serious-discussion

[leaden skiff]

i know people have suggested the "triangle of power" or whatnot for exp, nth-root and log

which is really nice

[fast ivy]

[leaden skiff]

but just using words for trig funcs feels weird. like there's gotta be a better way

[leaden torrent]

.

[leaden skiff]

i know, let me enjoy my youth goddamn it

i had a dream once

where like you could represent trig funcs with colors

so a red x represented sin(x)

and there definitely becomes some problems when you try to compose trig functiosn

but i do wonder if using colors in notation could be useful somewhere

[toxic schooner]

[leaden skiff]

can you do colors in latex?

[toxic schooner]

i suppose you can

[leaden skiff]

how?

[toxic schooner]

i dont know that, but i think i saw someone using colors

[cold needle]

rest in peace color blind people

[last oxide]

something with textcolor
I remember doing it before

[thorn brook]

maybe do like \changetextcolortoblueplz{text here}

idk

[pale orchid]

you can use the xcolor package

then make your own textcolor macros for stuff like \blue{beepboop}

[stable oar]

curious - does anyone know the demographics of the users here? like, mostly high school students asking for homework help, maybe some undergrads, a few postgrads, mostly americans, etc.?

[neat lintel]

that's pretty much it lmao

[stable oar]

rip

[neat lintel]

a massive chunk of the server is just people who joined, asked a homework question or two, and then never said anything else

[fast ivy]

How many Latin American are here

[neat lintel]

at least 1

[fast ivy]

[neat lintel]

how's that symplectic geometry going

[stable oar]

shame, would be nice to have a space where grads/postgrads can be active and talk about higher level maths, but i suspect those that are here aren't that active

[deep mango]

the advanced channels are pretty active

[fast ivy]

It's being really nice, we are mostly following Anna Cannas da Silva for the introductory stuff

[deep mango]

based

[fast ivy]

I have almost finished the 2nd pset

Give it a look

[stable oar]

yeah they're somewhat active, but not that much really

[leaden torrent]

the advanced channels are active enough but even that is mostly upper undergrad

there are a few discord servers targeted at grad students floating around but theyre pretty exclusionary typiaclly

[neat lintel]

COMPACT!

[leaden torrent]

invite-only, hard to get in if you dont know someone, etc

[stable oar]

shame

[leaden torrent]

there are also subject specific discords

but i dont know the details there

[neat lintel]

there's an algebraic topology one and an analysis one somewhere out there

[fast ivy]

https://w3.impa.br/~henrique/sympl21.html

Take a look at list 2

[neat lintel]

the AT one seems relatively active and the analysis one, idk, i got invited to it but didn't join, seemed like it had a decent number of members

[fast ivy]

The problems are in English

[leaden torrent]

the problem is that generalist math servers end up infested by high schoolers asking rote questions because they didnt pay attention in class or dont want to expend the brain power to reasoning through things themselves

[fast ivy]

Maybe you find one of those fun

[leaden torrent]

not all high schoolers are like this ofc

but a lot are

[stable oar]

yeah, you're right

[fast ivy]

Oh, that's from the second chapter of Anna

[neat lintel]

yeah by second problem set i thought you meant the problems in the book lol

[fast ivy]

Np

[neat lintel]

problem 3

[fast ivy]

These are problems my professor set up

[neat lintel]

looks fun

maybe ill try a few of these later and share my thoughts

[fast ivy]

I mean, just share them after the due date pls

[leaden torrent]

even exclusionary upper math servers end up with people who think the 0 map isnt linear

[fast ivy]

Here are my solutions to the first pset. I just erased my name and personal information obvious reasons

It takes a whole lot of time

to write all of this in LaTeX

I have also started to write the solutions to the second pset

[neat lintel]

Geometria Simpl´etica

[fast ivy]

I think I will maybe write those in English

[neat lintel]

you can submit them in either language?

[fast ivy]

Yup

[neat lintel]

mix it up

[fast ivy]

I mean

The course is in English

The lectures I mean

I just prefer to write in Portuguese

[neat lintel]

do the odd problems in portuguese and the even problems in english

[fast ivy]

Because I am more familiar

[fast ivy]

lmao

I will try 👀

Yeah so, so far Symplectic Geometry is being the most fun course

Riemann Surfaces too, but there aren't too many psets

[neat lintel]

someone's a geometer

[deep mango]

Symplectic geometry isn't geometry

Neither is riemann surfaces

The former is a mix of dynamics and category theory. The latter is pure algebra.

[bronze pelican]

Riemann surfaces is pure algebra

Thats so true

Even the geometry is algebraic

[jovial ember]

Riemann surfaces is algebra

[vivid halo]

Riemann surfaces of infinite genus have entered the chat

[untold sapphire]

i told someone earlier that compact riemann surfaces have finite genus and they were like "false, just puncture infinitely many holes in it"

can't argue with that logic

[vivid halo]

[deep mango]

[bronze pelican]

ultraproduct how do you do it

[ancient flame]

if you put an infinite amount of holes in something do you end up with nothing or a singularity?

because you cant put a hole in a singularity, right?

[vagrant kestrel]

a hole at every point

[bronze pelican]

why are those the only two options

[velvet dagger]

Did someone just call me out

[untold sapphire]

i wasn't talking about you dami

i was talking about angel

[velvet dagger]

I meant that picture

Because that's kinda me_irl

[light needle]

you are interested in ideas???? news to me

[velvet dagger]

I'm literally reading about the Kakeya conjecture over Z_p, partially because it's cool and all but mainly because it's a 6 page proof and probably the only thing I have the attention span for 🙃

[bronze pelican]

That got your attention

how can somethjing have lebesgue mesure 0 but hausdorff dimension 2

[deep mango]

We were wondering about this

[ancient flame]

We were wondering about this

[bronze pelican]

ok

just take products of this guy

and use the fact that

[deep mango]

Ok but like

Thats

[hidden bone]

hey

[deep mango]

Not

Super satisfying

[hidden bone]

@deep mango do u study real analysis

[deep mango]

There was a good answer where the factors by which you remove go like nlogn or something

Which is legit measure zero and hausdorff dim 1 on its own

[deep mango]

Yes

[hidden bone]

what application of it

im learning discrete math

[deep mango]

Understanding PDEs

And dynamical systems

[hidden bone]

thats more physics

then

[deep mango]

Are the main things I do

It really isn't

[hidden bone]

im a freshman in ug so pardon my lack of knowledge

[deep mango]

It's literally all just real analysis

I mean sure there are people who study physics who care about the equations I care about

But the problems I care about have very little to do with what the physicists care about

[hidden bone]

ph

oh

[deep mango]

even the most well-known pdes have tons of depth and a very broad subset of the math world and the physics world care about studying them in completely different ways

[hidden bone]

what do pthey care about

or what type of equations does the world ur interested in

[deep mango]

They care about understanding what solutions to these equations look like, approximating solutions, seeing their behaviors without rigorous proofs

I care about understanding properties like existence, stability, and dynamical structure. Sometimes physicists find these useful, but they're almost never proving them about PDEs. That takes real analysis, functional analysis, harmonic analysis, ergodic theory, differential geometry, complex analysis, etc.

So for example, a physicist thinks about the Schrodinger equation to understand how a particle might act in a system, or how a wave might scatter when it's launched at a boundary.

[hidden bone]

oh i see

[deep mango]

I would care about the spectral properties of a Schrodinger operator, the conserved quantities and how they govern the dynamics, statements across broad classes of potentials, etc

[hidden bone]

oh damn okay

[deep mango]

Physicists would find these results useful, but they wouldn't usually prove them themselves.

Dont get me wrong, there is a lot of shared ground! But a physicist does experiments and a mathematician proves theorems.

[hidden bone]

i see

see i love mathematics but i dont know if i can do them all day

thats my issue

but i want to be a math major

the thing is i need to apply it to another field

[uneven steppe]

@hidden bone hm

[hidden bone]

ya

wbu

[uneven steppe]

If you feel the need to apply your math in other fields, maybe you should do something like physics/operations research/engineering

[hidden bone]

im going into quant trading or swe

[burnt dune]

what are dynamical systems

[bronze pelican]

How do I address an academic in an email who I dont know if they are a professor or not

[burnt dune]

just say professor

whats the hurt

[leaden torrent]

do they have a phd

[bronze pelican]

yeah

wait

idk

[leaden torrent]

dr lastname

[bronze pelican]

They most likely have a phd but I dont see them on math geneology

[deep mango]

dynamical systems are functions that you iterate over and over on a set

like if X is a set and f : X to X is an invertible function, then the dynamical system associated to f could be represented by a function F(x, n) = f^n(x) where f^n(x) means f composed n times, or when n < 0, f^{-1} composed |n| times.

the questions people ask in dynamics are "what happens when n goes to +/- infinity? which x's are periodic and come back to themselves after a number of iterations? if x and y are close, are their trajectories similar or wildly different? etc"

you can also replace n by a continuous parameter, in which case you get F(x, t) where F(x, s + t) = F(F(x, s), t), and F(x, 0) = x. In other words, F is a flow where moving for time s + t is the same as moving for time s, then for time t.

and then you ask the same questions, as t increases/decreases.

there are a bunch of branches of dynamics. ergodic theory studies f's/F's which mix things up as time goes on. hamiltonian dynamics studies systems which have conserved quantities like "energy," and as a result are very organized - this is very connected with symplectic geometry. complex dynamics studies iteration of complex analytic maps, which leads to fractals like the mandelbrot set.

[nimble shuttle]

bro go outside 🤓

[deep mango]

just took a very pleasant evening walk you dunce

[nimble shuttle]

just took a very pleasant evening walk you dunce

[mild nebula]

just took a very pleasant evening walk you dunce

[astral marsh]

Touch some grass

[last oxide]

just took a very pleasant evening walk you dunce

[vale dawn]

Ya its the syllabus of 11

No its in 11

U studied from NCERT

It is when u watch the videos of fourier and laplace transform but dont even know to elementary calculus
Its me

[bronze pelican]

https://youtu.be/_gXlauRB1EQ

[vale dawn]

Some kids just found it on bprp videos and sending to me and asking if it can be solved?

[stable oar]

on first glance it looks fine, just lots of product/chain/quotient rule

[vale dawn]

So can we solve

Or anyone what is the asnwer for it

[stable oar]

you could try and put it in wolfram alpha, idk if the free version will like that

[vale dawn]

Dont know how to write it in there

[stable oar]

🤷 it's just a meme anyway so i wouldn't worry about it

[vale dawn]

[leaden skiff]

,ask d/dx of (((x^2e^x(sin(x))^pi)^(1/ln(2)))/(ln(x) * (integral from 0 to x of arctan(y) dy)))

[fathom swallow]

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

Requested by OfficiallyANinja#0413

[leaden skiff]

@vale dawn that apparently

[vale dawn]

@leaden skiff ur from cbse board

[leaden skiff]

i was yes

done with school now

[toxic schooner]

:nice:

[stray kite]

are all mathematicians soulless or just most

[stable oar]

the set of mathematicians with souls has measure 0

[rose dock]

[bronze pelican]

Your mom's soulless

[neat lintel]

blocked

I made this visualisation of the hailstone (3n+1) problem. the numbers doesnt look so random at all. they all seam to be somewhere on this line.

[wild jay]

I am soulless.

[neat lintel]

Sold my soul to the devil

[wild jay]

Do you also play the violin?

[neat lintel]

nope

😦

[vale dawn]

they have soul it also have a mathematical representation
Z=a+bi

[neat lintel]

[wild jay]

what

what

[cosmic coral]

is the term "hailstone sequences" widely recognised in maths? can i get away with not explicitly defining what it is (for a personal statement where i need to save characters)

[stable oar]

"Collatz Conjecture" probably does the job better

[cosmic coral]

yeah I'll try bend it that way thanks

[deep mango]

[broken scaffold]

just took a very pleasant evening walk you dunce

[deep mango]

Touch grass.

[neat lintel]

i only used it because i forgot how to write Collatz.

[west wind]

Okay people, I need help. Not math help, more like school advice. So, I'm in the final grade, and shits HARD. We are probably gonna get introduced to integrals and calculus, however my algebra and geometry knowledge is FAR from ready. Do I throw away my maths homework in favor of self-studying with Khan Academy?

[pale orchid]

that sounds like a terrible idea

if anything, you need to do both, and probably still more

[odd narwhal]

How much DE knowledge do you need for dynamical systems?

For an intro course say

[bronze pelican]

Touche de grasse

[deep mango]

Totally depends on the content of the course

Potentially none

Potentially a lot

[odd narwhal]

It seems to focus a lot on DEs and somehow the only prereq on the site is ODEs

Which is a bit fishy

Despite it being a grad level course

[deep mango]

I mean no PDEs will come up

And just having a basic ODEs know how is definitely enough

Dynamical systems isnt really about understanding ODEs super well

It's about looking at them from another perspective

(if at all)

[odd narwhal]

I expected you'd need some analysis and/or measure/probability background aswell

It seems pretty interesting honestly. My summer research advisor does homogeneous dynamics and ergodic theory stuff and he made it seems really cool

[latent forge]

ok it was ifc in change of coordinates

[woven axle]

@midnight grotto omg antisexleagueleadeer ur here too

[latent forge]

ift

i hate ift so much man

[midnight grotto]

I should participate in this discord more

[woven axle]

Me too bro

[woven axle]

I used to

[latent forge]

is differential topology just IFT and change of notation?

[slim meadow]

No

[neat lintel]

Are integration and differentiation considered as basic math operators like +-*/ ?

[latent forge]

btw this context #advanced-analysis message

[velvet dagger]

I don't think there's any reasonable way to formalize "basic math operator"

But calculus operations are harder than arithmetic

For instance, if you give me two numbers

Like written in digits

I can eventually tell you their sum

But there are functions whose antiderivatives you can't write down explicitly

[neat lintel]

Ok, I think you may be right. I have no idea.

[midnight grotto]

🤌

[vapid axle]

What grade are you guys in?

[cold needle]

14

[neat lintel]

What's a grade?

what's grade?

[vapid axle]

Like are you in elementary or stuff

[odd narwhal]

14

[neat lintel]

Ohh, We use class. Do anyone use class here?

[odd narwhal]

Yes we are all elementary schoolers LARPing as mathematicians

[vapid axle]

Or like how old are yall

[neat lintel]

Year 11

[vapid axle]

im so confusing

[odd narwhal]

Yes, you are

[vapid axle]

Lol

[vestal river]

So true

[vapid axle]

oh i see

[odd narwhal]

I'm 10 give or take a few years

[neat lintel]

I was half of my age 10 years back. What's my age now?

[odd narwhal]

10

Give or take a few years

[vestal river]

Any

[neat lintel]

Differential topological vector field over tensor surface.

[bronze pelican]

Automorphic functions and abelian integrals

[stable oar]

image a tense surface
now image one with more tension
that's a tenser surface

[neat lintel]

No, that's a tenses surface.

[odd narwhal]

Homogeneous dynamics on the space of lattices of covolume 1

[stable oar]

the surface with the most tension is the tensest surface

[odd narwhal]

Oh woops

[neat lintel]

True

[odd narwhal]

Meant to reply to this

[neat lintel]

This is a book name

[odd narwhal]

It is?

[neat lintel]

Yes, it has a second volume named.
Homogeneous dynamics on the space of lattices of covolume 2

[odd narwhal]

Lmao

[odd narwhal]

Yes

[upbeat fiber]

Google does not help

Could you please tell me what it is so i can look it up

didn't want to occupy a question channel

[odd narwhal]

Which part.of the notation isn't clear

[leaden torrent]

the function g takes an input from the cartesian product A x A and outputs an element of A

so g(x, y) = z where x, y, z are all from A

[upbeat fiber]

im just wondering what it represents so i can look it up and read about it

[leaden torrent]

its part of function notation.

[upbeat fiber]

aha okok

does it have a name?

[leaden torrent]

its the part of function notation that declares a domain and codomain

no special name

though this particular form would be called a "binary operation"

[upbeat fiber]

right i think i got it :p

[leaden torrent]

https://en.wikipedia.org/wiki/Binary_operation

[upbeat fiber]

perfect

thank you very much

[vast surge]

I'm setting up a math club for my college. What sorts of things do good math clubs have?

[pale orchid]

members

[vast surge]

How do I get those?

I have one other person interested in helping me set it up, so that's 2 members so far. How do I expand beyond that?

That is to say, what sorts of things should a math club do to attract members?

[cold needle]

hold talks

workshops

[blazing pawn]

Cyberbully people into attending

Have food

[cold needle]

advertise opportunities for math activities

(ie programs)

hold socials

[odd narwhal]

Hold collatz conjecture think tanks

[cold needle]

Don't do that. you will attract cranks

[odd narwhal]

You mean math club attendees?

[cold needle]

[latent forge]

obligatory ignoring other channels

what does this evaluate to

im guessing partial y over partial y evaluates to 0

because they are supposed to be same function

[leaden torrent]

uh

think

how much does y change as y changes

[latent forge]

er

[pale orchid]

why don't you take the example of y = x, and then write the derivative of y w.r.t. x in leibniz notation

[latent forge]

classmate did this work and im trying to verify

[fast ivy]

$\dfrac{\partial x_{i}}{\partial x_{j}} = \delta_{ij}$

[fathom swallow]

MisterSystem

[latent forge]

the hell is delta

[pale orchid]

i already took my glasses off so i'm not gonna read that :x but listen to nami

[fast ivy]

kronecker delta

it should be 1 if i=j

and 0 if i \neq j

[rose dock]

kronecker delta is just (int) (i == j)

[fast ivy]

so like

$\dfrac{\partial y}{\partial y} = 1$

[fathom swallow]

MisterSystem

[fast ivy]

think about this intuitively tho

if (x_1, ..., x_n) is a basis for R^n

why do partial derivatives behave like this?

[fast ivy]

This property is pretty important, when you learn about tangent spaces

[latent forge]

i guess to preserve change of basis

[fringe needle]

an orthogonal basis no?

[latent forge]

why does partial x partial y go to h_y

[fast ivy]

AAAAA

[fast ivy]

yup

[fringe needle]

yeah okay i was a bit confused

[latent forge]

wait

partial x partial y goes to hy

because

x=h(x,y)

so its really

[fast ivy]

do you remember the definition of partial derivatives?

[latent forge]

$\frac{\partial x}{\partial y} = \frac{\partial h(x,y)}{\partial y} = h_y$

[fathom swallow]

I Killed the Most

[latent forge]

Lol barely I guess

[fast ivy]

Ok so

[latent forge]

wait a second

partial y partial y

y=1y

partial y partial y should be 1

because you are taking detivative with respect to y

[fast ivy]

Suppose we have ${x_{1}, \cdots, x_{n}}$ the standard basis in $\mathbb{R}^{n}$ and we have a function $f : \mathcal{U} \subset \mathbb{R}^{n} \rightarrow \mathbb{R}$, for $p \in \mathcal{U}$, we define for $ 1 \leq i \leq n$, if it exists, the following limit:
\
\
$\left. \dfrac{\partial f}{\partial x_{i}}\right |{p} = \lim\limits{t \to 0} \dfrac{f(p + t x_{i}) - f(p)}{t}$
\
\
This limit is called the partial derivative of $f$ with respect to the coordinate $x_{i}$ at the point $p$.

[neat lintel]

p + tx_i in the limit

[fast ivy]

thanks

[latent forge]

ok yea

[fast ivy]

I was trying to make the |p bigger

[latent forge]

its like directional derivative along one of coordinate functions

right?

[fast ivy]

exactly

[latent forge]

woot

[neat lintel]

\left.\frac{\partial f}{\partial x_i}\right|_{p}

[latent forge]

geogebra incarnate fixing your latex

[fathom swallow]

MisterSystem

[fast ivy]

AAAA

[zealous pawn]

nice

[fast ivy]

THANKS

[latent forge]

i get the point

no worries

[fast ivy]

Yeah so

Try to prove that $\dfrac{\partial x_{i}}{\partial x_{j}} = \delta_{ij}$

[latent forge]

ok

[fathom swallow]

MisterSystem

[fast ivy]

Think about this intuitively tho

btw

this property is super important

[latent forge]

eh ok

[fast ivy]

Because this is used to show

[latent forge]

i sorta got jt

[fast ivy]

that partial derivatives actually form a basis

for tangent spaces

on a manifold

and you use this all the time

when computing stuff

[latent forge]

so like intuitively if you are looking at partial derivative of one coordinate function wrt another coordinate function you are looking at change in one coordinate as you go along another

since coordinates are supposedly independent of eachother this should be 0 when the coordinate functions are 0.

[fast ivy]

you mean should be zero when coordinate functions are different, right?

[latent forge]

otherwise you are looking at x^i(p+tx^i) -x^i(p) / t

[latent forge]

yes sorry

[latent forge]

I can only think of an example here being
(0,1,0)(a,b+t,c) - (0,b,0) / t

uh ew

[neat lintel]

notation abuse moment

[latent forge]

yea idk how else to express this

but ig you can multiply points now

coordinate wise

[neat lintel]

in the limit the x_i should be (0, ..., 1, ..., 0) (1 in the ith place)

[latent forge]

and that gets you (0,b+t,0)-(0,b,0) / t

yea im lazy

[fast ivy]

x^{i} is linear

so we can write

[latent forge]

im on phone forgive me

forgive me but are coordinate functions always supposed to be linear? no right

[neat lintel]

they are linear

at least the usual ones on R^n

[latent forge]

but like say ur describing points on ellipspods

oh wait lol

[fast ivy]

$\dfrac{x^{i}(p + t x_{i}) - x^{i}(p)}{t} = \dfrac{x^{i}(p) + t x^{i}(x_{i}) - x^{i}(p)}{t} = \dfrac{t x^{i}(x_{i})}{t} = x^{i}(x_{i})$.
\
\
But $x^{i}(x_{i}) = 1$

[latent forge]

nvm they should be linrar

[fathom swallow]

MisterSystem

[fast ivy]

Damn

Absuse of notation moment

[latent forge]

got me geeked up

[fast ivy]

x^{i} should be the coordinate function

i.e it takes a vector in R^n

and outputs the i-th coordintate of this vector

[latent forge]

yea

xi supposed to be basis boy?

[fast ivy]

x_{i} = (0, ..., 1 ,..., 0) where it is 0 everywhere but 1 on the ith coordinate

[latent forge]

x sub i

ok copy

[fast ivy]

x_{1}, ..., x_{n} is the standard basis on R^n

yeah

[neat lintel]

backslash the _

[fast ivy]

ohh

thanks

[neat lintel]

i still haven't thought about those symplectic problems you sent

i was kinda out of it yesterday

maybe later

[fast ivy]

I have done some, it's that I have also other hw problems to do

i am currently finishing my riemann surfaces pset

it is due 08/09

Once I finish the simp geo pset I will send you

Oh btw

[latent forge]

i am thankful for yall

[fast ivy]

Simp

[neat lintel]

Simp.

[cold needle]

yw

[deep mango]

[cold needle]

what

[neat lintel]

give me a cool analytic number theory fact

[bronze pelican]

Class number formula

[deep mango]

Log log log log log log.

[cold needle]

dirichlet.

[velvet dagger]

Metal just copying PTY smh

[bronze pelican]

Dirichlet theorem on primes in arith progs is often proved with a special case of class number formula

[neat lintel]

cool

[deep mango]

The heat kernel gives rise to Jacobi's theta function so you can use parabolic pde theory to prove things about number theory.

[bronze pelican]

Whoah

What is jacobi theta function

[velvet dagger]

Every number can be written as the sum of 4 squares, and there's a nice explicit formula for the number of ways in which you can do so

The way I know uses Eisenstein series

[deep mango]

I have no clue

[bronze pelican]

Is it an elliptic function

[deep mango]

I have no clue

It's a sum of exponentials of some kind

Like

Sum of e^(-n^2x) or something

Idk

It's very important I guess

[bronze pelican]

So it has 2 arguments

[deep mango]

Closely related to riemann zeta

Basically its renditions on the theme sum e^(in^2 z)

[leaden torrent]

ahem

i have a public statement to make

i would like to renounce this quote

#proofs-and-logic has confirmed to me that sometimes notation is, in fact, just that bad

writing (* a) \boxplus b \rightarrow ((* \oplus) \boxplus a) \boxplus b \rightarrow (* \oplus) \boxplus (a \boxplus b) hurt my soul

(not blaming the user, im blaming whatever course designer thought this was more clear than literally anything sensible)

[cold needle]

lmfao

[leaden torrent]

why are there two plus symbols and neither denotes addition

why is $\oplus$ the identity of $\boxplus$, but $\circledcirc$ is the identity of... $\diamond$ for some reason? instead of $\circ$???

[fathom swallow]

Namington

[leaden torrent]

does $\circleddiamond$ exist

[fathom swallow]

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

[leaden torrent]

nope

[velvet dagger]

@cold needle just to interrupt them less: do you see how good of a read I have on people?

The minute I stepped into the convo

It started moving forward

They weren't even listening to me as much as they should've but I guess they paid attention to some ambient noise

And boom it finally goes somewhere

[cold needle]

lmao

yeah the argument got much more interesting after

instead of just being terminology

[velvet dagger]

I am straight up a modern day enlightenment man

[cold needle]

lmao

[velvet dagger]

Honestly I should just go into philosophy and introduce my argument that kinda fixes some of the stuff in Kant

And just revolutionize the subject

[leaden torrent]

i cant tell what aspects of dami's egoism are unironic anymore

[velvet dagger]

@leaden torrent that was the whole point

Those who are susceptible to my influence will take it unironically and realize my greatness

Those who are skeptical can't exactly press because "Oh well ofc I'm being ironic"

My ability to throw people off about my own ego is truly a testament to my brilliance

[cold needle]

Clearly

[deep mango]

This is like believing any of my opinions are ironic just because I pretend they are after the fact

It looks more legit when I denounce some because I own others, but in reality they're all unironic and I'm just trying to cover my ass.

[blazing pawn]

of course the debate was terminological

Smh

[cold needle]

[uncut socket]

@west urchin What degree did you get from uni?

[west urchin]

my major was math

[pale orchid]

nami trying to prove circle circle dot dot

[ancient flame]

$\circ \circ \dot \dot$

[fathom swallow]

gmod

[sonic sentinel]

failed loss comic

[deep mango]

[fair tinsel]

Are you insinuating that gardeners and carpenters can’t do maths? I’ll have you know that those two jobs are where most mathematicians go after grad school

And the highest paying ones available

[wide vector]

I need some help in solving a mathematical problem

[wild jay]

ask in questions channels

[stable oar]

#❓how-to-get-help

[wide vector]

Done

No one is responding🥲🥲

[wild jay]

Just wait or tag helpers again.

[stable oar]

and only tag helpers after 15 minutes have passed, as it says in #❓how-to-get-help

[stray kite]

https://www.youtube.com/watch?v=ho3Z3NL4I4Q

[deep mango]

[blazing pawn]

#chill moment

[bronze pelican]

I've spent like 3 hrs trying to prove chain rule for wirtinger derivatives. Why is this so hard

[wild jay]

complex numbers right?

[bronze pelican]

Yes

[wild jay]

complex differential calculus

[fast ivy]

https://twitter.com/WKCosmo/status/1434529590949687296?s=20 Why tf is this so cringe

Will Kinney (@WKCosmo)

News flash: People in STEM already immerse themselves in literature, philosophy, and art, and think deeply about the human dimension of their work. Far more often than professors in social theory learn calculus or thermodynamics or quantum theory.

Retweets

119

Likes

862

Twitter · Sep 5, 2021, 2:51 PM

[vivid halo]

what's even more cringe is all of math twitter quote tweeting this and this becoming the discourse of the day

[fast ivy]

that too ig

[vivid halo]

also the original point is kinda true, although conversely STEM people often overestimate their competence in the humanities

[fast ivy]

The comments look worse tho

https://twitter.com/WKCosmo/status/1434559586233638919?s=20

Will Kinney (@WKCosmo)

@EliSennesh If you don't understand calculus, you are not a fully educated human.

Twitter · Sep 5, 2021, 4:50 PM

[vivid halo]

based though

yea this is the tweet that everyone is freaking out about

[blazing pawn]

No this is cringe

[vivid halo]

it is, but people's reaction is even more pathetic

[blazing pawn]

Remember

Every time someone is dumb on the internet in common ways

it is necessarily to talk about it endlessly

and give them attention

[vivid halo]

exactly!

don't block them and move on

you need to give them like 50+ replies and quote tweets

that way they don't repeat their attention seeking behavior

[velvet dagger]

Most STEM people overestimate their competence in the humanities

But not me

[odd narwhal]

i'm beginning to think dami is the ultimate life form

[velvet dagger]

When I say I'd be top 23 in any subject

I'm just right

[odd narwhal]

with such a specific number you can't possibly be making this up

[blazing pawn]

only top 23?

kinda pathetic

[velvet dagger]

Look Hegel I'm not gonna lie and inflate numbers here

[bronze pelican]

Lemme block dami and move on

[velvet dagger]

In music theory you know what? Maybe I'd only be 23rd best of all time

I don't know if my talent is that high

I'm willing to accept it

[blazing pawn]

i understand qrting if its like funny wrong

But most of the time its just people saying commonly held cringe stemlord beliefs

Like who cares

[velvet dagger]

What's qrting?

[blazing pawn]

quote retweeting

[velvet dagger]

Ah

Also now that PT has blocked me

You guys wanna learn about automorphic forms?

[blazing pawn]

No

wait

@vivid halo now that i have validated ur twitter opinions doesnt the corollary here implicitly require that every affine open subset of a k-curve comes from the base change functor from an affine normal bar{Q} curve

or am i crazy

[vivid halo]

no, why would it?

theorem 4.6.10 is the hard thing we talked about at some point, even for curves

[blazing pawn]

Yeah but like if i have X, U as above we cant necessarily base change from k to C, right

[vivid halo]

that's right, but you don't need this

[blazing pawn]

isnt that basically the corollary

base change to get an isomorphism of etale pi_1

[vivid halo]

no

k can be much larger than C here

[blazing pawn]

Uh then what is the proof being used

[vivid halo]

literally theorem 4.6.10

[blazing pawn]

Sure but to apply 4.6.10 you either need to base change U to C or you need U to come from base change from C, right?

[vivid halo]

no

well

[blazing pawn]

But thats... what the theorem says lol

that base changing induces an isomorphism on etale pi_1

[vivid halo]

yes I know you're not getting this

what's implicit in the corollary is that you have to descend to a smaller algebraically closed field of characteristic 0

say \bar{Q}

[blazing pawn]

Yeah

[vivid halo]

then base change

[blazing pawn]

thats what i thought originally

[vivid halo]

yes that's the correct way to read this

[blazing pawn]

so like for this to be true if we have k | bar{Q} then X must come from base change of some curve over bar{Q} for this to be true right

or at least to apply the theorem

[vivid halo]

not quite

do you know the trick of like

any variety you can descend to a finitely generated ring

it's similar to this trick

[blazing pawn]

i dont think so?

[vivid halo]

why not?

[blazing pawn]

No i mean i think i dont know the trick

[vivid halo]

oh like

your variety is defined in terms of polynomials, so you can just write down a ring that adjoins the coefficients of these polynomials in a minimal way

maybe \bar{Q} doesn't always work for this but C often does

since you can just adjoin transcendentals in the same way that you adjoin indeterminents when k has some positive transcendence degree

[blazing pawn]

Hmm

im not really sure how to use that in this context

do we want to get like an isomorphism of pi_1(U) with pi_1(V_L) for some curve V over bar{Q}

using this trick

[bronze pelican]

I didn't block you

[vivid halo]

over C, yes

this seldom works over \bar{Q}

[blazing pawn]

Uh sorry V is over C?

[vivid halo]

yes

[blazing pawn]

um does any such k necessarily contain C if it isnt contained in C

what about like bar{Q}(t)

cause if not then cant you not base change from C to k

[vivid halo]

uhhh

so ignoring the fact that \bar{Q}(t) isn't algebraically closed

[blazing pawn]

lmfao oops

[vivid halo]

you can embed \bar{Q}(t) into C by embedding \bar{Q} into C and taking t to be transcendental

so this is fine

[blazing pawn]

Hm

are algebraically closed fields of char 0 totally ordered by inclusion or is this just for C

[vivid halo]

definitely not

but again like

pass to a finitely generated subfield over which your curve is defined, embed this into C

this finitely generated subfield is Q adjoin some algebraic numbers and some transcendental elements

[blazing pawn]

maybe im being dumb but doesnt this just end up with the problem we had before where you cant necessarily base change from C to k but from some subfield of C to k

[vivid halo]

yes you are being dumb

[blazing pawn]

and that base change might not be essentially surjective

:catscream:

[vivid halo]

if this is some subfield of C you can base change to C first

do the comparison with topological π_1

and then base change to k using the theorem

[blazing pawn]

well sure you can like, pass from C to the subfield and then pass from the subfield to k and you'll get isomorphisms but what im not sure about is how you know that any curve over k comes from base changing from the subfield

[vivid halo]

every curve over k is defined over a finitely generated subfield of k

figure out how to embed this finitely generated subfield into C

[blazing pawn]

Ok i think i see

maybe

so instead of Qbar we want some other field L contained in both k and C where the base change thing will actually be true

[vivid halo]

yes \bar{Q} is often far too small

this is already true for curves defined over C: "most" of these aren't defined over \bar{Q}

[blazing pawn]

yeah only belyi curves

[vivid halo]

right

[blazing pawn]

Ok this makes sense i just need to figure out how to find L i guess

and how to show that every curve over both k and C will be defined over it

[vivid halo]

I mean you just have to show that any curve defined over an algebraically closed field k of characteristic 0 is defined over a finitely generated subfield k_0 of k

which is easy

then you have to argue how you can embed k_0 into C

this amounts to choosing some transcendental elements of C to take care of those elements of k_0 which are not algebraic over Q, with the correct relations

there's enough "room" in C to do this

[blazing pawn]

finitely generated here will mean over Q or something right

[vivid halo]

finitely generated over Q yes

[blazing pawn]

okay

[last oxide]

I never understand a word of these AG talks, if thats even AG

[deep mango]

Accidental Geometry.

[bronze pelican]

HOLY FUCK

[bronze pelican]

I've been trying to prove a false statement for 5 hrs

Thats why it took so long

[neat lintel]

[deep mango]

Read.

[last oxide]

true

[bronze pelican]

That took me way too fuckinh long

[narrow rock]

fuckinh

[deep mango]

Sinh, cosh, tanh, fuckinh

[limber perch]

how do you define fuck on a hyperbola

[cinder zephyr]

😳

[bronze pelican]

After several hours I've managed to complete problem 1 of my complex analysis hw

The most tedious sht ever

[frosty zinc]

Oh my. My condolences

[forest jackal]

lol

[cold needle]

pain

[leaden torrent]

yikes (ii)

[bronze pelican]

(ii) took me the longest because I missapplied chain rule for partial-x, partial-y

You'd think $(f\circ g)_x =( f_x \circ g)g_x$

[fathom swallow]

PTLanglands

[bronze pelican]

But thats wrong

Whats actually true is

This is the mistake that cost me several hours

[hidden bone]

hey]

[surreal sapphire]

that highly depends on language i assume

[neat lintel]

First one expresses shock and next one sleepy.

[unborn escarp]

Are you sure i just need a few practice tests to get 350 more points on the sat?

I’ve done many practice tests and a heck load of khan academy and i cant improve enough

[stray kite]

i mean depends on the languages using them but

the latter is almost always used for nasalisation

while the former might just show a different vowel is being used

idk of any lang which uses both

[stray kite]

how organised are people usually
do they do worksheets and stuff in separate notebooks and keep them

if they do physically write them out that is

[river linden]

I open my notebook to a random page (often with stuff already on it) and start scribbling in the margins

[surreal sapphire]

if i do homework, i usually do a nice enough writeup and keep that

scribbling i toss immediately

[surreal sapphire]

i have one folder per semester

[stray kite]

oof

id do that if i were typing but i dont do that if i dont need to submit it

[steel mantle]

I've somehow kept a catalogue of all my digital work since primary school through to now (honours graduation) similarly

Folder per year/semester broken down into subject

[velvet dagger]

Damn

[steel mantle]

I lost some stickman animation videos I made during grade 4 though, that's the biggest tragedy

[velvet dagger]

Oh my god that's so sad

[steel mantle]

I'm not even sure how, I have a story I wrote in that same year

I think because I had it filed away in school back then but the videos elsewhere when I got a new computer I forgot to back it up

Tend to not be that worried about backups when you're like, less than ten years old

[stray kite]

tbh ill just get a notebook exclusively for scribbling homework that i dont need to submit lol

overleaf'll take care of the rest

[devout nacelle]

Yeah, I do the same

[surreal sapphire]

scribbling i do on old paper

just the backside of wtv i can find

[devout nacelle]

Yeah I scribble anywhere as well but now I have dedicated scribbling notebooks since I ran out of backpages and notebook covers lmao

[surreal sapphire]

i have this three part paper storage

top is old paper with backsides/room left, middle is fresh printer paper, down is trash

[devout nacelle]

Interesting

I just have notebooks scattered all over the place, I don't use loose paper

[brave hollow]

I have the same setup

[surreal sapphire]

my scribbling is too shameful to use notebooks

half of it is crossed out

[devout nacelle]

A typical backpage with scribbling

[surreal sapphire]

imagine using lined paper

[devout nacelle]

[surreal sapphire]

my genius is too great to be contained by puny lines

[devout nacelle]

I might switch to blank ones

[surreal sapphire]

in uni i just take a clipboard and a stack of ~20 blank papers

[devout nacelle]

The only advantage with blank ones would be cleaner diagrams

[stable oar]

i use squared paper 👀

[devout nacelle]

The last time I use squared paper was grade 3

[light needle]

I use ipad.

[bronze pelican]

I still have 2 more problems to do on this fking complex analysis hw

[devout nacelle]

[surreal sapphire]

i am not rich enough

[devout nacelle]

Same

[surreal sapphire]

also my genius cannot be contained by a screen

[light needle]

its a good investment kek

[surreal sapphire]

sometimes i cba to get paper and write on my desk

[light needle]

The only disatvantage of ipad is like

[brave hollow]

is that the city block combinatorics problem?

[light needle]

battery life

and also the internet makes it a bit easier to get distracted

[surreal sapphire]

i have an ereader with wacom tech i can write on

but its a bit small

[light needle]

i c

[surreal sapphire]

i should get the bigger one

i use it in bus or when im elsewhere

also scribble on top of pdfs

when they are not worth printing

[light needle]

I would too but im p sure i would get robbed

[devout nacelle]

I don't know the name, the one I came across was "north-east lattice path counting problem"

[surreal sapphire]

this exam im studying for i printed the lecture notes and write on top

and some pages i added more stuff than is printed

one time i had to insert an extra page for my notes

[devout nacelle]

I feel like I should start printing notes too

[surreal sapphire]

i filled the page with cat memes

[devout nacelle]

[surreal sapphire]

tbf my prof did like a page of arguments for something that is just "universal property of inverse limit lul"

[devout nacelle]

Is category theory so overkill

[stable oar]

it certainly can be

[surreal sapphire]

it would take more time to introduce what inverse limits are

[bronze pelican]

my notes situation is a clipboard with loose sheets of paper

[surreal sapphire]

but if you know, then everything follows

[bronze pelican]

no organization

at all

[surreal sapphire]

that prof hates cat theory for some reason

and he's an algebraic geometer kinda

so that is odd

[bronze pelican]

good

[devout nacelle]

Oh btw Loch did your prof finish writing that crossover NT-algebra book?

[surreal sapphire]

doubt

[devout nacelle]

[surreal sapphire]

instead he published a book on history of mathematics lmao

[devout nacelle]

Lmfak

[light needle]

I enjoy reading history of math

[surreal sapphire]

ye same

[light needle]

specailly stuff from the 1800s

[surreal sapphire]

he is head publisher of a german math journal

[devout nacelle]

I'd probably want to read Stillwell's book at some point

[surreal sapphire]

and wrote a book about the history in terms of articles published in there

[devout nacelle]

Really nice

Is it in English?

[surreal sapphire]

no

[devout nacelle]

[forest jackal]

that's a clipboard more organisation than me. my desks in the office and at home are a nuclear explosion site of piles of papers/books/a4 for working on.

theres some vague organisation in that I can usually find relatively recent things if I need to, but generally this is done by rifling through the right geological layer :p

[delicate knoll]

Does $\sqrt[\frac{1}{n}]{x}$ make senss somewhere in math?

[fathom swallow]

THCampbell

[neat lintel]

ye

[delicate knoll]

I mean, rational index

[delicate knoll]

Seriously?

[neat lintel]

if root of y degree of x means x^(1/y) then root of 1/n degree of x means x^n

[leaden skiff]

sqrt notation sucks

use x^(1/n)

[ancient flame]

^^

[delicate knoll]

So we could say it is redundancy?

[ancient flame]

ye

[leaden skiff]

unless you're describing the square root specifically. and even then...

[ancient flame]

it just confuses students

[delicate knoll]

It is beautiful notation.

But i get it what you mean.

[leaden skiff]

it's needlessly confusing

[delicate knoll]

Yeah

[leaden skiff]

that doesn't sound beautiful to me

[stray kite]

do people commonly take courses from other years earlier

like
is it a thing lol

[odd narwhal]

Yes

Well if you have the prereqs

Or even if you don't depending on your department

[vale hare]

courses having a "year" they're supposed to be taken in is a spook

[stray kite]

hmm

ive done some stuff on my own so i was wondering if i would be allowed to take them as courses

[vale hare]

hmmm. at my uni at least only practical courses like in medicine are locked to a year and a major. in math you could take phd courses your first semester if you really wanted to

[odd narwhal]

Some departments are dicks about official prereqs tho

[latent forge]

question

[orchid zenith]

answer

[latent forge]

whats the most number of people that should be in any conversation

because clearly the more people the less progress

im thinking 2-4is probably ideal

unless we develop ways of talking over eachother and then recapping quickly

like maybe 12 people ina conversation

but they pair or triple

[orchid zenith]

obviously it depends on the conversation and who is involved

[latent forge]

in another lang

[orchid zenith]

this is a poorly defined quesiton imo

only good answer is "it depends"

that's my take anyway

[latent forge]

nice social skills but i was just postulating

clearly doesnt depend though

cant have w conversation with 1k people

so there are reasonable limits in communicating to large amounts of people

[orchid zenith]

are we assuming moderation of some kind? like for example a political party will conduct meetings with that many delegates

[latent forge]

mods here start sweating when they see 6 people typing at a time

[orchid zenith]

but in that case there is a chair moderating the meeting

[latent forge]

moderation ig would be a way to guide conversation

not necessary tho

[orchid zenith]

ok here is my claim: if you use robert's rules of order you can have an arbitrarily large conversation which is still productive

assuming technological assistance and good faith from the participants

[latent forge]

wtf robert rule order

[orchid zenith]

it's the standard rules for parliamentary procedure

like if you ever go to a congress or parliament, that's basically the rulebook

i bring it up because it's designed to moderate meetings with hundreds of people

[latent forge]

whats ur justification for it being productive?

i mean what if there is a more productive rule set

nine9s rules of order

[orchid zenith]

i mean there might be lol. I'm just taking the position that a discussion governed by rules and moderation can be productive no matter the size

it is easier to have a productive discussion with less people

[latent forge]

ig assuming good faith probably doesn’t work

like

[orchid zenith]

probably fair year, but then the constraint isn't the number of people but the nature of the participants

[latent forge]

think of a way rn in which you can get the most amount of ppl to have a conversation

im thinking if in America start yelling controversial things until small crowd forms

then have arguments

then release tensions and be in conversation mode

[orchid zenith]

yeah obviously that wouldn't be productive but also it would be unorganized

[latent forge]

i mean that comes later ig

im sure you can turn it into something productive and with order

[orchid zenith]

i think, perhaps, if there was a set or rules everyone agreed to follow, and there were impartial moderators enforcing the rules

[latent forge]

arguments naturally have order in them

[orchid zenith]

the conversation could be productive

and the limiting factor isnt the number of people

but the rules you choose, what people are involved, etc.

that's the point im making

[latent forge]

yeah but are u in a conversation if you don’t participate?

[orchid zenith]

number of people isn't the most relevant factor. it's just easier to not have rules with a small number of people

i would say you are if you have the right to participate

if there is an actual means for you to participate, even if you choose not to

[latent forge]

for that reason thats why i disagree with rules

because people have unspoken rules in speaking

like starting arguments with strangers

they will listen to your response if you start saying things controversial

and then maybe other strangers might pitch in

so no reason to formalize a set of rules

because that involves a lot of set up and limits number of people

ig the goal is to have as many people in one conversation without the topics splitting up

so interruptions could work

but maybe not talking over

something i noticed on this server though is that if there are too many people in one conversation mods want to remove people

and its interesting how irl people dislike large amount of conversation participants. i think its because its hard to pace the conversation

[azure kettle]

it's also because too many of the participants in the conversation would have to be passive and wouldn't get a word in

[latent forge]

thats a possibility but i think that shouldnt be a problem

they should be able to just interrupt if its text based without any social reprecussions

im not sure the statistics on this but i think a fair amount of people treat instant messaging apps like this as conversations irl

like if you are on a forum no one will ever mention the mumber of participants being a problem

[robust holly]

@compact tartan re: #discussion message
#serious-discussion since #discussion is occupied.
how tangible is a "kind" of the well-ordering-axiom?

i apologise for the late reply, i ate breakfast in the meantime

[compact tartan]

imagine being australian

[compact tartan]

I'm not sure I understand the question

[robust holly]

i ought to study, i'm incapable to elaborate

[compact tartan]

but then also again

there are multiple ways to define a well-order on a type

[robust holly]

that i'm aware of

[compact tartan]

and different recursive-but-terminating functions on the same domain might require different well-orders

[robust holly]

i.e. division of naturals can not take advantage of lexical size

[compact tartan]

I feel like completely automatic termination detection may be impossible

[robust holly]

halting problem.

[compact tartan]

unless such automation can also accidentally decide collatz for example

yeah halting I guess

every TM defines a relation on N which is a well order if and only if the TM terminates

[robust holly]

TM?

[compact tartan]

turing machine

[robust holly]

elaborate further

[compact tartan]

encode the state of the TM with a number

n < m if state m can lead in one or more steps to n

this is obviously transitive. If the TM never loops this is also asymmetric, and if the TM halts this is a well-order

[robust holly]

entertaining musings

i'm enamoured by opetopy, higher directed types seem to have open questions, i ought study to solve problems

[fair tinsel]

[hidden bone]

hey

whats up

can anyone help me

[fair tinsel]

#❓how-to-get-help

[jovial ember]

Lmfao muted

[neat lintel]

who is Lmfao

[fringe needle]

Gotta say that is a very accurate drawing of you

[molten acorn]

hii

[gentle bay]

Hi.

[sick dust]

hello

[robust holly]

@compact tartan i defined it!
https://gitlab.com/-/snippets/2172261
and yes, i admit i missed the point, equivalences to paths, not id types, not propositional equalities, etc

[wild jay]

[compact tartan]

missing the point once again I think

maybe?

I'm not sure

[sacred arch]

I did a thing

https://www.desmos.com/calculator/hvboxyiq3n

sunflower array

if you guys know any other cool things to do with the sunflower array tell me :)

[wild jay]

do v=8phi lol

looks like an ancient swas symbol

[uncut socket]

@magic smelt I'm moving that conversation to here since those are help channels, specifically math help and not career help

But I like electrical engineering

[magic smelt]

Kk

[uncut socket]

Pretty difficult at times

[magic smelt]

Heavy on math?

[uncut socket]

Very

[magic smelt]

Ah I don’t like that haha

I’m pretty bad at math

It sometimes feels like I’m dyslexic almost

Only when it comes to math!

[uncut socket]

I had to take, calc 1, 2, 3, diff eq, and linear algebra

[magic smelt]

I get confused and turned around very easily

Wow

That’s a lot

[uncut socket]

And on top of that, all the engineering classes, like circuits, power systems, electronics, etc

[magic smelt]

I could not handle that jeez

[uncut socket]

But as I stated, for you to be an electrician, I do recommend higher level classes so you know what to do

Real world experience is good to, but having that background knowledge is essential

[magic smelt]

I appreciate the recommendation but ahh probably won’t

I really want to just get my level 1 and get some experience

[uncut socket]

If you don't have the proper knowledge, you could make a mistake and things after that won't be good

[magic smelt]

That is true

[uncut socket]

Like amps is what kills a person, not voltage

[magic smelt]

My friend is already a 2nd year he would be willing to give me pointers

[uncut socket]

Well, good luck with that

[magic smelt]

I will try not to become human bacon