serious-discussion

[long matrix]

in more advanced integration things

[sharp cave]

More concerning is the choice of font….

[cloud latch]

wtf is that font lmao

[bleak spade]

#help-22

[woven whale]

no

[bleak spade]

Ty

[fast ivy]

where is this notion defined?

never seen this before

[woven whale]

in this chat

[fast ivy]

you introduced this notion?

btw

if you introduced this

what's the motivation for using the integral sign tho?

like, do you know if it satisfies properties analogous to the integral?

[long matrix]

i doubt he did

[full swift]

hola

alguien habla español

[flat harbor]

i think the fact that int = oint kinda defeats the whole point of using an integral sign to begin with

i conjecture that it was used bc it looks cool

[silver hawk]

sippppppppppp

[fringe needle]

Weird notation apart this seems false? Take F = F_p^2: if I’m not mistaken then only non trivial proper subring is F_p

So for any non zero f, oint f over F is just F_p

[reef carbon]

https://www.newyorker.com/tech/annals-of-technology/chatgpt-is-a-blurry-jpeg-of-the-web

[icy shadow]

neither they both suck

[bright hill]

Haitch

Bruh

Fr?

[ripe wasp]

@bright hill im thinking of joining the measure theory thing but the meeting time is kinda at 4 am for me...

[void tundra]

[long matrix]

early bird gets the measure

[ripe wasp]

is it full

[void tundra]

no

[amber orbit]

why

[bright hill]

hmm

that's a bummer

we'll figure it out

are you sure you want to join the group?

coz we're still early up into folland

we're still at sigma algebras and stuff

[neat lintel]

$\sigma$ algebra grindset

[long matrix]

darq

am i being dumb

or arent we just nowhere

we havent met yet?

[long matrix]

.

[bright hill]

well, yea

but we're supposed to read the material beforehand

and sigma algebras are next meeting's topic

[woven whale]

ic

do we have any example of a field F that is not char 0 whose integral is 0?

[long matrix]

yh where did u get that notation from

book?

[woven whale]

if it's char 0 we can embed Z into it

and integrating over Z gives us 0

so the intersection will also be 0

if you get what I mean

[long matrix]

[woven whale]

why sully

[long matrix]

ive asked u twice, someone else asked you too

where the heck is this definition from

https://i.imgur.com/FiY8mfv.png

[woven whale]

I've said twice

from this chat

[long matrix]

someone gave it to you?

[woven whale]

no

[bright hill]

btw @ripe wasp you didn't have to fill up the questionnaire lel

I already know you're a committed self-learner :3

but since you did, do you think asking to read that section was too much?

[vast surge]

Is this comic sans?

[void tundra]

oh yeah

[long matrix]

bruh dont ask me

[woven whale]

comic neue

[hearty shard]

Hey guys i am looking for some friends who are addicted to maths just like me, but i couldn't find anyone in my school so I came into this group. Anybody want to join please

[flat harbor]

pee whew what the hell just happened there folks

[neat lintel]

[fringe needle]

So you just happened to ask yourself a question about unions of intersections of subrings contained in ideals? What’s the motivation?

[woven whale]

there is no motivation

[fringe needle]

Then why are you asking this question

This seems like a completely arbitrary operation

[tall minnow]

he claims someone else came up with it in chat

I don't know who that is

[long matrix]

he denied that

[long matrix]

.

or maybe not technically

complete mystery

i bet hes keeping it to himself because hes on the verge of a breakthrough

[tall minnow]

breakthrough? sure.....

[neat lintel]

Hey morris 😊

[woven whale]

it's not arbitrary...

[neat lintel]

why did you use the integral sign for this?

what about this operation is integral-like enough to warrant using the notation?

[woven whale]

that's left as an exercise to the reader

[neat lintel]

so you just wanted to use the integral sign for fun

got it

[bright hill]

lumin the next mizlang, question mark?

[woven whale]

mizlang?

[frank orchid]

Guys have any of you got latex-workshop vscode plugin working?

[fringe needle]

If it’s not arbitrary you ought to explain what about it isn’t arbitrary if you want any help. Considering how convoluted it is im sure it’s not arbitrary and does come from somewhere but I can’t come up with that on my own

[storm sage]

where'd mizalign ever go

kinda miss them

[neat lintel]

those of you who self taught yourself, how??

w private tutoring i essentially finished my school's syllabus and i wanna work ahead for uni since i've acc learned to enjoy math

but idk how to do so alone

just reading textbooks feels dry and i just can't dedicate myself as hard (might be shite textbooks too)

[river moon]

well there's no other way than to read a book, watch a youtube lecture, read someone's blog post on a topic, etc

[dapper current]

youtube can be less dry, or khan academy, or different books

[river moon]

you'll have to adapt to the fact that you'll spend half of the time looking for information rather than just studying all the time

[sharp cave]

Yes

[river moon]

so better make a folder or something

and first year or so feels dry because there's not really many interesting applications to basic calculus/linear algebra

[neat lintel]

this too, so many times i've been hung up on stuff that I just had to ask my prof after a while bcz i couldnt find a good answer anywhere

[neat lintel]

tried khan and ngl i don't like it (might get lynched for saying this)

doesn't feel as rigorous as the normal classwork im used to

[dapper current]

well theres more than one teacher/video on there, but fair enough

[neat lintel]

ive just ran into sal for now

[dapper current]

doesnt have to be only resource also

[neat lintel]

what channel do you watch btw

if there was something like 3b1b but more depth, that'd be perfect

what topic are you trying to self study?

rn lin algebra

going to uni for comp sci

are u in the US?

nope, europe

ah

hmm

(not british despite my pfp)

[river moon]

there should be plenty of rigorous lectures on calculus/linear algebra which are recorded in class, when I was learning all of this I watched like multiple playlists of calculus/linear algebra

[dapper current]

ive watched some mathemaniac, but maybe thats too close to 3b1b also

[neat lintel]

yea theres probably alot of completed LA lectures on YT

i thought the MIT OCW was a godsend, but then i realised that they were just saying shit and the students had to take it for granted

[dapper current]

seems like a common issue

[neat lintel]

like even basic geometric interpretation of the determinant wasn't covered, whereas 3b1b does it really well

hence my hesitation for lecture vids

[neat lintel]

havent heard of mathemaniac, ill check it out

[river moon]

tbh if you ever find a linear algebra class that starts off with geometric interpretation of determinant it's either going to be a geometry-based linear algebra (which isn't going to last as far as applications are concerned) or it's some really abstract, high level view at algebra

[dapper current]

geometric algebra?

[river moon]

no, geometry-based linear algebra

[neat lintel]

isn't linear algebra fundamentally a study of space and transformations though? i get the applications are sometimes more important but i'd hate to learn it without really understanding the roots

[river moon]

using matrices, dot products, determinants, linear dependence in R^2 or R^3 to say something about some parallelogram, a pyramid or something

[dapper current]

ive found it helpful to use my intuition from group theory/graph theory, and of course theres the origins with systems of equations and stuff

like coexeter group matrices, lie group matrices

[neat lintel]

group theory? is that meant to be a pre-requisite??? if so ive gotta backtrack

[devout nacelle]

No

[dapper current]

its very helpful via group actions/representation theory, not sure about a prereq

[devout nacelle]

Certainly helpful if you've learnt it to get a hang of abstract algebra if nothing else, but not a prerequisite definitely

[neat lintel]

ngl i know absolutely nothing about maths (still in HS for perspective), but if this is a fun subset i'll look at it in parallel

[frank orchid]

How did you do it?

[sharp cave]

Just install the package?

[frank orchid]

I’m on mac and it couldn’t the the root file.

[sharp cave]

Have you installed MacTex?

[frank orchid]

No

I installed texlive

Tex live works

[sharp cave]

Youre able to write and compile a Tex document?

[frank orchid]

Yep

Got a vim plugin and it works fine.

[sharp cave]

I see. As long as you have all your documents in one folder and accessing the file from that folder, it should work. Other than that, I am not sure. Try opening an issue on the Github page

[ripe wasp]

nah section 1 was really short

and im fine with the group starting really slow

bc i needed to review anyway

i was kinda losing motivation bc of school stuff

and hws will be nice to make sure i don’t slack off

[bright hill]

[bright hill]

good good

we're gonna aggregate a bunch of interesting problems

(everyone can suggest a problem they find interesting)

they'll be in #problem-hitlist

I already sent you an invite btw

wait

I didn't wtf

lol

[ripe wasp]

an ok

is it in this server

or is it a group chat or smth?

can’t see it

[bright hill]

it's in a separate server

I sent you an invite

I actually should've mentioned we're organizing the thing in a server

welp

no matter

[desert mauve]

hi

[dense crow]

[split pawn]

Hi!

[grizzled grove]

Heyy..

[rough sphinx]

hello

@rough sphinxhi

[fading pulsar]

If X,Y are complete metric spaces, with X_1 and Y_1 being dense in X and Y respectively, and X_1 and Y_1 are isometric, are X and Y isometric?

[neat lintel]

hu

hi

[deep mango]

Not necessarily

Suppose X_1 is the interval (0, 1). Can you come up with different X and Y for this X_1?

[fading pulsar]

so just [0,1) (0,1]

[deep mango]

Those aren't complete

[fading pulsar]

oh yea

[deep mango]

Something like that though

[fading pulsar]

oops

hm

how about completions of a metric space

Are any two completions of a metric space isometric

I hate these prove or disprove problems

[neat lintel]

i would hope it's true

[static loom]

R isometric to Q_p

[jovial ember]

Why old ryc

Finally embraced ur baldness?

[long matrix]

meow

[long matrix]

https://i.imgur.com/gGxdjBf.png

fixed it

[jovial ember]

Lol

[jovial ember]

U just sully but don’t even answe??

[long matrix]

we're playing skribbl

want in next round (if there is one)

[jovial ember]

Oog

[deep mango]

dont join and leave dumbass!

[jovial ember]

Bruh every1 left

Also I’m on mobile

Skribl mobile is

Pain

[deep mango]

easier for me to beat you then

whatever

[jovial ember]

Yeah you’d need it

[deep mango]

you can play later when yamin can

no i got first in the first game by a large margin

im a skribbl god

[tiny saddle]

Wtf is this

[bronze pelican]

Yamin

Thats me

[dapper badge]

that's you

[old fox]

yo wtf?

[wooden flax]

walter honorable??

🥳

[icy shadow]

do you eventually improve at quickly understanding something you've never seen before

[vast surge]

Congratulations walter

[acoustic halo]

So im reading a book on dif eqs and im noticing that the author writes log instead of ln. Is this a mistake or a notational choice?

[static loom]

it's not an uncommon notation

[vast surge]

If anything I'd be more shocked that you got as far as diffeqs without having seen that notation

[acoustic halo]

So far I have only ever seen physicists do it, and I always assumed they just didnt care, however my math teachers were always adamant that log was for base 10

[prime adder]

@neat lintel
,w int_0^H pi*(R/H *h)^2 dh

[nocturne tusk]

THEYRE ALL SIDEWAYS NOOOOOO

[long matrix]

ill cope

its ok, on phone

[nocturne tusk]

@long matrix not letting me access the itemType class

despite it being public

no signal in class

[long matrix]

Dim is private declaration within class iirc

ull want to make a property

its complaining about the property not the class itself

[nocturne tusk]

I might just make it a structure

[long matrix]

also chatgpt might actually be somewhat helpful

@nocturne tusk so instead of going
Dim itemID as Integer

You should do
Public itemID as Integer

That declares it as accessible from outside the class

Well maybe im missing something

Cant remember whats the diff between
Public id As Integer
and
Public Property id As Integer

iirc ones static, ones instance var

===
Also you need to instantiate
Dim item As itemType = New itemType()

[river moon]

what language is this

[long matrix]

visual basic

https://www.tutlane.com/tutorial/visual-basic/vb-classes-and-objects

im staring at this

which is ok for example/tutorial

[deep mango]

public class variables

[river moon]

[long matrix]

yh vb is rather silly once ur used to py js etc

iirc it bijects with C#, that be better to use

[nocturne tusk]

sick, ty!!

[long matrix]

that tutorial probs help u a lot

[nocturne tusk]

Well uh

class ended

so

[nocturne tusk]

oh god constructor methods

I tried ages learning how class constructors worked for python

never got it

[long matrix]

yes

uhh

a class is like a factory

the constructor is your factory sorry

[nocturne tusk]

yeah its

[long matrix]

class is like a blueprint

[nocturne tusk]

instantiating a class

[long matrix]

constructor is the factory

instances are the cars

[nocturne tusk]

the way I've been taught in this class is to just have a single object

store it in a file

then clear it

[dapper current]

its like a partial equivalence

[dapper current]

is that the only thing in the file?

[fading pulsar]

This is rly depressing lol TA links is a paper from 1935 and he’s like I hope this paper is accessible to you by now

[static loom]

why is that depressing

[fading pulsar]

100 years to go

[static loom]

100 years isn't too much more, since you already covered stuff from a couple thousand years back when pythagoras was around

[dapper current]

turing was alive then

[devout nacelle]

So was I

[neat lintel]

Im too dumb for new shit

[tall minnow]

Undergrad class?

You learn way more in grad school and at greater speed so it's nothing to worry about

[neat lintel]

Im too poor for grad school

[untold sage]

Grad school is free

And you get paid

[tall minnow]

I'm thinking he's just trolling

[neat lintel]

If ur good

[neat lintel]

Im not trolling

[untold sage]

I think it's almost always free

[neat lintel]

If u get accepted to a phd program but i don't even have math undergrad. I had to read munkres topology, lang algebra, rudin's 3 analysis books, mac lanes categories for the working mathematician on my own. I am unemployed and I have no future plans

[neat lintel]

Im not joking i really did waste the past 7 years of my life reading stupid crap unguided on my own and im not in any school or program or future prospects or opportunities

[tight comet]

What are you doing now

[neat lintel]

Im reading Lectures on Functional analysis by Helemskii

[neat lintel]

I have no job and no school

[tight comet]

Where are you from, continent wise

[neat lintel]

Im in California

[tight comet]

So I assume your future plan is to get a job

[neat lintel]

Ya i applied to be a barista

[tight comet]

Is your aim to do math research?

[neat lintel]

I want to do that

[tight comet]

I think it's a bit hard to do unaffiliated research

[neat lintel]

Ya i know. I want to be a part of some school but im poor and don't have math undergrad.

[neat lintel]

Fuck this and fuck you i have to read functional analysis in my free time

[untold sage]

What do you do in your non-free time then

[neat lintel]

When i was working i had to do shitty work. I wasn't paid to learn math

[untold sage]

Yes but you said you don't have a job now

[neat lintel]

Ya i can learn functional analysis and scramble to apply for odd jobs like barista or janitor n shit

[untold sage]

If you're good at math, you can get good at programming relatively quickly

And get a programming job which pays better

You can get a certification from like freecodecamp

[long matrix]

You said you've read - but would you say you're proficient in all you've read

if you are, I don't see why there shouldn't be a way to somewhere

somehow

[neat lintel]

u had some school to force u to be proficient. I can't afford school. U can get paid to keep learning math in grad school and do research. U can devote huge amounts of time these next several years to learning and mathematical maturity. I have to do odd jobs, get a programming job, do what i can to learn math in my free time, eventually get some money to go to math undergrad where the classes aren't gonna teach u nearly as much as grad school. Maybe in 10 years i can be where you are now in grad school and get paid to learn math at very fast speed

[long matrix]

If you mean 'u' as in me - I can see you're likely to be more knowledgeable than me in many subjects judging from what you've read/reading

[neat lintel]

I should mean u as in this guy

[long matrix]

I'm asking like -

[tall minnow]

I was not speaking to you

[long matrix]

can you do most of the exercises in the books and so on

[tall minnow]

In fact, I don't even feel like explaining it

[neat lintel]

I don't read without doing exercises

[long matrix]

like you can read a book and barely understand. or properly understand

[neat lintel]

Idk i wasted like 7 years reading them

[long matrix]

My point is - if you really have learnt these subjects, I don't see why you can't get somewhere

Just... talk to people...

[neat lintel]

This is why

[tall minnow]

shuri is clearly not talking about research

[long matrix]

ngl I have little clue how instutions and so on work

I am referring to say a phd yeah

[tall minnow]

but about getting a job

[long matrix]

huh no

[tall minnow]

oh?

you mean you want to go into PhD?

[long matrix]

idk - i feel like you could right

[tall minnow]

could you?

[neat lintel]

I do

[long matrix]

look, idk

but they would have the mathematical prereqs

?

[neat lintel]

u tell me how unqualified and shitty i am. I obviously can't shit on myself because im not in grad school

[long matrix]

in which case its just a matter of finding somewhere that'll say yes

[tall minnow]

The only time I mentioned you at all was when you said "too poor for grad school"

that implies some monetary aspect

[neat lintel]

Im projecting my anger

[neat lintel]

Yes i don't have math undergrad

[tall minnow]

that's knowledge and diploma, not money

[neat lintel]

No it's money

[tall minnow]

[untold sage]

Ask them if you can just pay a small amount, do the exams, and get a degree

[neat lintel]

@tall minnow math undergrad is just money

[tall minnow]

I won't even bother explaining to you my life story but there is a 90% chance I was born poorer than anyone talking here

if they required money there's no way I could have gone into maths

anyway grad school doesn't require money, but knowledge and diploma and recommendation letters

[untold sage]

Would this work btw

[neat lintel]

Thats the biggest bullshit ever

[tall minnow]

believe it or not, that's your choice

not mine

I neither gain nor lose anything from you not listening to me about how it works

[neat lintel]

@tall minnow maybe read this message and try to understand a new perspective of my frustration rather than saying some clever last word gotcha

[long matrix]

why are you convinced its bullshit

[tall minnow]

no, maybe you read mine and every word

[long matrix]

Doesnt sound bullshit to me

[neat lintel]

No fuck you

[long matrix]

[tall minnow]

no one on admission board cares about how much money you have to go into PhD

[neat lintel]

Huge bullshit

[long matrix]

are you saying this having spoke to some people

at various universities

or something

[tall minnow]

clearly he doesn't believe someone who has experience with it

so he's on his own

[long matrix]

i have no experience myself, but it makes perfect sense to me they are after brains more than money

there are scholarships and whatevers offered.

not saying this is everywhere, but a good number of places at the very least

[neat lintel]

Clearly you wanna keep saying last word gotchas rather than putting in any effort. So i just wanna say ur not worth my time.

[tall minnow]

you were never worth mine

[long matrix]

[neat lintel]

Likewise

[untold sage]

Lmao "last word gotchas"

[tall minnow]

the absolute inability to disagree without calling everything BS

not a discussion but a shouting match

[neat lintel]

@untold sage basically this asshole can't not have the last word. Also his last word has to be a gotcha.

[tall minnow]

betting the guy is still raging over people instead of discussing the idea

[neat lintel]

See? He has to say a gotcha after anything I message. It's in his programming. He can't help himself.

[long matrix]

What is your problem.

We're giving advice, not tryna gotcha you or anything

It won't benefit us.

[neat lintel]

I have bad depression and anxiety and i frequently take my frustration out on everyone in my life including my therapist and psychiatrist

[neat lintel]

You aren't tryna gotcha me but @tall minnow is

[tall minnow]

believe it or not I only care to discuss the idea of "too poor for grad school"
I don't care enough about you to gotcha you

you are just unable to handle disagreement

[burnt dune]

not true

@neat lintel go to a math department in any good uni

be polite to a professor

tell him or her to examine you in fundamental areas

talk math with him or her

get a rec letter

rinse and repeat

and then apply

good luck

u need rec letters to say that yea this kid does not have in his trasncript analysis but he knows analysis enough he wont fail qualis

for exampel

example*

if ur aiming for good schools i dont think u have a high chance to be admitted

but u can be admitted for masters tho

as sorta a bridge

finding a funded one in the us is hard (ig)

[tall minnow]

funded masters are very rare

[burnt dune]

in the US

ye

he can apply to canadian universities where funded masters are the norm

also consider taking the GRE subject test

if u do well it might sugget that indeed ur talented enough that u self taught all this shit by yourself

[neat lintel]

Thank you @burnt dune this is good advice

[burnt dune]

but u need rec letters to verify this

you need to takee exams

and have professors vouch that you indeed know this shit

[neat lintel]

@burnt dune yes those are good tangible goals that get me where I wanna go

[burnt dune]

yea i am assuming u want to apply for good schools ( as in ranking )

u wont be accepted into a phd program ig

just too many math majors that are jut better than you (regardless of skill but atleast on paper)

[neat lintel]

Idc about school ranking

[neat lintel]

Im shit

[burnt dune]

maybe you are but you can improve

your application

maybe a professor really likes you and if that happens and he is in some admission committe he would want to work with you

who knows man

main thing is

do math and improve at it

[tall minnow]

I have seen at least one immigrant family, with the husband trying to contact a professor about trying to get into grad schools
it didn't work out well as the husband wasn't prepared enough for an interview

one would need to be very ready upon meeting the prof

[burnt dune]

those are not easy books at all

if u do atleast half the exercises then id say your p good ig

[burnt dune]

yes

be very polite

[tall minnow]

preferably get a good GRE Math Subject score to show you're not just a crank

[neat lintel]

Ya i assume u need to actually read what the professor has wrote or actually show interest in what the professor specifically has done

[burnt dune]

yes

[burnt dune]

no

just be polite and show that ur actually not going to waste his or her time

thats the hwole point

also some professors are less helpful than others

be lucky ig

if u can have letters vouching that you got eexamined ( and did reasonably well ) in grad lvl analysis, algebra and some topology or whatever (ie the basic math)

then u have a shot at good (masters) i think thats just in my optimistic opinion

[tall minnow]

rather than a cold email from nowhere, probably a person could appear at lectures or talks given by a professor
uni campuses are often publicly accessible

[burnt dune]

100%

do not email

[tall minnow]

then ask the professor if they are free for a lunch and talk

[burnt dune]

just literally go up and be polite

exactly

@neat lintel thats my two cents really hope u get somewhere and ig just do not give up

[neat lintel]

Thank you @burnt dune for giving helpful honest advice

[burnt dune]

deleriks stuff is important too like u NEVER want to sound cranky

in any way

make sure ur acutally half decent

say you just finished papa rudin

literally type up real analysis qualifyihng exams

do problems

see where ur at

math is about solving problems

proving theorems

if u cant do those but u know a thing or two it does not matter

[neat lintel]

@burnt dune ive been practicing https://jonathanlove.info/qual/makeit.html

[burnt dune]

standfords qualis are gigafuck hard anyways

but the point is

ur self taught

so ur approach with math might not invovle much problem solving as much as just theory learning

thats not good at all

atleast for grad schools ig

but that ur already practicing so u know whats good so good for you

[meager sonnet]

not really

not that it's easy but it's early undergrad

hmm?

no, most people don't have much idea of what high level or research mathematics is

[zealous garden]

C (with classes) was my first language

Based

[chilly hull]

i was about ask "wtf is this an undergrad qual"

its a grad qual

nvm

[long matrix]

[fading pulsar]

Why is every convex symmetric body in $R^n$ a unit ball wrt some norm

[fathom swallow]

Functional Kitten

[fading pulsar]

was casually mentioned at end of class but it's been bugging me

[eager reef]

is the picture clear?

like is formalizing the problem or is it the intuition

[fading pulsar]

Oh I get the intuition I just don’t know how a proof would start

[elfin ridge]

How is "symmetric" defined

[tight comet]

Didn't someone ask this exact thing

[tight comet]

symmetric wrt origin

[fading pulsar]

I would look it up online but I don’t want to be spoiled with a full proof

I just want a direction to start with

[tight comet]

Sorry I don't know the theorem/proof myself, but the last person who said this mentioned the Minkowski functional

[wooden flax]

Whats a good converter for pilot metro

[river moon]

yeah I've heard of something called steiner symmetrization which preserves convexity and in the limit as you repeat the symmetrization infinitely many times you get a sphere in R^n, perhaps this could be relevant?

[tall minnow]

Because if you scale up the "ball" you get the whole space. The norm of a vector is then how much you need to scale up to absorb the vector

[fast ivy]

One of my profs does research in convex geometry

and this is how he explained it to me

given a centrally symmetric convex body (compact convex with non empty interior) which contains the origin

you have associated to it what is called a gauge function

and this gauge function defines a norm

whose unit ball is this convex body

https://youtu.be/jLhKJRmKbUY

and the intuition of the gauge function associated to a convex body is precisely what delerik said before

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

this is the relevant wikipedia page

[ancient sequoia]

Is anyone else reading Euclid

[burnt dune]

this shit is metal as fuck

[ancient sequoia]

Yeah it is

[fading pulsar]

Prof: I’m assuming you read the book, because it’s pretty damn good (he wrote the book)

Class:

[river moon]

reads the book like gigachad

[zealous garden]

I have to write a book

[neat frost]

Why are you writing around your sketch, as opposed to above and below it?

Unless you sketched it first and then wrote, that would make sense lol

[long matrix]

the left is the dead zone

[amber orbit]

chad

[ancient trout]

had to do prop 17 book 12 for a final, it hurts your brain trying to keep up with all the proofs and what not

[potent kernel]

Hello

I’m doing algebra

I’m not sure where the 1 come from

If the coefficient is just x

[ancient trout]

3x is a fraction its just over 1

so when you multiply it by 1 over y it returns 3x over 1 * 1 over y which is just 3x over y

[potent kernel]

I’m not sure what you mean

Wouldn’t 3x be 3 whole numbers

[violet coral]

xxx=x^3

[potent kernel]

Oh

[violet coral]

i used asterisks it’s not going through

[ancient trout]

yes but every whole number is technically over 1

x over one times 3

[potent kernel]

But there 3

What’s that

[ancient trout]

3x over 1

are you working with three x, or x cubed

[potent kernel]

What can be done about it

3x

Just trying to understand

[ancient trout]

im not quite sure what you mean, you want to know different ways it can be represented?

[potent kernel]

3*x = 3x

But if do 1/y

What’s just 1/y

Is that equivalent to 1/1

So y could be anything

Out of the fraction

Ahh

Mm

Brb

What does that mean

How is 3x merged with 1/y

It doesn’t make sense

3x*1/y

@ebon pelican

Still there?

So it’s forks to the right numerator

Does 3x merge with the 1

And or does it also merge with the y and that can’t be true because it must only be y at the denominator

So 1*3x =3x

/y

[ancient trout]

3x == 3x/1 so the one in the denominator of the 3x multiplies with the y in the denominator and the 3x in the numerator multiplies with the 3x in 1/y

its pretty much (3x*1)/(1*y)

^^ alot easier to comprehend with visuals like this

[potent kernel]

Oh

So you have to balance
The equation

With what’s ever in the numerator

[empty spade]

how are yall so good at math

lord

[potent kernel]

How did I go

[empty spade]

i got a 25 on my last geometry test so we arent too far apart

[potent kernel]

Oh

For got the x

Sec

[bronze wedge]

<@&268886789983436800>

[tall badge]

ty

[velvet dagger]

How I had my finger on the ban button

[fading pulsar]

Can arzela ascoli's assumption be weakened from uniformly bounded to pointwise bounded

[bronze wedge]

Arzela-Ascoli establishes an equivalence between "F is compact in the uniform topology on C(X)" and "F is pointwise bounded and equicontinuous"

@fading pulsar

[fading pulsar]

I have been lied to in the class :_:

was introduced just as uniformly bounded urgghh

[bronze wedge]

This is actually false (the unit ball of C(X) is not compact although it is uniformly bounded)

[fading pulsar]

ok imma have to reread notes

it's highly likely that I just misread them

Ok I see this in the notes, is uniformly bounded different from bounded?

[bronze wedge]

No

[deep mango]

isn't the actual thing you need like "pointwise bounded" but for compact domains this ends up being the same

[bronze wedge]

Yes

[deep mango]

oh i guess for locally compact vanishing at infinity its the same too

[fading pulsar]

Yea I just noticed on the homework assignment he just tasked us to change the proof

I think it shows it for pointwise bounded

instead of just bounded

[deep mango]

i see

[bronze pelican]

I proved the inverse function theorem in class and I feel like it was a waste if time

Its such a technical proof

[deep mango]

it's a waste of time

🤡

dumb theorem

[neat lintel]

noooo haha it's good haha trust me

[tall minnow]

did you follow the terrible proof in Rudin

it's one of the most important tools for diff geo and diff eqs

[velvet dagger]

What's wrong with the Rudin proof?

Isn't that the one that works in Banach spaces too?

[neat lintel]

(47) (48) (49) (50)

[tall minnow]

looks ugly and uninsightful

this is how I would prove the injectivity

[velvet dagger]

Looks ugly because of the typesetting

But this is very clean

[tall minnow]

even the ideas

[velvet dagger]

Do you prefer it to be more like Newton method?

/is there a reference for your preferred proof?

(Or are you gonna give it right now lol, I didn't realize "this is how I would prove the injectivity" was referencing something forthcoming)

[tall minnow]

WLOG assume $f(0)=0$ and $f'(0)=Id$ (use translation and linear map)
Then for x near 0, we have the fundamental theorem of calculus
$f(x)-f(0)= \int_{[0,x]} f' \approx \mathrm{Id} x$
So injectivity is proven

[fathom swallow]

Delerik

[velvet dagger]

Huh

Wait how do you turn this into a proof proof

[tall minnow]

Just need to write out $| | \int_{[0,x]} f' - Id | |<\epsilon$

[fathom swallow]

Delerik

[tall minnow]

what's the dashed integral

how to write dashed integral in texit

I'm using the average integral

well you can understand

f' is so close to Id its average must be close to Id

this is how I proved it myself. In fact I bet others have proved it like this also

how did tao prove it

oh, he also uses FTC

yeah this is also why I like Tao.
he thinks naturally like me

just go for the obvious, like constructing real numbers by cauchy sequences

this is also how I would prove open mapping in complex analysis but there I split into cases of nonzero derivative and cases of the function being locally z^n

[velvet dagger]

Does FTC work nicely for Banach spaces?

[tall minnow]

yep. As long as you impose regularity from Frechet derivative

the inverse function theorem in Banach spaces is proved in the same way
and in fact it is what I use to prove the smooth dependence on initial data for Picard iteration / ODE

otherwise proving the smoothness manually would just be messy

the most advanced / famous version would be the implicit function theorem in tame frechet spaces that Nash used for his embedding theorem

[bronze wedge]

Arguably derivatives in general don't work nicely in Banach spaces

[tall minnow]

which leads to the story of fluid mechanics today

we don't use the exact theorem. But we use his ideas, especially the regularization to defeat the loss of derivatives

[neat lintel]

<@&268886789983436800>

[tall badge]

ty

[neat lintel]

Ja

[frozen seal]

what happened

[limpid maple]

lads how do I peak in high school maths

[frozen oriole]

hello

im very good at maths

lol

[velvet dagger]

By going downhill afterwards

[rocky tiger]

How does one go from 40% test scores to 70% in VCE Math Methods Unit 3 & Unit 4?

[neat lintel]

Im very bad at math

[real hill]

Proof it

[real hill]

You are on discord, what do you expect? Your grades go up because you ask on discord how to, rather then learning?

[split pawn]

Second derivative test

[fast moat]

learn

[jade garden]

anyone got tips to get better on algebra and just in general solve equations faster and calculate faster etc I think it's basically basics

it will save time on a test

[oak hemlock]

imo just practice the equations you wanna know

i dont really know any other way

[jade garden]

no but like I made a realy dumb algebra mistake last time it went like (a^n + b^n) / c^n and I thought it was ((a + b) / c)^n

so I want to prevent this

[oak hemlock]

oh

[oak hemlock]

does it usually happen?

[jade garden]

I guess if I am not too focsued or smth

[oak hemlock]

Memorize the formula alot of times beforehand and write it down when you're solving the question

[jade garden]

I didn't raely do it with the formula I most of the time know this is legal to do

[tall minnow]

if you want, I'm sure someone has generalized in clarke's direction as well
just as Ekeland generalized on Nash-Moser
and sobolev / holder spaces aren't exotic but what every analyst deals with

but I will settle for Nash being the most famous and impactful

and it's the idea of recovering regularity that still helps us till this day even when we don't actually use the theorem

[tall minnow]

Holder spaces are exotic ?

just confirming your opinion here

ok you are entitled to your opinion then

[runic charm]

can i also ask phy doubts in doubt section

help section*

[hearty marsh]

bruh

[runic charm]

nope

[hearty marsh]

look at the name of the server

[runic charm]

ok

[burnt dune]

yo

wtf are sobolev spaces

[tall minnow]

I think people in geometry are more familiar with C^k and Holder spaces

which expresses regularity / differentiation

Sobolev spaces are also like that (differentiable functions) but based on L^2 spaces instead. It's the setting for elliptic regularity which Hodge theory and PDEs depend on.

[fast ivy]

some areas of geometry actually depend a lot on sobolev spaces

like index theory for instance

and their connections to the topology of compact manifolds (stuff like atiyah-singer for example)

which is pretty cool

this is one of my motivations to learn about elliptic operators and sobolev spaces at some point

[zealous garden]

my motivation to learn about it is there's a dirac operator there

[warped creek]

My motivation to learn about them is to get a feel of other structures on manifolds and their geometry. I’ve worked w a C^k structure (book exercises involved). I’m in a class for smooth structures. I’ve worked with analytic structures (class setting). I’ve seen others work w a Riemannian and Kahler and Complex structure (all independently). Never worked w a W^(k,p) structure until recently

New ball game

[neat lintel]

Im not motivated

[autumn pumice]

hi my love

[sudden wren]

I have written an absolutely-stupid stats joke

Me, sitting at my desk doing frequentist statistics: ...
My wife, bursting in: WHO THE HELL IS EMILY

[bronze wedge]

Sobolev spaces are built on common sense

[tiny saddle]

My head feels kinda distant from mathematics rn thanks to a few videos on YT which talked abt the flaws of mathematics: Of how it is inconsistent, undecisive and flawed ._. Suddenly it feels as if maths ain't smth that great- it began to make me question if maths truly should be the thing I'm working on and studying.

[neat lintel]

We don't actually know whether ZFC is consistent or inconsistent. I think that most mathematicians believe it to be

What we do know is that ZFC is not complete

[tiny saddle]

mhm

fair ig

[neat lintel]

Therefore it's possible (and probable) for it to be consistent

[tiny saddle]

godel and turing be like slapping their whole ass thought experiments

[tiny saddle]

[neat lintel]

And also, ZFC is not all of mathematics

[tiny saddle]

XD true that

[neat lintel]

There are many axiomatic systems and it's probably not too hard to swap the foundation, because of the way theory is built up

[tiny saddle]

[neat lintel]

Like, if we were to find that it is inconsistent, we can always switch or modify, we don't have to 'restart'

[tiny saddle]

yeah, since the reasoning should be similar

With paid learning services such as Brilliant, Coursera, Datacamp, Udacity, Udemy and so on, it becomes quite a struggle for me to decide which one(s) I should enrol for. To provide some context, I'm looking into exploring these learning forums to further develop my skills and knowledge in STEM, mainly Mathematics, Physics and AI (programming and coding).

One that stands out immediately is Brilliant, given how it's widely advertised, with claims of providing an interactive and hands-on experience. It sounds and seems great and all from glimpses of the platform from YT vids- but something that made me think twice was how other learning platforms provided actual certificates from Universities, such as Coursera. I wasn't really sure if people would really... care about these certificates when it comes to applications into Universities, or maybe for a job, so I wasn't sure if perhaps other platforms which provided certifications would benefit me more. Honestly kinda confused on which to pick

[tight comet]

Avoid paying for anything. People may or may not care about certification, but mostly not really. Your degree and past experience matters more.

[tiny saddle]

was thinking that perhaps a learning platform would help me learn better and ahead of whatever is taught in the classroom. I agree that degrees and past experiences matter much more tho

[neat lintel]

Just pick a platform that will teach you what you want to learn. It's better to have a great understanding of a subject instead of some meaningless certificate. If you know things well you'll get into a good university and you will have a good career.

[tiny saddle]

[ripe wasp]

imo u should just use textbooks

i was really into self learning last year and i still am but i found the best way

is to just use free stuff

paid learning services teach the same things

one that i found genuinely helpful were the aops classes

[tiny saddle]

[potent dawn]

Well sorry for any inconvenience or disruption caused, but just wanna ask whether anyone can help me in #help-22 🙏🙏 I'm afraid I wouldnt receive a reply if I dun post this message here
(Please feel free to ignore this message, and tell me if this violates any rules, I will immediately delete for sure)

[rich rapids]

wut. paid services...?
why would u even consider those? use this server

[tiny saddle]

well, this server is mainly math oriented XD, there's still more

[rich rapids]

there are other servers

[tiny saddle]

well, tbh even then servers may not be the best options to learning

[rich rapids]

also, idk what lvl u on but learning every topic is not possible anyway

but yea, like the dude said, read books and ask questions

youtube has enough lecture videos if u need

coursera has free videos. and if u need more there are some stackexchange threads that list lectures in many different topics

[tiny saddle]

true that

[rich rapids]

high school?

[tiny saddle]

yep

[rich rapids]

do math major. will be fun. and easy to study. tho the topics themselves can get tough

[tiny saddle]

[ripe wasp]

education level doesn't stop anyone from learning, i'm also a high schooler and that's never gotten in the way of me pursuing my interests

[rich rapids]

dont sweat too much abt getting accepted into unis. ull be fine

[tiny saddle]

[tiny saddle]

tbh only thing that's stopping me from actually doing so is due to how all the information is scattered all over the place- it's like: "I know where I can search things up for resources, such as servers like these, YT, whatever, I also know where I can get help and practice- through textbooks, exam papers online and Wolfram's problem generator- but compiling and managing all of this is kinda a pain. This was why I thought a paid course where most info is already on the site for me would be best

ig it's a matter of "get gud"

[slate cairn]

It saves up a lot of time when someone has done the work to collect most of the information into 1 easy to access place.

[tiny saddle]

mhm

[rich rapids]

i would like to read this book...

https://m.doverpublications.com/0486409198.html

i want to download but cannot find it online. also my school library and some more around the area don't have it. i could buy it but that will be the last resort. doesn't anyone know where i can find it online?

except libgen cuz libgen doent have it

[tiny saddle]

yeah

it makes u more invested into it since it's smth yr investing in

[neat lintel]

It's still technically fallacious since you've already made the payment (sunk cost)

[long matrix]

yes if only they informed their customers

[solar hawk]

Hi

[neat lintel]

Anyone here take smart drugs (nootropics) ?

[random cargo]

Fr need to get my life together, Currently predicted CCB, in maths, computer science and business? ,. Fuck man, it's like 5 months in, I spend like on average 8 hrs a day on my phone, Really started to rethink my life choices, how can I get up to an A in maths😭

[plush moon]

Have you tried subliminals?

They helps me alot

[neat lintel]

just try to set up a schedule it might help

but account for when life happens (eg getting sick, etc)

[plush moon]

The key is to developed mental discipline in the face of adversity, countless failures, zero reward, and endless failures. If you can develop a Thomas Edison mindset of NEVER giving up you will get there.

[neat lintel]

yeah that's one important part of it

for like i guess meeting your goals and stuff

[night thistle]

Very debatable

[tiny saddle]

[tiny saddle]

true tho lmaoo

[dim needle]

Moving from #math-discussion

I don't know if I get it ;_;

I think I'm doing something wrong

[static loom]

go back I don't look in other channels

I'm probably wrong and should have picked the smallest not largest

[dim needle]

Ah, I felt bad because I didn't want to interrupt josemom2

[static loom]

nah

[neat lintel]

yo, can anyone help me? with bhaskara :/

[brittle socket]

!help

[quasi jetty]

Please read #❓how-to-get-help

[brittle socket]

You can literally just use wolfram or your calculator

Do not troll/meme here if you are doing so.

[tiny saddle]

How would you consider doing khan academy's math step by step (algebra 1, 2, precalc (trig, logarithms etc), calc, AP calc) as opposed to doing them at the same time?

[ripe wasp]

how would you do them all at the same time

i guess alg 1-2 and precalc may be feasible

but you would be pretty lost in calc without enough algebra knowledge

also no need to do both calc and ap calc

just do the ap calc BC course

its the same as calc AB but with more content

[random cargo]

Wtf is this😭

[tiny saddle]

Icic

[leaden shoal]

hello

I really need help understanding how polynomial ideals work

particularly, this question asks how I represent Z[1/6], I understand that this can be written as Z[x]/6x-1, but dk how to continue from there

[long matrix]

.

#groups-rings-fields more appropriate

I also don't get your full question

like 'continue' where

[leaden shoal]

like I don't understand how u approach the question

[long matrix]

you haven't written the question

Anyways - post in that channel, ill take a look

you'll need to pick up the undergrad role

[leaden shoal]

done!

[dim needle]

Here's the context, this is about the start of the conversation
#math-discussion message

I moved to this channel worried I was talking over someone else and was told to move back

[minor basin]

Damn, this makes my g11 Spec and Methods math look like kiddy stuff

lol

[loud whale]

i'm making a python number theory package

which functions should i add

[analog abyss]

#❓how-to-get-help

[neat lintel]

yo is any1 indian here

patriotism

no i have doubts

[halcyon lichen]

There are shit tons of Indians here

[neat lintel]

ikr

they r all ded

[karmic perch]

why VC has been deleted?

@everyone

[fading pulsar]

Because of people like you

“@everyone” to answer the question I couldn’t bother answering myself so I attempt to ping everyone

[karmic perch]

actually not everyone is lazy like you, so dont just assume anything @fading pulsar .

[tall minnow]

yeah, another rude rando to the blocklist

[eager reef]

[woven whale]

the person in your profile picture fits you

[molten quest]

bruuuuh this man helped me

[molten quest]

this man a goat

[long matrix]

go shitpost in #chill , not here thanks.

[fleet oyster]

damn wtf

why am I only learning about this characterization now

makes so much sense

[tall minnow]

because then what about R^4

[fleet oyster]

ternary inner product

[velvet dagger]

This is how I learned cross product in a way

[tall minnow]

sounds like you're just learning exterior algebra with extra steps

wait it is exterior algebra

[tiny saddle]

I am not understanding this at all.

[velvet dagger]

I had physics and just kinda suppressed that memory

[fleet oyster]

yeah I am

[velvet dagger]

And then at one point a friend of mine was like

Hey I get cross products now

Wanna see?

And explained it this way

[tiny saddle]

[fleet oyster]

the book is called multivariable calculus and differential geometry by walschap

pretty ambitious book that doesn't assume much prereqs but ends up doing diffgeo in considerable generality from what I can tell

[tall minnow]

I care less for R^3 but more about general Riemannian manifolds

in which case cross product is wedge product with the hodge star

[tiny saddle]

Hodge star?

[tall minnow]

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

[tiny saddle]

[halcyon inlet]

what is the mode of (14; 17; 18; 20; 20; 21; 23; 24; 25; 25; 25; 26; 26; 26 ; 27; 27; 28; 29; 32; 32; 33; 33; 34; 35; 37; 39; 45) is 25; 26 correct?

[fading pulsar]

#❓how-to-get-help

[halcyon inlet]

for such a simple question?

[velvet dagger]

Yes

[long matrix]

doesnt say anywhere in the guidelines no simple qs

[zealous garden]

The cross product is dual to the wedge product, yes yes

[tall minnow]

why doesn't apple pencil have eraser on its end

[dawn edge]

is it possible to find the complex conjugate of a longitudinal wave?

[marble delta]

25 & 26

[halcyon inlet]

lol. thank you 🙂

[quasi jetty]

As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.

[halcyon inlet]

bad bot

[velvet dagger]

Nah good bot

[woven whale]

beep boop

[halcyon inlet]

just saying, confirming a correct answer should not be a bad thing

[long matrix]

shouldnt be in the right channel

[lucid prairie]

Typo confirmed

y = 0.5, not y = 0.8

[neat lintel]

what does the bot use to pick up on this?

[dark shale]

I was wondering if anyone knows how solve the problem using the shell method

[sand zealot]

Oh that's easy

Just remember that the volume of a cylindrical shell is equal to the integral of the shell's circumference times the height times the width

And the width is always d(whatever axis you're rotating on)

The height is the function

And the circumfrence is the tricky one to calculate but it's 2 times pi times the radius

But the radius is always the hardest to figure out

[pearl eagle]

Whats the best free resource to learn math im confused

[neat lintel]

What math?

[pearl eagle]

Highschool math i wanna build a solid foundation

[tiny saddle]

khan academy would be a great place

[last otter]

and after that, u can learn a bunch of the harder stuff on youtube, MIT has good courses I reccomend them!

also various maths youtubers are good resources to learn from too !

[tiny saddle]

3B1B

[last otter]

i like him for overviews and conceptual introductions

but nothing is in-depth

[pearl eagle]

Oh alr then ty

[pearl eagle]

Whos him? Mit ?

[tiny saddle]

MIT is a university

iirc their website had quite a few vids on math?

[last otter]

they have the lectures posted on YouTube as ell

well*

[pearl eagle]

Oh

[pearl eagle]

Ok then thanks ill go study khan academy math now!

[last otter]

gl

[burnt kettle]

Yes, Spivak introduces cross product this way. I thought it was really neat when I first saw it

It also is a fun party trick when you're around other mathematicians

and you ask them what the cross product looks like in R2

[tall minnow]

https://github.com/vscode-neovim/vscode-neovim/issues/576

damn

[gritty hearth]

gawd forbid sum1 might give sum1 else an answer to any math homework!

[analog abyss]

#❓how-to-get-help
And be patient

[marble quail]

hellooo

is anyone interested in infinite series

[snow panther]

hiii

[neat lintel]

helo

there are many ways to do i think mayb

[snow panther]

geometric series

maybe

[neat lintel]

do u want a hint

its like

honestly so dumb seeming after u do it haha

[snow panther]

wait

i need to take paper

why do i sometimes mess up the sum symbol

qkshchuehdj

[neat lintel]

yeah dont do integrals in ur head lol

lmaoo

[somber musk]

Let me try

It's 1/(1 + sqrt(x)), right?

[neat lintel]

yes

dont give the answer though

let her do it on her own too

[somber musk]

It was easier than I expected

[neat lintel]

yes

i am telling you

lmao

it is hard looking but really dumb when u actualy do it

[hearty marsh]

Why not tho

[neat lintel]

uh

if u want to, then do them in your head

[somber musk]

If it's a simple u-sub, then you can do it in your head

[hearty marsh]

Who can’t integrate “x^2” in their head

[hearty marsh]

Lmao yeah

[somber musk]

One day

[neat lintel]

[somber musk]

I was trying to derive a formula

For that I needed to integrate sec^2

And I spent like 20mins

Before remembering that

I literally got that sec^2 from differentiating tan

While I was wasting my braincells instead of recalling that

[neat lintel]

lmao

[hearty marsh]

Lol

[neat lintel]

r u still dying

[snow panther]

i have a sum problem now

:(

[neat lintel]

alright

um

sums

are probably complicating it a lot more for u

ur hint: u sub

[snow panther]

aa okay

i think ln is going to be in the answer

[neat lintel]

u r not wrong

[somber musk]

There will be ln in the answer, yes

[long matrix]

ln 1

[somber musk]

= 0

[neat lintel]

do you want me to just show u it

[snow panther]

i messed something up

okay

[neat lintel]

yeah its basically

[flat harbor]

||do u sub sqrt x = t||

[long matrix]

i sub

u sub no

lixu

[flat harbor]

huh

[long matrix]

lixy

[snow panther]

i did

[long matrix]

u no sub

[neat lintel]

[
\int\f{1}{1+\s x} \dd{x} \textqs{take} u = \s{x} +1 \quad \dd x = 2 \s x \dd{u} \
= 2\int \f{u-1}{u} \dd{u}
]

[long matrix]

chet

[neat lintel]

lmao

[flat harbor]

u shuld get smth like t/1+t then rite