serious-discussion

[ember fog]

i also have to memorize identities of hyperbolic functions? but im not on that lesson yet (i am behind)

[flat harbor]

that

just sounds like calc

[ember fog]

yes i think we are doing calc 😭

but our subject is called elementary analysis

and so is the module that my uni made

[flat harbor]

oh

i mean it doesnt change the message

its just that with calc theres a lot of ppl who do it, and competition can get rough depending on where u are

[ember fog]

I'm constantly being told this is the easiest math subject ill be having

[flat harbor]

ppl tend to overemphasise the "difficulty of math" on the "math spectrum"

ure smart if u do well in subjects that punches above whats allocated to ur year in ur syllabus etc

thats a good way to get burnt out if u do bad and treat books uve read like a trophy even if u do good imo

what matters in the long run imo is if ure doing smth challenging for u and manage to overcome it, dont worry abt what comes next

[ember fog]

okay, I'll take that advice

[flat harbor]

awesomesauce

[ember fog]

I'm looking back at some problems and I'm also struggling to remember what I have to to in order to solve them? like onesided limits, limits with infinity, and continuity. Do I just need more practice?

[rocky shuttle]

It may be good to not see them as separate methods, but to try to reduce them to some basic principle in order to remember them. But no matter what you do, there is a certain amount of things that you have to memorize. There is no getting around it. So, do you need more practice? Always.

[bright hill]

Ok, this unhealthy lel

You'll not go very far with that mindset

You're prolly imposing absurd and even arbitrary expectations from yourself

You should prolly reevaluate whether you're studying as a mere masturbatory activity to stroke your ego or for something more healthy

I say "prolly" coz I'm merely extrapolating from passed experience

I'm not trained professionally to give such advice

Consider seeing a psychologist

[delicate mulch]

Bruh

A pyschologist

?

[bright hill]

Yeah

Don't tell me mental health professionals are stigmatized where you live

[neat frost]

Where do you want me to stick my ties?

Good morning DarQ!

[bright hill]

Good morning slurp!

I'm steaming something today btw

[delicate mulch]

They are

[brittle socket]

Streaming math?

[delicate mulch]

They will probably think I'm mad or something

Or they won't believe me and say that I don't know what I am saying

[bright hill]

Yeah prolly

[brittle socket]

Nice

[bright hill]

Not really, i don't think

That's what society might lead you to believe

But psychologists are trained to address a verity of mental problems

[delicate mulch]

Na na for real, you don't know Nigeria

Believe me, that's what they will say

[bright hill]

You can straight up just going through a bad time like a break up or a death of a relative and a psychologist can help you deal with that and walk you through the mourning process

[delicate mulch]

Remind me why I need one again

[bright hill]

Yeah, that's what I thought about my country too until I sought a psychologist

Maybe Nigeria is worse, I'm not sure

But seeing a psychologist is the best advice I can give

This is obviously causing you a lot of distress and anxiety having mentioned you cry every day

If that's not psychologist-worthy i don't know what is

[brittle socket]

Whether you need one or not, only you can decide yourself. But I guess just know that it isn't shameful or anything to look for one.

[neat frost]

Oh nice I don’t have too much time today though

[brittle socket]

Hi Slurpy

[neat frost]

Hola grass

[bright hill]

Oh

Welp, I'll just ping you and see if you're available

I'm open for time suggestions if you have one

[neat frost]

Hmm

Chemistry

[bright hill]

Chemistry is not a time

I'm also not streaming chemistry lol, that was a joke

[tender tulip]

I just came across some bullshit

Assume f(x) is a real polynomial such that f(x) > 0 for all x

let q(x) be a quadratic with strictly negative discriminant; aka q(x) > 0 for all x

by euclidean division

f(x) = q(x)p(x) + r(x). deg(r) < deg(q), i.e r is either linear or constant

[arctic grove]

did someone say chemistry

im gonna ask you to stop saying that

[tender tulip]

nvm I answered my own q.

[bright hill]

Good morning shyshy!

[arctic grove]

Good morning darq!

[bright hill]

...

Bitch.

[brittle socket]

Hi Shyshu

[arctic grove]

oh shit i wrote slurp by accident

im so sorry

[bright hill]

Lmfaoo

Tis ok

[arctic grove]

[bright hill]

I wanna stream today btw

Wanna tag along?

[neat frost]

Chemistry? What’s wrong with chemistry? Is chemistry not a word that you like?

[arctic grove]

depends on the time when u will be streaming

i am pretty busy today

[arctic grove]

yes

it causes me physical pain

[brittle socket]

Relatable

[brittle socket]

Bombed my Chemistry paper 2 yesterday

[arctic grove]

oof

[burnt dune]

grad school

[deep mango]

Wow

[deep mango]

He's already using emote screenshots after losing nitro. Wow

[arctic grove]

what

whats wrong with that!

also whats surprising in that

smh

[deep mango]

😐

[arctic grove]

What

ryc answer me clearly

[deep mango]

r u sure you want a clear answer?

[arctic grove]

yes

i want one

and look at u

[deep mango]

😐

[arctic grove]

using "u" after insulting me for using it countless times

[deep mango]

I just know what connotations it holds

I know how to use it for effect

[flat harbor]

i mean ryc

[arctic grove]

"effect" sure thing pal

[flat harbor]

u can probably remove shushu and only shushus image posting perms right

[deep mango]

I think I'd probably have to make a new role

[flat harbor]

hmm

[arctic grove]

what the fuck is this

[flat harbor]

bureaucracy

horrid

[arctic grove]

This isnt fair!

ryc dont u fucking dare!

[deep mango]

I don't think muted users can post pictures

[flat harbor]

i just said life isnt fair in a grumpy middle aged man voice

ur opinion invalid

[delicate mulch]

Alright

I will look for a psychologist

[arctic grove]

wtf

[arctic grove]

wow

you both suck

i hate you two!

[deep mango]

I don't suck. I'm great!

Anyway

[arctic grove]

no you suck, you are horrible

just absolutely disgusting

😭

[deep mango]

What's wrong with our emotes

[arctic grove]

nothing!

i just wanna use some other ones as well

that i have grown to using too much

in the past what

5 and a half months

[deep mango]

5 and a half months (unearned)

[arctic grove]

i cant let go of my muscle memory that easily

what do you mean unearned!

how was it unearned

[deep mango]

soon to be 6 and a half months (unearned)

Poor vlad

[arctic grove]

what the hell ryc

[deep mango]

Good thing we have blobcry here

[arctic grove]

oh we have blobcry here

thats good

how is it unearned!

[deep mango]

oh no i just looked at my arm

i have a big big welt

from the shot i got yesterday

[arctic grove]

whats a welt

oof

[deep mango]

it's just a big red spot

weird

[arctic grove]

i luckily dont have one rn

even thought i went for a blood test

[deep mango]

hopefully that goes away soon, that's not good if it sticks around

[arctic grove]

it was red for a while but its fine now

[deep mango]

i see

[arctic grove]

it probably will

it if doesnt then...

what

[deep mango]

what are you wishing on me huh?

[arctic grove]

im not wishing anything!

im praying it doesnt go bad

fuck you ryc

[deep mango]

[arctic grove]

you are too rude to me

[deep mango]

I'm sorry!

I'm just suspicious

[arctic grove]

why are you suspicious of me!

what have i done to get that treatment

thats not a good reply ryc

smh

[bright hill]

Whenever

It's the weekend

So I'm open for time suggestions

[bright hill]

Good luck

[arctic grove]

sadly i have classes tomorrow

[rocky shuttle]

classes on weekends

[delicate mulch]

@bright hill I've been so stressed by school that I stopped studying precalc( before calc1) now I have to review somethings from functions that I forgot

[arctic grove]

😭

i have them basically every week

its sadge

[lament flicker]

does anyone here know haskell?

how can I start?

like

what do you use to code in haskell?

is there an IDE for it? something like pycharm but for haskell?

yeah uh this is something I want to avoid, I really like IDEs for underlining errors and auto-completion

darn

how about some other pure functional languages?

ah rip

still thanks for the info

that's one I'm considering

but I heard that it's not as pure as haskell, that you can avoid using functional methods, while I want to focus on those functional methods as much as possible

[deft inlet]

can existence of transitive closure of a set be shown without using replacement axiom?

[bright hill]

Please tell me you're joking

[long matrix]

whats wrong with notepad

perfect ide

[static loom]

but it lacks vim keybindings

[long matrix]

🖕

u see with vim

if u sit on your keyboard

u probably lose your work

with notepad, itll probably live

[mint canopy]

Back in the days when I did Haskell, I would use editors with nothing but syntax highlighting

I really think if you're gonna do that with any language, Haskell's the one.

Notepad++ will be fine.

[long matrix]

i used to develop in chrome console with js. anyone else

[lament flicker]

is that a notepad with code highlighting?

[mint canopy]

It is. It has some other features

[lament flicker]

I see

[static loom]

download VSCode and in the editor you download the extensions for it

[lament flicker]

I tried, failed, so now I'm installing GHCup -> VSCode -> Haskell extensions

[burnt dune]

anyone can help?

[woven whale]

apply for what

[burnt dune]

grad school

[chilly hull]

#graduate-applications

[neat lintel]

TW: grad school.

[neat lintel]

sideline of a square is a line therefore its not a segment right?

like sideline of a square is a line and not a saying for side which is a segment

[carmine creek]

YOOO u got active role

[chrome anchor]

I have a quizz monday

about Average rate of change and absolute extrema

[neon glade]

Hey. I am looking for some good problem solving content and interested in reasoning and logic. Can anyone recommend some good content to me (books, videos, youtube channels)?

Am interested in critical thinking, emotional reasoning, logical reasoning, abstract logic.

[woven whale]

yes but you're a bit late to the party hehe

I got it like a week ago

[unreal raptor]

Hii everyone

I needs someone help in course selection

anyone please?

[surreal sapphire]

course selection?

[unreal raptor]

yes
Semester subjects selection

[rocky shuttle]

You need the axiom of choice for that

[unreal raptor]

Hmmm 🥲

[surreal sapphire]

why not just ask your question

[alpine kindle]

@mint canopy I found ||the crown|| 0_0
also ||vlad died in one jump|| so i got the cool cape

sadly died to ||olmec||

[mint canopy]

You are kinda cracked at this game

Looking forward to seeing you figure out what that does

[alpine kindle]

i assume ||it works like the ankh in HD and you have to die in a specific area||

[alpine kindle]

i only figured out ||you needed the eye at the drill|| when i ||bombed a different-looking block and noticed an unbreakable floor like there was a door there, and then saw the symbol||

[deep mango]

Wtf

Ally is way better at spelunky 2 than i was at spelunky 1

[alpine kindle]

spelunky 2 spoilers

[deep mango]

And spelunky 2 is harder

[alpine kindle]

it is?

[deep mango]

From what ive heard

[alpine kindle]

i never played the first game

[deep mango]

I havent played spelunky 2 just watched a lot of videos

[alpine kindle]

i mean you really just need to notice the patterns

all the ai is predictable

(some more than others)

[neon narwhal]

Hello!

[alpine kindle]

hi

[deep mango]

Yes I am pretty bad at games mostly

I'm only good at celeste from having hundreds of hours in it

I knew the truth long ago

I stand tall in the knowledge that I will never be an esports sweat or a speedrunning piss bottler

Yes, I think I would take a long time to learn the souls games

Insecure, or apathetic?

My careless response reflects the number of shits I give

[alpine kindle]

oh also I've played a fair bit of hollow knight which probably has helped

[deep mango]

That's cool

I also suck at hollow knight

But I want to get better at that

[bright hill]

Good morning ryc

[deep mango]

Ha, the effortless orator spends not a moment composing his thoughts

They spill out in perfect coordination like water cascading down the contours of a cliff

[alpine kindle]

hollow knight is the most broken game in existence lmao

by broken i mean glitchy as all hell

[deep mango]

I want to do a loose hose your mom joke

But I'm a moderator in this server so I won't

[alpine kindle]

eg framerate affects the speed of flying enemies

[deep mango]

Something something hose is loose once your mom is done with it

[alpine kindle]

oh you can also teleport entire rooms into other rooms

[deep mango]

What

[alpine kindle]

and you can use sth called "main menu storage" to bring all your items from one save into another

it's so broken that the "glitchless" speedrun category is actually called "no major glitches"

because a lot of the basic speed tech is arguably glitched

no it's a great game

it being broken is a bonus

the glitches improve it

well

"glitches"

some you can argue over

[bright hill]

Literally "it's not a big, it's a feature"

[alpine kindle]

idt room teleportation is a feature

[bright hill]

Ok, fuck you

I'm lazy

I use swipe type ok?

I wonder if I'm still good at games

I used to play a lot when I was younger

But for the last couple o' years the game with the highest frame rate that I've played has been like

Chess

I will though

Lol

I wanna stream my first play through stuff that came years ago

Like GTA 5 or smth

I think it's gonna be fun

[alpine kindle]

you should place spelunky 2 at the top of your play list

go in as blind as possible

[bright hill]

Yeah lel

[alpine kindle]

why sully yohan

[bright hill]

14 year old me have seen the ending tho

[alpine kindle]

of hollow knight?

[bright hill]

I don't remember it now but I think I will once I start playing

[bright hill]

GTA 5

[alpine kindle]

you are wrong in that thought

they are both excellent games

i wouldn't say one is better than the other

have you even played spelunky 2

[bright hill]

Lol

[alpine kindle]

then how are you judging it against hollow knight

oh

[bright hill]

Owned.

[deep mango]

GTAV

Who were the gtav people

Trevor was a nutbag

Franklin was sort of normal right

I forget what the other guys deal was

I think he was rich

[bright hill]

Yeah, I think

[deep mango]

Anyway

That makes sense

[bright hill]

I vaguely remember a mission where his daughter was riding a jet ski or smth

[deep mango]

The only part of gtav that i like is franklin because i actually understand wtf he is doing

I don't know anything about the other GTAs

Lol

Yeah

That is what i remember

Who was the gamer manchild guy

I remember that

Wasnt that a tennis instructor

That checks out

[bright hill]

Lol

[deep mango]

I bet it was a tennis instructor dummy

[bright hill]

I shouldn't be reading all these spoilers lmao

Later nerds

[deep mango]

Ratchet

Imagine being unspoiled on fucking gtav

Anyway none of this is substantive so dont worry about it

What

Goodbye

[bright hill]

I'm sure I am, i just don't remember lel

Oh, btw ryc

Are we gonna have obsidian vc back?

[deep mango]

Who knows~ only time will tell~

[bright hill]

Running at night while steaming music is such a vibe dude

I did that yesterday

Bliss.

[deep mango]

Steaming

Don't listen to that cringe ass song

[bright hill]

I listened to the entire discography of 美波

I need more j pop

[deep mango]

Only the strong-stomached can stomach the cringe

[bright hill]

@devout nacelle got suggestions?

[deep mango]

I reinterpreted it for you

Now it's less wrong

Superman does wrong. I did incorrectly.

[bright hill]

Btw I fell and scraped my knee literally the first lap

And it's still pink since yesterday

[deep mango]

So heroic, so brave

[bright hill]

But the vibe was just too strong

[deep mango]

Bury the light will carry you through the sore knee

[bright hill]

Lol

[deep mango]

You find similar comments under many linkin park and green day songs

If evanescence werent a meme

I bet the comments under their videos would all be that too

[bright hill]

I can hardly follow both of you btw lmao

Tf is evanscence

True

[deep mango]

CANT WAKE UP wake me up inside

[bright hill]

Also it's Linkin Park

[deep mango]

https://youtu.be/wXcdYBh3hgg

[bright hill]

[deep mango]

Linkin park lol

[bright hill]

Oh, it's a 2015 meme

[deep mango]

When i looked up wake me up inside it forced some bo burnham down my throat in the search results

Gross

[bright hill]

Yohan, the first time I entered the internet was 2014

[deep mango]

Darq has never watched an old YouTube tutorial

[bright hill]

It took me a few years to know what a "meme" is

[deep mango]

With no voice and the instructions typed in notepad with 24 point font

[bright hill]

That's literally one of the first things i did

[deep mango]

Then you narrowly avoided Evanescence

You probably heard Hey There Delilah

[bright hill]

Cracking windows 7 was such an adrenaline rush

[deep mango]

Or something like that

[bright hill]

Yep lol

The email I created back then is still my main lmfaooo

[deep mango]

I don't even know what that means

[bright hill]

[deep mango]

Crimes are meant to go unabated

[neat lintel]

do adults know about andrew tate

[zealous garden]

I am an adult

So yes

[neat lintel]

wait

really?

[frigid lark]

I heard his name quite often but idk him.

[neat lintel]

ok

[zealous garden]

I'm nearly 24

[neat lintel]

i mean like 40+ people

[zealous garden]

You said adults

Did you mean Gen X? Millenials?

[neat lintel]

gen x

[fair mural]

boomer

[zealous garden]

Whatever you say

[fair mural]

[alpine kindle]

24 is literally gen z

[zealous garden]

Correct I am barely Gen Z

[bright hill]

If you say you miss Skype I'm gonna slap you.

Gud

Acceptable

[woven whale]

I'm also gen z and I feel ashamed

[bright hill]

"...for unrelated reasons"

...?

[woven whale]

wut

[bright hill]

Stick that at the end of your sentence

Close the quotation marks and add question mark

[woven whale]

why would I want to be gen z in the first place

[bright hill]

Why wouldn't you wanna be?

Being ashamed is not the default here lmao

[zealous garden]

idk gen z kinda trash

I hope the alphapods are better

[bright hill]

Is that the new generation?

[zealous garden]

no

it goes from Z to Alpha

lmfaoo

[bright hill]

Finally

[alpine kindle]

can't wait for generation sigma

[bright hill]

We'll have a first look at alpha/beta females

(this joke was not funny enough to warrant the risk of being cancelled but w/e trololol)

[zealous garden]

one day at a time

also ideally talk to someone else you're close to

if you don't have one, try to make that connection

[green field]

if there was one thing you could change about the world, what would it be?

[flint thunder]

Change the physical environment so that people can live in walkable mixed-use communities that have low carbon emissions and encourage healthy lifestyle (more walking, more interaction with people who live around them, etc.).

[bright hill]

@open aspen no idea lel

But I like the emote

I think it's great

[fluid rapids]

ylyl

[rugged trench]

Hey guys, I'm in first year of master of Maths. And I was wondering (it concerns researchers and students) how do you organize your time : do you make a schedule every week with precise things you have to achieve or do you just make the things you must do when you have some time without scheduling it?

I will ask it in the discussion "maths pedagogy"

[rugged trench]

Oh no actually I can't

[rocky shuttle]

#get-advanced-access

[bright hill]

I think this question fits better in #advanced-lounge

[versed geode]

<@&268886789983436800>

I got removed from the physics server

For violating the rules

(Asking multiple doubts and pinging)

Can u add me to the server again?

I won't repeat my mistake

[bright hill]

Wtf, physics mods got no chill lmfaoo

Based

You should prolly take it with them tho

The mods here are hardly involved with the Physics server

[versed geode]

I need the server cuz I'm preparing for the exam viteee

Please consider my request gandl/g&l

Like my phone numbers blocked

[versed geode]

Oh okay wabbout gandl

Is he there in this server

[bright hill]

Gandl?

[versed geode]

Yea

[bright hill]

Oh, I've never heard of him

[versed geode]

I thought he owns all the servers

[bright hill]

So prolly not

[versed geode]

The science servers

[bright hill]

No lol

The owner here is mniip

I'm sure the physics server got a modmail or smth

You can contact the mods through that

[deep mango]

we're not directly affiliated with the physics server so unless you find someone who is also a mod there we're not in charge of that

[mental whale]

you can dm me darq

also yohan is this going to be a new thing now smh my head

im incapable of detecting sarcasm anymore but ig it's fine to ping me for these things

[bright hill]

Why? Lol

[mental whale]

sorry, meant ph118

[bright hill]

Are you one of the physics mods or smth?

[mental whale]

yeah

[bright hill]

Cool

[lean hemlock]

hi

hi

can anyone

tell

me

the

square root

of

124354657646563474637463746437463746374637463746374637463746656564754545655464

i bet no one can answer this

[zealous garden]

google can

[rocky shuttle]

,w sqrt(124354657646563474637463746437463746374637463746374637463746656564754545655464)

[fathom swallow]

Results provided by WolframAlpha

Click here to refine your query online
Upgrade to WolframAlpha Pro!

Requested by Zanarcane#6798

[dense musk]

Hey anyone good with big O notation here?

[river moon]

just ask

[rocky shuttle]

[dense musk]

I got these 2 algorithms and I wanna know how to get the O time complexity for this

I figured it’s some weird recursions in them

The ones from before basically was just look at the loop conditions and see if they’re nested etc etc but these are different i guess?

It’s abt the number of calls of the function f btw

[tender tulip]

24 is a whackass number:

$4! = 24 \$
$\nexists m : m|n \vee m | 24 \Rightarrow 24 | (n^2 - 1) \$
$\sum_{i = 1}^{24}{n^2} = 70^2$

[fathom swallow]

Mizalign

[dense musk]

What I figured out for the First algorithm was that its like n + 3/2 n + 9/4 n + 27/8 n and so on

So wouldn’t that still be O(n)?

[zealous garden]

what

[tender tulip]

it's a weird number

I wonder if the two bottom facts are related

[zealous garden]

I can't even interpret the middle one

[bronze narwhal]

what significance does the series of some arbitrary sum have?

the middle one is super weird too

I guess I can agree with 24 showing up a lot in combinatorics though but only by virtue of 4 being a common number

[tender tulip]

If n is coprime to 24 then 24 divides n^2 - 1

[zealous garden]

you mean \implies is the lowest priority operator here?

also you used $\lor$ instead of $\land$

[fathom swallow]

wraithlord_kotopology

[zealous garden]

so that's not what that says

[storm sage]

Lol

[storm sage]

Time to do the old timey awful notation where you write a dot, two dots, etc above the operation to show how tightly binding it is

[tender tulip]

whoops, thanks

[brave wraith]

hmmm

ima try something

.close

.reopen

ok nope

doesnt work

[storm sage]

Lol

[tender tulip]

$cong$

[fathom swallow]

Mizalign

[tender tulip]

$\cong$

moment

Is $xy \equiv 1 \mod{24} \Leftrightarrow x \equiv y \mod{24}$
related to $\sqrt{\sum_{n = 0}^{24}{n^2}} = 70$

[fathom swallow]

Mizalign

[tender tulip]

Actually there's sorta like 3 major identities tying 24 to taking "something" to the power of 2

$\text{gcf}(n,24) = 1 \Rightarrow n^2 \equiv 1 \mod{24} \$
$\sum_{n = 1}^{24}{n^2} = 70^2 \$
$\sum_{n = 1}^{\infty}{\frac{1}{n^2}} = \frac{(2 \pi)^2}{24}$

[fathom swallow]

Mizalign

[tender tulip]

Are these all connected somehow?

[vivid halo]

no

I don't think I've ever seen anyone write Euler's identity like this lmfaoo

[atomic haven]

if you travel along a path on a doughnut

will you always end up back at the same point

[vivid halo]

no

e.g. take a line of irrational slope

[atomic haven]

then you oscillate around the doughnut

but because its a wave

you end up back at the same spot

[vivid halo]

[atomic haven]

like you take slanted circles around the doughnut

[alpine kindle]

ryc did a talk on this

[alpine kindle]

if their phase doesn't align properly with the doughnut it'll never return to the start

[atomic haven]

fr?

[alpine kindle]

yes

[atomic haven]

how do you align your phase with the doughnut

by it's size?

[alpine kindle]

well

[atomic haven]

thickness is amplitude

[alpine kindle]

think of it like this

if you have a rectangle

[vivid halo]

if you're representing your torus as R^2/Z^2 (so the unit square with sides identified) then it corresponds to whether the slope is irrational or not

if the fundamental domain of your torus is more general you're basically asking whether the slope is a rational linear combination of the periods of your torus

in the case of irrational slope you get a space filling curve, the orbit is dense

in the case of rational slope you get periodic orbits

[atomic haven]

okay so im not too familiar with the geometry tbh

but lets assume for a second the cross section is a circle

in that case isn't the slope fixed

[alpine kindle]

cross section of what?

[atomic haven]

the doughnut

[alpine kindle]

ok so

[atomic haven]

or one side of the doughnut

[alpine kindle]

let's say your path passes through a point on that circle cross-section

[vivid halo]

right so if you're slicing the torus in the way I think you're referring to, that's not going to be a linear flow, the slope is going to vary along the cross section

[alpine kindle]

look at the small bit of path just before and after

[vivid halo]

like, the usual embedding of the torus into 3-space is very nonlinear, if you cut this with a plane the resulting cross section is also going to be very nonlinear on the original torus

[atomic haven]

if i iine integ over the entire path will i get the surface area of the doughnut?

if the case is that it never meets its original point like u said

[atomic haven]

oh because its a circle

i see

[alpine kindle]

no because

1. integrating over a line gives length not area
2. there's no function to integrate

[teal lion]

?

[alpine kindle]

ok well

nvm

[atomic haven]

alright but then the length of the path

[alpine kindle]

yeah it's infinite

[teal lion]

Define “integrating over a line”

[alpine kindle]

line integral

[teal lion]

ah okay

[rocky shuttle]

integral of a 1-form

[atomic haven]

thanks

[alpine kindle]

oh you never actually explained how integrating diff forms actually works

because i had to sleep

[teal lion]

Learn linear algebra first, I’d say

finish part 3 of Lang

[alpine kindle]

i know linalg

[rocky shuttle]

oh yeah, would love to talk about that again, but maybe later, can't rn

[alpine kindle]

pretty well

[alpine kindle]

ok that's fine

[teal lion]

How familiar are you with the tensor product?

[alpine kindle]

somewhat

[teal lion]

get really familiar with that, modules, and some alg top and homological algebra I’d say

[zealous garden]

so how do you make the delineation between directed integrals (f(x(t))x'(t)) and the other kind (f(x(t))|x'(t)|) [hold on this isn't what I wanted to say]

in diff forms

[atomic haven]

u guys rly messed up solid mechanics with that btw

[teal lion]

Then exterior products become much easier to understand

[alpine kindle]

i get exterior products

[teal lion]

oh okay

[zealous garden]

wdym

[atomic haven]

it was taught as a prerequisite and gave learning solid mechanics a pretty difficult learning curve

[alpine kindle]

they're just linear subspaces of $\bigwedge V$

[fathom swallow]

Ally (ea/eam/eius)

[atomic haven]

tbh so far 7 weeks in haven't used it much

[alpine kindle]

(which is just $TV/(v²)$)

[fathom swallow]

Ally (ea/eam/eius)

[teal lion]

In that case

[alpine kindle]

?

[teal lion]

integrating over a diff form is just locally integrating over a function over a parametrized subset of R^n, and patching it together

[bright hill]

Ping me when you do please

[bright hill]

What's the difference between integrating over manifolds and integrating diff forms?

[surreal kindle]

[bronze wedge]

"integrating over manifolds" could mean you are doing measure theory

[zealous garden]

integrating differential forms says what you're integrating, but not what you're integrating it over/on

integrating over manifolds tells you what you're integrating over, but not what you're integrating

[rocky shuttle]

@alpine kindle @bright hill alright, I'm back, we could continue if you want to

[bright hill]

Oh, im about to go to sleep haha

[rocky shuttle]

Haha, okay, it's fine

gn darq

[fluid rapids]

sussy baka sussy baka

[tender tulip]

I still haven't found a good way to construct the tensor algebra without referencing the tensor product but whatever

[tender tulip]

Well 2π is more fundamental than π

[vivid halo]

[tender tulip]

I realized the connection with 24 is there if you consider 2π or tau instead of π

[vivid halo]

[tender tulip]

Probably just due to the bernoulli numbers

[vivid halo]

yeah so the even zeta values are basically just coming down to Bernoulli numbers

[tender tulip]

I wish there was a way to combinatorically "comprehend" the bernoulli numbers instead of them just being like

[vivid halo]

the thing with 1^2+...+24^2=70^2 is weird

[tender tulip]

just some recursive sequence of numbers

[vivid halo]

it doesn't have to do with Bernoulli numbers

[sacred forge]

imagine having a family of mathematicians

those fucking bernoullies

[rocky shuttle]

the thing with 10^2+11^2+12^2 = 13^2+14^2 is also weird

which additionally coincides with the number of days in a year

[vivid halo]

why is that interesting

[rocky shuttle]

it's not, it's just weird

[vivid halo]

hmmm

1^2+...+24^2=70^2 definitely gets used places

so it's both weird and important

[tender tulip]

they also were at like war

fuckin math tf2

red vs blue

[tender tulip]

The bernoulli numbers are interesting but do they hold any combinatorical meaning

[rocky shuttle]

I didn't know that, thought it was just another mathematical coincidence

[vivid halo]

the Bernoulli numbers have a lot of arithmetic significance yeah

[tender tulip]

I just thought they satisfy

[vivid halo]

so famously they come up in Faulhaber's formula, that's one big combinatorial application

[tender tulip]

$\sum_{i=0}^{n-1}{\binom{n}{i}B_i = n$ by proxy of Faulhabers

yeah

[fathom swallow]

Mizalign
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[vivid halo]

there's other deeper stuff with number theory, like primes in the numerator of Bernoulli being congruence primes for modular forms

[tender tulip]

which are antiderivatives of bernoulli polys

[tender tulip]

?

[alpine kindle]

nooo i have to go to bed now

was playing spelunky so i missed the message

some other night

[rocky shuttle]

next time then

[alpine kindle]

yeah

[vivid halo]

like this congruence between the Fourier coefficients of the Ramanujan tau function and the Fourier coefficients of the weight 12 Eisenstein series (the divisor sum function)

[rocky shuttle]

it's alright, hope you got far

[vivid halo]

the 691 is the numerator of the 12th Bernoulli number

you get congruences like this if and only if you have (big) primes dividing the numerator of Bernoulli

[tender tulip]

[alpine kindle]

still grinding

[tender tulip]

is that whole 1 + 2^2 + 3^2 ... + 24^2 = 70^2 related to
xy congruent to 1 mod 24 means x congruent to y mod 24

[vivid halo]

no I don't think so

[tender tulip]

Both are related to modular forms apparently

[vivid halo]

yeah so 1^2+...+24^2=70^2 comes up in the construction of the Leech lattice

[tender tulip]

But like, the whole 1 + 2^2 + 3^2 ... + 24^2 = 70^2 seems like a particularly nice choice such that the 25D lorentzian norm on Z^n union (Z+1/2)^n is 0

Like, there probably is OTHERS

[vivid halo]

from the Leech lattice you can construct a theta function which is a modular form

so that's one relation

[tender tulip]

for n = 10 there's (1,1,1,1,1,1,1,1,1,3) afaik

which also has 0 norm

[vivid halo]

right yeah so this is a good question, why sums of consecutive numbers like this

like there are a LOT of other sums/differences of squares in lattices of different signatures that are sort of interesting

[tender tulip]

that whole "even unimodular lattice" thing sorta makes sense for quadratic forms

but the connection to the number 24 seems oddly coincidental

but it could be "just coincidence"

24 evenunimodular lattices in 24D, that fucking vector being consecutive

AFAIK any even unimodular quadratic form has a signature divisible by 8 or smth

[vivid halo]

I mean there are a lot of coincidences in general with small/highly divisible numbers like this

some of these coincidences are more direct than others

some of the "coincidences" you really have to reach to claim there's much of a connection

[tender tulip]

https://math.stackexchange.com/questions/1754111/which-role-does-the-frac124-in-the-dedekind-eta-function-play pretty phenomenal answer

[vivid halo]

yeah there's a lot of nice stuff like this around modular forms/elliptic functions

[tender tulip]

The existence of the leech lattice alone is weird but it doesn't feel any more intimately tied to quadratic forms than any of the other neimer lattices

[kindred ore]

y’all just be knowing shit

that’s crazy

[swift kite]

He said theta function and I noped the hell out lol I know it’s all English but sometimes I wonder if it’s not 😂

[neat lintel]

nuker
if nuker was 5ft, how much explosion would it cause

[neat lintel]

im still in jh and i understand

[neat lintel]

ok 🧍‍♂️

[neat lintel]

ok 🧍‍♀️

[bright hill]

[rocky shuttle]

morning darq

[bright hill]

Morning zane

I'm pretty much free today btw

[neat lintel]

this book from my brother has the most bugged out contour integral lmao

the circle is out of the integral font lmao

unless it's something else

[rocky shuttle]

Oh nice, tomorrow is holiday for me, so I have time this evening

[bright hill]

@alpine kindle you free?

[rocky shuttle]

You can take a look at Spivak's Calculus on Manifolds beforehand if you're free today anyway

[ripe wasp]

spivak

[rocky shuttle]

Any issues with that?

[bright hill]

Hahaha

[neat lintel]

Spivak

[bright hill]

It's hard lel

[ripe wasp]

dw im also a masochist so no problem

[bright hill]

HAHAHA

[ripe wasp]

darq where r u looking to go after spivak?

[neat lintel]

the graveyard

[bright hill]

Will that be your main reference?

[ripe wasp]

💀

[bright hill]

Also, I'm still at chapter 2 btw so is there anything I should know beforehand?

[rocky shuttle]

I didn't start with diffgeo using Spivak, but for integration of differential forms on manifolds, that's the most concise one.

[neat lintel]

I'm already taking some sort of mixed Calc I and II in my last HS year and I honestly don't ever want to do any further level math

[bright hill]

It is?

I should stop picking up books that're super terse lmao

[flat harbor]

takes calc1
skips mvc
skips spivak
introduction to smooth manifolds, John M. Lee

[ripe wasp]

theres do carmo's book on differential forms that's like 100 pages

i havent read it, but it looks pretty cool

[flat harbor]

i feel like whether a book is terse or not depends less on the content

and more its presentation

for example if its formatting is horrendous and makes me want to cry

(like spivaks com)

[ripe wasp]

yeah i also hate spivak com formatting

[light needle]

this is the correct path.

[flat harbor]

if u want a concise introduction to calculation on manifolds i recommend sean carrolls spacetime and geometry 👍

[light needle]

i recommend lee.

[flat harbor]

ull do all the funky convergence in analysis classes anyways....

if ure geoming might as well as make it fun

[light needle]

idk what ur talking about lol

[flat harbor]

why does everyone say that to me

[light needle]

anyhow a curves and surfaces class is super boring

doing it like lee is much better

[rocky shuttle]

For differential geometry on the whole, I would recommend Lee too. If it's only about integration on manifolds, Spivak gets directly to the point.

[rocky shuttle]

You once discouraged me from using Lee though saying that your lecturer's notes are better

[light needle]

well yes

the lecture notes are better lol

but they r based on lee.

[rocky shuttle]

Yeah, they were very helpful, thanks again for that

[light needle]

mhm

[surreal kindle]

Sweden ig?

[rocky shuttle]

No, Germany, depending on the state, we have holiday either today or tomorrow

[surreal kindle]

ahaaa

[bright hill]

At the beach, nerds.

@neat frost

[neat frost]

Where are all the people?

[bright hill]

They're here

I just thought it'd be rude to take a photo of them

[neat frost]

Ah

Fun

Why beach no school

[bright hill]

Dunno

[flat harbor]

maverick

dont respect da rules

respect da ocean

[bright hill]

The students' body just decided to take a week vacation

So they did lmfao

[flat harbor]

oh

humbug

[bright hill]

Have you eaten yet, Blo?

[flat harbor]

nah

i think ill have a few cheese crackers

oh yeah

these cheese crackers r poppin

[neat lintel]

reversed þ integral

[deep mango]

Wow, pretty

I love the beach

Do you swim in the ocean

[bright hill]

I woulda swam if my knee wasn't injured lol

[eager reef]

How did you injure your knee

[bright hill]

Got you guys a shout-out

[eager reef]

FOR FREE

[bright hill]

I was running with flipflop hahahaha

[eager reef]

HE GOT THEM DAWGS OUT

[deep mango]

What sort of injury

[bright hill]

Just a sorta deep scratch

[deep mango]

Ha!

I knew it

[bright hill]

Nothing serious

[deep mango]

DarQ can't take the saltwater on a scratch

[bright hill]

My bandages are drenched with sea water actually lmao

Also, i cleaned it with alcohol which is much worse

[brittle socket]

Hi Chalk

[fair mural]

[deep mango]

Weak!

Google is so weak

[frigid lark]

I fear the ocean but manage to always swim all the way to the buoy.

[deep mango]

Yea but you didnt do that for fun

[fair mural]

hey ryc you should uh swim in hand sanitizer with an open cut

[fair mural]

hi toge

[deep mango]

Hand sanitizer is so gooey that would be gross

[brittle socket]

Like pigeons?

[frigid lark]

Hi quantum. How are u

[fair mural]

good

i just woke up a bit ago

[deep mango]

Pigeons aren't gooey

what

[fair mural]

how are you

[frigid lark]

You were in college or uni?

I am fine rn. I passed my last exam. Now I only have my thesis and internship left.

[brittle socket]

Gross like pigeons? Why would i say pigeons are gooey

[bright hill]

It was actually surgery alcohol

[fair mural]

[brittle socket]

What's the difference

[frigid lark]

But my thesis will not be easy 😂i choosed to torture myself.

[bright hill]

Don't ask why I have that

[frigid lark]

I have to proof a protocol about bit commitments is secure. The prof said he "thinks" it is. I am doing the thesis with a prof from a different uni.

[neat frost]

Lol fucking snowflakes

Blah blah blah parasites who gives a fuck

[deep mango]

Yeah

Lol

Come on if it's like a little cut

nothing can get in there

[neat frost]

Yeah

Like

Too small

And if it is small enough to get in there, it’s too small to do any damage

[deep mango]

Yes

[neat frost]

“Oh I’m a gen-Z and I’m a little pussy” for shame

You millennials are at fault as well btw

[deep mango]

"my wittle fwiends, pwease weaken ur immune systems so that our superviwus can wipe u out :3 ~"

yeah right google

[fair mural]

ok but you’re gen z

[deep mango]

are you kidding

ok yes it's their fault

[neat frost]

Stfu quantum or I will drink your eyeballs like miso soup

[deep mango]

it's not mine i'll eat shit i drop in the dirt

[fair mural]

i will treasure this message

[brittle socket]

[bright hill]

Kaguya pfp

Cringe.

[fair mural]

[deep mango]

Not even the best kaguya

[fair mural]

who is the best kaguya

yamin

hi

[deep mango]

Kaguya Houraisan from touhou

[fair mural]

ok weeb

[brittle socket]

[fair mural]

ok sure she is cute

[flat harbor]

kaguya ranks
3. princess kaguya
2. touhou kaguya

1. kaguya kaguya

[fair mural]

but that is not really much of an accomplishment for an anime girl of all things

[flat harbor]

TRUE!

[bronze pelican]

Kaguya pfp

Based

[fair mural]

uwu yamin

[flat harbor]

kaguya pfps can do nothing wrong

[bronze pelican]

Don't you think an anime girl needs to take care of her appearance?

Its hard work

[deep mango]

Kaguya Houraisan is notoriously a shut-in NEET

who does nothing

[bright hill]

@neat frost wanna see me shirtless?

[bronze pelican]

Kaguya horse-raisin

[neat frost]

Wait

Don’t delete your goddamn messages

[bright hill]

I was gonna resend them, i just wanted to garner ryc sullies

Hahaha

[eager reef]

he already showed them dogs

[flat harbor]

haha slurp missed out

[neat frost]

I’m in a lecture rn

Don’t make fun of me

[sacred forge]

i dont thing we have frozen nuggies in belgium

[neat frost]

I can’t look sad in front of all these people

[deep mango]

I figured this was the case

[deep mango]

WHY do you call TOES DOGS

[eager reef]

https://www.urbandictionary.com/define.php?term=put the dogs away

[deep mango]

[bright hill]

OH

[neat frost]

@deep mango did you see what happened on big brother?????

[deep mango]

[neat frost]

Hi rycie

Good morning

Got your attention

[bright hill]

Lmfao

[deep mango]

Good morning

This morning is better

It's stressful but better

[sacred forge]

,w open wolfram

[fathom swallow]

Results provided by WolframAlpha

Click here to refine your query online
Upgrade to WolframAlpha Pro!

Requested by Lasha#1055

[sacred forge]

,w sudo pacman -S kolourpaint

[fathom swallow]

Wolfram Alpha doesn't understand your query!
Perhaps try rephrasing your question?
Click here to refine your query online

Requested by Lasha#1055

[woven whale]

@sacred forge #bots

[neat lintel]

hello i have a few questions about the SAT

is it multiple choice?

is it the same in every country?

and i khan academy a good place to practice for the SAT?

Yes it is multiple choice.

is khan academy a good place for practice?

I don't know.

I don't really do any practice for those things. They're just elementary math.

i just want to get a general feel for the test

im really nervous

you can download SAT samples online

where

google

okay do i google SAT samples?

pdfs?

[balmy zodiac]

there's the Khan academy official SAT practice

[neat lintel]

thank you

im just really nervous

not scared

i just want to get it done

its like a kid poking you with a knife, and the only way you can stop him is by doing the SAT

[glossy birch]

Yo can someone help me with this common app stuff

[hollow sundial]

#❓how-to-get-help

[glossy birch]

it says try discussion for non math questions

[umbral forge]

I got bored and was wondering if there is a trig function that has this shape cause it feels rly familiar

Well the general shape, when you zoom in it’s a ton of spikes

[long matrix]

(sin(x^2))/x

[umbral forge]

Ohhhh right thx

Yeah it’s like a weird version of that, the sum actually gets more and more “stretched” compared to (sin(x^2))/x

[lament flicker]

is currying somehow connected to homology?

[rocky shuttle]

@alpine kindle @bright hill up for some differential geometry?

[bright hill]

Sure

I can even vc if you want

[alpine kindle]

i cannot sadly

latin homework

[rocky shuttle]

oh, haha, I never vc'ed in a public discord before

[zealous garden]

Man I love spectating diff geo

[neat lintel]

what za flick is differential geometry

geometry with differential equations

[rocky shuttle]

I'm kinda shy

[neat lintel]

what happens after you graduate from your math degree

[bright hill]

It's aight lel

[rocky shuttle]

Well, you need to join, not only spectate!

[zealous garden]

[rocky shuttle]

So, ally's out, did you follow the discussion before? Is there anything specific you want to know?

Are you finished with Spivak?

Did you do all the exercises?

[eager reef]

Thats gonna be the prereq

[bright hill]

I saw ally asking for pre reqs

[eager reef]

[bright hill]

which I don't have

[eager reef]

Just listen

Im sure they’ll motivate the subject properly and you’ll get something out of it

It’s not a textbook

[zealous garden]

which Spivak

[bright hill]

On manifolds

[zealous garden]

I'm still on page 50 of spivak cat

oh

[rocky shuttle]

I think Spivak is pretty self-contained, you learn about functions in the first chapter, differentiation in the second one, and integration in the third chapter

[rocky shuttle]

Calculus on Manifolds

[zealous garden]

I haven't gotten that one yet

[rocky shuttle]

The interesting (new) stuff starts in the fourth chapter

[neat lintel]

swokowski has the best calculus book

[rocky shuttle]

But you did multivar, right?

[bright hill]

Uh

When I said I'm doing multi var I actually meant spivak on manifolds lmao

I'm still at chapter 2

What I would really like to know is why we care about the subject