serious-discussion

[barren anchor]

google's actual Plans

the Banks actual plans

[fervent notch]

Idk if it has anything to do with nuclear fission.

[barren anchor]

honestly this may be as late as we can go and still change our ways

in terms of capitalism

like do we wanna find out bezos is going to the moon without us in 20 years, in 20 years, or now?

certainly nuclear fission is a very propriety process in the details and very valuable

some fallen 1st worlds like russia would probably love to be back up to speed

I'm just saying top secret shit all over

but yeah I say just put it on PLoS or arxiv

security is just another way for the lumenprole to be marginalize

[signal oracle]

i never hit you

[devout nacelle]

Unfortunately no. I would have liked to work on a Bachelors thesis or similar but for some reason it is not an available option at all.

This is a surprisingly interesting class, I guess it's good to know about all these things but I'm mostly settled on moving in the math phys direction

[cinder zephyr]

I want to do an undergraduate thesis but idk how that's even done here

[devout nacelle]

Oooof

I hope you can make it work through an individual or directed project under a prof's supervision

Even if not a formal undergrad thesis

I cannot even do that because this place has only been open for a few months in person for me

And I graduate mid-year

So not enough time for anything

[cinder zephyr]

I'm doing CS-ish research right now

but I want to do something pure math maybe

idk what an undergraduate thesis would even consist of

[devout nacelle]

I'm guessing it usually amounts to a survey paper or similar most of the times?

Or presenting alternate/more polished exposition for some idea

[cinder zephyr]

not research?

[devout nacelle]

I think original research is pretty rare for a bachelors thesis in math

Even for a masters thesis, from what I know

It kind of is a prelude to research I would say, but yeah, I don't think attacking unsolved problems is that common

[surreal sapphire]

this is most common

folklore result that was never published correctly

or what i like: recent result that presents some kind of algorithm that can be implemented

this can lead to original research when you discover that the published algorithm is wrong and nobody noticed bcs it wasnt implemented

[buoyant plaza]

Hey I don’t know if this is the right chat, but I’m in urgent need of private tutoring maybe rover a few days to a week, I can’t explain it all here because I don’t want to interrupt anything, but if your willing to priv tutor me friend me. Thank you.

[bright hill]

@ripe wasp felt like we were going off topic so I'm moving the Convo here

[ripe wasp]

ah ok

wbu, what chapter u on?

[bright hill]

You did do the category theory stuff from chapter 1, right?

Those are quite important

Especially Universal properties

[uneven roost]

Hi, have friended

[ripe wasp]

i did that before, but need to skim over it again

[bright hill]

And canonical decomposition

[ripe wasp]

they don't quite do that rigorously i feel like

it was kinda iffy

something something terminal object

[bright hill]

I was on 5

[ripe wasp]

dang u made a lot of progress

how long did that take?

[bright hill]

I skipped 4 coz it seemed dreadfully boring and wanted to do it with someone else

[bright hill]

Way too long than it should've

Maybe a couple of months? I'm not really sure

[brittle socket]

Universal property of quotient sets

[ripe wasp]

hmm chap 4 doesn't look too boring tbh

i never learnt sylow

but fundamental thm of finitely generated abelian groups is cool

symmetric group stuff is cool too

except for laborious cycle multiplication

[ripe wasp]

ah yeah i just read abt that

[brittle socket]

I learnt that from set theory

[bright hill]

Meh

[brittle socket]

Probably the first commutative diagram I drew, and in latex

[bright hill]

Its very unmotivated imo

I have no idea why I should care

Which bugs me a lot

[ripe wasp]

i mean it's kinda like fundamental thm of algebra prime factorization things for abelian groups right

finite*

[bright hill]

Dunno

Never learnt about it lel

[ripe wasp]

i have a q abt universal properties

is it like something that holds in any category?

so with the quotient set property you just instantly get the first isomorphism thm for groups and rings and whatever by just considering their respective categories

oh wait nvm

it says set

anyway @bright hill how much of aluffi are u planning on doing?

the whole book?

[ripe wasp]

im thinking of up to chapter 7 perhaps skipping some things

[bright hill]

It's something that can happen in multiple categories

[bright hill]

You still need to verify the set function (which the universal property guarantees the existence of) is a morphism in your category

[ripe wasp]

by set function do u mean $\bar{\varphi}$

[fathom swallow]

sean

[bright hill]

Maybe?

There are stuff which i defenitely wanna do

But others I'm not in such a hurry

I can always refer back to the book if i ever need em

My main objective rn is to Speedrun to chapter 7

[flat harbor]

post it in chat again chat
if u havent read thru alg geo by age 12 ure too late

[bright hill]

Then maybe chapter 4 if i find someone to suffer through with

[flat harbor]

ill read things if u tell me to read them

[bright hill]

Or 6 too

I wanna see what that's about

I know it got a lot of modules theory

[ripe wasp]

ill do it with u if u want

i also kinda need to speedrun it

because i have math camps coming up and if i get into one i might get to take an alg top class during the summer

[bright hill]

But I'm not sure why I should care about Modules

So it's not very high priority rn, if you catch my drift

[ripe wasp]

albeit it may be pretty crap bc it's prob gonna be hatcher chapter 1-2 or smth 💀

[ripe wasp]

ah yeah, honestly, me too

i wanna learn the basic groups rings fields galois theory

then move onto smth else

[bright hill]

Sure!

Lemme know when you reach that

But you don't need chapter 4 for AT nor AG

It's finite group stuff

[ripe wasp]

i'm thinking to keep myself motivated i might start a yt channel or smth where i upload like a TIL each day of what i studied and aim for consistent daily uploads

[void tundra]

better yet

stream in the secret vc

well you don't have access yet so time to start posting good content

[ripe wasp]

LMAO

[bright hill]

I feel like by far the biggest disadvantage for us, self learners, is that the learning process is completely unsocial

[zealous garden]

Based

And true

[bright hill]

That's why I try as much as possible to learn stuff with people and make reading groups

And I've been mildly successful with that the last few weeks

Which did wonders for my motivation tbh

[zealous garden]

I wish I had people IRL to talk to about this

[bright hill]

Samee

I hoped I would once i joined uni

[long matrix]

people irl

dont exist

[bright hill]

But i have found none sadly

[zealous garden]

At least you have uni to try

[bright hill]

Which reminds me

[torn willow]

You know we should start a study group

[zealous garden]

Time to start lurking on local college campuses

[bright hill]

@void tundra wanna tackle 3.24 in a bit? :3

[long matrix]

whats 3.24.

[bright hill]

Rudin exercise

[zealous garden]

Unironically, I think some of them have libraries open to the public and that sounds potentially fun

[long matrix]

rudinmentary

[tulip jasper]

how can a public library be fun?

[bright hill]

[timid gale]

[zealous garden]

Aside from the access to books I don't have at home, it's a good way to remove yourself from distractions to get some reading done

[torn willow]

Well I go to class to get reading done

[zealous garden]

I don't have classes

Or I would

[timid gale]

got 5 problems from chapter 4 as homework due tomorrow

[torn willow]

You completed your degree?

[zealous garden]

I wish

I'll be back for my victory

I shan't lose the war

[ripe wasp]

u doing big rudin?

[bright hill]

Wuss dat?

Still baby rudin

[ripe wasp]

oh

isn't that the R as a completion of Q one

[bright hill]

Oh, btw, what anal book are you doing rn

[ripe wasp]

or am i thinking of the wrong one

[bright hill]

Yea

Lol

[ripe wasp]

i'm doing malliavin's "integration and probability"

[bright hill]

Round 2 babyyy

Ah, measure theory

Hmm

[ripe wasp]

ye but it also has probability which i like

also fourier analysis

[bright hill]

Why not folland?

[ripe wasp]

this is the toc

[ripe wasp]

i like the probability based view

i was thinking of folland, but im mainly learning MT for probability so i just said why not just learn from a book that has both

[bright hill]

You seem to have similar interests to mine lel

[bright hill]

So do I

But i also wanna do measure theory appropriately

And folland got functional analysis as well which might be fun

Anyhow

I should be done with rudin in a week or so

2 weeks max

After that I'm starting an analysis reading group around folland if you ever change your mind

How far are you into malliavin?

@ripe wasp

[ripe wasp]

ah i basically started last week

im on section 2.4 on chapter 1

Borel algebras. Measurability and continuity.
Operations on measurable functions

[ripe wasp]

ah yeah, thanks for offering

i might change my mind, but im enjoying malliavin so far

other than the fact that it's kinda old and the notation is a bit annoying

[surreal sapphire]

@woven whale because you might care and its relevant to what we talked about
DFG is known for not telling you why grant proposals are rejected or what they even care about and today we talked about sending them an IFG letter

[woven whale]

what's DFG?

[surreal sapphire]

deutsche forschungsgesellschaft

[woven whale]

ah

did you see my ping in discussy?

[surreal sapphire]

now yes lmao

true germany moment

[woven whale]

took 5 days to tell me that it's not their job

[surreal sapphire]

timely reply

if you message bezirksregierung, they will tell you to message whoever you messaged now :3

[woven whale]

Lol

the theaterstück was total garbage btw

they didn't use any requisites

it was 3 people

I didn't understand what was going

[surreal sapphire]

woyzeck?

[woven whale]

yes

[surreal sapphire]

ye so

the original is incomplete

unsure why its so important

there is an opera thats pretty good

[woven whale]

I noticed

it just suddenly ends

after the guy kills his wife or whatever

[surreal sapphire]

i only remember the barber scene

[woven whale]

what???

almost none of these people appeared

[surreal sapphire]

get scammed

[neat lintel]

why can't i imagine anything like in graph of geometric related chapter

[neat lintel]

@surreal sapphire

Question

Where is your pfp from

It looks so familiar

[neat lintel]

is there any set where a + 0 != a?

idk if wat i said makes sense

like identity

[surreal sapphire]

the album "ziltoid the omniscient"

[void tundra]

not in a group

[neat lintel]

ok

[void tundra]

if 0 is the identity

• is the operation

then a + 0 is certainly a

[neat lintel]

if the + is addition in the usual sense and 0 the neutral element of addition then no, but of course we can define them however we want to. We could define + to concatenate two strings together, which would result in a + 0 = a0

[void tundra]

by definition

[surreal sapphire]

see #❓how-to-get-help

[alpine cargo]

have anyone heard about mirror multiplication and mirror division

[neat lintel]

@fresh cairn

[fresh cairn]

hm?

[neat lintel]

U gave jee??

[fresh cairn]

what

[neat lintel]

Did u give jee mains exam??

Are u Indian?

[fresh cairn]

i am but i haven't taken it

[neat lintel]

Sorry

I might have misunderstood you for someone else

[fresh cairn]

oh it's ok

good luck

[neat lintel]

@arctic grove

Did u give jee mains

[arctic grove]

i did yes

[neat lintel]

Nice

My classmate shockshwat tokd

Told*

There is another shashwat

Preparing for jee

[arctic grove]

i see

[neat lintel]

Ok

[sacred marsh]

what does f(x)/f'(x) give you in the newton raphson formula

[static loom]

the correction to subtract off from x

[woven whale]

@sleek wing

for this

#groups-rings-fields message

can't you also like argue that anything not in [G, G] commutes with everything else

[storm sage]

Lol what why don't you just ask in the channel

[sleek wing]

^

[woven whale]

uhh because like

eh

you're right

[sleek wing]

think this works

but I prefer their solution using third iso

much clearer to m- wait nvm

nvm nvm, I do prefer it

[woven whale]

what's third iso

like

I probably know it

but they're not labeled like that in german

[sleek wing]

lemme get the latex right one sec

[onyx cape]

hi guys

[sleek wing]

$N \trianglelefteq K \trianglelefteq G \Rightarrow (G/N)/(K/N) \cong G/K$

[fathom swallow]

Wew Lads Tbh

[onyx cape]

i know this a maths server but i had a doubt in physics can anyone help?

[gray charm]

please

[storm sage]

why does third isomorphism thm have a name? I've never used it before, what do you use it for?

[sleek wing]

quotienting

[woven whale]

it's used in the fundamental theorem of galois theory

[sleek wing]

https://tenor.com/view/soyjak-spinning-spinning-soyjak-soyjak-jazz-hands-excited-spinning-wojak-gif-25231392

[onyx cape]

Guys do we need electric potential to create potential difference?

[alpine kindle]

#old-network physics server

[onyx cape]

I am so sorry

[open aspen]

!help

[quasi jetty]

Please read #❓how-to-get-help

[neat lintel]

interesting function i was messing with in desmos: q^(1/p)^q^(1/p)^q^(1/p)... where q and p are both real numbers greater than 1

i don't know if it's a thing that exists and has special properties but for all the values i've seen it converges

why did you react with that

i know very little math pls tell me if this is a thing

[long matrix]

iteration of ^(p/q)

[neat lintel]

also yeah i mean doing f(f(f(f(f(p) where f(x)=q^((1/p)^(x)) for like hundreds of f's is not very convenient

ok

[long matrix]

dont think so.

[river moon]

there are dual numbers q, p such that 1/p + 1/q = 1 for p, q >= 1

appears in a ton of places in functional analysis

[quasi jetty]

Please read #❓how-to-get-help

[neat lintel]

Sure

that's 6 to the power of 6/5 to the power of 6/5 to the power of 6/5 to the power of 6/5 which is slightly different

it's 1/p to the power of x, not x/p

[neat lintel]

this nicely converges to a value pretty close to 1 which is very different than ur function

[long matrix]

doubt thats what you wrote.

oh nvm

[neat lintel]

q to the power of (1 over p) to the power of q to the power of 1 over p

[long matrix]

ok

[neat lintel]

yeah if i wanted 1 over p to be times q i would include parentheses

and it'd be a lot easier to add

[deep mango]

You can probably prove that it converges to the solution to the equation x = q^((1/p)^x) if you're careful

Or, one of the solutions. There might be multiple

[neat lintel]

this interestingly becomes greater and then smaller as you move p or q from 1 to 1 hundred

but the greatest or smallest values depend on what p and q are

[deep mango]

That's hard to solve

[long matrix]

,w solve x=q^(p^(-x))

[deep mango]

Lol

[fathom swallow]

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

Requested by Shuri2060#9525

[long matrix]

[deep mango]

It's like

Maybe an iterated lambert W function or something

[neat lintel]

https://www.wolframalpha.com/input?i2d=true&i=solve+for+x\(44)+x+%3D+Power[q%2CPower[Divide[1%2Cp]%2Cx]]

uh

rephrasing it with z and x and y doesn't help

figuring out what this function is and interesting stuff about it could probably be very fun for someone who is much more advanced at math than i am but i guess i'll keep experimenting in desmos

i just think functions that converge when you apply them infinite times are really cool

[river moon]

this is just a contraction mapping and there exists a stationary point

[neat lintel]

ok but that's very different to q^1/p^q^1/p...

[river moon]

so yes no wonder it converges similarly to cos(x) = x or that other formula which is used to iteratively compute a root of any positive number

[neat lintel]

i mean not too different but

[river moon]

this is just investigating a function q^c^x for a stationary point tbh

it does have one for 0 <= c <= 1

[bright hill]

Anyhow, @alpine kindle we should organize an AT reading group

[fresh stone]

[long matrix]

meow

[storm sage]

shuri stop being so negative

:(

[dapper current]

you shouldn't joke about such things

[storm sage]

Please don't :(

[echo relic]

Whatuuup people

[teal lion]

life is valuable, I was in your spot many times

and I’ve grown to be glad I failed those attempts

[wraith geode]

if ur being serious please get help

reach out

i can send u multiple phone numbers

[rich rapids]

reply back dude, im worried

[woven whale]

<@&268886789983436800>

[hollow quest]

Shit went down

[grim patrol]

how does the bot detect if someone is asking help

Help me

hm

can someone help me with my homework

wait it doesnt?

[echo tundra]

There is already one going on by @tight sapphire for brendon if you wanna join

[tight sapphire]

it's not active anymore unfortunately

the group is still there but almost nobody followed

[arctic lagoon]

I can't stop wondering how i should let the free monoid generated by sharp and flat act on the set of all music notes. Surely the two generators don't have to act as inverse to each other, right?

[echo tundra]

Yeah, that's the problem with large study groups. Maybe small scale groups would work better

[tight sapphire]

why wouldn't they

[tight sapphire]

I think it's a problem with not large enough groups personally lol

[arctic lagoon]

I mean they don't a priori have to.

It makes sense to do so if you restrict to an infinite discrete set of frequencies, then one would reasonably make them act as the predecessor and successor maps...

[tight sapphire]

and they are inverses

nothing's preventing you from reinventing the definition of sharp and flat so that they aren't inverses

[bright hill]

I disagree

I think a study group can thrive with just 3 or 4 core members

Others can choose to commit

Or not

But people won't join a study group that's dead

[tight sapphire]

didn't say otherwise

it's just that when you don't know many people that you're sure will be very active, well you don't have a choice but to ask as many people as you can

[bright hill]

Yea, true

I tried that once

It didn't work

[bright hill]

That's why I'm looking for these 3 friends

Speaking of which

[bright hill]

@alpine kindle is ignoring me

[void tundra]

speaking of which

we like missed last sunday

measure theory

or we could switch to topo tbh

[bright hill]

[bright hill]

I pinged you yesterday for a substitute

[void tundra]

oh where

ping me in secret club next tome

time

[bright hill]

Here and in oby

[bright hill]

I did

[void tundra]

hmm

[bright hill]

If we could get the Munkres boys to switch to Lee that'd actually be sweet

[void tundra]

highly doubt it

we can just do our own thing tho

[bright hill]

True

But it'd just be us 2

And i already know most the content in chapter 2 and 3

I would ask ally but she did even more pointset than I did lel

[void tundra]

@brittle socket

[brittle socket]

What?

[void tundra]

topo

book club

[brittle socket]

Don't have the prereqs for Lee

[void tundra]

what prereqs are it

!help

[quasi jetty]

Please read #❓how-to-get-help

[void tundra]

not here

[brittle socket]

!help

[quasi jetty]

Please read #❓how-to-get-help

[brittle socket]

Goddamn you beat me to it

[brittle socket]

Uh lemme see if I can rmb

Nvm lemme pull up my copy

[void tundra]

p sure u dont need THAT much

[brittle socket]

But enough that im pretty sure I don't have the prereqs rn

[bright hill]

Yea

[brittle socket]

The set theory prereq should be fine based on what I saw last time

[bright hill]

You need multivar calc or smth

It's pretty weird

[brittle socket]

I know basically nothing about metric spaces and group theory rn also

[bright hill]

My brother in Christ, you can possibly have no reason to study set theory again in your life

[void tundra]

i doubt you need that much group theory

[brittle socket]

Specs into foundations

jk

[void tundra]

[bright hill]

There are annexes or appendices or w/e they called tho

[brittle socket]

Yeah but I haven't done much AA other than the bit my set theory and lin alg book has touched on so far lmao. Which are like just the definitions of some algebraic structures

[void tundra]

ah whatever

you can learn it as we go along

[brittle socket]

Sounds like a... bad idea

[void tundra]

[bright hill]

[void tundra]

we won't need it that early

[bright hill]

All that talk about "being a man", grass...

[void tundra]

if you need it im sure DarQ can crash course lecture you

[bright hill]

I am disappointed

[bright hill]

Yeah, sure lel

[brittle socket]

Just a joke lmao

[void tundra]

hey we won't need group theory for the first few chapters I bet

so

all good

[brittle socket]

I picked up Schroder instead of Rudin for a reason

[bright hill]

that was a joke too

[brittle socket]

Yes, I know, Dark

[bright hill]

Yea

[brittle socket]

DarQ*

[void tundra]

I picked the most pedagogical book ever

[brittle socket]

Schroder of course

[void tundra]

uh

[dim zodiac]

i am smart cus i joined this group

[void tundra]

!help

[quasi jetty]

Please read #❓how-to-get-help

[void tundra]

darn

I thought it was gonna be a help

[bright hill]

LMFAO

[bright hill]

Y E S

[void tundra]

[neat lintel]

guys is it normal to forget multiplications tables?

lol

[void tundra]

!help

[quasi jetty]

Please read #❓how-to-get-help

[void tundra]

aH? did you mean Ha

[brittle socket]

What's that really curly math font called again

[void tundra]

ok pretty sure we wont need much analysis to begin with anw

uhh

mathcal?

or mathfrak

[brittle socket]

[\mathscr{AH} \qquad \mathscr{YES}]

[fathom swallow]

grass

[brittle socket]

Hmm mathscr is not working

[hollow quest]

$\mathcal{AH}$

[tall badge]

theyre equal if a in G, H subset G, with G abelian c:

[fathom swallow]

NEONPerseus

[void tundra]

we could also just have H be normal in G

[tall badge]

we dont talk about that

[void tundra]

[brittle socket]

Hm

I think I want to complete some books before I start on Lee

[void tundra]

[brittle socket]

Namely, Enderton, Schroder, FIS, first couple chapters of Jacobson's Basic Algebra I

[brittle socket]

what

[void tundra]

just do it!

[brittle socket]

Sounds like a bad idea

I feel that getting my foundations (e.g. intro anal) down first would be better

[void tundra]

@bright hill convince this person

[tight comet]

we all support bad ideas

[brittle socket]

[tight comet]

also now I'm very active you can believe me

I lost my 'active' elite status

[brittle socket]

Real men get not very ppl

[bright hill]

point set IS foundational lmfao

[brittle socket]

Well, yes

[bright hill]

I personally did hatcher's notes instead of chapter 2 of rudin

I admittedly did a tiny bit of analysis beforehand

[brittle socket]

I literally haven't even completed one chapter of anal

[bright hill]

But still

Well

Chapter 1 of rudin barely even counts as analysis

Besides

[devout nacelle]

People who spent 10 days on proving n-th roots exist in R:

[bright hill]

You have us to help you

And you can always drop out

[brittle socket]

[bright hill]

You can just join and see how it goes :)

[void tundra]

yeah its not rly a competition lmao

[brittle socket]

Hmm I would be slightly irked to start another book when I haven't even completed one.. but hmm.

[brittle socket]

Yeah why would this be a competition lol

[bright hill]

Mfw i literally haven't finished a single math book

[brittle socket]

(I don't plan to read my math books end to end of course)

[void tundra]

ah now we know why

start 20 books and never finish it

[devout nacelle]

This should almost never be a goal in itself

[torn willow]

I have finished one

[devout nacelle]

Learning enough of the material that you need/care about should suffice

[torn willow]

It was not worth it

[bright hill]

I'm going to Finish rudin, ok?

[devout nacelle]

You're at chapter 7, right?

[void tundra]

dont people recommend you stop at chapter 7 or 8

for rudin

idk

[bright hill]

Yea

[devout nacelle]

It might be a good time to stop after the exercises here, and move on to more interesting things

[torn willow]

yea do spivak

[bright hill]

Oh, ofc

I don't actually want to finish rudin

Just maybe till chapter 8

Max

[brittle socket]

Im doing Schroder rn

Manan is typing

[devout nacelle]

I was about to say I try to find more concise sources now

[brittle socket]

[devout nacelle]

Lecture notes>>>textbooks most of the times

Textbooks are generally packed with too much information, more than what one needs to care about when learning the subject for the first time

[brittle socket]

I see

How do you find good quality lecture notes / materials to learn from? I guess as in, how do you assess if a random piece you found online, for instance, would be a good read?

[devout nacelle]

Hmm, this is difficult to tell beforehand but you can look at how polished they are for instance

The content organisation/has exercises or not/even formatting

And of course

The author and the source from which you obtained it

Course notes from an instructor would generally be more credible than notes on someone's personal webpage

[brittle socket]

Ah I see, that makes sense

[devout nacelle]

One of my active tabs rn: https://personalpages.manchester.ac.uk/staff/Charles.Walkden/hyperbolic-geometry/hyperbolic_geometry.pdf

[brittle socket]

[devout nacelle]

filetype:pdf (topic name) lecture notes can often reveal goldmines

Sometimes even dropping the "lecture notes" helps, not always standard to include it in file titles or similar

[brittle socket]

I see, thanks for the advice Manan

[devout nacelle]

All that said, the standard thing about being disciplined and focused still holds

Diffusing attention across multiple sources all the time will generally make progress cumbersome

Sometimes you just need to sit down and work through something

I say this with 6 browser tabs open So there's that

[brittle socket]

[brittle socket]

I see

[torn willow]

Why does 6 feel like the perfect number of tabs

[devout nacelle]

Seemingly 6 is the maximum number of tabs I can have without the title bars shrinking to accomodate others

[alpine kindle]

I don't want the pressure of having to keep up

sorry

[long matrix]

meowsies

[storm sage]

Understandable

[cinder zephyr]

Ask in this discord lol

That's what I've done

[outer glacier]

does anyone have good quality notes for calculus 1

[smoky lodge]

I am trying to open a server like this one but in a different language

I want to replicate the help rooms (how they are available until someone sends a msg and some other things)

is there a bot that does that that I could use in my server? or is it more complicated than that?

[void tundra]

bot is open sogrce

source

go to github and search for discord-math

[surreal sapphire]

https://github.com/discord-math/bot

[smoky lodge]

so I will have to run it on my pc or a server right?

sorry Im really bad at these things

[surreal sapphire]

yes

the process is a bit complicated then maybe and sadly we cant provide support

[smoky lodge]

oh its fine

thanks for the help 🙂

do you have any tips for running a maths server? something I should do or avoid doing?

[surreal sapphire]

we are struggling ourselves

[void tundra]

ban mathasking

[surreal sapphire]

a lot of what we do is copied from the libera community: https://libera.chat/guidelines/

this is more general and not specific to mathematics

but general knowledge about community management applies

seems to be an unsolved problem though overall

[waxen python]

hi

[bold ingot]

if you guys are working on a problem that you somewhat understand, like you know what your goal is, but you haven't done it before so you don't know exactly how to

how long do you keep trying before you just look up how to do it?

for example I have a rational expression in terms of x and the problem says to write it as a sum of an even and odd function

the expression itself isn't complicated, I know what even / odd functions are, I know how to add functions

but I still can't actually solve the damn thing

[severe swallow]

That heavily depends on the problem and how much I rely on knowing the solution in time to be honest

[bold ingot]

well I'm learning for the sake of learning, so I'm not on a time crunch

I'm on a time crunch in the sense of I want to gain understanding / mathematical maturity as efficiently as possible for the amount of time I invest

I feel like once I see a problem solved a few times, I can get a handle on it and do it

[severe swallow]

Not an actual hint but sort of a comment on the style of the solution: || whether you will figure it out or not, i can assure you you will be mad once you see the solution||

[bold ingot]

but this seems like the type of thing that I shouldn't need to see examples of before I can solve it, and I'm worried about my lack of problem solving skills

[bold ingot]

lmao

[torn willow]

That's a mad one,yes

[severe swallow]

This feels like the type of discussion I dont feel qualified enough to talk about. Its sort of how much is it pattern recognition vs actually you coming up yourself with something original. Honestly I have no idea. Some problem seem so trivial after seeing how they work. But sometimes you just simply dont spot that one trick that solves the entire thing super easily

[torn willow]

Do a bunch of similar problems

And you will get it

[bold ingot]

Right, that's basically my dilemma.

[torn willow]

Well I think at this point it's better to just give away the answer

[bold ingot]

jaijainaaojnaonao

nooo

stop typing right now 😭

[torn willow]

So ||a= (a+b)/2 + (a-b)/2||

[bold ingot]

nope, you guys telling me how mad I'm gonna be is kind of a hint

[severe swallow]

I mean eventually yes. But I feel like the discussion is more about. Once you run out of problems with solutions you should be able to somehow stand on your own feet and come up with approaches yourself. And how you encourage that effectively. I honestly dont know

[bold ingot]

I'm gonna try to come up with some funny ways to solve it

[torn willow]

Well what have you tried so far

[bold ingot]

staring at the paper real hard

[severe swallow]

That one sometimes works

[torn willow]

Well this is an even odd problem on generic functions

So you kinda should think about f(-x)

[bold ingot]

idk I've been considering different combinations of squaring and square rooting things

lol

[torn willow]

Because otherwise There's no way to incorporate the f(-x) anywhere

And hence use odd/evenness

[bold ingot]

ok one hint I will take is

does this involve squaring / square rooting stuff?

[torn willow]

No

[severe swallow]

No

[bold ingot]

ok, wrong track completely then

[torn willow]

Your domain may not allow square rooting

[bold ingot]

hmm let me take another run at it

[torn willow]

It's always addition that works

[bright hill]

I mean

We will be running the study group lel

We can go at whichever pace we choose

But sure ig

[long matrix]

We?

[alpine kindle]

i don't want to have to keep up with anyone including you

[long matrix]

It will be I who chooses when we start and stop

and I declare we never start

[alpine kindle]

i am already stressed enough

[alpine kindle]

to @bright hill

[alpine kindle]

sorry

[pseudo sleet]

aw i hope you'll get better :c

[bold ingot]

I'm dtf (down to form a calc/analysis study group)

[bright hill]

no comment lmfaooo

[alpine kindle]

thank you

[bright hill]

🫂

[alpine kindle]

this wasn't meant negatively towards you I'm sorry

[long matrix]

its ok, i wouldnt wanna keep up with darq either

[alpine kindle]

i can't phrase stuff properly

[bright hill]

No, i didn't take it negatively lel

It's just that

[alpine kindle]

that's not what i mean

[bright hill]

I wouldn't worry about my pace lmfao

[long matrix]

i joke

[bright hill]

Skill issue

[alpine kindle]

i do not want deadlines of any sort

[long matrix]

keeping up with u is like following the stock market i bet

zigzagzog

[bright hill]

True lmfao

[alpine kindle]

even if you're slow it's still a deadline

[long matrix]

AT right

[alpine kindle]

yes

[long matrix]

@bright hill is it possible to do reading groups without reading

thank you

i think the reading part is fairly problematic

[bright hill]

Yes

[alpine kindle]

i am going to read it but i might like

stop halfway for sth else

or take a break for other stuff

[long matrix]

darq is going to read me hatcher like a bedtime story

[bright hill]

We can just agree to do specific buts together

An exercise or a section

[long matrix]

i refuse to do anything of my own volition

[bright hill]

I am doing this rn with derpz

[bright hill]

Hmm

Why is it so hard to do math with people?

[long matrix]

wym

everyone thinks at their own pace

its hard to coordinate

[bright hill]

No like

[long matrix]

im very unlikely to understand something unless i go away, have a think about it for myself and come back

[bright hill]

Like doing a course together or smth

[long matrix]

[bright hill]

That's what I'm looking for

[long matrix]

i dont get what u mean

[bright hill]

Like working through stuff in tendem

Like how people take courses together

[long matrix]

idk what u mean but im really down to brush up on or learn math

i feel i want and need to

for a few things

AT was one of them

[bright hill]

[woven whale]

you can join our reading group

[long matrix]

ill join darq but not u

[bright hill]

Don't join lumin's reading group...

[bright hill]

THANK YOU

[long matrix]

I find it hard to do things of my own volition so lets see if this helps me learn

[woven whale]

we got cat bread ren and rakki

[bright hill]

Me and derpz already do stuff in oby semi regularly

[long matrix]

well ping me whenever u do AT and ill join

[bright hill]

We currently aren't doing anything very organized

[long matrix]

what helps me is talking about stuff

going thru examples

dont really get a chance to talk math

[bright hill]

Sure, but we prolly won't be doing any topology for a while

[long matrix]

thats ok

[bright hill]

Would you be interested in pointset stuff?

[long matrix]

sure

i never learnt it properly

i did AT in my final year, all they covered was chapter 1 of hatcher

[woven whale]

chapter 1 of chapter

[long matrix]

disappoint ngl

[bright hill]

Ok sweet

[long matrix]

the exam was silly easy

[bright hill]

I wished we could do a full blown study group around lee's Introduction on manifolds

(which actually does homology and AT stuff)

But the Munkres fan bois wouldn't agree to it

So ig I can just convince DerpZ to read through it together

I already know most the stuff from chapter 2 and 3

And a bit of 4

But the other chapters look dope af

Also, I'm doing folland very soon

Like

In 4-5 days I'll be done with rudin prolly

You might be more interested in measure theory

[long matrix]

i need to do both

[bright hill]

Sweet

I think i wanna commit to measure theory for a bit

[long matrix]

i know much less measure theory

[bright hill]

At least till folland chapter 3

Folland 4 is pointset so by the time I'd be done with chapter 3 i should've covered the pointset i needed with DerpZ

Then I'll see if I wanna commit to functional analysis, algebra or probability or multivar anal

That's my plan for the near future, anyhow

[bright hill]

Topology reading group confirmed? @void tundra

[woven whale]

darq you can join us

[bright hill]

Lumin, i already talked about this

Munkres sounds hellishly boring

[woven whale]

it's not

[bright hill]

Well, you love algebra

So I don't trust your word for it

[woven whale]

stupid analyst

[bright hill]

You still haven't answered why not Lee

[bright hill]

500 pages of pointset
It's perfectly reasonable bro, it's not boring at all bro

[woven whale]

it's 200 pages

the rest is algebraic topology

& we're using hatcher for at

[bright hill]

You think 200 isn't a lot?

Hatcher's notes are like 40

And he specifically made them for his book

[woven whale]

ok? you don't have to join

idk why you're hating on munkres

[bright hill]

:/

[alpine kindle]

oh i was using rotman anyway

so we wouldn't have been able to do the reading group

even if i could

[bright hill]

I wasn't settled on any book for the record

It's lumin that wants to do hatcher for AT

[long matrix]

what is this witchcraft

constructing Z+ from R???

[alpine kindle]

ig if you say R is dedekind cuts of the initial in Field

then you haven't defined what integers are yet

[long matrix]

idk what dedekind cuts are. witchcraft

wikipedia tells me its constructed from rationals

[bright hill]

Bruh

How did you guys construct R?

[long matrix]

Well I didn't

I just assumed it exists

[arctic lagoon]

iirc there are indeed axioms characterizing the reals that don't refer to the integers

[long matrix]

thats something we leave to the analysts

ok ok, my defn of R is just the completion of Q

thats the only one i had to care about

[bright hill]

Well

[deep mango]

surely dedekind cuts require you to construct the integers

[bright hill]

I suppose i can't judge

[deep mango]

then you have to be careful about how you define "cauchy sequence" because metrics are supposed to be R-valued, but sure

it works if you're careful

[bright hill]

Since i haven't seen a contruction of the reals yet

[long matrix]

meow meow ryc

[analog flame]

Guys hey

[long matrix]

Ive seen a construction of the reals from integer functions

fairly cool

[analog flame]

I wanna study math becaues I think I love it

[deep mango]

in particular, both the cauchy completion and the dedekind cut construction are important and generalizable

[analog flame]

But I don't know yet

Guys

I wanna study math major's classes

[long matrix]

so where should i have learnt about these dedekind cuts

[alpine kindle]

you need Q

not necessarily Z

[analog flame]

Guys

[deep mango]

nowhere in particular, they're in chapter 1 of rudin somewhere

[long matrix]

well i never really read books

so thats that.

[deep mango]

but they're not like

relevant to learn

[deep mango]

well, where are you starting from?

[analog flame]

I finished high school

I wanna knwo something

[teal lion]

euclid has an interesting dedekind-cut style argument

[analog flame]

I have a question

[deep mango]

if you want to go through calculus stuff, you could try Khan Academy or MIT OpenCourseWare. those are both free

[analog flame]

What am I gonna use universitie's math for?

Am I gonna use it for programming

Or Ai and mL

[long matrix]

wheres the best place for me to quickly learn dedekind cut? wikipedia verbose

[deep mango]

it depends, most STEM fields use a certain amount of university math (calculus and linear algebra)

[analog flame]

Because I want it to be purpsoful and useful in order for me to find it motivated

[deep mango]

in AI and ML they use a lot of multivariable calculus, linear algebra, probability, and statistics

[dapper current]

that's for you to do decide

also programming is AI and ML?

[long matrix]

hmm hmm, so tldr

we partition Q into an open interval (-infty, a) and [a, infty) <-- these being intervals in Q

this is a cut?

[deep mango]

why don't i just tell you. a dedekind cut is a pair of subsets of Q, (A, B). they partition Q, so that A cap B = 0 and A cup B = Q

and A has the property that if x in A, then y in A for all y < x in Q

[analog flame]

Are you saying ai and ml are not programming?

[deep mango]

that's not a good definition because not every cut is defined by such an a in Q

[dapper current]

im saying the opposite. I think i misunderstood the grammar of the sentence

[deep mango]

some of them are defined by such a's in R

[long matrix]

oh.

[deep mango]

which is what we're trying to define

[long matrix]

ill have a think

i have the defn in front of me yh

[deep mango]

for example, the dedekind cut that represents pi is given by ({x in Q : x < pi}, {x in Q : x > pi})

[deep mango]

but of course in order to define pi you need to know this

so

this is circular

[long matrix]

ok so this is very similar to completion idea

[deep mango]

it's completions for ordered sets

[long matrix]

and R is then the set of all these cuts, I take it

[deep mango]

yes

and you can define addition and multiplication and such on them

[dapper current]

seems like most things past high school could be used for AI in some roundabout way

[deep mango]

and an order, and then use the order topology

and so on

[long matrix]

Is choice involved here or not at all

[deep mango]

to get R as a complete metric ordered field

[deep mango]

not really, all of the objects are totally described

[long matrix]

I get this non-constructive feeling

idk.

[deep mango]

what's nonconstructive about it

well

[long matrix]

hmm

[deep mango]

if you give me a sequence of digits

i can define a dedekind cut from it

[long matrix]

well in the end u have to kindof manually come up with the subset for pi say

[deep mango]

by {x in Q : x < a1 or x < a1.a2 or x < a1.a2a3 or...}

which is how you show that this is the same as decimal expansions

[long matrix]

yeah thats kindof what i mean

[deep mango]

im not sure where choice is used

in just defining it

[long matrix]

no not choice

[dapper current]

but constructivists can still use infinite sets right?

[long matrix]

i just thought of it

because it has non-constructive vibes to me

[deep mango]

it's a weird definition

but to be fair the cauchy completion definition is weird too

[long matrix]

idk why that has a different vibe to me

[deep mango]

since the set of cauchy sequences in Q is way bigger than R (well, the cardinality is the same but tons of them converge to the same element of R)

[dapper current]

computers just use arbitrary precision or something

[deep mango]

and we just kind of like

squish it all together

and then what's the right cauchy sequence to think of when you think of an element of R?

[long matrix]

Ok ok

So for sequences

This is f : N -> Q

[deep mango]

in reality the best definition was always just decimal expansions and the others are just to make us feel better

[long matrix]

im fairly happy with this map

Whereas with these cuts... it feels 'more'?

[long matrix]

.

hm or maybe not

[deep mango]

im just doing a countable union of intervals instead of a countable sequence converging

in some sense a countable sequence converging is a countable intersection of intervals

[long matrix]

I see, countable union, thats fine then

very nice this easily defines extended reals

[deep mango]

this actually makes me think of another way to define R

which is like completions

it's sort of a compactification of Q, locally

[dapper current]

isnt there weird versions in synthetic differential geometry also? where its sometimes like heres a space its smooth now we make sheaves of it

[deep mango]

you could look at elements of R as being nested sequences of closed intervals in Q whose diameters go to 0

that's the same as the cauchy sequence definition but somehow it can be made more topological i think

anyway

sheaves :wg:

[long matrix]

add

[dapper current]

in this case they'd basically just be open sets, i think

[dapper current]

how do the diameters go to 0? like as a limit?

if so you could probably use nets to make it more topological?

[deep mango]

Yeah

i dont know

there's some problem here cause like

idk

i want to look at nested sets of neighborhoods

Oh this is just what i was looking for

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

[dapper current]

goes down an interesting rabbit hole

[hidden cipher]

Anyone DM me if you want to help me improve with Maths everyday, it would mean a lots to me as I'm failing it.

[woven whale]

I can assure you that no one will be dming you

[neat lintel]

https://tenor.com/view/cat-broken-cat-cat-drinking-cat-licking-cat-air-gif-20661740

what's wrong with just asking questions in the server

[analog flame]

It's hard bro, for many reasons.

That's why it's wrong or let's say hard

[bright hill]

I'm not sure where to post this

But I'm trying to graph the polynomials in the proof for the stone weierstrass theorem (rudin 7.26)

https://www.desmos.com/calculator/m3ufmbrep4

But i can't get it to work

It says "you can't use x as an integration parameter coz x is already defined"

Can someone knowledgeable with desmos (or any other graphing alternative) help me out?

[storm sage]

have you tried just using a different letter

x is probably reserved

[bright hill]

Yea

[tall minnow]

doesn't work

desmos can't deal with these things

[tall minnow]

this proof is another one of Rudin's crimes

like his construction of lebesgue measure

it relies on ideas students have not encountered

[bright hill]

Lol, yea

It makes no sense to me

[tall minnow]

don't bother. prove it yourself

[bright hill]

Like i can follow the argument

[tall minnow]

find a better proof to follow / prove yourself

[velvet dagger]

Hot take do measure theory starting from single variable calculus

[bright hill]

I would rather just accept it and move to smth else to be honest haha

[velvet dagger]

Half of the mess in analysis feels like "Oh we don't have measure theory yet :("

[tall minnow]

basically just the dominated convergence theorem

analysis makes no sense without it

[bright hill]

I might do that hmmm

[bright hill]

What's that?

[tall minnow]

the convergence to end all convergence

[brittle socket]

Enderton

[bright hill]

You and Wikipedia make it sound grand

But i still haven't done measure theory

Soon doe!

[storm sage]

fr? that sucks 😭

[bright hill]

Useless.

[tall minnow]

anyway the main idea of Rudin's proof is just convolution / mollification

an idea you will learn when you get to Fourier analysis

or any kind of real analysis really, because mollification lets you approximate any rough function with smooth functions. which is very neat. smooth functions are nice. That's how a lot of PDEs are solved

just that without knowing about mollification, the proof just seems like magic

[bright hill]

It does hahaha

[tall minnow]

I remember there was a cute proof from probability theory for weierstrass

law of large numbers I think

[static loom]

I think I fixed it by just replacing all your integration variables

in just f(n) changed x to v

pretty sure desmos can do nearly anything, although some things are pretty hacky or will lag it out

there are extra features you can enable as well called actions: https://help.desmos.com/hc/en-us/articles/4407725009165

[storm sage]

btw there are a ton of proofs of weierstrass's thm

one way our class did it was by approximating |x| with polynomials and then using that to build piecewise linear functions and then using that to approximate uniformly continuous functions

the reasoning was pretty simple

[tall minnow]

the real point is approximating |x|, which both Rudin and Folland noted

[storm sage]

there's also one involving binomial polynomials

[tall minnow]

that's the law of large numbers

[storm sage]

ah

it was this one I think https://en.wikipedia.org/wiki/Bernstein_polynomial

[static loom]

bernstein polynomial one is probably not too bad to make some kind of demonstration of in desmos I'd imagine

[storm sage]

yeah prob not

[tall minnow]

how engelking proves weierstrass

dini

[storm sage]

👀

[neat lintel]

Today I watched grand budapest hotel, brokeback mountain, and coraline. What movies should I watch next?

[tall badge]

if you enjoyed grand budapest hotel then i recommend other movies by the same director, eg fantastic mr fox and isle of dogs

[neat lintel]

I’ve seen them both and I enjoyed them a lot

I need to rewatch isle of dogs though it’s on my list

[tall badge]

yeah i only saw it once, back when it was released in theaters

knowing the director theres bounds to be bits of detail to pick up on a rewatch

coraline is great, ever seen nightmare before christmas?

[neat lintel]

I have but it’s been a while

Same thing with corpse bride. I liked them both but I would have to rewatch them to tell you what they were about

[tall badge]

hmm the director also made frankenweenie

i havent seen it myself but it seems to have a good dose of macabre humor like corpse bride and nightmare before christmas

ever seen any studio ghibli movies?

[neat lintel]

I actually have not but I definitely need to get on that

[tall badge]

awesome, yeah almost all of their movies are worth a watch

my favorites are spirited away, my neighbor totoro, how's moving castle, and grave of the fireflies (this one definitely isnt meant as light entertainment)

[neat lintel]

I am up to watching nearly anything

[tall badge]

and while we're in anime... hmm

[neat lintel]

I think all of those are on my list to watch

[tall badge]

ghost in the shell

ohhh lol

steins;gate (series adapted from a visual novel)

[neat lintel]

I’ve heard that it’s good

[tall badge]

its so good that i have one of its characters in my profile banner

ok change of pace, this isnt based on anything you mentioned

oldboy (original from 2003, not the remake)

the handmaiden

these are south korean movies if youre interested in that

[neat lintel]

Sorry I did not mean to leave you unanswered I just got sidetracked

I have heard of the handmaiden but not oldboy

[tall badge]

nw lol

yes finally a movie rec youve not heard of before