serious-discussion

[leaden torrent]

though idk how youd be interested in ag before even knowing what a ring is

[bronze pelican]

Yes its a prerequisite

[mint patio]

those two are the same thing?

[leaden torrent]

second one is a generalization for arbitrary k forms

[mint patio]

weirdchamp

[atomic hornet]

Bc algebraic geometry is hype

[fair mural]

cool name that’s about it

[crystal stone]

Some classes will like do this "learn as we go" type thing, especially topics courses in undergrad

Is it effective?

[fast ivy]

I'd say learning bits of commutative algebra/ring theory along with algebraic geometry may be a good way to motivate a few constructions here and there.

But that's about it

[neat lintel]

this is why a&m is cucked

[deep mango]

[neat lintel]

:blushsully:

[fast ivy]

Hi TTerra

[neat lintel]

hi mistersystem

[crystal stone]

A&M is a good school

[neat lintel]

i meant the book

[fair mural]

tterra can i get a hi too

[crystal stone]

I've only seen it referred to as Atiyah

[neat lintel]

i didnt even know there was an a&m school

[crystal stone]

Tejas baby, Tejas

[mint patio]

A&M is nice

except it's full of racists and every other -ist you could think of

also it's in the middle of nowhere

[crystal stone]

I don't think that's true

I loved my time in Texas (well at least partially)

[mint patio]

I don't think anyone's going to openly flame you for that kind of stuff but that doesn't mean it's not there

I'm just speaking based off of what I've seen other people say, I haven't personally been to A&M since middle school

[crystal stone]

I know some faculty at A&M, and I used to work with a lot of A&M alumni. Saw nothing but kindness from them

[atomic hornet]

I applied to A&M

[peak ledge]

telll

[tough pivot]

which question?

[fair mural]

@peak ledge #❓how-to-get-help

[tough pivot]

I've actually gone through this exercise in my previous grade lol

[chilly coral]

Might not be easy for someone new to the subject

[neat lintel]

captain obvious

ive missed you on your sea fares

[chilly coral]

It's mr. captain obvious to you

[muted rose]

i finally understand why linear algebra is in machine learning

finding euclidean distances is a technique in, like, figuring out which data are similar to each other

its called clustering and its used in recommendation algorithms

i feel like the other topics like dot product are also used for finding similarities too

[deep mango]

machine learning is entirely phrased within linear algebra and probability theory

the entire conceit of the subject is "apply linear maps interspersed with simple nonlinearities, and tweak the linear maps"

[muted rose]

lol

i just picked up a book from mit on data science

im an absolute beginner, but i do know how to program so it shouldnt be too steep a learning curve

[muted rose]

yeah the chapter on regression basically said "lul just tweak it"

well, more specifically start from a linear line of best fit and then do curves if you need to

and i just like

dont know how youd go about doing that 😩

they make it seem like its just guesswork

[tiny marten]

Yeah I am currently doing research on the adaboost boosting algorithm and linear relations of distance on data sets is a big deal

Adaboost is interesting because it sort of super imposes all these bisections of a data set embedded in a feature space

[muted rose]

oooh

not entirely sure what adaboosting is actually lol

[tiny marten]

Its very cool and an interesting algorithm in general

It has some mysterious qualities

[muted rose]

hm

how so

[tiny marten]

It has the ability to resist over fitting in its learning procedure and also exceeds the error minimization that was expected, a total surprise 20 years ago, and still isnt entirely understood

[muted rose]

damn

[tiny marten]

Yeah they are still working on the theory of how it performs so well

One theory having to do with linear distances

[icy forge]

While I think distances are involved I don't think they are necessarily linear

[tiny marten]

With adaboost or ML in general

[icy forge]

ML in general

[tiny marten]

Oh, yeah

[icy forge]

I'm not too sure on boosting itself TBH so

[tiny marten]

There are definitely models that dont deal in linear relations on the data set

Boosting is largely related to linear regression techniques and gradient descent

[muted rose]

hmm

i kind of want to learn more about it

[tiny marten]

You should look into the support vector machine

The basic SVM is linear I believe, and it is sort of pre-empts boosting and other linear things

And it gives you a way to understand nonlinear classification

You can classify a data set using something that isnt just a clean, linear hyperplane bisection

[muted rose]

aye

i just know the basics of linear regression lol

[tiny marten]

Yeah looking into SVM and boosting could be useful

They are easier to understand than perceptrons and neural nets at first

[near mulch]

Hello guys

I need to show an ez inequality

But I can't make it

I need to show that (a+b)^x<a^x+b^x where a and b are positive and 0<x<1

[frail sail]

Try this…power up both sides by 1/x…. LHS will be a+b. RHS will be logically more than it

[opaque patrol]

note that they're equal when x = 1 and when x = 0, (a+b)^x = 1 and a^x+b^x = 1+1 = 2 and 1 < 2
and then think about the fact that both sides are monotonically increasing as x decreases

that's how I'd go about it anyway

[crystal stream]

binomial expansion?

[opaque patrol]

x isn't an integer so that doesn't help too much unless you really wanna work with an infinite sum

[ashen bison]

Have you done calc yet or no?

[long matrix]

^I think they said they found it

[ashen bison]

oh wait what was the approach?

[near mulch]

Ok so I studied function -1 -t^x+(1+t)^x with parameter x and variable t

I showed it was negative on R+

And then I evaluated it at a/b and multiplied by b^x

And there we have our inequality

[near mulch]

If you needed an answer

[ancient flame]

have u guys ever dreamed about math

lmao

nerd

[jovial ember]

TFW

[deep mango]

I don't think I've had super weird math dreams

I've had math dreams about solving problems or presenting things to people, but super banal stuff

The weird dreams never have any math in them

[ancient flame]

lol

[ancient flame]

is $G\overset{f}{\rightarrow}H$ one of those category theory drawings representing a mapping of a function?

[fathom swallow]

the true embodiment of a sully

[ancient flame]

like a basic drawing

or am I completely wrong

[jovial ember]

It literally is just representing f:G -> H graphically

So sure, it’s a diagram or a drawing

[ancient flame]

but like is it one of those category theory diagrams?

it looks like them

[jovial ember]

Technically

It’s not a very interesting one

[ancient flame]

well yeah but still

so technically

[jovial ember]

Yeah it’s a commutative diagram

[ancient flame]

you could say that I'm a category theorist

[jovial ember]

I mean…

Okay

[ancient flame]

LOL

[surreal sapphire]

i use this notation all the time because i forget to name my maps and then notice that they need names

category theorist status: achieved

[ancient flame]

lmao

[deep mango]

Gmod give a talk on proving integration by parts using category theory

[ancient flame]

LMAO

IHY

is that even possible

[frank hedge]

ayo i have a quick question, i feel like everybody uses the part highlighted in red. However, I feel like the part highlighted in blue is more precise. Am i missing something?

[ancient flame]

it is more precise

but everyone ignores it

people tend to ignore the domain restrictions when taking derivatives

[deep mango]

Umm it might be rude to send it but my friend wrote a short expositional paper doing this lol

Using adjoint functors

So funny

[ancient flame]

lmao

[deep mango]

I think it might not be public

[ancient flame]

functors so relatable

arent functors like maps between categories

ohhhhh okay I get it now

makes so much sense

sense = 100

lol

oh

lmao

I see

Set

so smart

🧠

ohhhhh

that's interesting

because a category contains all sets right

so if a category was a set, then it would be the "set of all sets"

is this line of reasoning correct?

[vague lion]

the category Set contains all sets, sure

[ancient flame]

yeah just making sure

that's like the peak of my knowledge of category theory lmao

oof

idk

[unborn trellis]

Probably waiting until you've actually seen a functor in context would be good before doing category theory lol

[sick kite]

Define integration by parts in terms of category theory then prove the thing

how hard can it be?

[ancient flame]

lol

[hollow flame]

guys everybody hold up i solved integration

[ancient flame]

you just went in a circle

LOL

[hollow flame]

no look i evaluated F

[ancient flame]

bruh

[hollow flame]

obviously F is a separate variable that does not depend on x

[sick kite]

????

uhm

am I being dumb or

[hollow flame]

nah youre not dumb

its like one of those proofs that 0=1

[sick kite]

ah mkay

i just dont know enough calc yet lols

[hollow flame]

F depends on x so i cant integrate sinx with respect to it like that

[sick kite]

I was thinking that yea

[hollow flame]

e^x / sinx does not have an integral in elementary functions

also i believe that if youre integrating from 0 theres an asymptotic sliver with infinite area

so your integral would not even converge

well i guess thats why you usually start at 1 for 1/x

btw integration by parts could probably be proved in terms of category theory

my intuition says its something like a coproduct in the category of diffeomorphisms

[ancient flame]

yuck

[hollow flame]

right if the product rule is given by a product

[deep mango]

Lol

I mean it's expressing an anti self adjointness property of the derivative

It's gonna be an adjoint functor thing

[hollow flame]

in Set

or well i guess the category of smooth 2-manifolds

if you take the functions as your objects you could do smth with universal constructions

im gonna b honest i dont understand adjunction

i make everything into a 1-category with stupid arrows and then i can understand

[hollow flame]

ok yes i am correct

take ob = diifferentiable functions
take morphisms = an arrow exists from x to y if y is a component of a (n>=0) derivative of x

then proving integration by parts is just proving existence of all coproducts

and its a poset

so not super hard honestly

[unborn trellis]

brainrot

[hollow flame]

anything can be a category if you think about it for several hours

[neat lintel]

one time i was explaining what a derivative was in vc to a highschooler

and someone kept loudly interjecting about how we could view differential calculus constructs as category theoretic

i got angry and told them to shut up or something

this server is crazy

[untold sapphire]

hahahaha

I'm with you no worries. i would never do that to a poor soul

[hollow flame]

"y is a component of any derivative of x including the 0th derivative for identities" is incredibly stupid condition for a morphism

i think we should leave calculus alone

well actually now that i think about it
maybe mildly useful for differential equations?

easy natural transform to linear algebra right?

maybe not easy

not sure how the whole component thing would go

especially bc the derivative is acting more like a relation than an actual derivative so idk about turning that into a matrix

[tiny marten]

Lol

Why do calculus when categoryposting do good

[mint patio]

why be helpful at all to high schoolers who don’t care about higher math and just want to pass their class when you could flexpost all your advanced math to jerk your ego off to their confusion?

[jovial ember]

Category

[tiny marten]

"I mean I guess you could use the limit definition of a derivative in your calc 1 class but I am telling you that you can also take the double self adjoint k-category contravariant cohomological spectral n-form instead"

[untold sapphire]

so true

[mint patio]

half the fucking people who try to help here

[mint patio]

[mortal igloo]

I'll just say I'm not convinced by this category theory proof

[untold sapphire]

yeah i don't know what's going on there

I'm not sure what you're talking about

with the products and coproducts and stuff

[mint patio]

okay wait

so I was watching a cat theory meme vid a couple days ago

[jovial ember]

Is it the one with the coconut?

[mint patio]

and he said “co” just means like do the thing but backwards??

Yes

[jovial ember]

Yes

[mint patio]

Oliver Lugg or wtv his name was

Funny video

[untold sapphire]

was it this https://m.youtube.com/watch?v=H0Ek86IH-3Y

[mint patio]

so is cohomology just backwards homology and is covector just backwards vector? idk what homology or covectors are at all but that latter one doesn’t sound right

[mint patio]

yes

funny video

[mortal igloo]

A covector is definitely not a backwards vector

[mint patio]

LMAO right

[mortal igloo]

Cohomology if you use chain complexes could be thought of as backward homology:
... -> A0 -> A1 -> ...
ker d/im d is homology here
... -> A1 -> A0 -> ...
ker d/im d is cohomology here

[jovial ember]

Cohomology is homology of a cochain complex

[mortal igloo]

I'm not sure how enlightening that is though

[jovial ember]

The literal only difference is if the numbers go up or down

[jovial ember]

And if you write them as a subscript or superscript

[untold sapphire]

using a vector v in a vector space V you can define a linear transformation from R to V which sends 1 to v and r to rv. a covector is a linear map V->R, in the other direction

[mint patio]

I don’t have any of the prerequisites for this stuff

[jovial ember]

I don’t remember which is which, I just pick it at random

[untold sapphire]

this is the path

[jovial ember]

Is there a pneumonic for it??

Like for Ext and Tor

[untold sapphire]

fam

[jovial ember]

Or for (co)chain complexes

[untold sapphire]

are you misspelling this as a joke

[jovial ember]

I don’t remember where the indices ever go

Yeah

Mnemonic is the actual word

[mortal igloo]

Tor for tensor products, both start with T

[jovial ember]

[mortal igloo]

you're welcome

[mint patio]

so a covector’s a function?
it sends v to 1 and rv to r

[jovial ember]

No Icy

Lmfao

I know which is the derived fucnctoe of what

[honest veldt]

that was definitely intentional, wasn't it, chmonkey you strong fella

[jovial ember]

I forget if the numbers go in the top for Tor or for Ext

[mortal igloo]

Oh you meant top or bottom

[jovial ember]

Yeah

[mortal igloo]

Hmm I somehow just remember cohomology is top

and ext is top

[jovial ember]

And also for cohomology and stuff

[mortal igloo]

The thing I have the worst time remembering is |- or -| for adjoint functors

[jovial ember]

I forget which goes where

[mint patio]

Icy are you a top

[honest veldt]

[jovial ember]

That’s why I asked if there’s a mnemonic for it

[mint patio]

why’d everyone stop talking

[jovial ember]

Except I wrote pneumonic

[mortal igloo]

I disagree that everyone stopped talking

[honest veldt]

you did this featha

[mortal igloo]

Hm a mnemonic...

[mint patio]

I hate doing homework lol

[untold sapphire]

first half yes second half hmmm maybe but you also have to tell where the other vectors go that aren't linear multiples of v. an example of a covector is, if your vector space has a dot product or inner product, fix some vector v and then there's a covector V->R which sends w to <v, w>

[mint patio]

I’ve never felt as bad about learning as when I do math homework

[mortal igloo]

I think I remember cohomology is top indexes by sheer amount of usage

Then Ext is like cohomology while Tor is like homology

[untold sapphire]

i don't have this problem but i dont remember the top and bottom indexing conventions for covariant and contravariant stuff in diff geo.

[jovial ember]

Maybe I can remember it that way

Because the (co)homology I’m most used to is sheaf cohomology

Which is H^i

Or maybe

Cochain complex goes up in degree

So it go up top

Chain complex go down so it goes down

[untold sapphire]

ok

[hollow flame]

a covector is a linear functional

its the opposite of a vector if you think of constructing a vector as several component scalars

it takes in a vector and spits out a number

so it is a function, it's just a multivariable one

[tiny marten]

I have actually been getting the chance to use basic functional analysis stuff in my algorithm research lately

Functional analysis and convexity are so cool

[ashen bison]

i don't understand what you did there lmao? is this for analysis?

[near mulch]

What did you not understand

[ashen bison]

how'd you come up with the function?

[hidden bone]

What year are most of u in

[fair mural]

there’s really no answer to that

[ancient flame]

yeah, some in high school, some in college, some doing phds, some are teachers, just a mix of everyone really

[mortal igloo]

Imagine if discord existed in like 2008

Unfortunately facebook existed in 2008

[ancient flame]

unfortunately i existed in 2008

[fair mural]

unfortunately gmod existed in 2008

[ancient flame]

#sad

[deep mango]

lol! boomer!

[fair mural]

ryc is in his 20s therefore he’s a boomer

[mystic mountain]

imagine being old

[mortal igloo]

Man there are probably people in this server who were not alive in 2008

Y'all are boomers if you were alive in 2008

[fair mural]

i’m 17 and i’m a boomer

rip

[mystic mountain]

i’m 7

[tender musk]

#rules

[mystic mountain]

oh there’s even a rule

[ancient flame]

that's like

a discord rule

[mystic mountain]

fine I’m 77

[tender musk]

They can't be #rules

[ancient flame]

in fact that's more of a social media rule

united states law actually

[mortal igloo]

If you were born on January 9, 2009, you can be in here

[mystic mountain]

nobody reads the age rules lol when making an account on social media

does anyone have a suggestion for a name? it has to be cool tho x.x

[tender musk]

Questioning my own age...

[tender musk]

Nope... I know my own age

[fair mural]

drop the ..

[tender musk]

quantum2

[fair mural]

no

[tender musk]

Or just Quantum

[mystic mountain]

I don’t remember my password… and apparently I need it to change my username… give me a damn moment

[tender musk]

It is a good name.

[mystic mountain]

no quantum

refresh x.x

also I did not mean my username

[fair mural]

then what did you mean

[mystic mountain]

just names in general

[frozen merlin]

for people?

[mystic mountain]

yes

[frozen merlin]

I always thought cassian was a cool name

[mystic mountain]

it is, I am reminded of acotar when I think of that name tho

[hidden bone]

Anyone offer me a job

[fair mural]

[mint patio]

ACOTAR was good I need to read the latest one

after Frost and Starlight or whatever it was

why not just do “chloe” lol

[mystic mountain]

the other sister of feyre lol istg if she’s with the third male from the other trio tho…

[dense radish]

sorry if this is the wrong channel for ask this, but do you guys know any good programming help discord servers?

[fair mural]

@dense radish there’s a server with 112k members with the invite code programming

[dense radish]

Thanks a lot for help

[mint patio]

guys

https://www.google.com/amp/s/www.cnbc.com/amp/2022/01/08/cyprus-reportedly-discovers-a-covid-variant-that-combines-omicron-and-delta.html

doom.

[pale orchid]

https://tenor.com/view/transformers-decepticons-attack-soundwave-shockwave-starscream-gif-14693384

the new decepticon strain

[mint patio]

LOL

[fair mural]

deltacron

[pale orchid]

necronomicon

[naive orchid]

lol

I really want this shit to end ASAP

like who the fuck can stay at one place for hours together

[jovial ember]

hours

[fair mural]

hours

[jovial ember]

My guy it’s been a hell of a lot longer than hours we’ve had to stay put

[naive orchid]

true lol

[velvet dagger]

Oh noooooooo

Honestly the more time goes on the more I think covid is proof that God's there and he's enraged at us lol

[inner finch]

lmfaooo

ive honestly resigned myself to a covid life

it's going to be this way forever

[fair mural]

2 years already, 20 more here we go

[toxic schooner]

[neat lintel]

Im back bithes

[compact tartan]

took long enough?

[velvet dagger]

More like with time it increases in how strongly I feel this way

[flat harbor]

bayesian theology

[opaque patrol]

lol

[toxic schooner]

[stray kite]

god is real and i am him

i am the god(only one)

[ancient flame]

yeah that should be good

[granite lantern]

isnt it better to take calc1 then stat course?

[ancient flame]

either way is fine

they're completely unrelated to each other

[granite lantern]

i mean, dont you need to find estimated values/mgf/another characteristics of distribution through integration/differentiation?

[fair mural]

intro statistics has nothing to do with calculus

[ancient flame]

that's a more advanced stats course I believe

yeah

[fair mural]

that’s when it starts becoming more advanced

[tender musk]

It would be interesting to have a debate channel that has weekly non-sensitive mathematical topics

[tender musk]

Or daily...

[static loom]

wdym

you want to debate if 1=.999... or somethin?

[tender musk]

To possible create more quality conversations

[fair mural]

[tender musk]

There are plenty of un-answered mathematical questions like

[tender musk]

Does 1 -1 + 1 -1 + 1 -1 + 1 -1 = 0, 1/2, or 1

[granite lantern]

isnt transcedental number theory just the questions like this but interesting?

[fair mural]

this is so trash

[tender musk]

Maybe we could put forth our best efforts to solve un-answered mathematical questions... we probably would fail but have fun doing it

By mathematicians

[tender musk]

Ouch

[fair mural]

the answer is undefined

[tender musk]

is it?

[fair mural]

yes

undefined falls under divergent

[tender musk]

See we are already having a debate... and the question is not what is important currently but the concept is...

[fair mural]

this is me calling your answer trash and thinking my answer is superior

debate?

[tender musk]

What do you mean divergent?

It stays between the values 0 and 1...

Online if that counts

[tender musk]

Otherwise no

https://youtu.be/PCu_BNNI5x4

Si

Again the question is not the point

What mathematical youtube channel is consistently reliable?

I have no choice if I want to learn more about math, practically

[pure sun]

if you want to learn math

[granite lantern]

this one?
https://www.youtube.com/c/Aleph0

[pure sun]

dont rely on any math channels

get some math textbooks

depending on the topic, khan academy has some good videos

[tender musk]

Aren't they expensive?

[pure sun]

what kind of book are you looking for

calculus? differential equations? linear algebra?

an old edition of a calculus textbook can be purchased for $10 on used book sites

[granite lantern]

spivak's calculus is VERY expensive and its one of the best books on the calculus

[tender musk]

I am unsure, I just purely want to learn (where I can understand)

[pure sun]

you have to start by deciding what you want to learn

and what your goals are

[tender musk]

I have gotten a few books in the past... they were complicated and went way over my head, 3b1b delivers messages in ways I can understand them more easily

[tender musk]

hmm goals...

[pure sun]

3b1b doesnt actually teach math

[tender musk]

?

[tender musk]

Where do you suggest starting?

[pure sun]

lol i cant answer that until you tell us what your goals are

[granite lantern]

btw what are good and interesting problem books in calculus 1/2 in anglowold?

[pure sun]

and what math classes you've taken so far

do you want to become a mathematician? do you want to do physics? engineering? are you just trying to learn calculus so you can pass your calculus courses?

[tender musk]

In-Person Algebra 1, Geometry, Algebra 2... Online Too many to count (I exist taking math lessons online from youtube)

[tender musk]

I started with physics but I think I want to be a mathematician (hopefully a professor)

[pure sun]

do you know calculus?

[tender musk]

About 85% depending on the level (This is future me, What in the world was this statement)

[pure sun]

im not sure what that means

[tender musk]

And what the textbook consists of

Thanks...

I work mainly in differential calculus

[pure sun]

so learn integral calculus

sequences and series

multivariable calculus

[tender musk]

If I use calculus

[tender musk]

I think this would be good

Thanks @pure sun !

[pure sun]

np and gl

[ripe wasp]

3b1b just explains the conceptual ideas btw, yt should be used as a supplement to actually solving problems

i recommend stewart

it has differential calc integral calc and vector calc

all in one book

it's also pretty easy to understand

[broken crater]

I'm not sure if I am posting in the right channel, but can anyone tell me, relatively, how feasible it is to learn trigonometry on your own? I took precalculus I (college algebra) last semester and, well, it was rather easy. I figure if trigonometry is just as easy, or relatively easy, I can self-study and place out of it and into calculus I. I did not take trigonometry in high school, btw.

[mystic mountain]

if you already took precalc, trig would probably be really easy for you

precalc is basically taking those concepts and expanding? at least back at my school

[broken crater]

I took precalc I, which is mainly college algebra. We didn't go over trig, though

precalc II goes over trig

[mystic mountain]

you should just self study it

also what did you take in hs then? x.x

[broken crater]

Lol

I stopped at algebra 1 😐 , so I had to learn algebra 2 while in college. I learned a lot in algebra 2, though.

[mystic mountain]

I see, didn’t know people could do that

[broken crater]

precalc I was basically algebra 2, but maybe a tiny bit more advanced

plus exponential and logarithmic properties and equations

[mystic mountain]

did you take geometry?

[broken crater]

Do what? Take algebra 2 in college? If you are referring to that, I took a developmental math course lol

I did, in high school. However, I don't remember much from that class and I didn't do that good

I did ok, I guess

[uncut socket]

You can look at Khan Academy to see what concepts are in trig. It might be a different from actual curriculum but it's pretty close

[broken crater]

@uncut socket I just looked on Khan Academy and most of the material is new.

[broken crater]

Does learning trig necessitate a strong foundation in geometry?

[mystic mountain]

really depends on the curriculum, I was jw; all I learned in geometry was proof tables and the basic trig ratios, not that important

and proofs were so boring x.x

as they were basics x.x

[broken crater]

lol

[mystic mountain]

my one best memory from geometry was the end of semester party

so long ago x.x

[broken crater]

I probably need to learn the basics, seeing that I am not familiar with trig at all - I don't think

[mystic mountain]

I mean do you know sin cos tan

[broken crater]

Lol! I could use an end of semester party rn

[mystic mountain]

haha

well anyways if you do just do trig straightaway

[uncut socket]

Majority of classes teach new material. Only a few weeks, more like 1 to 2 weeks, is just review material

[broken crater]

I learned it about a week ago via an online course

[broken crater]

Heard.

[mystic mountain]

👍.

[broken crater]

Bet!

Thanks @mystic mountain and @uncut socket

[mystic mountain]

glhf

[broken crater]

I'll try lol

[neat lintel]

I need help adding and subtracting radicals

[pure sun]

maybe you should read #❓how-to-get-help

[past stone]

Anyone stare at the corner of a room where 2 walls meet the ceiling and briefly feel like you can comprehend the fourth dimension going through it but then snap out of it?

Douglas Adams was probably right smh

[mortal igloo]

All the time

[timber edge]

https://tenor.com/view/42-hitchhikers-guide-to-the-galaxy-answer-life-universe-gif-11206785

https://tenor.com/view/pan-galactic-gargle-blaster-hitchhikers-guide-to-the-galaxy-zaphod-ford-gif-10677595

[mellow magnet]

what REUs should I apply to, or how does one go about choosing which ones? I'm kinda broadly interesting in algebra/topology/algebraic geometry/logic, but I haven't been exposed to that much---I haven't really seen much number theory/diff geo, and I'm only starting some algebraic topology right now.

[neat lintel]

Girls

[blazing pawn]

Uchicago REU seems neat

Chicago is generally more expository/less focused on originality than other REUS tmk which does i think make it more accessible for things like AT and AG

[dawn bridge]

Do Math majors on average enjoy anime more than Engineering majors?

casue this server seem to have more anime while on an engineering discord im they consider it all cringe

[jovial ember]

This is purely a reflection of administration

We also have a ton of cat emotes

[fair mural]

tokidoki emote

of course

[fair mural]

i mean nami is a bigger weeb than almost everyone here

[leaden torrent]

a lot of engineering spaces feel really insecure to me

from what ive seen

so clowning on people for enjoying things is a natural corollary of that

but admittedly this is anecdotal

[jovial ember]

Unlike the chad mathematicians who feel secure in our own outstanding intellect

[toxic schooner]

[leaden torrent]

no you see we're insecure as well but we arent in denial about it

[fair mural]

nami i was about to say

[toxic schooner]

i mean, in any space, there probably will be people of many kind

some like me that dont like anime

some that adore it

[fair mural]

we gotta get back to posting these waifu labs pictures

[toxic schooner]

etc etc

[jovial ember]

In this moment, I am euphoric. Not because of any false gods blessing, but because I am enlightened by my own intellect

[fair mural]

objective cringe chmonkey

[jovial ember]

Why don’t you copy paste that into google and see what turns up

[static loom]

don't forget to reference the original quote maker

[jovial ember]

Oh right, they did that in the original post didn’t they?

[static loom]

lol

[fair mural]

chmonkey i know you didn’t make it lol

[wild lantern]

Plagiarized

[static loom]

I had a friend who memorized this and would say it all the time

[jovial ember]

I don’t quite remember, but it would track

I have that memorized

[static loom]

-AALewis

[jovial ember]

There’s a different one I wish I could find god damn it

It was some guy talking about how he was so smart and like

He said he would never hurt someone else unless the cost to his body was higher

Said if given a chance he would not go back in time to kill hitler to instead rehabilitate him

Said he’s well respected on some brony subreddit

[static loom]

lol

[jovial ember]

Said as part of how smart he is he’s disproven multiple of the theories of Freud’s theories

And that he knew calculus a lot better than his sister’s boyfriend or something who is an engineer

It was just a fucking goldmine

I just don’t remember any of the direct quotes so I can’t find it

[dawn bridge]

anime is art engineering

[untold sapphire]

this was me

[mellow magnet]

Hmm yeah that does seem really appealing. I’m in no rush to do something original, I’d be very content with getting some depth and writing up some good exposition

[pure sun]

@clever knot I sullied you for interrupting an in progress conversation with a completely unrelated question

[clever knot]

😬 oops

Would it be considered a proper subset?

Guess not I assume.

[pure sun]

No.

[clever knot]

Of itself I mean

But why do we need such a notion

[pure sun]

Of subset? Or of empty set?

[clever knot]

I guess because it is the same thing then it is a subset by default

Seems weird to question the subset of an empty set

[pure sun]

I think you are looking too much into this. It’s literally just a fact that comes straight from the definiton of subset

It’s not deep or meaningful

[clever knot]

Yeah

[pure sun]

If’s just true. We have a definition of “subset” and based on that definition the empty set is a subset of itself

Just like any other set is a subset of itself

[clever knot]

Why would someone care about an empty set?

Or is it just one of them edge cases that we filled in

[pure sun]

Why would someone care about the number 86?

It’s a set that exists because of how we have defined sets

[bronze pelican]

86

[clever knot]

I see.

[pure sun]

Asking “why does the empty set exist” is like asking “why does the number 7 exist”. It’s just how things are defined

[bronze pelican]

I'm sure there are several reasons why the number 86 is interested

[pure sun]

The empty set is useful because sometimes you want to be able to have “nothing” as an answer

[pure sun]

It’s nice that I can say “let X be the set of even integers greater than 2 which are not the sum of two primes”

Without having to check if that set is empty or not

[neat lintel]

wtfish, let me think

idts

[pure sun]

If you dont allow the empty set as a set, then you can’t make thst statement.

[opaque patrol]

how is this just a conjecture wtf

[neat lintel]

ik

[neat lintel]

freedom of speach/thought

[opaque patrol]

like we know 65536 is the largest power of two that does not contain a power of 2

[neat lintel]

are you sure you spelled that number right?

exactly

[opaque patrol]

thank you

[neat lintel]

your welcome

[crystal stone]

Truly an educated gentleman. Was this all unprompted?

[jovial ember]

I forget lmao

[crystal stone]

I do think it's more important to address grass roots issues if given a time machine to go back to Nazi Germany, it wasn't as if Nazi's didn't exist before hitler. He just became their leader

It'd probably be better to find a way to dismantle the nazi party before it hit critical mass

[jovial ember]

I think it was just that it was another point in this really obviously “I’ve never had to really make any hard decisions because I’m immature” “I’m above everything” middle of the road non confrontational attitude

[crystal stone]

but it is pretty cringe to hear people say stuff like that

[jovial ember]

Like he says stuff about how he’d be pacifistic and it’s clear the dude’s never been in any sort of altercation to be able to say that

[crystal stone]

I remember at my church youth group we'd have conversations like this a lot

On morality & ethics

[jovial ember]

And the hitler thing read as just naïveté from someone who thinks the world is far simpler than it is

Which isn’t to say someone who “has seen the real world” wouldn’t have that opinion, it’s just that in the larger context that’s how it seemed

[past stone]

i know people like that

what prompts them to be so pretentious

[neat lintel]

the world is so simple

[jovial ember]

I remember years later he followed up on it and recognized how cringe it was and obviously also full of lies

[alpine kindle]

if you went back in time it would be better to get hitler a better education than kill him

in that case

[jovial ember]

I forget if it was just “yeah idk what that was” or also partially defending himself

better education
Was Hitler uneducated?

Lmao

[neat lintel]

idts

[alpine kindle]

better art education

[neat lintel]

lol

[jovial ember]

Hurb

[neat lintel]

do you guys love william rowan hamilton?

[dawn bridge]

had to google it but hitler's art actually pretty good in terms of his technical skill

the subject matters he picked seem kinda boring to me tho

i dunno if that was the fashion at the time to draw those kinds of things only

[cold needle]

I Love William Rowan Hamilton.

[toxic schooner]

😌

[neat lintel]

noice, I love him not well

[cold needle]

lol

[neat lintel]

lol

you like that nabla sign?

[cold needle]

where

[deep mango]

who the fuck is this

[toxic schooner]

[deep mango]

oh it's just hamilton

who doesn't like hamilton

[toxic schooner]

i love hamilton

(the musical)

(and the quaternion dude)

[deep mango]

[toxic schooner]

whats so true in this

i do love the musical

a lot

[deep mango]

i think hamilton is a dumb musical

that went through several rewrites in my brain before i typed it

[toxic schooner]

[toxic schooner]

I love it
and i wont hear anything bad about it 🔫

jk

[deep mango]

🙂

[toxic schooner]

AAAAH

this emoji is so scary

[deep mango]

my brain is poisoned from growing up in the art world, i have been trained to hate almost all musicals

🌝

[toxic schooner]

wha-?

[toxic schooner]

this is worse than that smiley

[wild lantern]

West side story is kinda nice.

[toxic schooner]

never heard of it, but if its a musical i can find online, i will give it a try

[bronze pelican]

rycope

[toxic schooner]

Lmao wow

[deep mango]

hamilton is probably better than most other musicals

i was forced by friends to listen to the soundtrack several times over in high school, sort of fragmented?

because the big joke was that i hated hamilton

but had never seen it

[neat lintel]

I liked it

[toxic schooner]

Oo

[deep mango]

and i just never liked it

[toxic schooner]

i mean, that does make some sense as to why u wont like it

[deep mango]

it's not really lin manuel miranda, i kind of liked the new in the heights even if it was very very cheesy

[toxic schooner]

friends doing something like that will ruin it for u

[toxic schooner]

yeah it was good
it had cheesy points but i liked it

[deep mango]

well it was worth the sacrifice cause it was a good long running joke

[toxic schooner]

i see

wait when u were in HS?

[deep mango]

2013-2017

[toxic schooner]

oh hamilton is nearly 7 years old at this point

[deep mango]

hamilton was really big in my junior year

like in terms of the suffocating popularity

[neat lintel]

It was like the millennial wicked

Well

[deep mango]

oh yeah i remember wicked too lol

[neat lintel]

No wicked is still popular

[deep mango]

zoomer wicked?

[neat lintel]

I’ve never seen it actually

[deep mango]

wicked was definitely millenial

[toxic schooner]

never heard of that

again, i dont exactly live in a place where musicals are popular

so i had to scour the internet for a while before i managed to get to one i liked

[deep mango]

i see

[neat lintel]

Phantom of the opera has good orchestration the story is just cringe

[deep mango]

yeah

damn literally all my friends were so into musicals lol

[toxic schooner]

[deep mango]

and my parents were actors in non-musical theater, but i met a lot of musical-people

[toxic schooner]

musicals are the kinda thing i would be into

i recently heard the greatest showman

i loved it

[deep mango]

god i hate the greatest showman songs i've heard

[neat lintel]

The latest job I had was as an usher at a movie theater and I had to listen to the intro to west side story over and over I also just think it’s problematic. It doesn’t address its issues well enough and it doesn’t have any license

[toxic schooner]

why?

[deep mango]

boring and loud

[toxic schooner]

if u hear them out of context, they can be boring

its not a sung through musical

[deep mango]

i see

[neat lintel]

I kind of like Oklahoma

Some of the characters anyway

[toxic schooner]

its a movie with a lot of songs

i liked it

i heard "the other side" and it was catchy

[mystic mountain]

are they well known??

[deep mango]

Not particularly outside of the theater world

I mean

They are quite well regarded but not famous in any way

[mystic mountain]

oh

[mint patio]

Proofs are so zzz man They turn me off
I like the problems
I just don't like the formality

[wild lantern]

Different situations require different levels of formality.

[mint patio]

This is for self-study but I guess it's important to build those skills up for when I take a real class right?

I've always been a very foundational and intuitive person, I need to know the why and how behind things to feel like I understand and appareciate it

but I don't care about formality either

obviously handwaving is still bad but I don't want to have to consider every small detail

but ig if you don't then how can you be sure you didn't miss anything or you're not glossing over a "small detail" that turns out to be important

[wild lantern]

For my first couple proof based classes a lot more attention was paid to rigor. But I'm not fully done with my bachelors yet. But as the classes went on we were able to accept more stuff intuitively.

[jovial ember]

Your intuition sucks ass at the start

[wild lantern]

Part of it was in building up thms and constructions from foundations but I think some of it was our instructors not expecting us to belabor every little point?

[jovial ember]

Because you just pretend things that you want to be true are “intuitive”

[mint patio]

u know Chm I was about to say "idt so " to the first message and then you said the second and I guess I can't say no

[wild lantern]

Part of why things work is formalism maybe?

Well idk, that's not a great way to say what I mean

[jovial ember]

When someone says clearly and doesn’t expand on something later it’s because of a lot of experience that says “this is true, I know how the argument will go but maybe I haven’t checked every detail”

When you start out when you say clearly it just means “this seems true probably and I want to use it”

[mint patio]

HAHAHA

[jovial ember]

There’s nothing actually there to back up your claim

[mint patio]

Right

[wild lantern]

I just mean that part of why/how things work rests on formal details.

[mint patio]

(I'm laughing because it's funny to get called out and realize that yes, that is what I've been doing, not because I disagree or anything )

[vague lion]

half the songs are good, the other half and the actual non-music parts are kinda bad

[mint patio]

okayyyy I guess like

maybe I should just change my approach to it too

[jovial ember]

To be honest proving things is what’s fun for me

I think I enjoy it more than the larger overall picture of things

[wild lantern]

Proofs seem like they get more fun as you do them

[mint patio]

cause when I try to write proofs I always think about it in my head (but the handwavey "intuitive" way) and then immediately try formalizing it. but maybe if I just like let myself blabber on paper and speak my thoughts out loud it'd be more satisfying? because I can first get the details in a way that's casual and comfortable for me and then I can try to make it exactly right

[mint patio]

absolutely not me but I haven't done much

[jovial ember]

I mean that’s how most proofs work

You have an idea then you work out if it’s correct

[deep mango]

Proving things is what's fun for me but before I was super used to it it sucked in a lot of ways for sure

(also before I was doing proofs on cool stuff)

[jovial ember]

Like idk it depends on the field too

[surreal sapphire]

i wish i could start all my proofs with at least a vague idea

[jovial ember]

I enjoy algebra because the way the ideas translate to arguments is a lot more fun for me

[surreal sapphire]

i usually have to poke the objects for a while

[wild lantern]

Proving more interesting things makes a difference too I guess.

[jovial ember]

For analysis I felt like I had an idea on what to do then I spent a while trying to grope around to see why some delta would work

[wild lantern]

But there's a lot of pain that goes along with that lol.

[jovial ember]

Granted this was from freshman year so maybe now I’d be better at it

[deep mango]

And what chmonkey says is the opposite for me, trying to translate an idea to an algebra argument is painful for me, but it's really fun for me to put together an analytic argument

[jovial ember]

And combinatorics is again a completely different sort of way to go about it

In a sense combinatorics can at times be the most fun to translate an idea to an argument

[deep mango]

Yeah

But you have to be able to do it

Lol

[alpine kindle]

algebra feels so much more open to me than analysis

[deep mango]

I would say that that is a perception shaped by intro analysis books

[alpine kindle]

it feels like you can build any structure you want in algebra

[deep mango]

Which is very inaccurate

It opens up a ton when you start doing other kinds of analysis

[alpine kindle]

oh

[wild lantern]

Is there any way around that kind of thing for studying intro analysis stuff or is it like an "eat your vegetables" kind of thing?

[alpine kindle]

holomorphic dynamics seems interesting to me
because of the interesting fractals that result

[neat lintel]

[alpine kindle]

why the stares

[jovial ember]

I think that’s because they heard the word holomorphic dynamics

And are intrigued by the subject

[alpine kindle]

oh

[narrow rock]

[alpine kindle]

it's the study of iterated holomorphic functions

[jovial ember]

I think they know what it is

[alpine kindle]

oh

...

[jovial ember]

This server is full of dynamics simps

And by that I mean RYC and Slim

[light needle]

Dynamic slimp

[alpine kindle]

sorry I'm not good at parsing people's messages

autism moment

what would be the prereqs for holomorphic dynamics

ofc complex analysis

but what else

[neat lintel]

crack open milnor's book and see

[deep mango]

[deep mango]

[jovial ember]

Fuck you RYC you don’t even study cool math

[deep mango]

holomorphic dynamics... 😏

slim has probably been hiding a voracious appetite for holomorphic dynamics this whole time but it might be one of the fields of dynamics i am least interested in

I think it is very flashy and pretty on the surface, but actually engaging with it seems sort of unpleasant

[sick burrow]

Wow you just described all of analysis

[deep mango]

[light needle]

Who would ever describe analysis

As flashy

[deep mango]

[light needle]

Or pretty

Smh

[deep mango]

complex analysis...

you must be kidding

[light needle]

That’s just polynomials. Next

[deep mango]

😐

[alpine kindle]

why fo you say

[deep mango]

well

my perception is that it's very similar to analytic number theory in this way

uhh

that could be wrong

i don't have a good description of this

[young lagoon]

i like analysis, but analysis doesnt like me

[crystal stone]

It seems analytic number theory is an increasingly difficult field to work in due to the slow pace of progress, and the dwindling number of faculty members that work in it

Most people seem to either do some other type of NT, or analysis, and as a side project they do some analytic NT

[sick kite]

analytic nt meaning studying nt using tools from analysis?

[deep mango]

yeah

[sick kite]

mkay

[bronze pelican]

Analytic number theory is not dying lol

Its just incorporating more and more algebra

Modern analytic number theorists look like algebraists

[crystal stone]

I never claimed it was dying, I just claimed it's an increasingly difficult field to work in

[bronze pelican]

Well the dwindling number of faculty working in it part seems false to me, I don't have statistics tho

[crystal stone]

I wanted to do some research in Analytic NT, but I didn't find much on the west coast

[ancient flame]

look harder

[deep mango]

I am go to IAS.

I'm actually so close i wonder if there's any way at all to attend anything...

Highly doubt it

[crystal stone]

sorry just let me be terry's PhD student

y'know, I think Yitang Zhang will take me too

[deep mango]

well when is it happening? so soon?

is "next year" this year?

[neat lintel]

Is it Buddhist to not ask questions in class

[tiny marten]

i took an elliptic curves class that was supposed to incorporate analytic number theory but i really didnt recognize it

it's so broad and runs up against geometry/algebra so hard at times

well i guess the prof showed us some interesting integral bounds at times

[jovial ember]

You call it analytic number theory when there start being too many letters on the board and you feel like you can’t understand it anymore

[tiny marten]

lol

[jovial ember]

It’s a method of copium for “algebraic” number theorists

[tiny marten]

yeah pretty much, the names dont even mean anything anymore at times

[fossil kindle]

if someone is familiar with t test and distribution pls hit me up It'll just take 5 minutes

[tiny marten]

especially with like dynamics, physics, and CS in the mix NT is kinda crazy

[fair mural]

@fossil kindle #probability-statistics, i assume this is the channel you need

[tiny marten]

like i got into CS algorithms via number theory

[fossil kindle]

ok thank you

[cinder zephyr]

I'm getting into combo via algos rn lol

I just picked up Knuth's text on combinational algos (well, Volume 4A not 4B)

gonna be an interesting thing to work through

[tiny marten]

Nice do you do CS then?

Knuth and Conway have some really cool recursive and discrete stuff

[neat lintel]

Are these even real proffessions?

lol

they are leavubg'

guys

Man

I have this problem with hard math problems where when I cant solve them... I am like HOW IN THE FING WORLD IS ANYONE SUPPOSED TO THINK OF THAT.... I mean.... I am wondering if this feeling ever goes away?

your writing another paragrapgh

[carmine briar]

Yes it eventually goes away

[neat lintel]

its fcking demotivating

[neat lintel]

Well, I guess I sometimes think that, but I watch a lot of youtube so I havee control over that feeling

[neat lintel]

what kind of math problems?

school problems?
or mathematician-problems?

[neat lintel]

not school problems.... I am way ahead of my school curricula

me2

its like trying to prove ineqs..... sometimes without calc

that could be hard

Sometimes I look up how cauchy proved am-gm and I feel like this dumb creature that's like thinking will I ever be able to do this?!

who thinks about casework around 2^n......I'd never think of that in a million years

[bronze pelican]

I'm talking about people who call themselves analytic number theorists.

[neat lintel]

I think you could

ik

calculus is so lolly

I mean.. proving them with calc feels like cheating for some reason.....without calc you get beautiful proofs

like using cauchy induction

and also I have this commitment of doing every single exercise problem... but now I cant keep that up or i'll burn out

and not doing exercise problems feels that... maybe I'll miss a really nice problem which i'll like

[dawn bridge]

yes just practice doing more problems and reading proofs and stuff then u'll get better at this sort of thing

[hollow island]

HELPP

[scenic narwhal]

#cats

[idle trout]

Someone can help me ?

[noble linden]

2 days

[icy forge]

huh?

that's not how bags of Ramen work

[fair mural]

from what i’ve heard i’d imagine they can eat way more

[proven hornet]

if you live of your stipend its rough

[desert adder]

Anyone does gcse maths edexcel >

[velvet dagger]

Well there's still like, Green-Tao style NT. But if you mean Langlands then lol

[cobalt star]

idk if you have the time or want to but math olympiad helps for these kinda skills

If you're still in school

you could consider

But it's not necessary

[tired wave]

Hi is there a link for this server so my friend can ge jelp

[deep mango]

https://discord.gg/math

[tired wave]

Thx

[pure sun]

please tell your friend to read the rules before asking for help

[fair mural]

posts question in 20 channels

[deep mango]

we're so close to 75k

wowie

[fair mural]

we’ve been at approximately this many members for quite a while

[last oxide]

for a suitable definition of approximately

[ancient flame]

engineer's definition of approximately

I mean

we are at 75,000 now

since 75,000=74,976 for large values of 74,976

[deep mango]

[tiny marten]

Yes

[fair mural]

large values of 74976

guess constant numbers have upper bounds now

also it went down by 2

[deep mango]

yeah. i left the server

[brave hollow]

and deshawn got banned

that makes 2

[tiny marten]

Lol what happened?

[fair mural]

jerk being a jerk

[pure sun]

you know what they say. fuck around and find out.

he fucked around and he found out.

smh dont sully me that's a thing :P

[brave hollow]

it is

[deep mango]

i know it's a thing...

that's why i sullied you

[long matrix]

its just 1 grad student doing the eating. adding 1 doesn't change the rate 👀

[ancient flame]

if im taking one of the elements of a power set, can I use the \in symbol?

[pure sun]

use \in if you are talking about an element of a set

it doesnt matter what the element and set are

[ancient flame]

e.g. if my set S={1,2} then the power set is {{}, {1}, {2}, {1,2}}, can I say that {1} \in P(S)

[pure sun]

yes

[ancient flame]

ok cool ty

[pure sun]

because P(S) is a set and {1} is one of the elements of the set

👍

[ancient flame]

even though it's a subset it's still an element, correct?

[pure sun]

{1} \subset P(S) would not be correct

[ancient flame]

oh

[pure sun]

it's not a subset of P(S)

it's an element of P(S)

[ancient flame]

oh true

im dumb

[pure sun]

and therefore you would write {1} \in P(S)

[ancient flame]

ty

[worldly solar]

{{1}}

[wild lantern]

{{}}

[static loom]

describe all finite sets $S$ where for all $s \subseteq S$, we have $s in S$.

[fathom swallow]

Merosity

[neat lintel]

I mean... I dont have a affinity towards olympiads...

and they are two different things right.. math research and math olys

[ember fog]

hello there this isnt related to math at all but can I ask for help with an essay I'm writing

I would love to hear some critique on it and it's not too long

[frozen merlin]

ordinals?

[static loom]

give an example

[frozen merlin]

$\emptyset \subset {\emptyset}$ and $\emptyset \in {\emptyset}$

[fathom swallow]

∧res

[frozen merlin]

I assume you mean proper subset, because S \in S is impossible

by a cardinality argument if they're finite, but also by regularity

[static loom]

for finite sets yeah, there are no sets S

that's basically what I had in mind, {} is a subset, so it's in S, so then we have must have {{}}, etc... no way you can have a finite set

[frozen merlin]

yeah and ordinals doesn't even work because you need the subset to take the form ${0,1,...,n}$ for some $n < |S|$

[fathom swallow]

∧res

[static loom]

yup

[compact tartan]

wouldn't that mean S in S

[static loom]

😎

[mild nebula]

They're doing all the good math these days, I get it