serious-discussion

[vocal roost]

then it's multiplied by the derivative of the inner function

[wild lantern]

P much

For ex D(e^(2x))=2e^(2x)

[storm sage]

I mean understanding the partial derivative definition is really easy if you understand the regular derivative definition

[wild lantern]

Let f(x)=e^x and g(x)=2x

And recall D(e^x)=e^x.

[vocal roost]

Yeah I don't understand chain rule still

[storm sage]

that's okay

everything takes time

[bright locust]

You might need to put that in latex notation so that it’s easily viewable

[vocal roost]

I dont work with function in a function

wtf

[wild lantern]

Just gotta do some examples until it makes sense

[storm sage]

nesy do you know what function composition is

[vocal roost]

yes

f o g (x) for example

f(g(x))

g(x) is basically your input value and it maps to all x in the f(g(x)) function.

[storm sage]

yep

[vocal roost]

but 2x is not a composite

[storm sage]

anything can be a composition

of two functions

sometimes it helps you to view things that way in order to more easily take the derivative

for example, with e^2x, then you can take f(x) = e^x and g(x) = 2x

you already know how to take the derivative of f and g

so you can use the chain rule to take the derivative of f(g(x))

[vocal roost]

so you

can split the functions up?

into compositions

[storm sage]

yes

[vocal roost]

well i need to let this rule marianate in my brain

because im a bit doubtful that i understand it

[finite tusk]

Missing the most beautiful part

[vocal roost]

master oogway moment

"the peach can..."

[ancient flame]

...

[vocal roost]

säs

[ancient flame]

I still don't understand what that means

[storm sage]

nesy is the king of poor communication

[vocal roost]

säs is sus

[ancient flame]

so then why say it that way

[vocal roost]

its fun

[ancient flame]

...

[storm sage]

I mean

[vocal roost]

to do the slighest bit of trolling

[storm sage]

you can say it like that if you want

[ancient flame]

it's a whole different pronunciation

[storm sage]

as long as you tell other people what you mean

[vocal roost]

i've done that

countless times

[storm sage]

well

[ancient flame]

ur so weird

lmao

[vocal roost]

yes, now live with it

[storm sage]

yeah you should expect to do that since no one knows what it means

[vocal roost]

[storm sage]

xD

[bright locust]

Just say sus

[vocal roost]

no

[bright locust]

For math’s sake

[storm sage]

also wtf ä and u don't sound similar at all LOL

[vocal roost]

it doesn't

it's what I call

"slightest bit of trolling"

[bright locust]

Nonsense

[ancient flame]

how is that trolling

[vocal roost]

i mean you guys...

come on

[storm sage]

All language is nonsense

Except through interpretation

[vocal roost]

I still dont understand why 2x could be a composition.

[neat lintel]

2x is composition of 2 with x

[vocal roost]

learning anti derivatives before derivatives moment

[vocal roost]

a composite function

[ancient flame]

...

[vocal roost]

i mean

[ancient flame]

that's your fault

[neat lintel]

2*_ is a function that sends x to 2*x

x is a function from 1 to R or something

[ancient flame]

say f(t)=2t and g(x)=x, then f(g(x))=2x

[wild lantern]

You can always let f(x)=x and then if you have any other function g(x) you can write g(x)=g(f(x))

You can always come up with compositions, they just might not be interesting lol

[storm sage]

2x can be a composition in an infinite number of ways, it's just not useful if you want to take the derivative of 2x

since you can already take the derivative of 2x

[ionic star]

i think you learn anti derivative of y'=x before derivatives

[storm sage]

without expressing it as a composition

[vocal roost]

i mean... its

literally not helpful

to do that yeah

[storm sage]

yes

you are correct there

[wild lantern]

It is for derivative of e^(2x)?

Oh wait nvm

Lol

[vocal roost]

so i need to find some convinient way of using chain rule

[ancient flame]

even just x could be a composition

[storm sage]

you only use the chain rule on problems where the chain rule is useful (although you can use it on any derivative problem if you really want)

[ancient flame]

let's say f(t)=ln(t) and g(x)=e^x, then f(g(x))=x

[storm sage]

it's useful to evaluate the derivative of e^(2x) with the chain rule

[vocal roost]

f(x)=e^x
g(x) = 2x

f(g(x)=e^(2x)

I dont know how to take the derivatives of e^x

yet

[wild lantern]

Try cos(2x+1) with chain rule. What is a good choice of f(x) and what is a good choice of g(x)?

[ancient flame]

$\dv{x}e^x=e^x$

[fathom swallow]

gmod

[vocal roost]

f(x) = cos(x)
g(x) = 2x+1

f(g(x)) = cos(2x+1)

[wild lantern]

Yep

[storm sage]

👍

[wild lantern]

Then just use the chain rule formula basically.

[vocal roost]

so the derivative of cos(x) wrt x

was it sin(x)

[wild lantern]

Almost

[vocal roost]

-sin(x)?

[wild lantern]

Yeh

[vocal roost]

-sin(x) done

2

-sin(2)

is the answer

[wild lantern]

Nah

[vocal roost]

wat

the derivative of 2x+1 wrt x

its 2

[wild lantern]

There's more to it

[vocal roost]

oh right

the other part of the chain rule

-sin(2) * 2

?

[wild lantern]

Also the argument to -sine is wrong

It's (f(g(x))'=f'(g(x))g'(x)

[vocal roost]

is it -sin(2) * 2

tho?

[wild lantern]

For the f' part you evaluate it at the original g not the derivative of g

[vocal roost]

oh

the inner function stays intact

[wild lantern]

Yep

[vocal roost]

wtf, aight

thats interesting

-sin(2x+1) * 2

?

[wild lantern]

I kind of imagine it like I'm taking the derivative around the inner function then multiplying by the derivative of the inner function

[vocal roost]

doot

[wild lantern]

Yeh

[vocal roost]

ye

So i need to multiply that

(which i clearly dont know how to do)

lacking trig

[wild lantern]

[wild lantern]

Most ppl would just leave this as the answer.

[vocal roost]

so you'd allow it to be in this way

[wild lantern]

Unless they had a reason to write it another way

[vocal roost]

?

ok

I guess chain rule is starting to make sense

[wild lantern]

You can sit around coming up with other random compositions and using chain rule to compute them

One really common exercise is telling people to compute stuff like the derivative of a(b(c(d(x)))).

It gets kinda nasty ofc lol

[storm sage]

ehh it looks a bit ugly, I prefer -2sin(2x+1)

[wild lantern]

Yeah yeah lol

[bright locust]

The proper way

That’s what it should be

[vocal roost]

well...

the more i think about it

the more easier it seems to become in my head

[storm sage]

yay!

[vocal roost]

but trying to do 2xy for example

[storm sage]

what do you mean

[vocal roost]

derivative of 2xy

[storm sage]

but what is y

[vocal roost]

2xy with respect to x

not partial derivative but derivative

[storm sage]

but what is y

is that a function of x

[vocal roost]

a variable

multiplying 2x

[storm sage]

is it a function of x

[vocal roost]

f(x,y)=2xy

[storm sage]

like y = f(x)

well right but

what is y

[vocal roost]

wait

these are multivariables

ah

you need partials for that i realised

[vocal roost]

then nvm then

because non part derivatives work with terms that have only 1 type of variable

right?

like cos(2x^2+2) and etc.

[storm sage]

yes

if y is a function of x then you can take the derivative of 2xy

[vocal roost]

but it needs to be partial

right?

[storm sage]

no in that case it's an ordinary derivative

if y is a function of x

[vocal roost]

so the derivative of

f(x,y) = 2xy

[storm sage]

no that's a multivariate function

[vocal roost]

that's what I ment tho

if you can take derivatives(non part) of multivariable functions

[storm sage]

however if you have f(x) = 2xy where y = some function of x, then you can take the derivative

[storm sage]

in general the derivative of a multivariate function is a matrix (I will not explain this though because it will probably be unhelpful if you don't know how ordinary derivatives work)

[vocal roost]

so for example:

Taking the derivative of 2xy with respect to y.

that's 2x

right

[vivid halo]

yeah

[storm sage]

that is a partial derivative

yes

[vocal roost]

ah

i get it

hold on, isn't that 2y then?

no wait

im mixing it up, nvm

2x would be treated as a constant, so it makes sense for it to be 2x if it's with respect to y.

[storm sage]

yes if it's a partial derivative

[vocal roost]

ye

[finite tusk]

Let F(x,y(x))=0
Then dF/dx(dx/dx)+dF/dy(dy/dx)(dx/dx)=0
Then dF/dy(dy/dx)(dx/dx)=-dF/dx(dx/dx/

dF/dy(dy/dx)=-dF/dx
dy/dx=-(dF/dx)/(dF/dy)
dy/dx=-(dFdy)/(dxdF)
differentials anti commute so
dy/dx=-(-dydF)/(dxdF)
dy/dx=(dy/dx)(dF/dF)
therefore dy/dx=dy/dx
Since differentials anti commute dxdF is also -dFdx

[mint canopy]

This is gibberish

[vocal roost]

säääääääääääääääääääääääääääääääääääääääääääääääääääääääs

[mint canopy]

F(x,(y(x))

what

are there missing brackets, or is there an extra comma, what is this

differentials anti-commute
Why are you doing this if this is a multivalued fn, this makes no sense for partials

therefore dy/dx=dy/dx
????????? I could've told you that beforehand

[finite tusk]

It's an actual proof from a multivariable calc book

F is a function of x and y(x)

[mint canopy]

I think you MIGHT have missed some details out

[finite tusk]

I did not

Lol

[neat lintel]

post a screenshot

[finite tusk]

If I did then elaborate

[mint canopy]

I literally just put up three things that don't make sense

[finite tusk]

Missing commas?

Where

[mint canopy]

F(x,(y(x))
Count the brackets.

[finite tusk]

The equation is set how it is lol

[neat lintel]

geo post a screenshot of the book

[finite tusk]

Sorry F(x,y(x))

This is what I meant

Thank you

Typo

[mint canopy]

Explain this one. Your conclusion is trivial

[finite tusk]

To be quite honest the burden is not on me to prove the equation it's on you to disrpove this theorem

[finite tusk]

It's not

[mint canopy]

Oh my fucking god

[mint canopy]

So are you saying that in general dy/dx is not equal to dy/dx?

[neat lintel]

holy fuck you're obnoxious lol, all i asked for was a screenshot

[finite tusk]

Let's say F=x^2+xy^420+ y^69 which is in R^3

But you would want to find dy/dx whcih is spanned on R^2

[mint canopy]

I'm so glad I don't live in a drywall house

[finite tusk]

Then use dy/dx=-F_x/F_y

There happy?

[finite tusk]

You kept asking like I was a god or something

I'm pretty sure you can find it

[mint canopy]

You said it was from a book

[storm sage]

what is going on lol

[neat lintel]

no you fucking knob, i just want to know what book it was

[finite tusk]

Calc 3

[mint canopy]

But what even is this, what

[storm sage]

😭

[storm sage]

this is true

I believe

[mint canopy]

Like your "theorem" concluded that dy/dx = dy/dx,

[storm sage]

when F defines a level curve

[mint canopy]

so wtf is your theorem proving

[finite tusk]

Thank you

[storm sage]

What

[neat lintel]

i can't wait for you to get banned

[mint canopy]

Also, are you using d as a partial or an ordinary dervative?? You are not giving us all the info

[finite tusk]

The thing I showed was 1st differentials anti commute

[storm sage]

I can't tell if you are trolling

[finite tusk]

Sorry not you wrong person

[mint canopy]

Hhaaaaaaaaaaaaaaaaaaaa

Oh my god

[finite tusk]

If you can't see what I'm saying then I can't help you

[mint canopy]

Oh my god

[storm sage]

.-.

[dapper badge]

geo, people have explained to you what an empty space is and what a ring is

[vocal roost]

AAAAAAAAAAAAA

[dapper badge]

the least you could do is provide some context for your "result"

[sleek wing]

Ban central

[mint canopy]

Yeah, you made the right choice switching to physics for sure

[finite tusk]

1st I showed differentials anti commute
2nd you can find the line tangent to F spanned on R^3 starting from some F which is in R^3

Like a level curve

When z=0 plane

[finite tusk]

Lol

[mint canopy]

I don't think differentials anti-commute for partials, I think this is just not meaningful

[finite tusk]

Seriously I'm amazed you don't know this

I'm actually laughing so jard

[storm sage]

me too

[mint canopy]

Jesus christ

[vocal roost]

my brain is bleaching

so hard

[sleek wing]

Bit of a rude quip imo!

[finite tusk]

If you take Calc 3 you'll see this

[finite tusk]

He was shitting on me

[sleek wing]

I’ll see utter bullshit? Yeah probs

[storm sage]

what do you mean by multiplying differentials? are you taking the exterior product?

[finite tusk]

It was only fair

[neat lintel]

geo stellar, may i ask what book you got this proof from?

🙂

[vivid halo]

tfw rediscovering the exterior algebra but worse

[sleek wing]

PauseChamp

[finite tusk]

Yes

This book

Go to the chapter that talks about trees

And the problem is right there

[storm sage]

okay I will look

[finite tusk]

It's literally the exact same thing

Ok

It's nearing the end

[mint canopy]

I can't wait to see this

[finite tusk]

If it's not in the examples then it's one of the actual problems that ask you to prove that dy/dx = -F_x/F_y

[wild lantern]

What chapter?

I own that book lol

[finite tusk]

I owned two of them

[storm sage]

Lol

[finite tusk]

What school do you go to?

[mint canopy]

But this isn't what your "proof" was showing

[finite tusk]

Lol

[wild lantern]

Oh fuck me too actually lmao

[finite tusk]

Bruh it's the exact same thing

[wild lantern]

An older ed and the one you posted lol

[sleek wing]

Why did you own two copies of the same book

[finite tusk]

That's very sick jajajaja

[storm sage]

👀 are you spanish-speaking

[sleek wing]

Unless...

[finite tusk]

I overused the other book and I always carried many books

And it looked like trash carrying it around

[wild lantern]

I bought one used before I did calc to work thru then they updated our curriculum to req the new one

[finite tusk]

So I got another

[storm sage]

wait they required you to own a specific textbook?

[finite tusk]

That's actually true the same thing happened in the school I go to

[finite tusk]

Yes everyone

[wild lantern]

Yes lol

[storm sage]

tf

[wild lantern]

Welp not super heavy req

[finite tusk]

Expensive book

[mint canopy]

America moment

[storm sage]

why???

[wild lantern]

Usually the profs don't care if you own it

[finite tusk]

I believe that book was about 220 dollars

Or 200

[wild lantern]

It's just the one they all followed at the time

[finite tusk]

In hardcore is all I knew that they sold it in

[wild lantern]

They switched to stewart now i think

[finite tusk]

Hardcover

[vivid halo]

undergrad courses: you must buy this textbook
grad courses: here's a site where you can pirate the three books for the course

[finite tusk]

Same too what the

[wild lantern]

It's pretty popular textbook geo

[vocal roost]

https://tenor.com/view/1984-gif-19260546

[vivid halo]

"if you feel uncomfortable pirating the book just email me and I will send you my pirated copy"

[vocal roost]

mods: ^^
do not talk about pirating things

[vivid halo]

you can talk about pirating things, just not about where you pirate things

[vocal roost]

its a joke

💀

[vivid halo]

[velvet dagger]

[wild lantern]

I pirate at my computer

It's not a secret

Jk lol

[velvet dagger]

Measure theory prof: "The content of this class is covered by finitely many books"

[finite tusk]

Banned

Lol jk

[mint canopy]

you know, what if there was some kinda library at the beginning of time. Like a library of genesis

[velvet dagger]

Not lol jk

I'm about to ban dootdooter

Any last words?

[wild lantern]

Pls no bulli

[velvet dagger]

,ban_irl DootDooter

[fathom swallow]

Couldn't find a member matching _irl DootDooter!

Jul 24, 2022, 10:58 PM

[finite tusk]

I see nothing wrong

[mint canopy]

HAHAHA

[finite tusk]

Lol

[storm sage]

imagine if there was a person whose name was _irl DootDooter

and they just got banned

[velvet dagger]

It'd ask me to confirm lol

[storm sage]

Lol

[finite tusk]

When the power gets to the head

[wild lantern]

_irlDootDooter is a pretty good choice of username ngl

[storm sage]

do you know what chapter this is

[finite tusk]

You get P=W/changet

[finite tusk]

Nope

[storm sage]

pain

[finite tusk]

But it's with the differentials in 3d

Like I said nearing the end

Before curls and flux

And divegrence

[storm sage]

okay I will look

I am curious what you were trying to say now

[finite tusk]

After normal tnagent accelerations

[wild lantern]

Ch 12 in my older copy?

[finite tusk]

You should find it and I hope you find it because it's actually very interesting

I'm not here to lie I am a seeker of truth

[mint canopy]

Seek that truth

You keep seeking

Wait no

[finite tusk]

I genuinely like this type of thing and I don't like to lie or mislead

[chilly hull]

https://tenor.com/view/jinx-cat-attack-hand-fast-gif-25112967

[mint canopy]

Not the best at writing proofs tho

[wild lantern]

This?

[mint canopy]

Maybe work on that

[finite tusk]

Yes

Thank you

Justice has been made

[wild lantern]

Yeah this is from sec 12.5 in my copy

[mint canopy]

LMAO I WAS RIGHT, YOU WERE MISSING OUT THE PARTIALS

[finite tusk]

Except the partial can be a d

[mint canopy]

HAHAHA

[finite tusk]

They have d for dx/dx

[wild lantern]

But idk how this shows differentials anticommute?

[mint canopy]

And there's nothing where you commute the differentials, bc you can't do that with partials mixing with ordinary diffs

[finite tusk]

Because using the right hand side you can get the left hand side

[mint canopy]

Yeah like Geo, you wrote nonsense

The notation wasn't even there

Thanks for being like, "I can't believe you don't know this"

[finite tusk]

Sometimes they used partial

Sometimes they used the standard d

[mint canopy]

Yeah, and you never used them correctly

[finite tusk]

Bruh you can literally switch some D's and partials and the idea is literally the same

[mint canopy]

They are extremely different

[finite tusk]

dx/dx is the same a partialx/partialx

[mint canopy]

It makes, dare I say, all the difference

[finite tusk]

They are different but on on some cases

[eager reef]

[mint canopy]

Especially in this case, the distinction is important

[finite tusk]

Not everytime lol

[neat lintel]

geo stellar doing their best mochizuki roleplay (it doesn't matter how good you are at something if you explain it poorly and rudely)

[mint canopy]

This time.

[storm sage]

do you mean this

[finite tusk]

partial f/partial y is distinct from dF/dy

[storm sage]

this theorem is correct

[finite tusk]

Yes

[storm sage]

I couldn't find what you were talking about earlier though

[finite tusk]

I forgot to simply put some of the D's to partial

[finite tusk]

You found it

Before it should be a proof

[wild lantern]

Interuniversal Geo_Stellar theory

[storm sage]

do you mean this

[finite tusk]

yes sir

[storm sage]

okay but what were you saying when you said "differentials anticommute"

[finite tusk]

dy/dx= -F_x/F_y is what I said but I forgot to put partial for the dF/dy partial

And for dF/dX

[mint canopy]

you literally just ended your proof with "therefore dy/dx = dy/dx"

[eager reef]

Differentials do what

[wild lantern]

Therefore 1=1

[mint canopy]

Also, you mixed partials and ordinary differentials, so you can't even mix it

anticommute* it

[finite tusk]

So inorder to get the left hand side from the right hand side you must manipulate the right hand side to get dy/dx and then you see differentials anticommute

[storm sage]

oh

[finite tusk]

In physics in grassmanian Geometry we see differentials anticommute

So which is why I don't see it necessary to justify that to someone that doesn't believe me

[finite tusk]

Jajajaa

[dapper badge]

ok but you didn't show it

[finite tusk]

Yeah

[storm sage]

okay I don't think that's the right way of putting that

[mint canopy]

This is the exterior derivative tho, it's not true that dxdy = -dydx, this is still wrong

[storm sage]

because you can't literally multiply out dy and dx in this equation

[finite tusk]

Its the idea that is used

[mint canopy]

Eric brings up another point

[finite tusk]

Not multiplying out

[mint canopy]

I'm going to implement some self-care

[storm sage]

I don't really understand, but I think you are struggling to articulate what you want to say formally

[finite tusk]

Idk how else to put it then it write it out in in paper

I'm not struggling to articulate what I'm saying

Simply differentials anticommute

[dapper badge]

are you claiming that you proved this or not

[finite tusk]

It's already proved

I didn't prove it

[storm sage]

what is dF dy / dx dF?

[finite tusk]

Prof Nima Arkani Hamed proves it in his lecture on Grassmanian

[dapper badge]

Ok it's just confusing because earlier you said "I showed differentials anti commute" when you didn't

[finite tusk]

You mean (dF/dy)/(dx/dF)?

[eager reef]

Are you referring to the fact that differential forms are skew symmetric

[storm sage]

you start with $$\f{\dd y}{\dd x} = -\frac{\f{\partial F}{\partial x}}{\f{\partial F}{\partial y}}$$ which is correct, and then you cancel out the fractions which is nonsensical

[fathom swallow]

Eric Tao (he/him)

[finite tusk]

Yes thank you

Ime that

[storm sage]

I'm referring to what you wrote

[finite tusk]

Like that

It's cuz you're not adding / so you're not making any justice

[storm sage]

what on earth do you mean by (dF dy)/(dF dx)

[finite tusk]

I was very clear with what I wrote

[storm sage]

okay you are either trolling or are unwilling to answer the question, I will just ignore you

[bright locust]

He’s probably trolling

[finite tusk]

I'm looking back for it

[dapper badge]

timo is that a new pfp

[eager reef]

Different account

[dapper badge]

ah

[mint canopy]

King shit

[eager reef]

What algebraic structure are you feeling like today @dapper badge

[finite tusk]

I put -(dFdy)/(dxdF)

[dapper badge]

mmm

[mint canopy]

I don't think they're trolling fwiw ;)

[storm sage]

yes

[dapper badge]

woke up feeling like a local ring

[storm sage]

what on earth do you mean by that

[mint canopy]

Damn you got some ideals???

But one big one??? sick

I respect that

[dapper badge]

i'm noncommutative

[eager reef]

Might compute the maximal ideal later?

[mint canopy]

Well, nobody's perfect

[eager reef]

Ooh the left or right one then

[storm sage]

noncommutativity is a plus

you are more general

[dapper badge]

I actually forgor how the conditions work for noncommutative

is it that left and right jacobson coincide?

[finite tusk]

Can you write it in latex ?

Just to expand upon it plz

[mint canopy]

Not a clue, damn

[finite tusk]

So I can explain

[mint canopy]

Making me feel bad about my knowledge of local rings

[dapper badge]

it's ok

[eager reef]

Think so

[mint canopy]

Hey did you know that you can detect singular points on a variety by looking at the global dimension of the local ring? Pretty cool huh

No idea how that works

But I know it does

[eager reef]

Funny words magic man

[dapper badge]

need to work on algebra stuff today, I been slacking

[mint canopy]

The global dimension is infinite exactly when the point is singular

[vivid halo]

have you thought about what this looks like for some simple examples?

[eager reef]

Need to work on diffgeo stuff

[storm sage]

okay $$-\frac{\partial F \partial y}{\partial x \partial F}$$

[fathom swallow]

Eric Tao (he/him)

[storm sage]

what on earth do you mean by this @finite tusk

[mint canopy]

I realised recently that the Galois theory course that I took in my final year was really bad, so I want to read a good Galois book

[dapper badge]

i'm just getting to the good stuff but feeling a bit burnt out

[mint canopy]

I should look into this in the future

[eager reef]

Instead I am here reading that someone is saying differentials are anticommutative

What’s wrong

With my English

man

[vivid halo]

differentials do anti-commute in a certain sense but idk if we are talking about that sense here

[eager reef]

Read above for context

[mint canopy]

Do some self-care. Get those messages out of your face

[finite tusk]

https://youtu.be/fCi195e9QD4

At 2:29:09 he describes that differentials anticommute

Watch at least like a minute it's right there

[vivid halo]

do you know in what sense he means this

[finite tusk]

As an anti synnetrized product

[mint canopy]

He doesn't mean in multiplication, I have said this a couple times now ughdhudsahjfd

Idk why I'm replying

[finite tusk]

But he only said as an anti synnetrized product to make the equation work

[mint canopy]

I said it was nonsense from the start

[eager reef]

Take your time. There’s no rush

[mint canopy]

Here's something cool

[eager reef]

Take care of yourself

[mint canopy]

I notice that the number of help channels that are open increases/decreases at different times of day

[vivid halo]

lmao him swearing before this

[mint canopy]

I just thought that was cute. I guess it's clear that most people asking questions are from the US and Canada

[eager reef]

Geo stellar what you’re saying is correct in a sense

But in a sense that you don’t seem to know about

[finite tusk]

lolLLL

I just heard it too

[mint canopy]

Cargo cult math lol

[vivid halo]

also to be clear the explanation you gave isn't really a proof

[eager reef]

That’s the thing

[vivid halo]

like it's morally true but there's a lot more work you need to do to make this precise

[dapper badge]

thanks friend. sometimes I set personal goals for myself so I feel a bit disappointed when I don't meet them. I wanted to finish Aluffi this summer (ideally by the end of July) but that's probably not happening. You're right though, think I ought to take a small break so I'm not already burnt by the time fall semester starts lol

[vivid halo]

and you seem to be handwaving those steps

by like

[finite tusk]

I understand can you elaborate

[vivid halo]

idk citing Nima

[finite tusk]

I understand

Can you show me on a proof then

[storm sage]

this comes down to 1) how are you defining differentials 2) how are you defining multiplication of differentials

[finite tusk]

What exacrly it means for differentials to anticommute

[mint canopy]

How are you finding Aluffi? I am looking for graduate books in algebra

[eager reef]

Do you know what those forms are

[finite tusk]

According to the video

[vivid halo]

you have to know what differential forms are

[finite tusk]

Yes

Go on

[mint canopy]

Idk why you guys are still going ngl

[eager reef]

Now you look at the definition

[vivid halo]

and then you have in the exterior algebra e.g. dx\wedge dy=-dy\wedge dx, this is the sense in which they anti-commute

[eager reef]

As sections of exterior powers

[storm sage]

Lol

[eager reef]

You need more background here

[mint canopy]

Like fr Eric, your goals are beyond me

[finite tusk]

I understand

So when this grassmanian Geometry is something I've been recently going in with another person

I'm not fully 100 percent knowledgeable at like most physicists

[storm sage]

My goal is now to learn about grassmannian geometry

[finite tusk]

But I guess I heard him say differential anticommute

And I applied it to some basic calc 3

[storm sage]

it was mentioned in our linear algebra textbook

[vivid halo]

the way you have to make these arguments that involve algebra with differentials precise is using the exterior algebra an making heavy use of like, isomorphism between a vector space and its double dual, and evaluating vectors on covectors and so on

[dapper badge]

I absolutely love it, I had little experience with algebra before aluffi (I think I had only read Pinter's book) but I like his exposition a lot and the categorical perspective feels pretty unifying. My only gripe is the field theory chapter, but that might just be because this is my first time learning field theory. I found it a little too abstract for a first run so I want to go back and be more hands on with it

[finite tusk]

Thinking that differential form would work

[mint canopy]

Lmao. Lol even. Perhaps even a ""

[finite tusk]

Sorry if I made a hassle out of it honestly

[storm sage]

yeah I don't think it applies there

[finite tusk]

Elaborate more please

Its difficult in text

[storm sage]

there is something called the "wedge product" which is how you multiply differential forms

[eager reef]

Nothing ever really goes as planned my friend, important is simply that you know when to stop for the day or for the week and take a break. The maths will still be there by the time you come back

[finite tusk]

Really?!

[mint canopy]

I'd like to hear your gripes with the field theory stuff. I took a terrible course in Galois thy this year and I want to get more perspective

So hearing about Aluffi's approach is very valuable for me rn

[vivid halo]

the point is that when you write dxdy you're really talking about dx\wedge dy in the exterior algebra

[eager reef]

Do you know what the exterior algebra is

[finite tusk]

Can you write in latex something about the wedge product? Is this something you have studied?

[storm sage]

Basically, you can imagine dx wedge dy being oriented in the opposite direction as dy wedge dx using the right hand rule

[storm sage]

There is a nice michael penn series on differential forms

[eager reef]

How are you gonna have this talk without knowing what a wedge is

[finite tusk]

Interesting

[eager reef]

You need way more background

[storm sage]

https://www.youtube.com/watch?v=PaWj0WxUxGg&list=PL22w63XsKjqzQZtDZO_9s2HEMRJnaOTX7

[eager reef]

I thought bprp only solves funny looking integrals

[storm sage]

it's michael penn, not bprp

[eager reef]

Oh

LOL

Saw penn

Brain went to bprp

[finite tusk]

I understand the wedge product

[dapper badge]

personally I just feel like a first course in field theory ought to involve a good bit of rote computation to gain a better appreciation for the abstract tools. He brushes over primitive element theorem which I feel like is one of the most important theorems to grapple with.

[finite tusk]

a^b=-b^a

We can say one is a positive orientation and the other a negative orientation

[mint canopy]

Fair enough. I'll give Aluffi a chance then

[finite tusk]

When I say this I mean to think of it in a space in not just saying it

[storm sage]

basically

a wedge b is like a signed area element

[dapper badge]

Yeah, overall I highly recommend anyone to at least give it a shot, but ofc it'll mostly come down to personal preference. Lmk if there's anything in there you ever wanna discuss!

[mint canopy]

Ya might be fun

[storm sage]

b wedge a is the same area with opposite sign

[finite tusk]

https://youtu.be/Pw1ejJzsCPA yes this one

[finite tusk]

Yes

I would say it is

Like a cross product of a and b if a was a vector and also b

[storm sage]

yeah it's like a cross product

sort of

[finite tusk]

The abs value of cross product of dx x dy is dA in vector

Almost close yes

@storm sage @vivid halo if I have more questions on these type of these y'all think y'all can help?

[plucky zodiac]

@finite tusk sorry did not answer as have to take care of things but did reply

[storm sage]

prob not my diffgeo knowledge is limited

[vivid halo]

if I'm around I guess, just don't ping me specifically for this kind of stuff

[finite tusk]

Not 1form or 2form stuff?

[finite tusk]

Not dif geo?

Thanks guys, but just as far as you can help is always fine

[plucky zodiac]

Did it Eric

[finite tusk]

Wait why though 🥺

[vivid halo]

I mean I'm happy to talk about this stuff I just have other stuff to do

[finite tusk]

I understand

[vivid halo]

I am happy to answer quick questions though 🙂

[finite tusk]

Of course thank you very much 😊

[storm sage]

wait is it not diff geo lol

aren't you doing geometry with diff forms or something

[neat lintel]

you can also just ask your questions about differential forms in #multivariable-calculus or #diff-geo-diff-top :)

[finite tusk]

It is

Yes

[plucky zodiac]

Did it

[rotund cove]

just ripped a fat one on the last day of class. not even flustered

do any of u smarts ones hold it in? i swear i've never seen a smart guy fart

[ancient flame]

can we pin this

[cold needle]

bruhnion

[ancient flame]

hi metal

[cold needle]

hello

[ancient flame]

how's life

[wooden flax]

Hi Moddy!!

[ancient flame]

hi invictus!

[wooden flax]

how r u

[ancient flame]

im good

hbu

[wooden flax]

p good

[ancient flame]

that's good

[wooden flax]

yeah i guess

[fierce abyss]

How do you read those kind of letters in English? Flourish A/B/…?

[full isle]

$\mathfrak A$

[fathom swallow]

Mary Majok

[fierce abyss]

I mean read

[full isle]

script {letter}

[fierce abyss]

Like giving a speech or lecture something

[full isle]

Yes

just call it script

[fierce abyss]

Thanks

[full isle]

you usually only need to prefix with script,italic,bold,big,small {letter}

when speaking

script is just anything that looks like different font

every other prefix self explanatory

[fierce abyss]

Thanks. I have one more question. How do you read $^{b}A,{b}A,A^{b},A{b}$ respectively. Where $A^{b}$ doesn’t necessarily represent power, could be something like cohomological groups

[fathom swallow]

Cogwheels of the mind

[full isle]

you will never see first one or second one really atleast for me

[fierce abyss]

I have seen them several times

Just don’t know how to read it

[full isle]

what context

for the last two you can say a upper b or a sub b

or a lower b

[full isle]

also it depends on context

[fierce abyss]

Above proposition 11

[full isle]

they are using it for indexing?

personally that just looks like notation that you shouldnt be verbalizing

but if you need to you can just say what the object is

[fierce abyss]

Yeah, Those symbols have upper-left, upper-right,lower-right subscripts

Okay so if I want to read $^{I}E_{2}^{p,q}$, does “E sub 2 sup p comma q of the first type” sound natural to you?

[full isle]

you most definitely shouldnt worry about verbalizing this though

[fathom swallow]

Cogwheels of the mind

[full isle]

its bloated notation with double indexing too. its never going to sound natural

you can just say what is understood to whoever you speak to

if its actually relevant to address the object

the whole point of notation isnt so that you can compactify the verbalizing

its just compactifying the idea of the object

no need to worry about verbalizing everything

[fierce abyss]

Okay, thanks. As long as i can make others understand what I am saying right

[full isle]

yeah and it shouldn’t be a problem if they have all senses

[fierce abyss]

Okay got it

[rich rapids]

wow, Gauss was mean af

[charred mortar]

Yeah Gauss had some savage moments

Once Jacobi came over to Gauss to discuss some cool new stuff Jacobi had found

Gauss opens some old drawer and is like “oh cool, I discovered that years ago but didn’t think it interesting enough to publish”

Jacobi counters by responding: Funny, you’ve published worse results

Gauss was honestly an ass

[rich rapids]

terrible human being

[charred mortar]

It’s a classic case of never meet (or in this case read about) your heroes

[rich rapids]

poor Bolyai was 21

[rich rapids]

very true

[charred mortar]

Yeah Gauss really didn’t need to do that to poor Bolyai

[rich rapids]

wholesome:

'If this depresses you, turn your thoughts to the uplifting counterweight of Leonhard Euler. An intellectual volcano erupting
with wildly original thoughts (some of which we shall meet later) he was also a kind and generous spirit. We cite one, parallel example. When the then-unknown 19-year-old Lagrange wrote to him with overlapping discoveries in the calculus of variations,
Euler wrote back: “. . . I deduced this myself. However, I decided to conceal this until you publish your results, since in
no way do I want to take away from you any of the glory that you deserve.” See Gindikin (2007, p. 216). Incidentally, Euler
also personally intervened to rescue Lambert’s career!'

[charred mortar]

Oh yeah Euler was a great guy

He could certainly afford to give some credit to other mathematicians

Gauss could too tbh, he just chose to be a dickhead instead

[rich rapids]

Visual Differential Geometry and Forms: A Mathematical Drama in Five Acts (2021) by Tristan Needham

in case anyone is interested

[mint canopy]

Euler was apparently a favourite punching bag of Voltaire, who also worked in the court of Frederick the Great. Perhaps he learned not to do the same to others

[surreal rose]

What is this equation

[rich rapids]

stokes

[compact tartan]

generalized stokes law

[surreal rose]

what does the subscript mean on integrals

[compact tartan]

what you're integrating on

[surreal rose]

like dx?

[compact tartan]

no

[odd narwhal]

The region you are integrating over

[compact tartan]

there's some region Omega and the theorem relates an integral over Omega to an integral over the boundary of Omega

[surreal rose]

Is this first year uni stuff?

And is it more physics or maths

[compact tartan]

no that's closer to 2nd or 3rd year

[surreal rose]

Don’t understand lol but sounds cool

Alright fair enough

[compact tartan]

it's math but it's closely related to physics

[surreal rose]

If i do a maths degree will i be able to learn it?

[compact tartan]

special cases of this formula come up in electromagnetism

in fact stokes was working on both kinda

[surreal rose]

As in physics and maths?

I want to learn electromagnetism too, maxwells equations are taught first year uni right?

[compact tartan]

depends but also probably not?

I had EM in third semester

[surreal rose]

I’m in my last year of high school right now, we briefly looked at maxwells equations in physics but didn’t go into any of the maths, they look interesting

[surreal rose]

What degree did you do

[compact tartan]

applied math and physics

[surreal rose]

Cool, i wanna do maths too

[compact tartan]

we didn't actually discuss the fully general stokes theorem in any class

but I was aware of it due to my own reading

[surreal rose]

Oh alright

[compact tartan]

intuitively it is a simple result but the proof is complicated by technicalities of analysis on manifolds

[surreal rose]

Is analysis on manifolds the same thing that made the poincaré conjecture proof so hard

[compact tartan]

uh

I'm not too familiar with that result

seems unrelated other than the fact that they're both involving manifolds

[surreal rose]

Oh alright

[odd narwhal]

Poincare conjecture is a result on topological manifolds

iirc

[surreal rose]

Ahh yeah

[compact tartan]

yeah I would be very wary of generalized stokes with relaxed smoothness conditions

[green sapphire]

I was doing a physics question and it was to calculate the displacement of an object when it covers 3/4th of the circumference of the circle of radius r
answer is D=sqrt2*r
=> That D/r=sqrt2

but sqrt2 cannot be represented in p/q

[pure sun]

Sqrt(2) = sqrt(2) / 1

[bright hill]

lmao

[neat lintel]

its not funny

[bright hill]

if you say so

[woven whale]

it wasn't meant in a sarcastic way lol

[woven whale]

only if p and q need to be integers

[green sapphire]

2x=0
2x/x=0/x
2=0

how

[surreal sapphire]

the first equation implies x = 0, so you are dividing by 0

[green sapphire]

transposing

we can transpose x also

[surreal sapphire]

what does that mean

[green sapphire]

like
2x=4
x=4/2
x=2

but

2x=4
2=4/x

also

[bright hill]

[surreal sapphire]

you can only divide both sides by a number if this number is nonzero

[green sapphire]

what?

[surreal sapphire]

what you call "transposing" is dividing both sides of an equation by a number

this is only possible if that number is not 0

[green sapphire]

oh

ok

[surreal sapphire]

[neat frost]

Wat

Why math not in math mode

[surreal sapphire]

slurp you found the one issue

[neat frost]

Yessir

I bet it would all make sense if typeset correctly

[surreal sapphire]

proof by nicely typeset

[green sapphire]

umm.

What do you want elaboration of?

[neat frost]

Everything

None of it makes sense

[green sapphire]

hmm

[surreal sapphire]

ye, this is mostly word salad

and i dont feel like trying to decypher it by asking more questions, since the conclusion is also just wrong

and i doubt this is a good faith misunderstanding

[mint canopy]

Could be written by an ai lol

[sacred forge]

pretty funny

[bright hill]

is this a copypasta?

this must be a copypasta

[wispy pike]

Does anyone have a recommendation for some sort of ipad/drwawing pad for roughly 200 euros? I have ver ybad vision so one short problem fills almost half a page haha

[neat lintel]

Finitists be like

[eager reef]

@sleek wing found your alt

[queen sierra]

Fit a 7x7 matrix in 2 lines :))

[arctic grove]

that is most definitely easy still

considering they fit a 5 by 5 in 1 line

lol

[neat lintel]

I found the flow of the PDE

i can fit a 20x20 matrix in 1 line

It took hours of online reading/repeated solving

Yeah

[shrewd cliff]

Hey, does anyone ever get humiliated for loving maths here?

[chilly coral]

You love maths? 🤮

[shrewd cliff]

Um, yeah, I do. I thought this was a maths group?

[woven whale]

no wtf???

this is a math hater group

we all hate math

🤢

[chilly coral]

It's a very toxic relationship

[shrewd cliff]

are you joking?

[neat lintel]

dont listen to them, people only get humiliated for not loving math, not for loving it

[shrewd cliff]

I don't know how to do that. You see, even my parents don't seem to get it for some reason🙁 it's like they just don't care about the things I like and don't like

[neat lintel]

well if they don't care about you, you shouldn't care about them either

just do your thing, and fuck everyone else in the world

[shrewd cliff]

Well, it's hard, I just can't stop myself from taking every small thing they say to heart

[neat lintel]

Yes

yeah, its just like an hard theorem. at first it seems really hard and you feel like you cant prove it. but keep trying it

in the future you'll look back at it and find it trivial

[fervent flame]

kid who do u think u are

change ur pfp

[shrewd cliff]

Did this sort of thing happen to you too?

[neat lintel]

well noone humilliated me for loving math

and its really weird if someone does that lol

if they do that they're weirdos and you shouldn't care about them

[chilly coral]

I get called a nerd sometimes but it's never in a bad/humiliating way

[fervent flame]

shut up nerd

[chilly coral]

[shrewd cliff]

I think math is amazing. I don't get why they act so weird either. thanks for your kind words.

[shrewd cliff]

That's nice. I also don't dislike being called a nerd . I just don't like it when they act like I'm invisible when I talk about it.

[neat lintel]

i m curious btw, what kind of math you like?

[shrewd cliff]

what do you mean by what kind?

[rich hamlet]

7x7 in one line

on a computer tho

so ig i cheated bc i can zoom in

[neat lintel]

what areas

[zenith forge]

shut up sideurk ur so bad at valorant get carried by zoph and Gabe radiant players

[fervent flame]

stfu silver

[shrewd cliff]

Hmm, I love basically everything, like any math topic seems interesting to me. But I especially love trigonometry ,algebra and patterns. What about you?

[rich hamlet]

what area in algebra do you mean?

[neat lintel]

i like category theory, set theory, algebra, idk much about them yet tho

[rich hamlet]

i have had awkward looks

[neat lintel]

polish space stuffs seems interesting

[rich hamlet]

where its like "you like math?? the fuckkk?"

its either "wow thats cool" or "i suck at math"

but in reality they think we are a different species lets be honest now /j

[neat lintel]

idk why people only say that for math usually

i suck at everything

[rich hamlet]

its bc its accepted to suck at math

like its a desirable quality

math is not something most people want to "improve" in

[neat lintel]

why would it be a desirable quality

its fine if you dont want to improve in it

[rich hamlet]

dont ask me lol its just what ive seen

[rich hamlet]

yeah its whatever they want

u dont have to love math

theres nothing wrong with not loving math

its really not that big a deal tho

[neat lintel]

i dont really want to learn politics or biology, but i dont think its "good" that im bad at those

[rich hamlet]

oh yeah i always dont feel good about being uneducated in a topic

but i dont go out of my way to learn it

[rich hamlet]

category theory is cool take a look at aluffi's algebra chapter 0

he starts with categorical principles

[neat lintel]

yeah i already did

[rich hamlet]

ah yeah

im not knowledgeable at all in algebra compared to analysis

i am just touching the tip of analysis too, but ive definitely done more in analysis

[neat lintel]

im not much knowledgeable in anything tbh

[rich hamlet]

yeah i think as i learn more theres just even more that i dont know

[queen sierra]

Grow up lol

[rich hamlet]

which is the expected outcome

[queen sierra]

Beautiful

[shrewd cliff]

@neat lintel are you in high school?

[neat lintel]

no

im just an undergrad

[rich hamlet]

@shrewd cliff are u in hs?

[shrewd cliff]

@rich hamlet yeah, 10th grade

[rich hamlet]

from the us?

[shrewd cliff]

no

[rich hamlet]

i see

@neat lintel i mainly got lost at universal properties

i dont get the langauge that they use

like "object A in C is universal in that there exists a unique morphism from A to Z for any object Z in C" vs. just saying "A is initial in C"

i mean ig its pretty cool that initial and final objects are isomorphic but its not exactly clear to me why we care

[fervent flame]

ur my biggest fan holy

[neat lintel]

initial and final objects are not isomorphic in general

[fervent flame]

so cringe

[rich hamlet]

initial objects are isomorphic to other initial objects

[neat lintel]

yeah

[rich hamlet]

thats what i meant

sorry bad wording

[neat lintel]

uniquely isomorphic even

[rich hamlet]

yeah ofc

thats the whole "universal property" part

from what i understand its basically about uniqueness

its about unique relationships between certain objects from what i understood

the product/coproduct example made it clearer

[neat lintel]

universal properties are kinda the most efficient way to construct something

for example the product of 2 sets AxB

[rich hamlet]

yeah

[neat lintel]

actually let me talk about the disjoint union

[rich hamlet]

my goal is to be able to write abstract nonsense proofs basically

[neat lintel]

AuB

[rich hamlet]

mhm

[neat lintel]

its all that you need to have to have inclusion of A and B into it

you could have more elements

but its not needed

AuB is the most efficient way to do it

[rich hamlet]

this is shown in 1.5 of aluffi right

i remember this

[neat lintel]

probably

[rich hamlet]

ur an undergrad right?

what year

also who is the girl in ur pfp @neat lintel

[neat lintel]

i am last year undergrad

[drifting wharf]

Can someone help me with a physics problem

[ancient junco]

Who is stronger, Goku or Sans?

[bright hill]

[deep mango]

Goku was a big part of big brother season 23. Final 4 eviction was messy!

[bright hill]

I've googled big brother a couple of days ago

shit got the lowest imdb score I've ever seen

I noped out so fast after seeing that lol

[deep mango]

What

Idk what that even means

How do you give an overall IMDb score to a game show with like 24 seasons

Some of the seasons are shit and some are godly

[hollow sundial]

episodes with vegeta: 9.0+
episodes with master roshi: 5.0-

[deep mango]

Lol

The episode with goku is very polarizing

Watching a car crash vibes

[bright hill]

24 seasons

how do you know which seasons to watch?

[queen sierra]

Ik 😝

[hollow sundial]

seasons where goku makes a spirit bomb: 8.0+
seasons where goku makes a kamehameha: 9.0+
seasons where goku is scared of needles: 5.0-

[fervent flame]

ratio

[queen sierra]

I love Dragon ball

Watched all of them basically even the films

[hollow sundial]

oh yea there are like 15 movies

[queen sierra]

Yuppp

[hollow sundial]

i think i stopped after Cell

but then watched Buu again. I never understood that saga

[queen sierra]

Gohan was my fav character :((

[queen sierra]

Understandable

[hollow sundial]

Gohan is badass

[queen sierra]

I liked his mystic Form without the yellow hair and the fight with buu was one of my favourites

[eager reef]

But can he beat goku

[deep mango]

You look it up or ask someone who knows.
Better than survivor, there's 42 seasons of that (although those seasons are 13 episodes instead of like 30 in bb)

Honestly big brother the tv show is garbage and not worth watching mostly

The old seasons are quite good

Seasons 2-8, 10, 12, and 14 are all excellent. Then the show kind of gets up its own ass

[queen sierra]

If he kept training hard like before then yeah but hes more focused with his studies now

I feel like Chichi brainwashed him 😭

[deep mango]

I just follow the big brother live feeds and podcasts cause I enjoy the gameplay and social strategy

I dont care about competitions or silly stuff

Survivor is a much much better show

[ancient flame]

hi ryc

[deep mango]

Hi gmod

[ancient flame]

how are u

[eager reef]

Let the guy study

[hollow sundial]

okay but everyone else likes you. parent approval is overrated

[eager reef]

They need an educated one

Goku be stupid as hell sometimes

[queen sierra]

True

[ancient flame]

🍿

[eager reef]

Don’t summon it

[ancient flame]

LOL

"it"

[delicate knoll]

it what?

[ancient flame]

.

[storm sage]

lol what why