serious-discussion

[tall badge]

you know what, maybe we can move this to dm if youd like me to give more recs

[neat lintel]

Ok sure

[sly forge]

Is there a channel I can send math commands in
Where a bot gives you the answer / even the working out

nvm

[bright trout]

You can use Wolfram alpha using @fathom swallow in #bots

[sly forge]

ohhh theres the channel thx

[vale plover]

saw this in my university bookstore

the art of proper bookbinding isn't dead yet

🥹

[tight comet]

Cool that they are doing that for a digitally free book

[neat lintel]

axler vomit

[vale plover]

i have ladr 3rd ed. and it's bound well too

but they might do this for all colored books

idk

[neat lintel]

okay this is little off topic, but how come some colleges require self-reporting grades? does it accelerate the admissions process?

[void tundra]

yeah it makes life easier for them

[dull pilot]

exactly, they don't have to wait for your high school to send them the transcripts

[bright hill]

@naive chasm slurp gives you his love

[void tundra]

!help

[quasi jetty]

Please read #❓how-to-get-help

[void tundra]

get a calculator

[brittle socket]

@neat lintel Memes do not go in here.

[void tundra]

ok uh

call in mods if u want

[brittle socket]

Uh I think that's a little unnecessary

You're actually not allowed here then. The mods might have to kick you because of tos

idk if I should ping mods tho

Ah well I guess I can just modmail it and let the mods decide

[bright hill]

Both pings mods lmfao

[dense hill]

Hi guys, I have some free time and I would like to start working on my math, the thing is I forgot a lot of math, so if there is a math master here, can u tell me where to start, and at which points to focus at the start

[long matrix]

this is an implementation flaw

our interaction with the interface is perfectly logical

[oak locust]

Which is best mathway or wolfarm alpha??

I was thinking about buying primium

Can anyone tell me which is better

[long matrix]

[woven whale]

your brain is best

[oak locust]

Hehe ikik thank

[alpine kindle]

use sage
it's free

[oak locust]

Okay i will check it out

[bright hill]

I haven't seen okay written out fully in a looooong time lmfao

[slim shale]

Sup so sorry I only begin my math journey like I learning is in school but also I wanna learn it a little bit at home for programming and just idk for fun 😊☺️☺️

[bright hill]

cool!

[slim shale]

So what should I do?

I know EdX heve some courses

[bright hill]

https://tenor.com/view/senator-palpatine-anakin-skywalker-phantom-menace-gif-10607636

[slim shale]

Or should I use books ?

[slim shale]

Thanks

[latent sage]

Help me enter state of NY

[slim shale]

Go to LA

[bright hill]

depends on your level

do you know calculus?

[slim shale]

I'm in 8 garage

So I Yung guy

[bright hill]

what?

[neat lintel]

8 garage

[bright hill]

I...

see

[split island]

blo\"e <3

[flat harbor]

the current state of discussion gave me a concussion and i feel lightheaded

omg hi kirbs <3

[split island]

I understand

[regal scaffold]

ello

[flat harbor]

hi

[split island]

discussion 2 is cooler discussy

[hollow zenith]

o/

[regal scaffold]

but a lot less active

[static loom]

mute and hide the channel lol

save urself

[flat harbor]

its a disappointing fact that a lot of cool ppl just dont visit discussion 2

myabe ill just ping them here?

[hollow zenith]

Politics sux ngl

[regal scaffold]

im not even old enough to vote im just staring like

[hollow zenith]

Haha same

[split island]

I don't think a lot of people in that discussion are either

[hollow zenith]

Tho next year maybe

[static loom]

wdym maybe lol

[hollow zenith]

18 next year

[static loom]

if you fail your birthday test they'll hold you back a year and you'll have to stay 17 another year

[hollow zenith]

But election may or may not happen

[flat harbor]

u can participate in varuous methods

[hollow zenith]

Wth is that

[flat harbor]

its a good mango

[tall badge]

a true fountain of youth

[flat harbor]

its a lighter one

but then again frieren was a bit light too

and u were all over it

[hollow zenith]

Immortality

Ez

[static loom]

imagine if we could stay young by being dumb and failing our birthday tests

[tall badge]

are u implying that doesnt work?

[static loom]

to be fair, it's a bit nerve wracking taking the birthday test after getting dressed up for it in your

[hollow zenith]

But if I purposely fail them doesn’t that make me smart 🤔

[flat harbor]

tests dont necessarily test smart testability

[hollow zenith]

Ye

[split island]

Yeah

exams are a good metric for some, but not for others

so that means they aren't a good metric

[flat harbor]

the standardised test and its results have been disasterous to humanity

[hollow zenith]

Is it even possible to design a good metric for that

[flat harbor]

yeah its called bribing ur way into positions

the fairest way to test someone is to just hire them after some simple screening

and see how well they learn to do their job

[hollow zenith]

Tbf that can be done with almost any test

[flat harbor]

oh yea? u think u can bribe me into giving u a pass into my dms?

[split island]

I don't even need to bribe you

[flat harbor]

u passed :)

[neat lintel]

[flat harbor]

im just starin

[split island]

starin

[long matrix]

meow

[errant peak]

Does anyone have introductory resources to understanding what norms are and how to prove stuff about them because I'm actually stupid and my real analysis prof assumed that we all knew going into the class and I've literally never heard of any of the things he's saying and I'm so confused

[long matrix]

wikipedia at least has a defn probably

i assume u have that in front of u?

[errant peak]

Yeah

[long matrix]

iirc its 3 axioms/properties

its gotta satisfy

Thats all the norm is

You can think of it is a kind of 'length'

[errant peak]

Ok that makes so much sense

[long matrix]

The norm will assign a length to each vector

But this is not necessarily the usual length

That's the euclidean norm

You can have 'distorted' norms

Can't think of a good example from top of head 😶

What you will likely come across at some point is function norms

========
For example, {f : R -> R} is a vector space over R. ||f|| := sup({|f(x)|})
This defines a norm (check it satisfies all properties)

[long matrix]

In words, this norm assigns the length of the function as the sup of the absolute value of all y-values the function takes

[long matrix]

Ah in this case, it norm maps to extended Reals, unless you restrict that space to bounded functions

[errant peak]

Ok wonderful

And that would satisfy the triangle inequality?

[long matrix]

you can try prove it.

but it should

,,\abs{\abs{f}}\coloneqq\sup({\abs{f(x)} : x\in\bR})

This should be a common introductory exercise to do

[long matrix]

Let's say you're only considering bounded functions (so the norm is finite always)

[bright hill]

I love this norm

so cool

using this norm on C(X) functions a convergent sequence is a uniformly convergent functional sequence

which I just find delightful for some reason lel

[long matrix]

to each their own

[errant peak]

I'm starting to think that maybe I don't actually want to take topology next semester lol

Thanks for the insight though

[long matrix]

I think its quite different from analysis

Especially algebraic topology

I'm not a fan of analysis, no.

topology was ok for me

[errant peak]

Are you in grad school?

[long matrix]

ive graduated

not in school

[errant peak]

Oh cool

[long matrix]

@bright hill continuous map from compact space to compact subset of R attains its maximum value right?

So whats a non-example where that sup is relevant
just tryna think

[solar sparrow]

anyone applying/applied to the uchicago reu? do they not have topics and just cover what u say u want to do in your research statement?

[long matrix]

(thats me guessing the statement, if its wrong or more general, correct me)

[bright hill]

yeah, you actually just need the "from compact" part

[long matrix]

oh right from compact implies bounded

ah i see

so if we map from R but still bounded function

we could have sup be asymptote

[solar sparrow]

the image of a compact set under a continuous map should also be compact

[long matrix]

#graduate-applications might be relevant for u (im not sure - check channel description)

[bright hill]

I mean

[velvet dagger]

Think arctan

[long matrix]

yep

[bright hill]

bounded means it attains its max, no?

[long matrix]

no

arctan.

[bright hill]

oh wait no

[humble laurel]

hello everyone ∫ln(f(x))d(f(x))=∫ln(x)x dx . What is the expression of f(x)? As x belongs to R*+

[long matrix]

f is a generic function

[solar sparrow]

what's the problem exactly, i don't get it. why is arctan relevant for compact domain functions?

[long matrix]

probably needs to be continuous? maybe monotone? idk

[long matrix]

.

as a non-example

thats what i was hunting for

[long matrix]

of where that sup in this defn is relevant (else u can replace with max)

[solar sparrow]

oh i see.

[humble laurel]

F IS a function from R to R

[long matrix]

I don't understand your question tbh

I think f needs to be monotone and continuous for that to hold

[humble laurel]

Thé question is to find the expression of f in function of x.

[long matrix]

[humble laurel]

F(x)=something with x

[velvet dagger]

He's insinuating that this equation actually specifies what f is

And is trying to find it

[long matrix]

oh wait i didnt notice the extra x on the right hand side

Id approach by differentiating wrt x both sides?

[velvet dagger]

I mean it holds for f(x) = x

[solar sparrow]

yeah this is a weird non linear de though unless i'm mistaken

[long matrix]

that extra x

[solar sparrow]

it does not

[long matrix]

ln(f(x)) vs x ln(x)

[velvet dagger]

Oh oh

Yeah I missed that x too

[bright hill]

x^2

[velvet dagger]

Lmofa

[bright hill]

times some constant

[long matrix]

u guessing boi

[solar sparrow]

https://www.wolframalpha.com/input?i=ln(f(x))*f'(x)%3Dxln(x)

[long matrix]

[velvet dagger]

d(x^2) = 2x dx tho

[bright hill]

I'm not lol

yea

[bright hill]

.

[long matrix]

ok i see thats clever

[velvet dagger]

ln(x^2) d(x^2) = 4 ln(x) x dx

[bright hill]

the constant is 1/4

[long matrix]

wait but srsly - doesnt f need to be monotone

to consider this kind of expression

[bright hill]

yes

[long matrix]

or did i misremember something

ok

[bright hill]

they said x belong in R+

[long matrix]

oh

[bright hill]

inwhich x^2 is monotone

[solar sparrow]

wait x^2 is actually such a troll sol

[long matrix]

[velvet dagger]

Troll solutions are always fun

[long matrix]

differentiating both sides should be the way to do it right

[velvet dagger]

I kinda wanna make a math career out of it

[solar sparrow]

but idt the constant is 1/4

[solar sparrow]

i have a problem for you

wait lemme remember

crap i need to ask someone

[velvet dagger]

No, no remembering allowed

[humble laurel]

Maybe

[solar sparrow]

there is a very epic problem

[long matrix]

integrate sqrt tan x 😶

[bright hill]

becomes paul zeitz

[long matrix]

troll question

[bright hill]

dude's a math professor

and his research output is non-existent

all he does is train HSers for the imo

[solar sparrow]

paul zeitz is a temp instructor at my friend's high school

[velvet dagger]

I mean getting jobs was easy back then

But also I wanna have a research career

[solar sparrow]

wait not anymore?

[velvet dagger]

Just that I want my papers to be a lot of like

[solar sparrow]

does he still do that

[bright hill]

I'm not sure

[solar sparrow]

cuz po shen is imo team coach rn for the usa

[velvet dagger]

Oh here's this big open problem you guys have been struggling with for decades

Hehehehehe just do this slaps knee

[bright hill]

lmfao

that'd actually be so funny lel

becomes erdosh ig

[velvet dagger]

Unironically I'd love that as a research career

[bright hill]

(or however his name is spelled)

[velvet dagger]

Just being slick

[bright hill]

that wouldn't be very sustainable tho

unless you're literally god or smth

[velvet dagger]

Skill

Issue

[humble laurel]

The solution of my problem,is it already done ?

[bright hill]

are you saying you're literally god?

[humble laurel]

God is one

[solar sparrow]

actually not sure that x^2 actually works with any constant

[velvet dagger]

More I'm saying that thinking it requires being God is indicative of a skill issue

[solar sparrow]

because if you put a constant in front you get a constant added to the entire expression but maybe i'm tripping

end up with an unwanted log(k)

[velvet dagger]

Oh maybe you just got got tru

[humble laurel]

Constant is a variable witch belongs to a singleton.all her values repeat in one value.

Singleton :a set witch contrains one number

This IS why repeating some objects in a set doesnt have any effect.

As {1;2;3}={1;2;3;3}

[tardy barn]

@neat lintel I'm not gonna disturb that channel. So Imma answer you here: originally we made it a set condition that the bracket gives only 1 solution.

[neat lintel]

vulcano is a hero 🦸‍♂️

[whole garden]

fys

[neat lintel]

yes

i remeber

but is that why it is =0

[long matrix]

<@&268886789983436800> spamming this suspicious image link across channels

[wooden flax]

i mean at university of san francisco

different schools prioritize different things

IDT USF is R1

[neat lintel]

@tardy barn 🌋

hello

can you guys tell me the time?

[neat lintel]

<t:1675982098>

[neat lintel]

WRONG

it's jello time baby

[tardy barn]

Because originally our derivative was equal 0

And our goal was to find a value of k that makes the derivative have one x value that makes the derivative = 0

[neat lintel]

idk why i sotrue it :^)

[dapper current]

2 minute difference for some reason

[neat lintel]

the pure charisma and strengh coming from that procamation left no doubts, it was so true, indeed

[neat lintel]

oops

[brittle socket]

Yeah i know

[zealous garden]

[tardy barn]

Looks to me like you wrote a sample time lmfao

12:34 AM

[neat lintel]

we are reaching veracity levels that shouldn't even be theoretically possible.

[heady fog]

Whats wrong with this argument for calculating molar mass, M of substance X.
M=m(1 mole of X) in grams
=N_{A} m(1 atom of X) in grams =N_{A} m(1 atom of X) N_{A} in amu

This is obviously wrong since the Avogrado constans should cancel each other

The last equality holds since 1 gram = N_{A} amu

[leaden torrent]

uh, is molar mass not mass / moles?

it seems youre multiplying instead of dividing

if you divide then the initial N_A ends up in the denominator

so you do indeed have cancellation

[neat lintel]

yeah

sometimes it works

more often than not it goes terrible

[storm sage]

yes

[rigid river]

Oh what univ?

[brittle socket]

So many math books

I went to one local uni's bookstore last time and it was so small bruh

[void tundra]

yeah it has bloody nothing

[vale plover]

csulb

[torn willow]

Yeah, although if you can do that the class isn't worth taking

[teal lion]

ah, so my high school wasn’t worth it

[topaz peak]

how do u finish pre algebra bruh

I fail it last year

And im struggling again

Pre algebra so hard. Algebra 1 must be impossible

[wooden flax]

I just saw Han-Na Chang and she was amazing

[fast ridge]

its ok. it can be learned. you will get it.

[shell cave]

me late but i saw this and fr wanted to wish you good luck

u will get it! 🙏

[neat lintel]

Algebra is indeed difficult

I will never understand solvable groups

[long matrix]

idk if finding pre algebra is a prereq in the usual sense to algebra

I mean it is but it also isnt

You might find things in pre alg hard but things in algebra 'make so much sense'.

But this is probably rare

[neat lintel]

i dont understand

[neat lintel]

Would anyone teach Integration

[long matrix]

khan academy

[neat lintel]

can you differentiate?

[hollow quest]

honestly "no" would be a hilarious answer

[teal lion]

You don’t need to

[neat lintel]

but it is best to learn that first

[teal lion]

I was just reading about de rham cohomology

I was going to give cool fun facts

but now I can’t think of any

and it also looks like it has to do with my first message

which wasn’t intentional

[dapper badge]

de rham cohomology fun facts

[zealous garden]

fun fact, if you spell it with a k, it can be used as my username

[neat lintel]

ke kham kohomology kun kacts

[split roost]

lol i made a program which convert drawing into math

[regal scaffold]

like a script? cool af

[neat lintel]

sorry do u have time to talk about ISO 8601

[abstract mantle]

funny joek

[dapper current]

i've had a similar experience after reading about cohomology

[split roost]

https://www.desmos.com/calculator/hri2yiobak this turned out great

[neat lintel]

Woww

Math is amazing

I should dedicate time to drawing something in desmos

[cobalt furnace]

Hello. Does anybody know, what is it curly arches means ? How to solve this example ?
(You need to find period of function)

[long matrix]

wheres my catgirl

,w catgirl curve

[fathom swallow]

Results provided by WolframAlpha

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

Requested by Shuri2060#9525

[long matrix]

smh wolfram

trash

[split roost]

no catgirl but

[long matrix]

meow

mandatory amogus

[junior jolt]

who will enforce it

[lavish kayak]

anyone seen the music movie about tar?

if you were in the julliard lecture hall in that early scene, would you have said something?
she has good points, but she rails on that guy to the level of cruelty, I believe. I do not know whether she is trying to teach him or to break him into her thoughts about music and its place.
My only counter-argument to standing up and trying to either stop or ease this interaction is that stressful encounters like that build character, and that anyone trying to be a conductor probably has a good spine or knows how to deal with egotistical characters (and the guy getting railed on is, all in all, faring rather well, and in the end decisively walked out), but her behavior is really pushing the limits.
Obviously it's easy to say but hard to practice, but what are your thoughts?
please ping me if you reply

[uncut socket]

@obtuse hearth Stop interrupting in #help-6. You're not even helping

[obtuse hearth]

I am helping

[uncut socket]

No you're not

[obtuse hearth]

yes i am

[uncut socket]

You don't even know what the question is asking

[obtuse hearth]

whatever

i am see which "help channels" i can help

[uncut socket]

Well, you aren't helping in help 6

You're not even doing it right

[split roost]

heheha

[flat harbor]

twice fan in 2023????? zamn

[alpine cloak]

hey just a question - I'm a math student taking an introductory course in newtonian physics and I really like figuring out things by myself so I'm basically re-deriving all the results in a more rigorous way, often generalising things , so I've come up with what I think is a nice set of notes that can help students see the bigger picture when taking a similar course. Is there any way I could publish them or is the idea just ridiculous?

[burnt dune]

probably they wouldnt be worth publishing but like u can upload them on the internet or something for others to use

[neat lintel]

Imo, better ask your prof/course coordinator/advisor. Not internet strangers.

[halcyon inlet]

How much are they charging for copies?

[neat lintel]

guys i have a question, to study architecture can i take IB math AI SL?

[torpid frost]

so what do i do after khan academy

[sturdy quarry]

Khan academy is plan for like 3 months if you are gonna spend 100% of your free time on it

and if you really want to understand the topic including proofs

https://www.youtube.com/channel/UCYO_jab_esuFRV4b17AJtAw

[torpid frost]

ive seen that guy

good videos

[sturdy quarry]

truly

[neat lintel]

I see you are men of culture of as well

I also enjoy Grant Sanderson

[torpid frost]

[sturdy quarry]

What grade are you?

[torpid frost]

like

[sturdy quarry]

$\frac{d}{dx}x^{2}$ Can you compute e.g. this?

[fathom swallow]

MathIsAlwaysRight

[torpid frost]

12th in aamerica

no

i cnt

[neat lintel]

@torpid frost what topics have u done in school so far, perhaps we can help you based on that ?

[sturdy quarry]

on this level of math khan academy is one of the bests

[torpid frost]

uh

[sturdy quarry]

if you dont mind paying brilliant.org is also good

[torpid frost]

i aam so poor

[torpid frost]

ive done differentiation

[sturdy quarry]

wait really?

[torpid frost]

o think thats the "highest level"

[sturdy quarry]

Can you differentiate x^2?

or 5x?

[torpid frost]

its only derivatives though

[neat lintel]

d/dx x² is diffferentiation

[torpid frost]

i only know 1st and 2nd derivative

and idk what u mean by "compute"

[sturdy quarry]

evaluate

or sth like that

simplify

Or differentiate x^2 or find first derivative of x^2

[torpid frost]

then just 2x?

[neat lintel]

Yep

[sturdy quarry]

Is there any topic you would like to get better at?

[neat lintel]

What's that for sin x?

[torpid frost]

not a clue

[neat lintel]

Oh

U need to work a lot on Calculus

[torpid frost]

is that like trig identities

[neat lintel]

Yeah

[torpid frost]

yeah i dont even know what calculus is

[sturdy quarry]

$\sum_{n=0}^{100}\left(-1\right)^{n}\frac{x^{2n}}{\left(2n\right)!}$

[fathom swallow]

MathIsAlwaysRight

[sturdy quarry]

oops forgot to add infinity

[neat lintel]

Average approximation

100

[torpid frost]

whats cculus

[sturdy quarry]

If I were engineer I would say it's 1

[neat lintel]

[torpid frost]

calculus

[neat lintel]

Calculus is the study of change

[torpid frost]

ill staty with calculus then

start*

[sturdy quarry]

Example usages of calculus: Approximate functions, work with rates of change, find areas under curves, proving volume of sphere and lots other area/volume formulas, computing infinite sums, finding behavior of functions at infinities

[torpid frost]

thanks

[neat lintel]

U need a lot of trigonometry got calculus tho

[sturdy quarry]

Maybe start with Algebra 2 or precalculus, you need a decent amount of algebra and trigonometry

[neat lintel]

Atleast the basics

U also need Algebra

And pre Calculus

[torpid frost]

alright

oh wait no

im not 12th grade 😭

lmao

im so silly why did i think 12th

im like 10th grade in the US i think

[agile willow]

i made a background for my phone can you rate it or some wut

[neat lintel]

It just feels math with no purpose ig
U should focus on like one particular branch that u love and stuff related that perhaps ?

For now, it looks like one of those things gifs about people thinking have

Like this

Random math with no focus on anything

[long matrix]

theres nothing wrong with it

[neat lintel]

Indeed

[agile willow]

i put the things I like so

[neat lintel]

Oh

[agile willow]

i think its fine with me

[neat lintel]

That gives it a certain personality then

That's good

[bright hill]

[neat lintel]

Why math when you can meth?

[long matrix]

should edit Jesus to ryc or something

[bright hill]

I would fill it with memes ngl

[long matrix]

id fill it with catgirl(s)

[bright hill]

$(a+b)^2=a^2+b^2$ ftw babyyy

[neat lintel]

I would feel it with some graph of a complex function

[fathom swallow]

DarQ

[bright hill]

[neat lintel]

$\cos(3a) \cdot e^{-i2a}$

[neat lintel]

It has a very visually beautiful graph

On the complex plane

Between a from 0 to 2π

[modern shard]

does anyone here know the school mmstc ?(Michigan -Butcher)

[split roost]

meth and ethics

[pseudo sleet]

methics

[long matrix]

@deep mango quack quack

are all well ordered sets order isomorphic to some subset of N

[bright hill]

Fancy way of saying "bijective" lel

Anyhow

[long matrix]

no it has to preserve the order structure

silly cow

[bright hill]

@deep mango teach us about transfinite induction

:3

[bright hill]

[deep mango]

every set can be well-ordered

[long matrix]

i just noticed

[deep mango]

How can a set be isomorphic to N if it has a larger cardinality

[long matrix]

oh which means not true

idk bruh, i just saw this defn for realsies

and im thinking whuddaheck u know

Ok, so apart from subsets of Z bounded below

What 'good' examples of well ordered sets are there

===
im now aware there is one with ordinals

[bright hill]

inb4 you just assume they exist

[deep mango]

Umm

N union infinity is one

[long matrix]

brehhh but this is boring

[deep mango]

yeah subsets of ordinals

idk

[long matrix]

ok do they all look isomorphic to some ordinal

subset

[deep mango]

sure

[long matrix]

subset of ordinals

ok, very boring then

comprehending transfinite induction rn

[deep mango]

the ordinals themselves aren't boring

they have a pretty interesting structure

[long matrix]

but theyre like a line init

because theyre in order

but that makes them boring

So therefore they are inherently boring

[deep mango]

maybe you'd be more interested in partial orders

[bright hill]

[deep mango]

total orders are pretty boring

[long matrix]

no i wouldnt be

whenever they started talking bout orders in class

i just didnt care

[bright hill]

Based

Sounds like discrete math stuff

[long matrix]

hurr durr this is less than this

[deep mango]

I think this is boring too

[bright hill]

An excuse to do proofs

[deep mango]

I don't care about any of this

[long matrix]

im reading chapter 0 of folland

[deep mango]

And I barely know it besides the basics

[long matrix]

and it introduces transfinite induction

[bright hill]

Do we need transfinite induction for measure theory, ryc?

Functional analysis?

[long matrix]

its just frigging induction on ordinals

clearly

yes?

[deep mango]

No

[long matrix]

you did induction on N before

now u do it on slightly bigger N

[deep mango]

It's one way of understanding some things in functional analysis

But the typical proofs are just done with choice

/ zorns lemma

[long matrix]

should i bother understanding choice

/zorn

never did

i definitely couldnt regurgitate the statement

[deep mango]

that's a tricky one to learn

[long matrix]

'all vector spaces have a basis'

[deep mango]

it took me a while of seeing it used in many contexts

to really interpret it

[long matrix]

alright

ty for your wisdom

[deep mango]

i'm eating couscous

[bright hill]

EAT YOUR WORDS CATTY BOI @long matrix

[deep mango]

what

why are you me

and why are you honorable

[bright hill]

Lmfaooo

[long matrix]

BAHAHA

[bright hill]

It's a long story

[long matrix]

it literally isnt

[deep mango]

oh this is your dumb reading group server i bet

[long matrix]

i joined their server

and named myself ryc

[deep mango]

the story is long because it involves lots of ryc-lore

[bright hill]

Cringe.

[deep mango]

i know the long part already though

[long matrix]

i told em to name themselves mods

so far only the owner has followed suite

[long matrix]

oh yes, derpz commented he was freaked out by seeing 'ryc is typing...'

[bright hill]

Hahahah

[deep mango]

what's freaky about me...

nothing@

[long matrix]

it means you do command some respect

from some people

[bright hill]

He said, and i quote, "Jesus fuck, holy shit"

While running in despair

[deep mango]

yeah but it's a good kind

like how people love jesus or whatever

[long matrix]

i wouldnt think that highly of yourself

its more like a school kid being scared of their teachers

[deep mango]

some would call jesus a teacher

[long matrix]

darq asks me how long to read 2 chapters of folland, but istg i cant stop myself stopping at every pitstop like this

[deep mango]

ok ill stop bothering you

byeeee

[long matrix]

ok no fck chapter 0

bye

[vale plover]

about $58

[halcyon inlet]

that's better than amazon

[flint thunder]

Do you recommend the book over e.g. Schilling?

[vale plover]

it's legally free online

you can check for yourself

[flint thunder]

I have 😀 But I'd like your opinion on the content

[vale plover]

axler is probably more traditional than schilling

[flint thunder]

I got stuck on Schilling in various places but I also just moved on to other things. So when I go back to that kind of content I'm thinking of switching books and Axler looked like a good option

I want to avoid reading one of these measure theory books that isn't general enough (i.e. and then have to go read yet another one to get the full picture or whatever)

[vale plover]

https://zbmath.org/?q=an%3A07150964

[flint thunder]

Oh great, thank you 😀

[long matrix]

@woven whale @woven whale

feed me some intuition for the argument principle

[kindred hatch]

Does anybody have good YouTube videos suggestion for

Thomas' Calculus: Early Transcendentals 14th Edition

[woven whale]

I don't really know any intuition for it

the proof is relatively simple though

[long matrix]

complex analysis isnt complex analysis without intuition

im almost there revitalizing it

[undone cobalt]

I am doing PDE now

I'll crunch this into some finite element analysis thing. Could you guess what's that equation?

[long matrix]

u should really clock some intuition for complex if u havent already tho

trust me its so worth

[woven whale]

no I have intuition for things

[long matrix]

i got it almost after i finished iirc

[woven whale]

just not for this

[long matrix]

[woven whale]

I don't think there is any visual intuition for this

[long matrix]

id have to draw to show but nvm

yes there is

maybe when i have a chance on vc i can

[woven whale]

do you mean the rotations of the outputting path

or whatever it's called

like

[long matrix]

yh

thats the intuition

[woven whale]

I don't see that as intuition

[long matrix]

theres more to it

and why u can intuit that equality

[woven whale]

hmmm what's the intuitive connection between it and Z - P though

[long matrix]

ive yet to fully get that, almost

i can certain explain the Z

the poles, you kindof think of the zero at infinity iirc

[woven whale]

explain it

[long matrix]

to visualize a complex function i imagine 2 planes, the domain and codomain

idk if u do that

[woven whale]

I just imagine a 4 dimensional space

[long matrix]

bah its hard without a diagram

bruh

[long matrix]

@bright hill listen to this kid

[woven whale]

go on

with your explanation

[long matrix]

ok so this is the domain space

now what does the function do in the image space

for now erase all but 1 blue dot

Its clear the function just goes around 0 once?

[bright hill]

Lol

Right

[long matrix]

in the image space

because your map has to be continuous

and so it looks the same

you have to go around 0

[woven whale]

if there's only one zero then it would go around 0 4 times?

[long matrix]

huh no

[woven whale]

but 1 - 5 = -4

[long matrix]

ive erased all but one blue dot

[woven whale]

yes

[long matrix]

no reds

[woven whale]

ah

1 - 0 = 1

yes ok

[long matrix]

ok now 2 blue dots

you know the answer needs to be 2

we go around twice

but how to achieve that

with the continuous function requirement

Well visualizing this is the intuition i meant

[woven whale]

I don't get what you mean

[long matrix]

That single loop in the domain

maps to a double loop in the image

phone, cant draw.

[woven whale]

what does that mapping have to do with it having 2 zeroes and 0 poles

[long matrix]

the 2 zeroes have to overlap

mapping from domain to image

that has some implications on what the map 'looks' like

and the topology

and how that single loop in the domain transforms into a double loop

[woven whale]

wdym

[long matrix]

the 2 blue dots in the domain

map to the same point in the image

[woven whale]

yes

[long matrix]

so you need to come up with some continuous deformation of the domain to achieve this right?

kindof

[woven whale]

but S^1 doesn't have a trivial fundamental group

[long matrix]

and considering what this must do to the loop is key

[long matrix]

maybe continuous deformation isnt the right word

===
For the red dots its the reverse

For the blue dots you consider the R^2 topology as the image space

this is also the riemann sphere with a hole at infinity

For the red dots you consider the riemann sphere with a hole at 0, hence the rotations are reversed

I think thats how it works

[undone cobalt]

what do you want to pass into the dude?

what's the idea?

[long matrix]

yh rather than this, consider a concrete example

like z^2 on S1

You can move the blue and red dots around - overlap them onto the same point, because topology

so its z^b for blue dots

maybe this is better explanation

z^-r for red dots

it averages out

The continuous map must be some deformation of z^b/z^r

[rain ruin]

I didn't get it can u explain what is this ??

[long matrix]

me rambling about some intuition for the argument principle in complex analysis

[undone cobalt]

just cross the branch cut and ruin the game of contours

[rain ruin]

Sounds interesting

[long matrix]

@bright hill hi u said i can ping u any time

complex analysis

how much did u do

Oh yeah i just remembered. the number of zeroes inside is equal to the number of poles outside iirc

[bright hill]

... you wanted to ask smth anal related 🙂

[long matrix]

complex

[bright hill]

Up till sigma algebras

[long matrix]

complex analysis

not blumming real and measure

[bright hill]

Oh

0

[long matrix]

missing out clearly

complex is very good

[bright hill]

I don't even know what a holomorphic function is

[woven whale]

complex differentiable on some region

[bright hill]

It doesn't interest me atm

[undone cobalt]

do you mean principal value?

[long matrix]

its so visual

[long matrix]

no

[bright hill]

I might do some after AT and measure theory

I heard from a few those two pre reqs are pretty nice to have while doing CA

[long matrix]

@woven whale whats the theorem which says number of zeroes equal to poles with whatever restrictions

inside outside, cant remember

[undone cobalt]

the counting principle?

[frozen seal]

am i getting factoring by groups correctly?
for ax^2+bx+c, can rewrite as ax^2+gx+hx+c where g+h=b and gh=ac
and then you fuck around with what you get

[long matrix]

yes

[rain ruin]

Chess ??

[woven whale]

do you mean rouché's theorem?

[long matrix]

probably lets see...

[rain ruin]

Come then

[long matrix]

dont think its quite rouche

if u have a loop

no wait

hmm

[undone cobalt]

https://i.stack.imgur.com/xbR8u.png

avoid the phrase

[long matrix]

i think im thinking the one counting the poles at infinity

andor zeroes

[woven whale]

you could also maybe means riemann roch theorem

[long matrix]

and how the total must cancel

[rain ruin]

Boring world

[undone cobalt]

That's a series.

[woven whale]

I saw that already

[long matrix]

im gonna dig out my old notes tomorrow

cant remember wut i wanted

[undone cobalt]

Bad teaching

[neat lintel]

no, dipshit

[long matrix]

rude

they were only politely requesting some assistance

[subtle osprey]

Hey man, I couldn't figure this out myself but after doing some research it seems to be some kind of automobile, here's a link to help https://www.jdpower.com/cars/shopping-guides/what-is-a-4-x-2-truck

[neat lintel]

Hey

[cyan goblet]

i also found a properly bound baby rudin in my bookstore which i got charged $170 for!

[neat lintel]

Lol, I thought all Springer books are print-on-demand now.

Bad ones.

[void tundra]

wow that is genuinely probably not worth it

[ripe wasp]

folland?

hows it going

[peak tide]

it's all relative, $170 could be a few crappy DoorDash deliveries, i'd say Rudin is worth more than that

[sharp cave]

Here is one way to think of it. First recall that winding of a curve around a hole gets you 2πi.
Now if f(z) = (z - a)^n then f'/f = n/z-a so the contour integral of the curve around f'/f will pick 2πin if the contour contains a, aka the zero of f.
For general f, you can write f(z) as (z - a)....(z-k) g(z) where a,...k are zeroes of and g is a non-vanishing analytic function.
Doing f'/f will give you 1/z-a + ... + 1/z-k + g'/g so the contour integral just becomes 2πi*(number of zeroes inside the curve).
With poles, you have things like f(z) = (z-a)^-n so the integral turns out to be -2πin.

The another intuition is to realise that \int_C f'/f is nothing but just n(f(C), 0). But n(C,0) is just winding of C around 0 so the number of zeroes of f in C is just the number of times the curve f(C) winds around 0.

The latter interpretation is basically why we call it argument principle. Precisely if you want to find the zeroes of f in a region, if you can estimate the change in the argument of the curve under f, then you can find the number of zeroes. This is especially useful when you wanna find zeroes of f in unbounded regions like the upper half plane (because Rouche's isn't useful anymore).

(As an exercise, use this fact and the fact that n(C, z) is constant over connected components as a function of z to prove the open mapping theorem).

[sharp cave]

Are you talking about sum of all residues including at infinity is 0? This just follows from the fact that for a large enough contour C that contains all the (finitely many) poles, we have 0 = \int_C f + \int_ -C f = 2πi sum of all residues + residue at infinity

[swift pilot]

[long matrix]

thanks

[ripe wasp]

anyone know of some like theorems that "overkill" olympiad math solutions?

for example, using muirhead's inequality

for am-gm

or smth like polya's enumeration thm/ burnside's lemma in counting problems

probably some like graph theory results too

[turbid spear]

İn this question mod is good idea?

[ripe wasp]

!help

[quasi jetty]

Please read #❓how-to-get-help

[ripe wasp]

try newton sums tho

[bright hill]

Yep

[ripe wasp]

nice

what part of folland r u on

[void tundra]

probs more than me

i am on ligma algebras

[turbid spear]

@ripe wasp yes but

Only öne day I wait for answer And I don't get answer

[void tundra]

interesting cat pfp lmao

[bright hill]

Pretty gud

[void tundra]

!volunteers

[quasi jetty]

Helpers are just people volunteering their time to help you. Be polite.

[bright hill]

I'm planning for the reading group before studying in earnest

(I haven't done any exercises yet)

[turbid spear]

ı know but

[void tundra]

ofc to join the reading group click link in my profile

[turbid spear]

Three times thats again and again

[void tundra]

people are VOLUNTEERS

alright

[turbid spear]

Yes man

[void tundra]

exactly

[bright hill]

First chapter

Sigma algebras and stuff

[turbid spear]

But I write disccussion

[void tundra]

man if only slurp was here

[turbid spear]

For the idea

Not solve

[void tundra]

what would slurp say

[turbid spear]

You understand

[void tundra]

I understand that you should read #❓how-to-get-help

[ripe wasp]

ok but go ask for the idea somewhere else lol

[turbid spear]

I don't want get help

[void tundra]

in a help channel for example

[turbid spear]

Only discuss about

[void tundra]

no you do

this isnt a discussion

[ripe wasp]

ah i see

[turbid spear]

Yes 8 do

[void tundra]

theres nothing to discuss

[turbid spear]

Discussion

I say my think is good or bas

[void tundra]

sure go to #discussion

[turbid spear]

Bad

I write it

[void tundra]

see how they take it

[turbid spear]

But any people write it anthying

[void tundra]

again #❓how-to-get-help

you aren't owed a response btw

!volunteers

[quasi jetty]

Helpers are just people volunteering their time to help you. Be polite.

[turbid spear]

Be polite

I am still polite

[ripe wasp]

they're being perfectly polite

[turbid spear]

And you say again again same think

[bright hill]

[turbid spear]

@ripe wasp yes I know

[void tundra]

I'm telling you you want to get help

So follow it

[turbid spear]

I didnt want help

[void tundra]

.

[turbid spear]

I need idea

Not answer

[void tundra]

you sound like you are whining

[bright hill]

DerpZ, just <@&268886789983436800>

[void tundra]

thats what how to get help is for

[turbid spear]

I am say this kan

[bright hill]

They should handle it

[turbid spear]

İ think so

[void tundra]

they dont give you answers

[turbid spear]

No they give

[void tundra]

they guide you

[bright hill]

Wtf is that i?

[ripe wasp]

tall i

[void tundra]

im so confused now

[bright hill]

Is that a capital letter i

With a dot???

[turbid spear]

Im from another co

Country

Thats why

[void tundra]

you sound ungrateful that people didn't respond after you asked "3 times again and again"

[surreal sapphire]

hm?

[void tundra]

just be patient

we didnt need mods for this mate

-.-

[surreal sapphire]

this is a turkish letter, there is a distinction between dotted an non-dotted i, so this is necessary

[turbid spear]

Yes

[void tundra]

now THAT is interesting

[bright hill]

It seems Symet is refusing to read #❓how-to-get-help

[surreal sapphire]

turkish is a very weird language

well

[bright hill]

Or smth

[surreal sapphire]

its weird that they adopted the latin alphabet

[turbid spear]

No @bright hill I dont

[void tundra]

[turbid spear]

I read it

[surreal sapphire]

its not very suited for turkish (arabic would be better)

[bright hill]

And the two were squabbling and i thought it best to let the mods handle it

[void tundra]

Ehhh I was gonna log off instead of continuing

[surreal sapphire]

so they added a ton of diacritics

[neat lintel]

That's a very bold claim to make lol

There are many current sounds that were nigh impossible to represent in the Arabic script era

[surreal sapphire]

same for latin

ideally they would just invent their own script

[neat lintel]

No but like

Turkish is just a very rich language in vowels, while Arabic is not

Arabic is heavily consonant-rich

Spoken Turkish and written Turkish often were hard to work well together

Not saying the Latin was perfect, but it DEFINITELY was an improvement from the Arabic script tbh

Take it from someone who can speak both Arabic and Turkish

[surreal sapphire]

oh ok

i read some argument that a modified arabic would be better than modified latin

[neat lintel]

I'm not sure about that. Literacy rates were very low with the Arabic script

[surreal sapphire]

thats just because of the times?

latin script was adopted in like 1920ish?

[neat lintel]

Anything Arabic is almost always 10 times harder for a non speaker to learn tho

[surreal sapphire]

quora, but the top answer addresses your concerns: https://www.quora.com/Why-does-the-Turkish-language-use-the-Latin-alphabet-instead-of-Arabic-alphabet-1

though i dont know much more than that

[neat lintel]

Like I learnt Turkish and became fluent in it in 3 years; I wouldn't expect a person learning Arabic to even come close to a native in 10 years of constant learning without much much effort

Hello

People underestimate how UNBELIEVABLY difficult Arabic is to learn in all of its aspect

It's an absolute nightmare that is rivaled only with Mandarin in my opinion

Sure

Here is the word "الملك", do you notice those little strokes under the specific letters? Those are the short vowels and they absolutely change the meaning of the word

This word can mean either, "King" "Property" "Angel", " Sovereignity " And a lot more

And those short vowels are almost always omitted in every casual talk

So when you see a sentence containing one of them, you are always meant to deduce the short vowels contained in it, and even the word itself

Yeah even I, a native, struggle to deduce the meaning of some words if presented without its certain short vowels

This also goes to show another thing: there is at least fucking 5 variations of every word and it's absolute cancer

All those short vowels that make such a slight change in pronunciation, and are often omitted, make up a whole plethora of new words

Oh yeah we have something in Arabic called " اعراب " Which basically roughly translates to "parsing"

It means you pick off a word and find all of its original roots and all of its affecting grammatical structures

Its so so so hard

I am so glad I don't have to ever take an Arabic class again

There is a reason why Arabic is so fragmented as a language

[sharp cave]

Is this just the dialect difference or are these also missing things like where you combine letters (like the w), and tanweens?

[neat lintel]

Every region has its own version of Arabic that is so accent-heavy it is practically non-legible to another Arabic speaker

[neat lintel]

No definitely not just the dialect difference

Absolutely no Arabic speaker writes Arabic words with their short vowels unless absolutely needed to

It just makes you seem either incredibly formal or religious

Like I can say a sentence like "انا احب اكل التفاح يوميا بالبيت" In Arabic but I wouldn't even know where the short vowels go in that, I just forgot

formal Arabic is incredibly hard and accents have always been the thing that eased it up a bit

[sharp cave]

Does this also result in difficulties with people with different dialects in being able to read each other's sentences?

[neat lintel]

Yes

Daily

I often don't understand some of my family's messages due to that, and vice versa. And we also tend to write words that don't actually exist in the Arabic vocabulary, but are in fact a written manifestation of their accented spoken counterparts

This is the reason why I said I wouldn't expect someone learning Arabic to even come close to a native in Arabic even after 10 years of learning

It is just... Impossible even for me

[velvet dagger]

Oh yeah short vowels

It makes it confusing to try to read for me too

Because everyone's like "Oh just interpolate them using grammar"

[sharp cave]

So does school curriculum in different countries teach the local dialect or do they teach some universal dialect?

[neat lintel]

Yeah they teach standard arabic

There is no school that teaches accented Arabic

That's just a whole other language you have to pick up solely from speaking to others

[velvet dagger]

So it's like yeah you have a language for which you basically need to know the grammar to be able to read. Compared to Spanish or smth

[neat lintel]

Arabic isn't that hard tho, how hard a language is depends on the languages you already know

Lmao

English speakers might find it hard but Hindi or Urdu won't

Similarly, Latin and English will be hard for those from Asian languages like Korean or Japanese

You only find what you "perceive" to be easy as easy, I would like to see you parse incredibly complicated Arabic sentences and still tell me it is not difficult

Korean might be more easier for Japanese than for English

[velvet dagger]

Duck that is true but the impression I get is that there is still a comparison that people are kinda able to make

[sharp cave]

I don't think so. Urdu speakers can learn to read Arabic fast but grammar and whatnot is very difficult for them still.

[neat lintel]

And Urdu grammar is easy ?

[sharp cave]

As compared to Arabic? Yes

[neat lintel]

80% of Arabic native speakers do NOT know the grammar. Even me. We just find it incredibly difficult to remember and keep a hold of

What is difficult about Arabic grammar?

[velvet dagger]

In particular a lot of people who know n \ge 3 languages seem to say that English is comparatively easy to learn

[neat lintel]

I don't think those forms of comparison are sensible as universal standards, they might be good for people individually, but u can't really rank hard to easy on a single universal scale

[velvet dagger]

You can't do a clean ranking but my impression is that there's more one can meaningfully say than what you suggest

[neat lintel]

If the natives even forget language, it means languages will change and evolve then

No

That's also impossible

Languages aren't fixed boxed with defined rules

They evolve as people change and they pronounce stuff changes

[neat lintel]

When you say this, I think you mean standard Arabic when you say Arabic grammar, right?

There are still remarks of old English to modern English as well

You still speak your dialect of Arabic perfectly, and have perfect command over it.

You have to remember the reason why Arabic is so traditional and hasn't been reformed is due to religion. Altering the language means altering the language of the Quran which is what 90% of Arabic speakers follow and believe in. Arabic has not been majorly reformed in 1400 years due to the fact that the Quran is meant to remain unaltered

People back in the day genuinely pronounced K in knife even tho now we don't
Languages changed cus we changed and we changed how we spoke them, leading to change

[velvet dagger]

Duck Arabic is gonna be more rigid, in the sense that there is "standard Arabic" that is not really allowed to change, e.g. because it should be a modern version of the language of the Quran

[neat lintel]

^ exactly

[velvet dagger]

So what people speak day to day are dialects, and there's a ton of variance and perhaps those are gonna be simpler

[neat lintel]

Why so ? What's unique in Arabic that it can't change ? Is it the perfection of a language ?

[velvet dagger]

But there is what's called "Standard Arabic"

[neat lintel]

.

[neat lintel]

Arabic changes all the time, at least the dialects people actually speak

[velvet dagger]

Which by definition is basically the modernization of the Quran

[neat lintel]

Formal Arabic will never change. Accents will come and go though

[velvet dagger]

That is considered proper Arabic

[neat lintel]

So, u will change the way u pronounce knife but never change the spelling ?

Yes that's the reality

As a metaphor

[velvet dagger]

Idk about other dialects, the Moroccan one is only spoken rather than read

[neat lintel]

Nobody speaks like the Quran is written

[velvet dagger]

When you read you read standard Arabic

[neat lintel]

anymore

Idk, sounds like most of Arabic fanbase is motivated by religion rather than genuine language

[velvet dagger]

Fanbase?

[neat lintel]

Idk what they call people who speak Arabic ?

Arabians ?

Arabic natives ?

Arabs ?

Seems like an incredibly uneducated and shallow remark to make lmao

What's complicated about Arabic?

Fanbase is a good term

[velvet dagger]

Arabs are people who speak Arabic but idk if you'd call that a fanbase lol

Nah it's pretty stupid

[neat lintel]

People often say that the grammar is very difficult, but I don't see any grammatical features that are very out of this world