace
velvet dagger
#

I think quality of life is good in eg Scandinavia but they might not be as good as somewhere like Germany for career advancement

timid bronze
#

hm

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lets add 2 more children

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sharp and deltoid

velvet dagger
#

Like there's the question of where I'd wanna work and build myself vs where I'd wanna retire

jagged forge
timid bronze
#

kawaii~chan will be upset to hear this

#

unc daminark wish he had kids
so be grateful

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he hasnt been able to found his furry partner yet

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Unlike u

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Bc ur very furrizzmatic

velvet dagger
#

My WHAT

celest terrace
#

that is a word

velvet dagger
#

I disavow this notion of a furry partner

celest terrace
#

triple combo goes crazy

timid bronze
#

ur furry wife will treat u well

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her name is um

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idk what u like i forgot

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manifolds

velvet dagger
#

I pre-emptively divorce

timid bronze
#

well too bad u waggle ur tail at idk real analysis

#

ur a furry

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be proud

velvet dagger
#

Absolutely not

timid bronze
#

its ok to lack charisma

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at least u have furrizzma

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or well

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developing it

celest terrace
#

furrizzma >>> charisma

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it’s fluffier

timid bronze
#

Right and dami is a fluffy meowing cat for his discord mod team

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he meows at them

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and purrs when he doesnt wanna do work

celest terrace
#

if that’s not marriage material, I don’t know what is

velvet dagger
timid bronze
#

hes already laid his eyes on some furries

celest terrace
timid bronze
#

hopefully they dont find him too furry

velvet dagger
celest terrace
#

your local Petco does a decent job usually

timid bronze
#

to clean his fur yeah

vivid halo
#

damn none of these words are in the bible

jagged forge
#

fr

timid bronze
#

dami u dont even read the bible

velvet dagger
#

If the alternative is being called a furry...

timid bronze
#

omg yes!! suremark and his senpai kawaii chan from mystreet had the most adorbs slow dance ever~! ✨💕 they were moving suuuper gently, like fluffy clouds floating on a soft spring breeze ☁️🌸. suremark held kawaii chan close, all careful and sweet, making sure not to step too hard so their dance felt like a soft, cozy hug 🥰🤗. kawaii chan’s cheeks turned the cutest shade of pink—like a little sakura blossom blooming just for him 🌸💖—and she smiled all shy and sparkly, resting her tiny head on his shoulder like the sweetest little kitten 🐱💞. the whole room felt like it turned into a magical fairy tale, with sparkles ✨ and soft pastel lights all around them, making their moment feel like a dreamy bubble of happiness 🎀🌈. every beat of the music was like a heartbeat just for them, making the world slow down so they could stay wrapped up in their soft little love story forever~! it was seriously too cute, like straight out of a magical anime episode~! 🥺💫💕

deep mango
jagged forge
timid bronze
#

what

#

u wrote it

#

dont be delulu

celest terrace
timid bronze
#

it was in ur journal

celest terrace
#

they just spelled things differently in the old testament

timid bronze
#

ok shower time brb 🧼 🚿

deep mango
#

ew whats that smell

timid bronze
#

i shower unlike ryc

#

shut ur bitch ass up

#

i knew what ud say

deep mango
#

i showered 2 times today

deep mango
#

good thing i did

timid bronze
#

math ppl r stinky

celest terrace
#

erm hello??

timid bronze
#

that one room in the math building smells

#

So i dont redact my statement anymore bc of u

deep mango
#

idk wtf youre talking about

timid bronze
#

u smell awful

velvet dagger
#

Imma be honest ryc you did kinda walk into that one

deep mango
#

even my armpits smell like petunias

hidden isle
timid bronze
deep mango
hidden isle
#

dami dislikes chip more 100%

velvet dagger
#

Do I?

hidden isle
timid bronze
#

@coarse bridge water beam ur romantic partner is missing u

velvet dagger
#

I might just ban you in my indecision

hidden isle
timid bronze
#

Not mine

tender heron
celest terrace
timid bronze
#

Ok brb

deep mango
#

speaking of fantasy ig ur shower was fictional

hidden isle
jagged forge
#

lil vro

tender heron
hidden isle
#

3 messages ah yes -> a lot the fact u care so much makes me think u want in

#

dw i can dm him for u

#

tell him that u have a fat crush

#

💔

velvet dagger
#

How does he have this much a stranglehold on your minds LMFAO

hidden isle
#

who even uses this channel cuh

velvet dagger
#

He's a chill friend of mine but you guys are gonna be writing fanfiction at this rate

fresh comet
velvet dagger
gentle birch
steel vessel
#

hi

gentle birch
steel vessel
gentle birch
#

no

tender heron
# gentle birch hi

Yoooo, wait wait wait 🫸-----🫷
Flux with a bunny tag?
bugs bunny flux bunny!!???

timid bronze
#

i mention them

#

including u

#

hes not special dude

#

☠️

gentle birch
#

iykyk

velvet dagger
velvet dagger
gentle birch
tender heron
timid bronze
#

Gn

tender heron
velvet dagger
timid bronze
velvet dagger
#

Goddammit

steel vessel
gentle birch
velvet dagger
#

Go to sleeeeep

fringe summit
fresh comet
#

have a wonderful night ally EB_EspeonLove

timid bronze
#

@coarse bridge Lmfao dumb fuckin muted ass

timid bronze
velvet dagger
#

Sounds good, gn fr this time

jade kindle
#

Guys i built Pi:

#

Abs[(2*Integrate[Sqrt[(r^2-x^2)],{x,10,-10}])/10^2]

granite hound
#

I feel like using calculus to generate pi is cheating somehow

jade kindle
granite hound
#

Hm, I was gonna say summations or something, but I guess that's still more or less calculus

#

Perhaps I shoulda said, using integration to generate pi feels like cheating

jade kindle
#

why

granite hound
#

¯_(ツ)_/¯

jade kindle
#

ok

#

I like Integration though

granite hound
#

Nothing wrong with integration, there's a lotta neat stuff there

jade kindle
#

atomic storm
granite hound
#

Well that's what pi is

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But you've gotta calculate it if you wanna use it

atomic storm
#

oh well without a circle

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😭

neat lintel
#

hi

verbal gazelle
wise bloom
#

use picks theorem

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take a square of side length 2

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plot a circle in it

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of radius 1

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find the distance of all points in the square from the origin by using cond r>1 or r<1

#

divide no of points in circle/no of point outside + in circle

#

look we know area of circle with radius 1 is pi and of a square with side lentgth 2 is 4

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so like Nin/(Nin+Nout)=pi/4 for so like you can approximate pi using this

#

@jade kindle

neat lintel
#

how are you @verbal gazelle

#

anyone?

jade kindle
jade kindle
# wise bloom i know

or just integrate a circle with a given radius and divide it by the radius squared

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the only issue is

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The Antiderivative is weird

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the antiderivative of the half circle function looks like the integral symbol

#

Coincidence?

#

I dont think so

cursive fossil
#

2arcsin(1) in radians

north topaz
#

,w 2 arcsin(1)

neat lintel
#

hello

delicate apex
bleak prairie
#

can u do middle terms in scientific calculator

north topaz
#

you would need a calculator with a CAS

#

computer algebra system

bleak prairie
#

bruh

#

those are expensive af

#

monopoly

north topaz
#

I mean Wolfram Alpha can do it for you

#

so can a lot of online tools but

bleak prairie
#

nah i need to use it in exams to save time

north topaz
#

then just learn it properly then

#

if you can't be bothered to factor just use the quadratic formula

bleak prairie
#

im slow at it thats why lol

#

idk whats that lol

north topaz
bleak prairie
#

nope

#

its in my book but not for this year

north topaz
#

search it up dude

bleak prairie
#

we gotta learn it next year

#

okay

north topaz
#

it's actually pretty dumb that they don't teach it this year

#

they should teach that and factoring and completing the square together

#

then your unit would be complete

bleak prairie
#

ok thanks

north topaz
#

not knowing transformations or vertex form isn't the end of the world but those are also important

north topaz
wise bloom
#

@jade kindle

#

wanna do something fun

#

hello

timid bronze
#

it was alr

#

just tiring

#

tyfa

#

how was ur day??

median knot
#

It was good slept until 12 so 😭

#

I slept a lottt

timid bronze
#

omg jealous

#

i can sleep in more today however i get bad headaches from naps most
of the time

#

or if i go over 8

median knot
#

Ahhh that sounds very tiring, not getting enough sleep ☹️

#

When do you get vacation?

#

From work

timid bronze
#

8 hours

timid bronze
#

i just cant rly get myself to go beyond it

timid bronze
#

but im fully done once mid july hits

timid bronze
#

its not a longterm job

timid bronze
gentle birch
#

hi ally

timid bronze
#

hi flux the furry

median knot
#

Oh I’m still in high school, have two more years left, then it’s uni time

timid bronze
median knot
#

Like in a day?

timid bronze
#

Yea

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for hs

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btw nat meet flux the furry and flux the furry meet nat

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@gentle birch

median knot
#

8-16 then I have work then I have job from 17-19

timid bronze
#

wtf

median knot
#

Hello flux the furry 🤩

timid bronze
#

8 am TILL 4 pm?

median knot
#

Yeah 😭😭😭

timid bronze
#

thats crazy

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along w work

gentle birch
timid bronze
#

learning from other people aside from that stupid brainrotted older brother u have

median knot
timid bronze
#

Sounds good

median knot
#

What should I address you then :D?

timid bronze
#

im just pulling his leg

#

hes done worse stuff to me and everyone in this server

#

he can handle it for one last time

#

Call him flux

median knot
#

Is that alright? That I call you flux? 😄

median knot
deep mango
gentle birch
#

shut up ryc

median knot
median knot
unreal brook
#

can somebody help in bio (dna replication drawbacks)

timid bronze
gentle birch
#

good night

timid bronze
#

no flux

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/j .

timid bronze
gentle birch
timid bronze
#

@deep mango says gn too

deep mango
#

dont speak for me

timid bronze
#

be kind

#

hes just a kid

twin flicker
median knot
ocean harbor
twin flicker
cursive fossil
#

6 hours of sleep a day

ocean harbor
#

I get 12 hours of sleeping SCchilling

lone orchid
#

Has anyone tried both fxcg50 and fxcg100 if so which one is better?

ocean harbor
#

I stay up all night

cyan wharf
cursive fossil
#

i remember this

#

there was a (roblox) sex game creator involved in their latest event

ocean harbor
#

wtf

timid bronze
#

but im only working in the summer

jagged pendant
timid bronze
#

it makes ur eyes tired

jagged pendant
#

I feel bad for flux sometimes, but then again... I don't

timid bronze
#

LMFAO

jagged pendant
#

Hi, shy girl

tropic cobalt
#

calc 2 is decent

#

not as hard as i thot it would be tbh

ocean harbor
twin flicker
timid bronze
timid bronze
twin flicker
#

bruh its so hot in this mf gym

#

im burning

jagged pendant
timid bronze
#

my shoes r so soaked

latent edge
timid bronze
novel shell
#

Ouch

twin flicker
novel shell
#

Wet shoes give blisters

velvet dagger
novel shell
#

Or some people did and it went away to here

#

Literally been raining all week in finland

latent edge
peak tide
#

<@&268886789983436800>

velvet dagger
#

Wait I did not see what happened

junior veldt
#

probably for the best

peak tide
#

you didn't miss anything good

latent edge
#

I thought I was going to get banned lmao

peak tide
#

just ascii "art" spam

junior veldt
latent edge
#

hi :3

calls mods

junior veldt
#

"mods, kill this man"

novel shell
#

“Art”

#

Maybe good i didn’t see

latent edge
#

I'm gonna guess some sussy ascii art

fresh comet
#

@novel shell welcome to the mathcord! happy

novel shell
#

Thanks😊

#

Math is fun

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Very logical

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And there’s (usually) always a reason for something

timid bronze
#

its smth i prefer keeping confidential now

twin flicker
#

ok

timid bronze
#

So u admit ur a tiny kid now?

#

Shortie

velvet dagger
dapper badge
#

Dami can you property (T) pill me sometime

rocky shuttle
#

omoi wa rain rain

velvet dagger
dapper badge
#

swag yeah I hear about it in the context of lattices in Lie groups but idrk how to think about it or why it's interesting

velvet dagger
#

I will say most of what I know of it is fairly impressionistic

#

So I'm not sure eg of the proof that lattices in higher rank groups satisfy (T) or anything

#

But I can tell you the story

latent edge
timid bronze
#

Ur 4’8

velvet dagger
#

Brutal

timid bronze
#

btw dami atp i dont even wanna go to the dining hall for dinner im just gonna skip it and stay in this building

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i dont wanna walk in the rain

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My shoes have never been this wet before

velvet dagger
#

Ah yeah valid. Esp given that dining hall food... May not spark joy

timid bronze
#

Real but salads r the only decent thing there

#

So it suffices

latent edge
timid bronze
#

dami do u wanna see a vid of how wet my shows are

near mango
#

The only place on this campus thats open for food has 10 dollar breakfast sandwiches

#

Pretty #epic

velvet dagger
timid bronze
dapper badge
timid bronze
#

so u cant rly tell

timid bronze
#

Embrace it

latent edge
timid bronze
latent edge
#

stop it get some help

timid bronze
latent edge
#

:3

timid bronze
#

Automorphic forms r banned then

latent edge
#

:3

jaunty ibex
#

Deltoid short? Lol I hope it was true

latent edge
#

why would i enjoy this

#

this is bad

#

oh

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yes loo bad

#

what class btw

timid bronze
#

Dami how tall r u

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Ur tall right

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U like 5’11

jaunty ibex
#

1 more year and I'm out of waterloo

latent edge
#

u after loo

velvet dagger
jaunty ibex
timid bronze
latent edge
#

:3

twin flicker
#

im the shortest in mathcord

latent edge
#

I played a game called catgirl

#

peak gameplay

#

and memes

agile fiber
#

there are 13 year olds in mathcord

velvet dagger
velvet dagger
latent edge
#

are we talking about kazhdan lusztig polynomials?

velvet dagger
#

I think there's a bit of a dynamical/"spectral gap" interpretation in play, but I'm not recalling the details offhand. That said, I can give a graph theory mini story that might have some bearing on things

timid bronze
dapper badge
#

Yeah, I guess I'm trying to learn some of the dynamical side of things too. This feels reminiscent of like ergodic actions vs mixing actions and realizing these things via the representation of G into L2 and characterizing invariant vectors there

latent edge
#

Fell topology?

timid bronze
#

i never realized how tall traffic lights were until i saw the pic of a person standing next to one

velvet dagger
#

Namely, you can define the notion of a Cheeger constant of a graph, which measures connectedness. Cheeger = 0 iff disconnected

Given a family of graphs (say k-regular for some k), you say they form an expander family if their Cheeger constants are bounded uniformly away from 0

There's an inequality relating the Cheeger constant to the spectral gap (smallest non-zero Laplace eigenvalue), so really an expander family can be thought of as a family of k-regular graphs which have a minimum spectral gap

If you study random walks on regular graphs, that spectral gap being larger implies a faster mixing rate for the walk

timid bronze
#

Almosg as tall as me

latent edge
#

smh dami graph theory pilled

velvet dagger
#

Now, you can show probabilistically that most large k-reg graphs are good expanders. But constructions of explicit families usually used property (T)

#

The theorem here is, if Gamma is a finitely generated group with (T), say S is a symmetric generating set, then the family of Cayley graphs Cay(Gamma/N, S) are expanders

timid bronze
#

Dami im gonna take notes of ur math

#

Ur rly knowledgeable

#

In this

#

Smartie very impressive

twin flicker
#

roughly

jagged forge
#

it's like he nearly has a phd or something

twin flicker
#

graph theory mentioned

velvet dagger
timid bronze
velvet dagger
velvet dagger
#

Because this lets me set up (T) vs amenability

#

How much do you know about amenability? The answer is probably more than me because I only know one and a half things

timid bronze
velvet dagger
#

Okay that does ring a bell actually

#

Yeah I figured as much, thanks for resending!

velvet dagger
# velvet dagger How much do you know about amenability? The answer is probably more than me beca...

But yeah there are a few characterizations of amenability.

One is that the group carries an invariant mean, i.e. an invariant linear functional on L^{infty} which is non-negative and has norm 1

One is something about fixed points if it acts in a nice way on an appropriately adjectivized subset of a TVS (maybe it was affine action on a compact convex subset?)

One is that the regular representation of G on L^2 has almost invariant vectors

timid bronze
#

Ur fine

velvet dagger
twin flicker
#

short

flat smelt
#

what is 12+5x(4-2)+8

#

i gotta go

agile fiber
#

,calc 12+5*(4-2)+8

fathom swallowBOT
#

Result:

30
agile fiber
#

isn't it wonderful what modern technology can accomplish

dapper badge
velvet dagger
#

The action is translation

timid bronze
dapper badge
#

oh wait this is bc we're in L2

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yeah

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ok that's dope

velvet dagger
#

But yeah so amenable + (T) => compact already has some nice consequences

#

For one, you can show that Z is amenable. Because it's not compact, it doesn't satisfy (T)

But then it's not too hard to show that a quotient of a property (T) group has (T). If π:G/N -> U(H) has almost invariant vectors, okay pull that back to G, tada.

In particular, any group with (T) can't have Z as a quotient. This is a cohomological property, since H_1(G,Z) is its abelianization

#

You can phrase this as H_1(G,Q) = 0, or H^1(G) = 0

dapper badge
#

Is property (T) preserved upon passing to finite-index subgroups?

velvet dagger
#

Yes

timid bronze
#

Dami im gonna brb to take more Note later

#

But dangthis sounds toooo hard cries

velvet dagger
#

In fact finite covolume

dapper badge
#

I see. I like this a lot. I didn't know why people cared if mapping class groups satisfy property (T) but I guess it's evidence for/against Ivanov's conjecture on H_1 of finite index subgroups

velvet dagger
#

That's exactly where I was going with this

twin flicker
#

i didnt mean it in a mean way

velvet dagger
#

I'm pretty sure this inspired Ivanov

timid bronze
velvet dagger
#

At least is post-hoc motivation

timid bronze
velvet dagger
#

Since okay we think cohomological stuff for lattices in higher rank groups probably should mirror stuff in MCG for higher genus surfaces

velvet dagger
dapper badge
#

I still haven't actually taken a GGT course so I'm missing a lot of motivation for questions people care about in this area

dapper badge
velvet dagger
latent edge
#

lmao

visual breach
#

Group homology bleakkekw

velvet dagger
#

Even if I don't, I still wanna learn this recreationally

#

It's so surprising how deep that goes

latent edge
#

Sheaf cohomology scary

velvet dagger
#

But yeah my first application was that (T) was (possibly time traveling) inspiration for Ivanov because I know you like MCG

visual breach
#

It also sounds scary to me tho

#

Like, what does group homology/cohomology truly measure

latent edge
#

replace Group with Galois and it won't be as scary trust

velvet dagger
visual breach
latent edge
#

Lie algebra cohomology is goated

visual breach
#

Wait, is Lie theory connected to this somehow

velvet dagger
#

Oh I was saying it because it was a lie

latent edge
#

from my experience if you tell me H^43(X,Z) = Z^44 or something that doesn't tell me anything

visual breach
#

Damnit, I got whooshed

timid bronze
#

Scary math people talking math language

latent edge
#

but like if you explain connections with other stuff then yeah it gets a meaning

visual breach
latent edge
visual breach
#

It has 44 43-dimensional holes (or whatever yapping one can think of)

latent edge
#

I meant for general cohomology theories

visual breach
velvet dagger
visual breach
#

A take: Homology should not have been generalized beyond bounds to give birth to motives and the like

timid bronze
#

Can this be renamed to math-discussion-2

latent edge
dapper badge
timid bronze
visual breach
#

Well tbf, if you think about it, who IRL cares about holes anyway

latent edge
visual breach
#

Damnit, true

visual breach
velvet dagger
#

Showing amenability is quite hard as far as I know. But (T) is easier. I would explain it but I don't know exactly why

Some general theorem which is true up to maybe being a bit false: if G is a higher rank semisimple algebraic group over a local field, then it has (T)

Also, if H is a closed subgroup of G and G/H has finite volume, then G and H have (T) together

Okay so that means lattices in higher rank groups satisfy (T).

velvet dagger
timid bronze
velvet dagger
#

I may be saying wrong things, add adjectives as needed

#

But if nothing else, SL(n,R) and thus SL(n,Z) has (T) :P

dapper badge
#

Good enough for me

timid bronze
#

Dami do u think u could win a topology bee

visual breach
#

It sounds important

dapper badge
#

Thanks for explaining all of this, helps a lot to appreciate it more when I see it randomly pop up

latent edge
#

tbh idk how to explain H_1 and H_2 with english terms other than 1 or 2 dimensional holes

#

lmfao

visual breach
#

Also interesting that lattices are everywhere

latent edge
#

I remember there was a specific term for these but i forgor

visual breach
#

Oh, wow
Quite simple

timid bronze
#

Reality bc i dont study this stuff

velvet dagger
#

So yeah Margulis normal subgroup theorem, cohomology, expanders, vague idea of spectral gap are the main kinda nice facts associated with (T) in my mind. Also something about rotation invariant measures on the sphere, though I know that story much less. Look up Banach-Ruckiewicz (modulo spelling) if you're curious about that

timid bronze
#

Too many theorem

visual breach
#

If only I knew what T is, but anyway

velvet dagger
#

You need to ask what the topology is on that space, it's called Fell topology

visual breach
#

Any direction you go, there are so many facts and perspectives you have to take in, so overwhelming tbh

timid bronze
#

too too many topology

latent edge
#

you see where im going with this

velvet dagger
#

So irl it means that if you can find unit vectors v_n in a unitary irrep such that gv_n - v_n goes to 0 (say uniformly on compact sets), then you can find a single vector for which gv = v

visual breach
#

Space of irreducible reps, now that is scary I guess irealshit

latent edge
#

I could be studying cohomology of arithmetic groups but instead I'm required to compute character formulas for unitary representations

dapper badge
#

rotation-invariant measures on the sphere

velvet dagger
#

Not just your explanation but the topic at large

latent edge
#

it's hard to explain in text

#

the only time i got it working is when i was using a blackboard explaining

velvet dagger
#

True but also it's the kinda thing where... Idk if you're not used to topology already it might be a bit tricky to imagine "data in a space" or to think about spaces combinatorially

dapper badge
#

I think I will check out this book

flat smelt
#

hi

timid bronze
#

Does solids of revolution help me with this XD

visual breach
dapper badge
timid bronze
velvet dagger
# visual breach Time for you to explain then

LMAO I mean Deltoid is giving a fairly good explanation, and probably comes as close as possible to explaining it understandably to a very early student.

I just think it's one of those things where it's hard to appreciate algebraic topology at all if you're not as used to certain ideas that typically come later

timid bronze
#

(Except me still not doing it)

flat smelt
#

give me a hard math equation please

timid bronze
#

Just giving interest to U pure math ppl

visual breach
#

Anyway I hope there would be a way to more simply present these all

velvet dagger
visual breach
#

Or maybe there lies the innate complexity in the property of (topological?) groups and stuff

velvet dagger
icy heron
#

It's so funny when ally is typing, because discord gets very confused by the unicode directional marks

velvet dagger
#

TRU I do notice that haha

velvet dagger
flat smelt
#

yea

#

same

velvet dagger
#

Like Ally is in calculus, so homology and such is tricky to explain at this stage

visual breach
velvet dagger
#

Tbh if she does calc 3 I can start to explain a tiny bit of algebraic topology. Just talk about winding numbers off curves

latent edge
#

yeah that sounds cool tbh

#

winding numbers after calc 3

visual breach
#

Maybe there is a way to present it to highschoolers or something

velvet dagger
#

There might be a way? Like tbh I don't really know a ton about the Fell topology myself

timid bronze
velvet dagger
#

My background is hypersketch

timid bronze
#

Ally not listed on me profile

velvet dagger
#

But yeah I know the interpretation as just almost invariant vectors vs invariant vectors

dapper badge
#

Ok time to learn about stationary measures catking

timid bronze
#

What that mean

#

Ik u know me ultra but

#

Who sheddiw

icy heron
velvet dagger
#

I need to learn those one day

dapper badge
#

perhaps

flat smelt
#

what that mean

velvet dagger
#

Honestly I should get an industry job with excellent work life balance and just learn a lot of math on weekends with no research pressure or smth

latent edge
#

industry job
work life balance

#

hmmmmmmmmmmmmmmmmmmmmmmmmmm

#

it's probably possible with some shenanigans

solid snow
#

That’s a perfectly reasonable expectation

#

I’m confused

timid bronze
#

Who did good in diff equations

solid snow
#

me :3

timid bronze
#

Me scared of them in linear algebra

#

U tutor me

velvet dagger
#

I mean... Arguably any job is tricky to have work life balance for. Industry might be slightly better in some ways because for many types of jobs you can just kinda clock out and that's it

visual breach
solid snow
#

I cannot

dapper badge
#

maybe if I can use Von Neumann algebras to prove certain cohomology groups vanish or stabilize

solid snow
#

I am too busy

velvet dagger
solid snow
#

I can at most answer one off questions or concerns in the relevant topic channel from time to time

dapper badge
#

well I am wondering if I can do that. Idk anything about Von Neumann algebras

latent edge
visual breach
velvet dagger
#

My superpower in math is guessing tbh

visual breach
#

Maybe each of these are complicated concepts which somehow is gathering interests.

velvet dagger
#

Suremark was right about GPT brain

latent edge
#

a regular ODE class is just some tricks getting thrown at u

#

hard to appreciate DEs at an undergrad level idk

velvet dagger
#

Yeah that's the vibe I get tbh

solid snow
#

This recent class I took we got justifications for the tricks and some cool theory thrown in :3

timid bronze
velvet dagger
#

I only had a couple weeks of ODEs in my analysis class

jagged forge
solid snow
#

But not quite yet full fledged proofy ODE

timid bronze
latent edge
jagged forge
#

i showed up right on cue

latent edge
#

tbh I still get amazed when I learn new stuff about DEs

visual breach
#

Isn't ODE just like, Pattern match using the tricks given to you

velvet dagger
#

Like the whole oh particular and general solutions is just first isomorphism theorem

latent edge
visual breach
#

Yeah, never got further than first ODE class

jagged forge
visual breach
#

Idk I dont like Analysis

ocean robin
#

SAME

timid bronze
#

Dami r u gonna give up calc 3 tutoring position to someone else so i dont botber u too much with it

latent edge
#

I still get exposed to DEs in number theory. The ideas make my mind go crazy

junior veldt
#

Isn’t everything pattern matching to some extent

timid bronze
#

Maybe suremark