serious-discussion

[normal sparrow]

i suppose i will have to accept that rotation is all there is to C

oh actlly

[leaden skiff]

i wouldn't say that

[deep mango]

well, it's a very organized, algebraic kind of rotation

that makes it very good

[leaden skiff]

C is a natural language with which to model rotations

[normal sparrow]

i thikn i found what i was rlly asking for

"How do we apply this rotational nature of C into the real world?"

[leaden skiff]

rotations use trig functions like sin and cosine

and eulers formula relates trig functions and complex numbers

[normal sparrow]

for example, what if we are modelling a spring hanging from a ceiling, going up and down

[deep mango]

yeah

[normal sparrow]

that's an oscillation, and so it would require C. But how???

[deep mango]

you can model that with complex numbers really easily and then take the real parts at the end

instead of having to work with messy sines and cosines

[leaden skiff]

it doesn't require C, but you can use it

[normal sparrow]

GUYS

Hooke's Law

omg

[leaden skiff]

the spring equation has complex solutions

[normal sparrow]

i finally found it

[leaden skiff]

the DE gives you a complex exponential

[normal sparrow]

aye

i was thinking of a DE that i glanced overr

hooke's law

now ur mine

[leaden skiff]

y'' = -kx

you get e^irt

well that sorta form

[primal crater]

[ancient flame]

so u guys know the math joke

$i 2^3 \sum \pi$

[fathom swallow]

gmod

[ancient flame]

2^3 doesn't feel like it fits in there well

so I propose a small change

make an italian person say this in english

$i \eta \sum \pi$

[fathom swallow]

gmod

[fair mural]

lol

also it’s 8 not 2^3

i two to the power of three sum pi

[wooden flax]

LMAOOOO

[ancient flame]

2^3=8

@fair mural

in fact there's the √-1 instead of i as well

[raven vector]

inverse eta

[ancient flame]

lmao

[raven vector]

$i \eta^{-1} \sum \pi$

[fathom swallow]

2217

[ancient flame]

?

why inverse

[raven vector]

$\eta = eta$

and $\eta^{-1} = ate$

[fathom swallow]

2217

2217

[fair mural]

upside down e upside down t upside down a

[ancient flame]

ohhhh

I didn't even notice that

what I meant is

say "I ate some pie" in an italian accent

[raven vector]

lmfao

[wild jay]

I two to the three sum pi?

[ancient flame]

lol

[wild jay]

what's 2^3 supposed to mean

[ancient flame]

8

[wild jay]

-_-

[ancient flame]

I ate some pie

[wild jay]

200 IQ

[ancient flame]

lol

[wild jay]

I failed

[ancient flame]

gg

[raven vector]

F

[wary swift]

my sixth sense tells me ur indian

[sharp mulch]

I'm hiring a TFT booster. Please submit applications in dms. Thanks !

[wary swift]

yes

[sharp mulch]

Lol

[wary swift]

WAIT THATS U ANGE?!

wtf why did u change

unrecognizable now

[sharp mulch]

What did I change

[wary swift]

ur pfp

[sharp mulch]

I didn't though

[deep mango]

you're a different anime boy

[sharp mulch]

Server profile pic

[wary swift]

i thought u were some rando

[sharp mulch]

Server specific

[wary swift]

yeah

i always knew u as the blue anime guy

[sharp mulch]

Yeah different anime boy

[wary swift]

and now you're not a blue anime guy

and my 6th sense tells me that luna is swiss

or sweden

or german

[ancient flame]

don't you disrespect the fuckin caterpillar

🔫 🐛

[inner finch]

love this

[ancient flame]

me too

[placid notch]

@abstract ravine just out of curiosity, are you this same DM Ashura? https://en.wikipedia.org/wiki/DM_Ashura

[neat lintel]

O2 jam, DDR, beatmania IIDX, and Pump it Up

[placid notch]

I know him from FFR actually

Played that game a lot until it got updated and started running really slow in my computer

[hybrid zephyr]

Ya same one he hasn't been that active lately tho

Well. maybe he is in #math-pedagogy

not sure

[neat lintel]

[placid notch]

Damn, that’s epic

Truly a small world

[hybrid zephyr]

Ya!!

[gentle bay]

Wait really?!!?

[hybrid zephyr]

wait now I feel bad about leaving ur serveer

Someone on here was using polytope emojis then I clicked it

Yea it says on the wiki page that he was studying math and is a math instructor now

[placid notch]

Wait, how did you find my server? Haha

[hybrid zephyr]

He's really into pedagogy

[neat lintel]

I knew him from o2jam lol

[leaden torrent]

every few months someone finds out that mniip probably helped make a program or two that theyre familiar with

like powder toy or whatever

[neat lintel]

i have not been playing this for few years

[leaden torrent]

and theyre like "wtf"

https://github.com/mniip

[hybrid zephyr]

[hybrid zephyr]

I'm trying to find the context but I was talkin to some dood somewhere and they were using polytope emojis

and I was like What the heck; wasn't there this youtube video a while back that got super popular about 48 polytopes or something

[placid notch]

Like 95% of our members come from that video alone haha

[hybrid zephyr]

Hahahahaha

[placid notch]

Eh, PD is a lot of things

Any of the OG members that overhears this will hate me for it, but I don’t think it’s even accurate to call it Polytope Discord for the most part haha

That’s only like a third of what goes on over there

It’s more of a math-oriented general talk server with a large amount of shape discussion

[hybrid zephyr]

I C

I think lots of general talk is important

Places that are super serious all the time are

too serious idk

It's weird

[leaden skiff]

BROOOOOO

WHAT

i need to do something with my life goddamn

[leaden skiff]

jan misali?

[neat lintel]

wait really? that's pretty cool

wait mniip's from russia??

https://tenor.com/view/soviet-cat-sovicat-soviet-ussr-cat-gif-21826197

soviet anthem intensifies

[fair mural]

where does it say that

[neat lintel]

his github

[fair mural]

hmm guess i don’t see it

cool though

[neat lintel]

damn I remember playing powder toy on my phone like 4 or 5 years ago

[neat lintel]

Mniip is one of the koolest on the server

And so am I

[compact tartan]

internet celebrity moment

[fair mural]

mniip i’m your biggest fan

can i get your autograph

[leaden skiff]

i actually spent way too much time on powder toy man

[hollow jackal]

mniip i love powder toy

[neat lintel]

Where is your yt?

[neat lintel]

mniip can you add a way to change the physics sim resolution? like it simulates stuff in blocks right? can you add a way make the blocks smaller or larger (hence yk "physics simulation resolution" lol)

[compact tartan]

you mean air?

[random kelp]

<@&268886789983436800> can I get streamer

thanks

[pale orchid]

you got it

[random kelp]

thanks edd, ily

[pale orchid]

[random kelp]

👨‍❤️‍💋‍👨

[primal crater]

@latent meadowerator can I get mod

[pale orchid]

lol who'd you ping

[primal crater]

idk lol

[wild jay]

Randomly pinging someone without their consent is a sin.

[neat lintel]

bannable

[wild jay]

sinnable

[vivid epoch]

@quasi jetty

@quasi jetty help

@quasi jetty avatar

[deep mango]

[wild jay]

lol

[fair mural]

[neat lintel]

hey ryc what does $\int f(dx)$ even mean?

[fathom swallow]

kanga gang drug mule no. 2

[neat lintel]

do I need to know analysis to understand it?

if so, what topics?

[primal crater]

looks bs to me but there are ways you can define it

not worth my effort

[neat lintel]

he integrated it a while back, so pretty sure it's not bs lol

[wild jay]

it's basically d multiplied by the variable x

[neat lintel]

[primal crater]

yes you can integrate it, but it belongs in a museum

[neat lintel]

lol wdym?

[wild jay]

,w integral of f(dx)

[fathom swallow]

Results provided by WolframAlpha

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

Requested by alepk#4230

[primal crater]

idk could be wrong, ryc showed me something on wierstrass func so

[wild jay]

kek

[neat lintel]

lol it didn't interpret it correctly

[wild jay]

is it f(dx)dx?

[neat lintel]

f(dx)

[fair mural]

ask him later when he’s active

[wild jay]

:/

[neat lintel]

the differential dx as an input to something real function f

[wild jay]

trivial

[fair mural]

,w integral of 0

[primal crater]

yes, you have to go back to the drawing board and define f(dx) from scratch

[wild jay]

lol

[fathom swallow]

Results provided by WolframAlpha

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

Requested by quantum#6320

[primal crater]

like $\lim_{h\to 0} \sum_{i=1}^n f(h)$ or something

[wild jay]

,w integral of dx without a constant 1 before dx

[primal crater]

with limits

[neat lintel]

i guess this is integral of f(dx) for a f(x) = 0x

[neat lintel]

hm

[wild jay]

f(h) is f(dx)?

[primal crater]

you can literally redefine anything for your needs

yes

[neat lintel]

lol like the gamma function

[primal crater]

no gamma is an essential definition

[neat lintel]

it is very useful

[wild jay]

not more useful than delta

[primal crater]

like if there's a possible extension of factorial, it's gamma

so you are not actually redefining it

but instead discovering the real thing

[neat lintel]

pretty sure it's more useful than the dirac delta function

at least in math

[wild jay]

dunno in math

[primal crater]

bruh

[neat lintel]

right

[neat lintel]

can you extend the gamma function to quaternions?

[primal crater]

green's function is literally a sol of a LT system with unit impulse, i.e. dirac delta

you solve differential equations with it

[primal crater]

it's very common in complex analysis

[neat lintel]

makes sense since it's a complex function

what about quaternionic analysis

[primal crater]

just like a^2 used to mean a times a

[fair mural]

pretty sure that’s a thing

[primal crater]

now imagine a^i

[neat lintel]

lol yeah extending the definition

[primal crater]

nope

[neat lintel]

rotation in the complex plane?

[primal crater]

they aren't even commutative, so f+g and g+f matters if you are defining functions on them

[primal crater]

not exactly

[neat lintel]

rotation and scaling?

[primal crater]

wasn't the point, I was saying there's no possible interpretation of a^i, compared to a^2 where it means a times a

[neat lintel]

right yeah you have to extend the definition in math a lot of times

[primal crater]

but it's a logical extension of exponentiation

[neat lintel]

like the gamma funciton

[neat lintel]

sure but that doesn't mean it's impossible to define functions on them though

[primal crater]

analysis is not all about defining functions

[neat lintel]

I never said it was

[primal crater]

lims continuity approximation etc

well if there's something on quaternion analysis, I sure haven't heard of it

[neat lintel]

me neither

[primal crater]

why don't you do your phd in it

[neat lintel]

[primal crater]

show the world how it's useful

(ahem)

[neat lintel]

it's too easy, I'm going for sedenionic analysis

[fair mural]

https://en.m.wikipedia.org/wiki/Quaternionic_analysis

boom

[primal crater]

lol

[neat lintel]

"useful"

no one cares about uses

[neat lintel]

oh wow

[primal crater]

mathematicians really are crazy dudes

[fair mural]

i also had that thought once

[neat lintel]

i know right

[primal crater]

[fair mural]

so i looked it up and it was a thing lol

[neat lintel]

Lol

it bet it's like 1000x harder than complex analysis with commutativity gone

[primal crater]

any possible word our brain can come up with, is already a branch in mathematics

lol

[neat lintel]

lmao yeah it does seem like that

[fair mural]

what properties do complex numbers lose again

[primal crater]

quantum mechanics, quantum gravity, quantum analysis, lol

[primal crater]

order, as compared to R

[neat lintel]

I found a way to order complex numbers

but this chat is too small for me write down the proof

[primal crater]

sure, every set can be well ordered

fermat moment

?

[neat lintel]

(V, M) where M is a ring of 2x2 matricies?

that could be?

[distant vortex]

Matrix vector multiplication? Isn't this just applying a linear transformation to a vector? I don't understand what you mean

[neat lintel]

I think they mean, an algebraic structure that has (represetantion of those linear transformations)matricies along with the vector space

[primal crater]

[neat lintel]

so it'd be something like (V, M, *) *: MxV -> V

I think

Idk

[primal crater]

that's not a vs

[fair mural]

me looking at this gibberish

[primal crater]

module is more appropriate

[neat lintel]

I'm not sure if that would be a module either, since modules are basically vector spaces but it takes it's scalars from rings instead of fields

[primal crater]

you are defining an operation from MxV to V

[neat lintel]

right

[primal crater]

M is a ring, V is abelian (wrt addition)

with the operation defined *(M, v) = Mv

[neat lintel]

I guess it's a module

[primal crater]

it is

[neat lintel]

@fresh juniper ??

is that what you're looking for?

[neat lintel]

I think it's a module

M is a ring of 2x2 matricies with real entries

[neat lintel]

yes

I think they're defined using groups

commutative groups

lol don't trust anything I say, I barely know any abstract algebra ask in #groups-rings-fields if you have a doubt about abstract algebra stuff

[fair mural]

i just find it amazing that you know so much only at 17

and i thought i was cool for knowing odes at 17

[neat lintel]

dude I don't know anything!!! this is just stuff that I found out googling and watching others talk in the server

this is just superficial knowledge

I've yet to read an abstract algebra book

[neat lintel]

you are!

[fair mural]

lol thanks

[neat lintel]

like you're actually going through a book (well a resource) and doing and learning stuff

and I'm just wasting my time googling stuff lol

[fair mural]

to be fair i often rush through stuff

[neat lintel]

well it's still better than not even looking at it, seeing you talk about odes made me curious and now I know how to solve does like y' + p(x)y = g(x) lol

[fair mural]

probably how i got halfway done with the de section on pauls notes

[neat lintel]

nice

oh lol

[fair mural]

wait i forgot to mention that was in a week lol

so i was probably way too fast

[neat lintel]

lol you should probably work through the stuff instead of rushing through

[fair mural]

i do work through it, i just often need to see a worked example first

[neat lintel]

that's okay though since you're doing it for the first time

I wish I had enough time to learn math, but I don't because of school

[fair mural]

i wasn’t doing good in school even before i was addicted to math

so now it’s terrible

[neat lintel]

Lol, same for me, that's why I've stopped reading the linear algebra and real analysis book that I just started

I'm gonna do those in the summer

[fair mural]

i’m not disciplined enough to stop lol

[neat lintel]

Lol neither was I, it took me like a year to stop

also the way schools teach linear algebra is just abhorrent

"matricies are a grid of numbers" or some stupid shit like that

[fair mural]

i don’t know how to describe them so

[neat lintel]

instead of teaching the intuition behind them and saying that they're a linear transformation

lol they're a linear transformation

from and to vector spaces

[brave hollow]

matrices can describe all the permutations hence they can describe all the finite groups

[neat lintel]

finite groups of?

[brave hollow]

matrices are objects that form all the groups

groups(algebraic structure)

[neat lintel]

ah those groups

[hollow ginkgo]

anger

[neat lintel]

I don't get it

[brave hollow]

this is the time to ignore analysis and join the algebra gang

[neat lintel]

I wanna be in both the gangs

analytic algebra

[raven vector]

Quit analysis, return to algebra

[neat lintel]

pls explain

[brave hollow]

its just matrices can form symmetric groups (i.e. groups isomorphic to the symmetric groups) and then cayley's theorem(every group G is isomorphic to a subgroup of the symmetric group acting on G)

[neat lintel]

the only thing I understand in that is "isomorphic"

other than that

it's

but nvm, I'll get it when I do learn abstract algebra

I should have a catchy personalitiy

[brave hollow]

I should have a sneaky personality

[neat lintel]

Oh, that is a good idea

ulw

*ukw

today I will be a snake

a sneaky dastard

[leaden skiff]

oh how do you construct one?

[brave hollow]

rename basic vectors <e1,e2,e3,..,e_n> any linear transformation from this vector space to itself would be isomorphic to permutation so the group of those matrices would form the symmetry

[surreal sapphire]

🤔

[brave hollow]

...

[surreal sapphire]

i think there is at least some info missing

[brave hollow]

1 sec I know the word that is missing

[surreal sapphire]

or maybe i don't understand the original statement lmao

but like

if you start with a finite group, you consider the free vector space generated by that group and then the permutations are linear maps (which correspond to the permutation matrices)

[brave hollow]

yeah like I know how to write down the construction explicitly

but I ate some words there

like you need the transformation to map the basis vectors to the basis and it needs to be bijective

[surreal sapphire]

(also existence of a free vector space might be a bit fishy, but it's the correct way to think about it)

[mortal igloo]

Why would the existence of a free vector space be fishy 🤔

[surreal sapphire]

well, what kind of object is it?

how do you construct it, how do the elements look like etc

[mortal igloo]

$\bC[G]$

[fathom swallow]

Icy001

[mortal igloo]

Take the vector space of formal C-linear combinations of elements of G

With no relations

[surreal sapphire]

formal linear combinations is a bit fishy

[mortal igloo]

Hmmmmm how

[surreal sapphire]

wtf is a formal linear combination

as a mathematical object

if you call them linear maps of finite support, this goes away

but the formal linear combinations pov is better i think

[mortal igloo]

Ya if you use linear maps, multiplication of elements is convolution

[surreal sapphire]

you dont need a multiplication (of elements)

[mortal igloo]

It just came to mind

How do you think of Q[x] then

The polynomial ring

What is a complex number? What is i?

[surreal sapphire]

Q[x] via universal property

if i want to know it exists, sequences that are eventually zero

complex numbers are a quotient ring that turns out to be a field

[mortal igloo]

Well formal linear combination of elements of a set is tuples of numbers indexed by the set then?

Well that’s the same as what you said minus finite support

[surreal sapphire]

works i guess

you need eventually zero

i also think existence of polynomial rings is fishy btw

at least when you first hear about them

[mortal igloo]

Did you think i was fishy?

[surreal sapphire]

yes

wait

you?

[mortal igloo]

Hah

the square root of -1

[surreal sapphire]

i first learned of C as R^2 with weird multiplication

which i believed in

i thought polynomial rings are fishy though

so by extension, this construction of C as well

[mortal igloo]

Interesting

[surreal sapphire]

but i cleared up the fishiness by then

and learned not to worry

[mortal igloo]

I guess all free functors are fishy?

[surreal sapphire]

functors are fishy in general

they arent even maps, so what are they?

[fair mural]

what in the world

[surreal sapphire]

i spent so much time convincing me that sets exist and hoping that i could understand everything in terms of sets

[toxic schooner]

[mortal igloo]

Amazing sticker

Well yes understanding everything in terms of sets is ZF

[surreal sapphire]

i guess

young me just wanted to be very formal

and funnily enough "formal combinations of ... " isnt very formal

maybe its me being weird

i learned to just go with the flow though

now i understand all objects through examples

[tiny marten]

yeah i thought i could understand everything using logic-y stuff

formal logic that is

ofc that is pretty absurd and everything you do ends up being way too complicated/not even correct

[icy forge]

Loch, truly random question here but if people write 'Goldbachschen Satz' they mean Goldbach's conjecture right

I have no other people I know who read any form of German

[surreal sapphire]

i am not aware of any Satz (theorem) named after goldbach

the correct term is Goldbachsche Vermutung (conjecture)

@icy forge

[icy forge]

But we have this
https://eudml.org/doc/58472

(It's not Lev Landau but still)

I didn't read the german or the math but I assume it's related to Goldbach's conjecture

Unless some of Goldbach's theorems got renamed into something more/less descriptive

[surreal sapphire]

this is referring to goldbach's conjecture

maybe naming conventions were different back then

this text also seems to assume that a proof is close

[icy forge]

Yeah I suppose, they thought someone would prove it

inb4 iutt memes flood the channel again

[surreal sapphire]

they cite 2) which calls it an "empiric theorem"

maybe the words were used more loosely ~100 years ago, i dont know enough math history to answer that

[sick kite]

"empiric theorem" meaning "eh it looks right" (probably)

[icy forge]

Wiki says it is verified for up to 4 * 10^18

[surreal sapphire]

they say its probably true in the very first sentence

[icy forge]

That's actually really low considering 3x+1 is verified to higher orders but I don't know what's the computational complexity in verification of each number

[surreal sapphire]

but their reason is more sophisticated than "it worked for all numbers we tried"

[icy forge]

nice

[surreal sapphire]

this was roughly 40 years after riemann's über die primzahlen ...

[tiny marten]

Empirical theorem proving sounds cool

[surreal sapphire]

so there were lots of really good results about analytic nt related to those kinds of things

and its maybe fair to assume they thought they were close to a proof but 🤷

(the prime number theorem was proven just 4 years earlier)

[icy forge]

Seems like the weak one is true (I can't find any commentary doubting it) so maybe it's good progress in about 300+ years I suppose

[leaden torrent]

it would be quite surprising if goldbach was false, intuitively

i have no intuition for collatz

but there are a shitton of primes as n gets large

[surreal sapphire]

reading this paper i have to agree

it makes a good point

[leaden torrent]

i think thats why it hasnt been checked to very large values

even if its false, the probability that we actually find a counterexample in any set of numbers we randomly sample is ridiculously small

just because of the sheer number of pairs of primes that sum "close to" a large n

whereas we dont really have any probabilistic info about problems like collatz afaik

so checking numbers until it breaks seems more sensible

(also its computationally much faster to check collatz, just run the algorithm and keep track of a list)

[icy forge]

Isn't Tao's result on probabilistic collatz

[leaden torrent]

okay, fair

but even that doesnt tell us anything about counterexamples really

it rules out a specific TYPE of counterexample

probabilistically

(the jettison-off-to-infinity one)

but not the weirder type where we have another loop

[surreal sapphire]

why check if tao will solve it

who will solve collatz

[icy forge]

Interestingly arxiv lists one UCLA grad student as working on a collatz-related problem

[surreal sapphire]

actually i wonder

say we prove its true for all numbers greater than a number that is not accessible by computers ever

will there be more or less interest in lowering the bound to something manageable

eh, let me rephrase

will there be more or less interest in producing an actual proof

[leaden torrent]

probably not

no one actually cares about the statement of collatz besides pop math videos

we care about what a proof would potentially tell us about the structure of N

[icy forge]

You mean prove for some large C but C>10^128? and space from 10^60 to 10^128 not computationally searchable?

[surreal sapphire]

yes

fair nami

[icy forge]

It could still result in some computation since I think GIMP is a waste of computation to be quite honest

[surreal sapphire]

i think some people would want it on their CV still

[icy forge]

Changing bounds isn't very interesting in math unless the methods are very novel though

The approach is very unlike applied math where bounds kinda matter

Matmul in n^2.22222222 instead of [insert current bound]? PRIZE TIME

[neat lintel]

this is a very funny exponent

I like it

[mint patio]

Could someone explain this to me?

It's a Desmos thing I think?

So I have this function

[fair mural]

feather your new pfp is cute

[mint patio]

And I need to plot the antiderivative of it right

So in Desmos I just did this

Which gave me the right answer

But when I tried manually (on my own) antidifferentiating it and graphing the function

It gives me this

(the function in black)

Now I can see that it's only off by a constant

[deep mango]

that's cause your +C is fucked up for the second part

[mint patio]

So how does Desmos determine the constant?

[deep mango]

it just does riemann integration i think

like

a riemann sum

so there's no constant

it's just the right answer right away

[mint patio]

o

[deep mango]

constant comes from taking an antiderivative

[mint patio]

Interesting

Ok I figured out the constant

It's 27

How would I show analytically that it's 27? Like where does 27 come from...is there some initial condition?

[deep mango]

it comes from where the last piece ended

the integral has to end up being continuous

[mint patio]

Oh

[deep mango]

that imposes a condition on the constant at 3

[mint patio]

I didn't know that

So antiderivatives are always continuous?

[deep mango]

yeah

well

[mint patio]

Even if the original function is only piecewise continuous

[deep mango]

as long as the function is bounded i think

yeah

think about it this way, if you look at the area under the graph up to x

and then you add another little sliver past x

the new little sliver will still be really small, it doesn't matter if the function jumps around or not

the only thing that could cause a problem would be like

an asymptote

where the function gets really huge

and the area of the bit you add is big no matter how small you make your sliver

[mint patio]

Do you have a visual 🥴

[deep mango]

no

lol

um

[mint patio]

sorryyy

Is it cause like

If you have asymptotic behavior

then a little sliver extra adds a lot more area? I think you'd need a more exaggerated asymptote though lol

[deep mango]

yeah

i don't even know when you can actually make the indefinite integral discontinuous

it might always be continuous

idk

[mint patio]

or maybe just isolated discontinuities

unrelated but can you imagine my surprise after three semesters of calculus realizing that differentiating y = mx+b gives dy/dx = m

sully moment

[fair mural]

big brain move

[crystal stone]

@leaden torrent I have a lot of misgivings about the CA education system as a whole, but to be quite honest it does a pretty good job

Comparatively speaking to times when there was no education system

It's been in steep decline since bush era stuff

[deep mango]

it's the channel pivot for me

[crystal stone]

But I still think it's possible to get a great education at an average public school in CA

The de-tracking of math before 8th grade

isn't so great

[digital wing]

Not sure where to ask this, but I wanna ask about the difficulty of real analysis course. I'm taking math as purely electives, and I've already done a bit of math courses like calculus I and II, probability, linear algebra and discrete math. I'd like to know if I'm capable of handling the supposedly cancerous real analysis. Technically I meet the prerequisites but most courses have 'hidden' prerequisites so I'm not quite sure if I can

[distant vortex]

Did you do proofs in your linear algebra and discrete math classes?

If you did, then you are perfectly capable of doing real analysis if you are willing to put in the work. Just up to whether you want to take it.

[digital wing]

Yeah I did

I did pretty badly in discrete math, a B+, which is only above average, tho.

[digital wing]

I don't mind the work tbh. I take math electives partially because I enjoy it. But enjoyment doesn't mean grades and...yeah. I guess this is a dumb question

[distant vortex]

No, it's a fine question

But you do meet all the prereqs

That doesn't mean you will find the course easy

[digital wing]

It's never easy yeah

I've never actually found a math course easy I think

They're meant to be hard

[distant vortex]

I can't gauge what grade you will get. But you can definitely do the course. If you were to continue with math, real analysis would be the next step.

[digital wing]

...yeah, you're right.

Plus I'm an econ major so real analysis is kinda mandatory

In postgrad

Just would like a gauge on difficulty to see if I can't run more math courses alongside it

Like, relative to a first timer doing calc or something

[distant vortex]

What are the other courses? How difficult it is can vary drastically from university to university, and also from student to student. So I can't tell you that.

[digital wing]

Statistics

It's a stats mod that's after probability

[distant vortex]

Ah, I don't know any stats but I'm sure it should be fine to do both

[digital wing]

Reason why I'm trying to squeeze so much stuff together is because as a non major I have barely any time to do math. Like, the math I did I pushed pretty hard to complete.

But yeah thanks man. I'll give it more thought and see if I can't run more math before I graduate

[neat lintel]

wait what? why is real analysis mandatory for economics?

[digital wing]

As much as I can without completely screwing up my grades

[digital wing]

For post grad

It's a 'hidden' prerequisite

Nobody tells you to do it but you have to know it

I kinda asked around for this because it's not on any requirements or guides or anything.

[neat lintel]

but aren't you guys concerned with the applications of calculus? real analysis is pure math though

[digital wing]

I thought so too

[brave hollow]

real analysis is prereq for big boy stats

[neat lintel]

what really?

[digital wing]

Yeah my prof did mention a lot of stats theorems need real analysis

Like continuity

[neat lintel]

oh cool

[digital wing]

Theorem?

I think the name is

How big boy stat tho

My level 3 mod only teaches up to

Method of moments, max likelihood, Neyman Pearson

I have no idea what this last thing is

Dunno what exactly big boi means here

[brave hollow]

its just me trying to not say real analysis is prereq for stats that you would learn in hs or early ug

[digital wing]

Fair nuff

Well eventually I'll have to learn it anyways cos ...job

Oh well

Hopefully it'll be fun

So far math has been pretty good to me. My biggest rages and biggest enjoyments

[jolly junco]

hi guys, I'm trying to get help on a question of derivatives and extrema: I noticed that the rules say that the helping channels should be dedicated for pre-university topics. Do derivatives count as pre-university in that definition? should I move my question to calculus instead?

[icy forge]

Yes you can post in #calculus

Unless you're pre-pre-university? Or post university?

I'm not sure what's pre-pre university extrema

I don't think it's post uni since even the proofs on derivatives/extrema are not post uni. Generalisations maybe

[jolly junco]

I'm taking AP calculus AB, it's technically a college course covering a semester of calc but I'm not sure if I should be in #calculus

[icy forge]

It's fine to be in #calculus

[jolly junco]

thanks!

[fair mural]

basically just ignore the category name in this case and only look at the channel names

[neat lintel]

F

[neat lintel]

Hi guys , I am providing a free maths class for 30 minutes for class 9 students , if anyone wanna join please DM me personally thank you 😊☺🙂

[neat lintel]

do you teach group theory?

No

Otherwise it would be easy to learn

[neat lintel]

if I want to learn anything in math, this is what I would do

and then later experiment with the ideas

in a really weird scenario that just pops in my head, but was not mentioned in the video

to test the ideas, and to have fun

So, you overwhelm yourself?

that is not fun

ic

What I would do

is google/youtube it

click on the first video you find

if you understand how to do the stuff in the video

then I think you should do stuff anyways

and forget watching other videos before you have understood how to do the stuff

ofc, doing fun problems from your head would help, so you have experience

and then I would move on to other videos

If they explain new aspects of that stuff

Then only pick one source

that is what I would do

I know khan academy and krista king

If you are "impatient" when learning, I would recommend faster and denser (krista king), but it might come at the cost of understanding

If you like math, and have time on your hands, I would recommend the opposite

and for all videos

I would also recommend to enjoy the video aswell

perfect

i can imagine that

very good for you

your welcome

[neat lintel]

lol

[sick burrow]

How did this server get created

[vagrant kestrel]

someone wanted to make an A.I. server network but only the math one survived because people have homework

[sick burrow]

How did we get discord.gg/math

Were we just the first ones there?

[fair mural]

we were probably the first server big enough that was interested in it

[sick burrow]

Oh do you need to be big enough for a custom server url

[deep mango]

it's an official discord science network server...

see #old-network

[sick burrow]

Is discord science network an official thing though?

[deep mango]

i have no idea

[sick burrow]

[jovial ember]

Bruh #old-network isn’t an official discord thing

It’s something Seph made

[jovial ember]

I think you needed a certain amount of server boosts and you can grab one. We have lost it for periods of time because the # of boosters fell too low

[deep mango]

seph is very official

[ancient flame]

it's just a major partnership

[leaden torrent]

yeah lmao its just boosts

we are by no means an official discord thing

[deep mango]

are you sure namington?

[leaden torrent]

in fact, there is a partnered math server that is not us

[deep mango]

i just figured you were with the feds or something

[jovial ember]

We keep saying we will

For the last 9 months

[leaden torrent]

(we are not partnered)

[jovial ember]

That’s why honorable lost our pin and messge delete privilege

So we can’t mini mod anymore

[leaden torrent]

that was for discovery

[deep mango]

what?

[jovial ember]

Oh isn’t that the same as partnered?

[leaden torrent]

not partnership

[jovial ember]

Oh

[deep mango]

we have pin privilege

[leaden torrent]

nope

[jovial ember]

No we have to use the bot

[deep mango]

oh

[jovial ember]

We used to be able to do it normally

[deep mango]

hmm

[jovial ember]

Basically like

For discovery

There’s restrictions on who can have moderator type privileges

That was one of them

So it would’ve required every honorable to have 2FA

Which tbh I was like whatever

But I guess some ppl took issues with it, I guess there’s an equity issue if ppl don’t have a cell phone or something

[deep mango]

well

uhh

[jovial ember]

But I know Max like

Said he wouldn’t ever do 2FA

[deep mango]

only the ones who want pin and delete privileges right

can't there just be 2 honorable roles

one with and one without

[jovial ember]

Idk I don’t feel like complicating it

Also we haven’t needed to delete stuff

[deep mango]

mostly true

[jovial ember]

In the past IMO more sus shit happened

[deep mango]

mods are usually available anyway

[jovial ember]

It’s cooled down a lot the past X months

[deep mango]

it's because i joined chmonkey

[jovial ember]

I pretty much only ever used it to like troll my friends in good fun

[deep mango]

i'm a cool cucumber

[jovial ember]

And ocassionally someone said some shit

So I’d delete it

I think Liquid used it once to clean up really old messages with slurs

From yeaaaars back

[deep mango]

that's nice

was the server slurry

[leaden torrent]

slurs like "formalist"

[mint patio]

:o

where/what is it

[jovial ember]

No I don’t think so

It’s just with like, millions of messages

Some stuff just gets said in help channel 5

[deep mango]

chrew

[jovial ember]

That no one noticed

[leaden torrent]

i have no clue what democratic means here

[deep mango]

A democratic server for the appreciation of maths

[leaden torrent]

do they elect mods

[deep mango]

literally under 10k members

pathetic

[mint patio]

yeah lol is that really it

[light needle]

what a bunch of losers not even 10k

[mint patio]

why aren't we partnered this server is massive and mniip needs more responsibilities

[light needle]

hostile takeover when

[leaden torrent]

personally i prefer juche servers for the appreciation of math

cult of personality around jacobian and woog (pbut) when

[hybrid zephyr]

Waiut what

wat does pbut mean

[ancient flame]

we should be a communist server for the appreciation of mafs

[ancient flame]

ppbutt

[hybrid zephyr]

oh Peace Be Upon Them

[ancient flame]

oh

[jovial ember]

Watch out John you got green guardian3.14 on your ass now

Wanna join?

🦘

Kanga Gang

[deep mango]

kanga gang does not endorse the views of kanga gang enforcer john

we need a crocodile

if you want you can be the crocodile and eat all the snitches

[light needle]

wow im being betrayed by my gang

guess ill just become a kosher

[river linden]

yes please

[deep mango]

hmm

would you like to be the treasurer?

[river linden]

sure

[deep mango]

alright

i am not pinging a mod to do this

it's too silly

[river linden]

if only i could change my own nick

[deep mango]

lol

[jovial ember]

@cold needle

Always ping Metal for name changes for Kanga Gang

Altho wait Metal rn is

[deep mango]

yes bother someone else

namington just did it

surely he'll do it again

[ancient flame]

is this proper at all?
$\ \int f'(x)dx = \int \frac{df}{dx}dx = \int \frac{df}{\cancel{dx}}\cancel{dx} = \int df = f(x)+c$

[fathom swallow]

gmod

[deep mango]

no

[ancient flame]

fuck

why does it work tho

[deep mango]

because people chose notation that is suggestive of what should happen

[ancient flame]

oh

[deep mango]

if no one ever came up with the "df/dx" notation then this would not be something you could ever do

[ancient flame]

fuck

[deep mango]

you can see why it's true

by writing down what a derivative is

it's a limit of difference quotients

[ancient flame]

that's true

ty

[devout nacelle]

What would you like to change it to?

[leaden skiff]

if you do this in limits is there ever any actual cancelling of a dx that's going to 0?

[neat lintel]

bruh

where do I learn matrix calculus from

is this commonly taught in pure math classes?

[toxic schooner]

matrix calculus?

[leaden skiff]

it's data science I think?

[neat lintel]

I was reading a ML book

matrix differentiation came up

seems like something only used in stats, econometrics

[wild lantern]

I remember it getting mentioned in the appendix of my ode book.

I also saw some stuff like that in one of those schaums work books.

Maybe it gets covered in some kinds of de courses?

[neat lintel]

or is this just doing vector calc over the spaces of matrices

[wild lantern]

The stuff I'm talking about was not at all that different from vector calc stuff.

Idk about anything more advanced though.

[pale orchid]

its usually taught in optimization courses

as you mentioned stuff like econometric and ML, signal processing, etc. usually deal with optimization problems in several variables

one way to write and deal with them is via matrix calculus

the derivation of the expressions is done with your usual calculus on each coordinate of the vectors, but once you're familiar with the results, it can let you differentiate wrt several variables more quickly

and well, ML deals with optimization and statistics

[serene rover]

Here first I was not getting what this second question meant, after finally getting it I searched for an answer and got following answer from stackexchange.
Please explain last line, why is it "contradictory"???

[jovial ember]

Cuz it’s just, not true

There’s always some k for which that isn’t a power of 10

Also in general check #❓how-to-get-help

[serene rover]

Didn't get it

[jovial ember]

think about what it means to be a power of 10

if 10^n + kd was a power of 10

then you should be able to show that like 10^n + (k+1)d is not a power of 10

or something like this

[serene rover]

I see

Proving by mathematical induction?

[jovial ember]

No…

I think you can just try out what I did

[serene rover]

:-|

[jovial ember]

If it does hold for some k

It won’t hold for another one

Then it’s obviously not true for all k

Since… you just produced a counterexample

Think of it this other way

As a function of k

This increases linearly

For these to all be powers of 10

It would have to increase exponentially

If d > 0 then this is increasing

So if 10^n + kd was 10^m

When you go to k +1 it would have to become at least as big as 10^{m+1}

But this just isn’t possible, 10^n + kd doesn’t grow fast enough

There’s a plethora of ways for you to show that this statement can’t be true

I think you should just try to prove it for yourself in whatever way you find works for you

[serene rover]

Okay. Thanks a lot. I will try

This method which u r mentioning looked similar to mathematical induction.
Proving for k, then k+1

[jovial ember]

But that's not what I"m doing

It might be true that for some k

it is a power of 10

you won't be able to prove that for any k, it isn't a power of 10

you can prove that it isn't true that for all k, it's a power of 10

Like you could even do this

Let k = 1

if this isn't a power of 10

you're done

if it is, then d must be something like 10^m - 10^n

then when you try k = 2

you'll get something that isn't a power of 10

[serene rover]

Ohkkkk

Finally got it

Thanks

[jovial ember]

that's why it isn't induction

because the setup was different

this is like if our statement was false for k, it's true for k + 1

which isn't how induction works

[serene rover]

I almost forgot it's method.

[jovial ember]

I see

[serene rover]

Yup

[still coral]

a random question, and if anyone has an answer it would be great but; I was writing an essay on figurate numbers when i started to think about if there exists a number that can never be used in any figurate number sequence. anyone got an idea? it feels like you would be able to fit at least one geometric form to any given number

[neat lintel]

what's a figurate number?

[neat lintel]

any number that's not a positive integer?

[still coral]

ahhh sorry yeah a positive integer. i mean would be hard to create one from a fraction XD sorry !

[neat lintel]

what about 2?

[random kelp]

Triangular numbers?

The term figurate number is used by different writers for members of different sets of numbers, generalizing from triangular numbers to different shapes (polygonal numbers) and different dimensions (polyhedral numbers). The term can mean

• polygonal number
• a number represented as a discrete r-dimensional regular geometric pattern of r-dimensional balls such as a polygonal number (for r = 2) or a polyhedral number (for r = 3).
• a member of the subset of the sets above containing only triangular numbers, pyramidal numbers, and their analogs in other dimensions.

[neat lintel]

so would 2 be a linear number?

since you can only make a line with it

oh wait it has to be a polygon?

[random kelp]

im not sure what they mean by figurate number

[neat lintel]

me neither

[neat lintel]

what exactly do you mean by a figurate number?

like an exact definition

from what I've seen 2 would not be a figurate number

[still coral]

gonna be honest not sure if there is one. tho 2 i the start number for the oblong numbers

[neat lintel]

an oblong number?

[random kelp]

yea i've never heard of these terms

[neat lintel]

lol yeah me neither

[random kelp]

could you explain what oblong and figurate numbers are?

[fair mural]

are you just coming up with these names yourself

[brave hollow]

no its real

I googled

😮

[random kelp]

yeah they are, but figurate has multiple definitions

depending on the author

[neat lintel]

is it just recreational math stuff?

[brave hollow]

the only other time I have seen this was the first time I joined the vc here

[random kelp]

anyway, if you can provide us with a definition of figurate and oblong, that'd be great

[brave hollow]

and the guy gave me a number theory problem to solve just after showing what triangular numbers are

so I assume its just old number theory

[still coral]

"a number represented as a discrete r-dimensional regular geometric pattern of r-dimensional balls" i think this would be the closet you get to a definiton

[neat lintel]

without an exact definition it's not possible to find such a number, but from what I've seen every positive integer can be a figurate number

[random kelp]

So yeah, intuitively its "numbers which given N number of pebbles you can forma geometric shape (often the outline)"

[still coral]

and an oblong is just a rektangel that is r*(r+1)

[random kelp]

Right okay

Yeah that works

Okay, so one way is to say:
Given some number 'm'

$m = \frac{n}{2} ( (V - 2)n - (V-4) )$

If you can solve for some integer n and V, then you know its figurate.

[fathom swallow]

ryn

[random kelp]

But this seems like overkill method

[neat lintel]

what's V?

oh some integer

[random kelp]

The left is the general formula for figurate numbers

And "V" is the number of sides I think

and "n" is the "nth" figurate number for that polygon

[neat lintel]

ah okay

[random kelp]

@still coral I think it shouldn't be too hard to prove that any number can be figurate though

If we allow n = 1, I think we can generate all integers

[neat lintel]

yeah linear numbers

[still coral]

i mean i just thought; shouldn't you just be able to create different sized rectangles like n*(n+r) cuz every number is either a composite number or prime. the primes would be the start cases for all the sequences right?

[random kelp]

Sorry n = 2

The formula for figurate numbers is:
$\frac{n}{2} ( (V - 2)n - (V-4) )$

Let $n = 2$, then
$$\frac{2}{2} ( (V - 2)2 - (V-4) )$$
$$( 2V - 4 - V-4))$$
$$( 2V - 4 - V + 4))$$
$$V$$

[fathom swallow]

ryn

[random kelp]

So now if you want me to make any number to be a figurate number:
$$P_V(n) = \frac{n}{2} ( (V - 2)n - (V-4) )$$
$$P_V(2) = V$$

[fathom swallow]

ryn

[random kelp]

Does that work @still coral

More geometrically speaking, every second figurate number for a given polygon, has the same number of 'pebbles' as the number of sides of the polygon (since the first figurate number is 1)

[still coral]

true, yeah that answers my question

[neat lintel]

oh, I feel sorry for you

are you a second account?

[river linden]

Kanga Gang Treasurer uli

[devout nacelle]

[pale orchid]

this turned into like a yugioh archetype

we need some spell and trap cards

something like

kanga's return from the D.D.

blazing fist of the kanga

Nr. 307 cosmic kanga, rank 8 xyz

[devout nacelle]

[leaden skiff]

hey I was teaching my sister prime numbers and I told her that we didn't always know there were an infinite amount of prime
numbers, and that eventually someone proved there were.

and the first question she asked me was "oh what YouTube channel was this?"

[bold ferry]

Nice

[primal crater]

kids these days

[gentle bay]

[tiny marten]

That's kinda cute

[gentle bay]

By the way who was it and how did they do it?

Euclid.

IT WAS PROVED SO LONG AGO?!!?

[tiny marten]

Yes you generally prove it by contradiction

[leaden torrent]

euclids proof is noncontradictive

[tiny marten]

Oh yeah? I didnt know that

[neat lintel]

euler's youtube channel

[gentle bay]

How did he prove that Namington?

[tiny marten]

Tho the first way a lot of people learn is by way of contradiction

[leaden torrent]

Euclid is often erroneously reported to have proved this result by contradiction beginning with the assumption that the finite set initially considered contains all prime numbers,[6] though it is actually a proof by cases, a direct proof method. The philosopher Torkel Franzén, in a book on logic, states, "Euclid's proof that there are infinitely many primes is not an indirect proof [...] The argument is sometimes formulated as an indirect proof by replacing it with the assumption 'Suppose q1, ... qn are all the primes'. However, since this assumption isn't even used in the proof, the reformulation is pointless."[7]

[tiny marten]

Neat

[gentle bay]

https://www.cantorsparadise.com/six-proofs-that-there-are-infinitely-many-primes-33037bc2c54e

Let me read this.

[tiny marten]

I guess everyone attributes the usual proof to him

[leaden torrent]

it is the usual proof

the point is that its not a proof by contradiction

You suppose you have a finite list of primes and show there's a prime not on this list

[gentle bay]

Okay this goes advanced.

[gentle bay]

Yes, but how?

[leaden torrent]

You never contradict anything

[gentle bay]

Can you explain us, Namington?

[leaden torrent]

Cases

[gentle bay]

Cases?

[tiny marten]

Oh then I guess the proof I use isnt strictly Euclids

[tiny marten]

Ah yeah my proof actually does do contradiction but is otherwise v close

[neat lintel]

proof by contradiction is my favorite type of proof

[tiny marten]

Proof by contradiction is nice tho it is always good to have a feeling for when you dont need it

[gentle bay]

Let me read.

[leaden torrent]

You don't need to ping me to tell me youre reading

[pale orchid]

or do they?

[neat lintel]

vsauce theme plays

[dense belfry]

that's the same style as cantor's diagonal argument, would you consider cantor's diagonal argument a proof by contradiction?

I think I would say euclid's argument is a proof by contradiction because the assumption is "there is a finite list of all primes of size n", which is what is contradicted

but idk if there is a more formal reason to say it's not proven using contradiction (eg there is a proof theoretic framework which does not allow for proof by contradiction in which euclid's proof is formalized)

[vague lion]

i love proof by contradiction because it gives you somewhere to start

[leaden torrent]

That isn't what's contradicted

We prove that this list cannot contain all primes

By finding a prime not in this list

This is, unambiguously, a direct proof

And not for low level logic reasons

We have a finite list of primes
We find a prime not on this list
Therefore the list of all primes is not finite

No contradiction involved

[leaden torrent]

Cantor's diagonal argument explicitly contradicts the claim that there exists a list of ALL real numbers

We never use this assumption in Euclid's proof

[gentle bay]

Sorry didn't see ping notification turned on, and that was a reply literally after like 2 minutes when you were in the chat.

[dense belfry]

I mean you can phrase the proof as an algorithm (if I'm given any finite list of primes I can find a prime not on the list)