serious-discussion

[hollow ginkgo]

indepth [sic]

[cold needle]

Hurb can we not have this sort of discussion on this server its just immature

[proud hill]

Hey guys, would I be able to show off a program I wrote to generate consecutive integer sums? I'm really happy with how it's turned out, but I don't really have anyone to show it to.

That's alright, it's not really about the attention. I've just been obsessing over it recently and wanted to show someone it.

It's just a thingo where if you give it a number, it finds all the consecutive integer sums which add to it.

So the number 100 for example, could be written as 18 + 19 + 20 + 21 + 22 or 9 + 10 + 11 + 12 + 13 + 14 + 15 + 16.

Thank you :)

That sounds interesting. Could you give an example?

That's cool. I imagine it's one of those things where once you write it in its general form it becomes obvious why it works.

Yep, it is.

[covert portal]

did you come up with it yourself?

neat man. i always have trouble being creative like that when learning to program

with exercises

[proud hill]

I first read about it in Things To Make And Do In The Fourth Dimension by Matt Parker.

There's a puzzle in the book about finding the numbers which cannot be made by consecutive integer sums.

And I just got really interested in why certain numbers have the amount of unique sums that they do and I started looking into how you could generate them.

Turns out that highly composite odd numbers are what have the most amount of unique sums.

[digital mortar]

hey guys

im new

needed help

anyone free?

[neat lintel]

#❓how-to-get-help

[hidden pecan]

does anyone know how to use java? I have an urgent problem

[grave leaf]

Yeah tell me mate

[hidden pecan]

how to make "return true" in bool not actually write "true" when executing the program?

[grave leaf]

sorry mate i am also a beginner in java

[woven whale]

you're printing the return value of isAvailable somewhere

also don't return Boolean

use the primitive type boolean instead

[hidden pecan]

ok

But I still don't get how to make the word "false" or "true" not appear in the window below

[woven whale]

did you read what I said

[hidden pecan]

yes

[cinder zephyr]

your issue isn't the function itself

it's wherever you're using it

somewhere you're printing the result

[neat lintel]

is computer science worth it

[cinder zephyr]

depends on what you want to do

[neat lintel]

maths or maybe data science

i don't liek amking websites
i am more into making kernels , programming languages and stuff

[cinder zephyr]

then sounds like CS is for you

kernel engineering and compiler engineering is a thing and ofc there's always ongoing research in those areas

if you want to go the academia route

[neat lintel]

is kernel making still relevant though?

like obbiously, you need a job, too

[cinder zephyr]

I know someone who does kernel work at Google

and then also maybe not specifically kernel but low level systems work is everywhere

[rustic wyvern]

what's the "not very ppl" role?

[storm sage]

for people who don't like their role colour

they can switch to a slightly off-white colour

[neat lintel]

lebesgue

[storm sage]

lebesgueric

[neat lintel]

oh btw congrats on being an honorable

[storm sage]

thank you!!

[neat lintel]

it's an honor

[neat frost]

You're welcome!

[azure nymph]

My friend is a kernel engineer at Apple so yes

[neat lintel]

wow that's cool
I still have a looong way to go.

[zinc shoal]

Rust is good lang

for systems programming

[neat lintel]

i am learning C and Rust rn

[onyx pagoda]

if I hadn't read this I wouldn't have known it looked any different

[odd brook]

kernel engineers when image and cokernel engineers walk in

[bronze wedge]

kernel when integral kernel walks in

[cold needle]

cofe when fe walks in

[torn willow]

I guess it's more computer engineering?

[frigid matrix]

are you grad student and what are you researching?

[torn willow]

Ok, apparently that is uni dependent

[turbid night]

how do i do

[frigid matrix]

A quarter is 25 cents. US have 1,5,10 valued coons less than 25.

x+5y+10z=25

Count the number of solutions

a way to make this more systematic is to sum coefficients degree 25 terms of (1+x+x^2+…)(1+y^5+y^10+…)(1+z^10+z^20+…)

[torn willow]

That's much better than the dynamic programming solution I had in mind

[static loom]

idk actually getting an answer out of the generating function is not really that easy

[frigid matrix]

there are easier ways to think about the counting though

just start big

[static loom]

although I wouldn't write the generating function that way either

just do all x, it's really the exponents that are making the equation

[turbid night]

thank

u open my eyes

[frigid matrix]

Yeah counting big is the easiest

usually the problem becomes unruly when the sum of the components is less than half the goal

[static loom]

like this $$f(w)=\sum_{x=0}^{25}\sum_{y=0}^5\sum_{z=0}^2 w^{x+5y+10z}$$

[fathom swallow]

Merosity

[frigid matrix]

oh thats cool way to write it

using all x makes more sense too

i dont know when using distinct variables makes more sense

also going by big cases seems to be the easiest way

[slim path]

not really a math hw question but

me and my friends trying to figure out how much we can fail our midterm by

and

I came up with this

it makes sense right

[small dust]

yea i think so

the grade after the midterm will be 0.9C + 0.1N?

so yes algebra checks out

[slim path]

oh nice

tysm

[small dust]

yep ^^

[slim path]

i feel so smart after writing that im like woah

taking 3 years of calc paying off so i can fail chem 😭

[small dust]

loll 😭

[slim path]

worst science frfr

like

IK ITS LOGICAL BUT ALSO NOT.

[small dust]

[bronze wedge]

Probability, functional analysis, applications to finance

[zealous garden]

have I already asked you if you'd encountered multifractals VMM

[bronze wedge]

I believe so

[zealous garden]

I can't remember

ty

[torn willow]

You can apply functional analysis to finance?

[zealous garden]

I don't know much about functional analysis OR finance, but that sounds right

[vast surge]

As far as I'm aware half of finance is throwing buzzwords at people until they buy your stocks or whatever

So if you know enough big functional analysis words you can probably use them in finance

[zealous garden]

excellent

[bronze wedge]

That's not what finance academics do

[bronze wedge]

Eg. Delbaen and Schahermayer

[torn willow]

There is finance academia?

[bronze wedge]

Yes lol

[zealous garden]

why are you surprised that money has nerds

[torn willow]

Wait then why does economics exist

[zealous garden]

because of nerds

[torn willow]

Finance academia sounds like it would be superior in every way

[zealous garden]

some people aren't real nerds

every subculture has its posers

[vast surge]

I am the posers in math

I hope I am good enough at pretending to get into a PhD

[torn willow]

So can I think of economics vs finance as pure math vs applied math?

[bronze wedge]

Not really lol

[violet wraith]

probably like topology vs geometry

ish

[zealous garden]

At risk of offending VMM, I'll compare it to Physics and Engineering without specifying which is which

[frigid matrix]

cool

im currently sending in my grad apps

i am decided. if feb 1st hits and im rejected from more than 4 out of 6 schools then I will spend the rest of my time preparing to be a quant trader or analyst

im not really sure how to prep properly for this though

[rustic wyvern]

how can I get access to the math help (hidden) section? what's the point of it?

[rustic wyvern]

thanks

[inland raft]

Im in phisics class rn

[mint canopy]

My commiserations

[bright hill]

Wtf

Why can't I react to boytjie's message?

[mint canopy]

Wym?

[bright hill]

Uh

[mint canopy]

I don't understand the reactions

[bright hill]

Nvm

[mint canopy]

Wth does

mean

I will never understand them 😔

[tight comet]

[bright hill]

I was mainly just testing

Lel

[mint canopy]

Wth does mean

[bright hill]

To me, it's like a softer

[bright hill]

That one is the satirical version of 😔

[mint canopy]

I kinda see that

[small dust]

[bright hill]

Sup layla

[small dust]

haiii

just debating with myself on sleeping or not haha

[bright hill]

Sleep!

Sleep is very important.

[small dust]

but

i could sleep later instead 🙂

[bright hill]

You could technically do a lot of things

Doesn't mean you'd wanna do them

[small dust]

yea like sleep

i'd have to get up in like 3 hrs

[bright hill]

Omg

[small dust]

so i wanna just not sleep

[bright hill]

Layla, what the...

We've all been there tbh

[small dust]

i think i'm there way too often

[livid spoke]

Guys got a math exam tomorrow (linear algebra) I am wondering if you guys got any tips on not making stupid mistakes.

[small dust]

gets lots of sleep

[livid spoke]

Lol except that

[turbid spruce]

wassup

[neat frost]

Good morning DarQ!

[neat frost]

Sleep or else I'll bully DarQ

[turbid spruce]

wassup

[small dust]

ohhh 😭

i'm asleep i promise

[umbral zodiac]

​

[long matrix]

in who's sleep is slurp bullying ppl

[bright hill]

Good morning slurp!

I just took a nap for the first time ever

[deep mango]

[bright hill]

Why ?

[neat lintel]

@deep mango sorry for the ping, but what are your thoughts on Evan's text for PDEs (I'm guessing you've definitely heard of it)? It's something my tutor and I are going through but I wanted to know if there's anything less dense available... should probably ask in #book-recommendations but I thought you might know about it

[deep mango]

Umm, it's definitely the standard resource for advanced undergrad / early grad level PDEs. I don't know about less dense, there's not a lot out there that covers PDEs at the same level of rigor while being more readable.

It's a good book

There's a tone shift from ch 1-4 to ch 5-end

[neat lintel]

what would the prerequisites be to have a relatively okay time going through the book? I've only skimmed through it so far

[deep mango]

ch 1-4 is more classical PDEs, focused on the important kinds of equations and classical techniques for understanding them. this section is dense but more understandable for an undergrad with real analysis and linear algebra done

and multivariable calculus

[neat lintel]

so real analysis, multivariable calc, linear algebra are realistically the prerequisites?

[deep mango]

ch 5-end are when it introduces more modern methods (ch 5 is all about sobolev spaces, ch 8 talks about calculus of variations, etc). here it's more important to have basic functional analysis + measure theory

[neat lintel]

ah

i've done some measure theory but no func analysis

[deep mango]

you can kind of learn it as you go

it's not super advanced stuff. just here and there things you need

L^p spaces are the important thing

[neat lintel]

gotcha thanks ryc

oh btw

what's your opinion of international students applying for less competitive programs to top universities and then switching after they get in

[deep mango]

Taking your time with ch 2-4 is totally fine. that's really important material and he definitely moves through it swiftly.

[deep mango]

for graduate school?

[neat lintel]

even undergrad tbh

[deep mango]

Well, for graduate school switching programs is pretty rare. For undergrads, it's more common

[neat lintel]

I've heard people apply to shit like Art and then swapping to CS

pretty despicable

[deep mango]

But I definitely am not the person to give any advice about how that looks for international students

[neat lintel]

oh are you a home student?

well, were you

[deep mango]

Yes

[neat lintel]

when you applied for undergrad

I'm international which makes applying to berkeley 2 times harder

[void tundra]

a ton of places are actually putting in measures against that rn tho

[deep mango]

And I went to berkeley, where everyone is admitted without a major. there was no benefit to saying one thing or the other

(except for with engineering I guess)

[neat lintel]

the acceptance rate is like 8 percent

vs 16% for cali students

[void tundra]

probably lower for international

[deep mango]

I was out of state to berkeley, so I also had a pretty low admissions rate. But higher than international I assume

I don't know

[neat lintel]

ah

yeah I just checked it's 10 percent

for international

its my dream school

[void tundra]

cost to attend university of california is expensive as hell if ur international tho

[neat lintel]

their math program is so fucking cool

[void tundra]

discussion-2 > discussion

[neat lintel]

fr

idk what they doing in #discussion rn

[cinder zephyr]

If discussion 2 is so good why don't they rename discussion to discussion 2

[void tundra]

seems cranky af

something about time and blackholes

yeah that will end well

[neat lintel]

sorry can i know what language your friend uses?

[void tundra]

C probably

[azure nymph]

Ruby was always their preferred language iirc but they're proficient in several languages including c, basic, and java @neat lintel

[fringe needle]

Im only now properly appreciating the content of one of my courses but it’s so satisfying

I love when it all just comes together 😌

[neat lintel]

what course?

[bright hill]

Which course? And how come?

Don't leave us hanging

[fringe needle]

Lie algebras

Whole course is basically one big proof which can be weird to follow until you’ve finished it and can put the train of thought together

[woven whale]

@fringe needle how would you explain lie algebras in one sentence?

[fringe needle]

I wouldn’t lmao

At least not in one sentence

Im not sure I can really motivate them since we’ve really looked at them in a completely closed setting, so without reference to Lie groups

But ig here’s a sort of motivation: the prototypical sort of associative algebra which doesn’t commute is an algebra of matrices. One way to measure the failure of two matrices to commute is to investigate the commutator operator [x,y] = xy-yx. It turns out if you investigate algebraic structures closed under this operation (lie algebras) you get a very nice representation theory which allows you to understand a decent bit of their structure. In particular we have a full classification of finite dimensional such algebras over algebraically closed fields which can be formed by taking a direct sum of simpler parts.

Ig this is the closed approach to a motivation

The wider point of view with Lie groups is more interesting but someone else could explain that far better than me

But basically the idea if I understand correctly is that when you have a group which is also a manifold, the tangent spaces of this group come with a natural Lie algebra structure. If you look at the tangent space at the identity the idea is that elements of this Lie algebra represent « infinitesimal » elements of your group. For example if you take GL_n(C), the invertible matrices, and linearize at the identity you get a space of « infinitesimal invertible transformations ». This is the Lie algebra gl_n(C) which happens to coincide with the standard algebra of matrices M_n(C). I haven’t really ever touched on this part of lie theory so I’m not exactly sure how the correspondence goes but it’s something to do with derivations and the exponential map

Someone else can cut in and explain that

[bright hill]

He wasn't writing it for you.

[desert field]

1415926535897932384626433832795

[neat lintel]

Pi?

I forgot the 1000 digits I knew

It's funny how now for me it's hard to even remember the 5th figure

!help

[quasi jetty]

Please read #❓how-to-get-help

[odd narwhal]

Tangent space of the identity

[wooden flax]

Algebra satisfying jacobi

[frigid matrix]

so what is the main theorem

[neat lintel]

"the main theorem"?

maybe lie's three theorems?

[frigid matrix]

#serious-discussion message

[upper patrol]

hey yall

me and a bunch of friends are writing a paper for this competition: https://hlma.hanglung.com/en/

any tips for writing research papers in secondary school? (or in general maybe)

also thoughts on our topic shortlist

1. Solving chaldani patterns for shapes other than rectangles, see https://physics.stackexchange.com/questions/90021/theory-behind-patterns-formed-on-chladni-plates
2. Distribution of roots on complex plane like https://mathoverflow.net/questions/182412/why-do-roots-of-polynomials-tend-to-have-absolute-value-close-to-1
3. Fractional Derivative: we have g(x,a)=D^a f(x) (where D is the diffintegral and a is real/complex), then analyse if g is continuous/differential/analytic. Might replace D with F (for Fourier Transform)

[cinder zephyr]

Read papers to see what the style of writing is

Have a professor who can proofread and be honest with your writing

[upper patrol]

sure i'll discuss with my IMO trainers then

p sure that none of the teachers in my school are professors (why would they be?)

[fringe needle]

Not like it’s the inky theorem of the theory but this course was pretty much centered around showing the classification of finite dimensional semisimple Lie algebras over an algebraically closed field

[woven whale]

when you don't know what the words mean it sounds almost as scary as classification of finitely generated modules over principial ideal domains

[eager reef]

It’s scarier

[fringe needle]

It’s quite a bit harder to prove but it’s in the same kind of spirit: semisimple Lie algebras are those which can be written as a direct sum of simple components: Lie algebras that do not have any ideals (ie that can only map onto themselves or 0). There’s a really rich classification which associated these algebras with this geometric structure called a root system, and these are much easier to classify

[neat lintel]

Lie algebras is a year 4 module for me

we don't have that in undergrad

[wooden flax]

this is a nice proof

root systems are mindblowing 🤯

lets you concretely work with abstract shit :)

[fringe needle]

Root systems themselves I don’t find insanely interesting but getting the correspondence between semsimple algebras and root systems is very neat

[hollow ginkgo]

Speaking of root systems, what’s with the weird correspondence between H₄ and E₈?

[neat lintel]

3.14159265358979323846264338327950288419716939937510

[desert field]

71828182846

[vivid halo]

can you say more?

[hollow ginkgo]

Regarding their root subsystems

[vivid halo]

H4 is the Coxeter diagram with 4 vertices and one edge of weight 5 right?

[hollow ginkgo]

H₄ has A₂A₂, H₂H₂, A₄, A₁H₃, and D₄ as maximal subsystems.
E₈ has A₄A₄, A₂E₆, A₈, A₁E₇, and D₈ as maximal subsystems.

[hollow ginkgo]

Yes, among others.

[vivid halo]

Ahh interesting I see what you mean now

[wooden flax]

Huh that’s weird

[odd brook]

Interesting lol I've not thought about this

[lucid sigil]

Does anyone know of a material that has a good classification or list of real functions?

[woven whale]

[velvet dagger]

R^R has literally all of them

[oak oxide]

In the definition given by my teacher, an H-group is an homotopy associative H-space which has an homotopy inverse map but only along the right hand-side of the multiplication map. Is it also a "left inverse"? Or is it the case if and only if the space is contractible?

[woven whale]

try asking in #groups-rings-fields

[oak oxide]

ty, I hesitated because I already posted it in #point-set-topology

[cinder zephyr]

I can't imagine there's a good classification

Right?

Or at least not one that lists out functions like "all functions of the form f(x) = ..."

[woven whale]

I can list some

f(x) = 0

f(x) = 1

f(x) = 2

should I go on?

[cinder zephyr]

Yes

[woven whale]

f(x) = 3

f(x) = 4

f(x) = 5

want even more?

[neat lintel]

yes

[snow coral]

Hello guys can you tell me why this statement is true please

[woven whale]

bézout's lemma

[wooden flax]

nG do you have any ideas?

[snow coral]

Thx

[frigid matrix]

its divison algorithm

[cinder zephyr]

https://en.wikipedia.org/wiki/Bézout's_identity
The proof isn't too hard to understand tbh

[cerulean kestrel]

most humble mathematics enjoyer ^^

[frail lagoon]

I mean tbf this is easy by many people's standards and hard by others

[eager reef]

If it’s not a concrete math question it doesn’t belong in that channel

Mentioning philosophy of maths makes me doubt that it’s appropriate there

[frigid matrix]

copi?

like copium?

tysm im not familir with this type of study

my only understanding of syntax/semantics are the uses in casual speaking

so does self referentially incoherent mean that statements about the theory of types written in the theory of types arent coherent? I dont know definition for coherent

this is true right

but golly

doesnt this devolve into ‘how do we know what is truth’ type questions?

i dont see how any meaningful remedy could be made to this contradiction

[neat lintel]

Anyone here?

no

oh

ok

[brittle socket]

Lmao tera

[neat lintel]

So is there a formula for prime numbers out there that gives you a lot of numbers that all end in 7, except for the first one which is 5?

I think the 28th number in the sequence is over 40 million digits

[neat lintel]

wait-that's the Fermat sequence; nvm only 5 of those are prime

[modest geode]

https://www.youtube.com/watch?v=EVTccVmTNEg&ab_channel=AndrewTejedor

why is this sound so yucky

does it have anything to do with mechanical resonance?

[surreal kindle]

#❓how-to-get-help

[willow hearth]

if your good at financial mathmatics let me know

[smoky lodge]

I am trying to teach a group on kids in 7 grade basic set theory and I have no idea how to explain Cantor’s theorem without confusing them
so If anyone has an intuitive or fun way it could be explained I would like to hear 🙂

[void tundra]

are you talking about the diagonalization one?

theres also cantor schroder bernstein

[smoky lodge]

the one with the power sets

For any set X, the power set of X (i.e., the set of subsets of X), is larger (has a greater cardinality) than X.

[bright hill]

Literally the exact same message

[tall badge]

just do examples for small |X|

[smoky lodge]

I want to teach them the proof

[tall badge]

not a proof

[neat frost]

THAT WAS LIKE 5 MONTHS AGO

Also that was on my bday look at that

[bright hill]

dude

How come i remember?

[neat frost]

Because you have eerily good memory? Idk

[bright hill]

My memory isn't even that good

[neat frost]

Obv it is

[bright hill]

Fr?

[neat frost]

Yeah

Same bday as Percy Jackson and Andy samberg

Massive flex

[bright hill]

You should've told me

Also

You said your b day was in July?

[neat frost]

I lied then

I don't remember

[bright hill]

Omg

Wtfff

I can't be the one losing his mind here

[neat frost]

No you're not dw

[bright hill]

@arctic grove you remember slurp telling us his bday was in July, right?

[neat frost]

You never had one

Hahaha gottemmm

[neat lintel]

hello

[smoky lodge]

I wasn't precise (and my english sucks)

I want to show them why it works for infinite sets
idk if its called a proof but you could use a function to show why its true but I doubt they would understand

[tall badge]

yeah for 7th graders i think its best to stick to small finite sets

[arctic grove]

i think so yeah

[cunning compass]

Solve for gf 😔

[neat lintel]

LMAO got too real

[fading tusk]

Oh if I changed 9 for 2 I could find an article talking about what I wanted

https://www.johndcook.com/blog/2017/06/20/leading-digits-of-powers-of-2/

[deep mango]

Chatgpt math 🙃

[undone wren]

The extent of what people do not to do their homework

[frigid matrix]

hi

so cauchy goursat is just greens theorem and cauchy riemann equations. and greens theorem is just change of variables twice

[surreal kindle]

#❓how-to-get-help

[frigid matrix]

but what about integrating complex valued functions in multiple variables on things homeomorphic to S^n

what would be the the generalization for cauchy goursat and what are some cool use cases

[sacred arch]

Technically nullary is the best base

• the prime factorization of 0 is 0 and every prime number, hence from a theoretical standpoint, all numbers should have a finite decimal expansion
• appropriately, in any base, any place without a written digit has an implied 0. Thus, all unwritten decimals are equal to 0*0^-n, aka 0/0, which could equal any number in the limit of some function.
• In addition to any irrational number, I'm pretty sure that includes imaginary and complex numbers, so they can written just as easily as the real numbers
• Don't have any digits in nullary anyways, so in a sense the number was always there and thus never needs to be calculated, instead pre-existent within the universe itself.

Of course, it does unfortunately suffer from the impractical issue of all numbers being the exact same, but since when did we let silly things like that get in the way of some good math?

Excuse my lack of proofreading

[deep mango]

"greens theorem is just change of variables twice" is a mighty statement

You know what, i changed my mind

It's not that mighty

[frigid matrix]

its just true

im just guessing any generalization would b using ift

[frigid matrix]

lol didn’t know they had the sticker

[brittle socket]

Best sticker

[sullen bone]

anyone have good resources for knot theory (beyond the wiki page

[simple field]

Wanna hear my theory

[untold sage]

I do knot.

[wraith whale]

pickles

[undone atlas]

joreggelt kivánok

[brittle socket]

Which book

[void tundra]

evening grass

i didnt touch grass today due to corona :(

[brittle socket]

Good

Don't touch me smh

[void tundra]

Dont u want corona tho

If u have corona u get to escape conscription for a few days

[brittle socket]

Who said I'm in NS

[void tundra]

i guessed

[brittle socket]

Besides, I gotten it earlier in the year lmao

[void tundra]

Hey you can always catch a different strain

[void tundra]

Im gonna guess u caught it from another conscript

Due to the complete neglect of any sort of safe management by the conscription authorities

[brittle socket]

That's assuming im in NS lmao

[void tundra]

Its a safe assumption

A ton of my friends got it from there

[void tundra]

and thus by extension the government

watch as I get disappeared

[brittle socket]

Prove by assumption

[void tundra]

axiom1: you are conscripted

[neat frost]

No I decided to read the other one, it's more straight. I am not cut out for philosophy

😭

I HATE philosophy yohan I hate it I hate it I hate it

I am NOT obsessed with programming

Also wtf is 22/05

[fast moat]

is traumatized incorrect

[neat frost]

I'm a 22 out of 5 on the hotness scale?

It's not tho

I'm a summer babe

You were never my friend, you were merely a plaything

Dude looks like a lady

[fast moat]

friends are for inferior, lesser beings

[brittle socket]

Cope

[main steeple]

[long matrix]

slurp refuses to think

[deep mango]

I hate philosophy too

[deep mango]

Mikey is based. Get fucked

[neat lintel]

@neat frost you smell

hi ryc

[deep mango]

Hello

Today im very achey

[woven whale]

what does achey mean

also hi ryce

[deep mango]

I have aches

My muscles are sore

And hurt

Cause yesterday I exercised a lot

[woven whale]

get well soon

[void tundra]

DOMS moment

[deep mango]

Thank you

[eager reef]

[deep mango]

[neat frost]

Haha jockman. Noodle brain. Rock brain. Stupid. Lolol

[dry leaf]

!!

[snow coral]

Hello guys can you tell me please why the gcd of (a,b) * lcm of [a,b]=a*b . Thx

[neat lintel]

if a and b have no common factors other than 1, say like 2 and 3, then their lcm has to be their product, 6

[gusty star]

Do you know about unique prime factorisation?

[bright hill]

Youre strad, aren't you?

I can just smell it

[neat lintel]

what

[bright hill]

But how would strad get nitro

[neat lintel]

who is strad

I said Slurp smells because he is emanating an odour known only to the most vile of animals

[bright hill]

@honest veldt just come of it

I'm onto you

[neat lintel]

im not strad hello

[bright hill]

How?

[neat lintel]

Slurp smells, that's how

[bright hill]

That is true

However

[neat lintel]

However?

[bright hill]

There's no casual relationship

[flat harbor]

@lament peak @sleek wing @zealous girder might hang here. might sleep idk

[zealous girder]

hiiiii

[flat harbor]

leave the nerd brigade to nerd out

what a bunch of mahogany amirite

[zealous girder]

i want to

die

no i don’t

guys we are the

highbrow

group of people

at. aparty

[flat harbor]

we are the "sociables"

i love listening to ppl talk abt their recent hyperfixations its awesome

except if theyre NERDS and talk like robots

[zealous girder]

dude

the like

ruled guy

99% sure he is an actual ai

being tested by chat-gpt

[flat harbor]

beware the debater in chat...

yea sure i got nothing else to do

[zealous girder]

hi guys

[zealous girder]

no don’t worry i’m just excessively high

[flat harbor]

im not a music person so like 95% of this went over my head

and maybe thats why its refreshing compared to whats in discuss

but ye u made it out in one piece u did well honey

[flat harbor]

i feel like im losing common sense talking to these ppl

need to literally touch grass

and connect with my fellow man..

[bright hill]

Baseddddd

[zealous girder]

actually

it’s like

insaaaaaaaaa

[bright hill]

Why's discussion invaded by white names?

[zealous girder]

Johnny appleseed

[flat harbor]

the abstract concept

[bright hill]

@neat frost come and keep me company!

[flat harbor]

coincidence that most antiwar ppl have never been in war..?

[bright hill]

You Korean?

Nice

[flat harbor]

에옹 난 집에있을거야

[bright hill]

What does kyuukurarin mean doe?

[zealous girder]

So True

[zealous girder]

bang

bang

bang

(gun shots)

[flat harbor]

thats hot

yoo... everyone rise for the national anthem

[deep mango]

[bright hill]

I see

[deep mango]

i will pause my chopin scherzi to listen to your song

[flat harbor]

listen to urself

[deep mango]

but i dont have headphones in so it had better not be a screamer

i can't say im surprised

how whimsical

[flat harbor]

do u speak the language

[bright hill]

I don't know enough japanese to understand the lyrics

It sounds cute tho!

I love the visuals

[flat harbor]

역시

믿고있었다고 꺼무

[alpine kindle]

조 바이던

[onyx pagoda]

hmm it's sharing songs with non-latin scripts time now huh

check this out

https://youtu.be/6qO_PdDGuR8

[neat frost]

Good morning DarQ!

[bright hill]

Hello!

[long matrix]

no.

[bright hill]

Good morning!

Shut up shuri.

[long matrix]

no

[bright hill]

Shlurp, what interesting stuff are you learning about lately?

OwO

[deep mango]

Good morning shuri!!!!!!

How are you!!!!

[long matrix]

no.

[deep mango]

Waaaaa

[bright hill]

Shlurp ignored me

[deep mango]

at least he didn't just say no

[neat frost]

Nothing

It's all boring

I was looking forward to my algo course because all of my lectures have been BUTT BORING but the man fucking cancelled two hours before it was supposed to happen

[still latch]

i have a ques6ion which i feel like isnt worth opening a doubt channel

where do i ask

[onyx pagoda]

#help-5

it's never not worth it to open a help channel

[still latch]

okay ty :))

[onyx pagoda]

turn this off on settings so it doesn't automatically convert to emoji

[still latch]

thanks lol

[jolly scroll]

How come physics server has maths section and maths server doesnt have a physics section. rude

[onyx pagoda]

because physics is applied math

[bright hill]

🍑

Sadge

[neat lintel]

because math is physics

[neat frost]

Though maybe after my tests I'll continue Royden

But I also want to continue doing TeX and I have such shitty time management so I bet I'll end up doing neither

[bright hill]

When're your tests?

[neat frost]

For example I should be studying rn

[neat frost]

All my finals for this semester

[bright hill]

This semester?

💀

[neat frost]

Yes

?

[bright hill]

How long till then?

[neat frost]

Uh

Lemme see

Last test 22 of February if I don't retake any

[onyx pagoda]

In set theory, physics can be thought of as a subset of mathematics, where a subset is a collection of elements that belong to a larger set. In this case, the larger set would be mathematics and the subset would be physics. This means that all physics concepts are a part of mathematics, but not all mathematical concepts are a part of physics. Therefore, it makes sense for a physics server to have a mathematics channel, as mathematics is an integral part of physics. On the other hand, not all mathematical concepts are related to physics, so it may not be necessary for a mathematics server to have a physics channel.

[deep mango]

I bet youll get stuck

[neat frost]

I probably will

[deep mango]

No, don't say that

I was trying to motivate you

[neat frost]

Oh

[neat lintel]

?

[neat frost]

Didn't work then

You're shit at this ryc

[deep mango]

Usually you'd go "fuck you ryc!!!! i bet im gonna know analysis better than you by the time im done with royden!!!!"

[neat frost]

I'm not that arrogant

[untold sage]

You can't control getting stuck beforehand

[neat frost]

I respect that people have put in more time to learn a subject than I have, and I wouldn't belittle their efforts like that

Personal pet peeve of mine

[bright hill]

Oh

That's not very far away

I wonder if I'll be done with the algebra i wanna do by that time

[neat frost]

Yes and first test on the 6th

5 tests 3 weeks

[bright hill]

Nice

[neat frost]

I have a test one day then another test the next

[bright hill]

I have 10 exams next week

:))))

[neat frost]

Finals?

Also what?

[bright hill]

Yea

And yea

[cinder zephyr]

finals now?

[neat frost]

In one week?

[cinder zephyr]

finals before winter break >> finals after

[bright hill]

Like

[neat frost]

It's the end of the semester

[cinder zephyr]

finals after winter break should be illegal

[neat frost]

Winter break was like a month ago 🥱

[cinder zephyr]

break is better when you don't have to do anything

[bright hill]

Yep

[cinder zephyr]

what???????

I'm still on break lol

I go back Tuesday

[bright hill]

LOL

Based

[neat frost]

How in one week

[bright hill]

I dunno

[neat frost]

No sense

[bright hill]

You just do it

[neat frost]

Anyway I need to study

[neat frost]

Well obv

[bright hill]

:))}

[neat frost]

And I assume if an entire uni does it then it's possible

But weird

[bright hill]

I hate my uni :)))

[neat frost]

You missed a du

[neat frost]

I love it

Kiss it

Stroke it

Rub its back

Wait

Wait

Not what I meant

Wait

Don't sully that

I didn't mean it that way

[bright hill]

Ofc you didn't

Anyhow

[neat frost]

No I meant stroke their face or their back or whatever

[onyx pagoda]

nice kink

[bright hill]

Me 2 tbh

[neat frost]

This algo hw is dumb af

I haven't had a lecture in like 3 weeks I don't remember anything

I need to do your mom

Oh

[bright hill]

Aight

[neat frost]

Nitro moment

Aight

Chow

[bright hill]

I really gtg lol

Byee

[zealous garden]

Nice kink

[zealous girder]

seychassssss

[bright hill]

@neat frost what were the courses you were taking this semester again?

[deep mango]

uhh.. algorithms... computer architecture... image processing... uhhhh

[pastel storm]

I wrote a triangle solving Android app. Does anyone know if there is a channel or server to get feedback for what I wrote? It's free and doesn't have adverts, so I'm not looking to make money, just see if it helps students with solving triangles.

[neat frost]

Ofc you only remember the CS courses

[neat frost]

What ryc said + group theory and calc3, and postmodern Jewish philosophy

[bright hill]

[bright hill]

only two math courses?

Cringe

[neat frost]

DarQ I do also have HS to deal with

[deep mango]

ofc i knew about jewish philosophy...

[neat frost]

My time is limited

Also there weren't really any other math courses I could've taken

I'm taking 3 next semester though

And possibly 2 Jewish courses

[bright hill]

Nice

How do you feel about group theory so far?

[neat frost]

I feel it like your mom

Uh it's fine

My courses this semester are for the most part quite dull

Group theory and algos are the interesting ones

[bright hill]

Image processing was dull?

[neat frost]

No it's okay but I suspect it's only because I only do recordings so I can do it at 2x speed

I used do too much in that sentence

[deep mango]

i do your mom

[bright hill]

I can't parse that sentence lmao

[neat frost]

Oh

Okay

[deep mango]

"i used the word 'do' too many times in that sentence"

[neat frost]

It's okay but I only watch the recordings at 2x speed, so I suspect that's why I'm not dying of boredom

Oh

Wait

You meant that sentence

Meh

Idfc

Fuck this

[bright hill]

Lol

How's group theory interesting tho?

We've roughly done the same stuff and for me it was just a big pile of definitions

[neat frost]

Sure there are a few definitions, but not that many

[bright hill]

The only "interesting" thing about group theory I've seen is how Lagrange easily proves Fermat's little theorem

And Fermat's little theorem is number theory

[neat frost]

Huh actually

No a lot of definitions

[bright hill]

And i don't give a shit about that so

[neat frost]

Idk like I said my other courses are dull

[bright hill]

Yes...

[neat frost]

Relatively group theory is quite good

[bright hill]

Lmao

[neat frost]

That's the most interesting thing?

Actually I see your point

[bright hill]

Actually, i did some group actions stuff

But only a tiny bit

So like

[dapper badge]

group theory is awesome and darq should grow up

[bright hill]

I can tell this concept can be interesting

[static loom]

I feel like that sort of stuff like burnside's lemma, polya's counting thm, orbit stabilizer, etc are cool I just never really use them

[bright hill]

But i don't know why yet

[static loom]

maybe if I did more combinatorics

[neat frost]

I forget what the lemma which isn't Burnside's is

But we talked about it a lot

Hmm is it like

The number of orbits is the sum of the number of fixed points?

[bright hill]

Maybe i will once i do aluffi chapter 4

[dapper badge]

Tbh chapter 4 made no sense to me the first time

[static loom]

the number of orbits is an average over the sets fixed by elements of the group

[neat frost]

DarQ does like aluffi chapter 20-25 but not chapter 4

[neat frost]

Oh yeah right you have to divide it

I need to upload my latest lecture notes ;-n

[bright hill]

I'm actually still at chapter 3

[neat frost]

And calc3 is soo fucking boring rn

[bright hill]

;-;

[neat frost]

Not because the material is bad

Like it is

But the professor is getting gradually worse and worse

[bright hill]

I'm telling you

We should just do spivak on manifolds

[neat frost]

No I'm gonna continue Royden

I wanna be a probabalist I've decided

[bright hill]

[neat frost]

Probability of DarQ not being a nerd 0

[bright hill]

I wanna do probability stuff too

[neat frost]

Haha lol

Trolled

I don't

[bright hill]

Well

[neat frost]

I'm tired

[bright hill]

Your loss

[neat frost]

Okay fr I need to study now

[zealous garden]

Is it?

[neat frost]

Yeah mostly the prof's fault though

[bright hill]

Wdym???

Dude

[neat frost]

Algos

I have a quiz on Thursday

[bright hill]

It must be 4am there

You can't be serious

[neat frost]

3:30

[neat frost]

I am serious

My friend is all like "I don't study after midnight" and I made fun of him for it

If you need to study study

[bright hill]

Dude...

Are you not exhausted?

[neat frost]

Idk

[bright hill]

You can't be studying optimally

[neat frost]

Feelingless

I haven't been studying at all I do like a question then am like "I wonder if DarQ has sent me another stupid message"

[bright hill]

Have you ever heard of the close button?

You click it

And BAM

Discord is closed

You should try it sometime

Slurp left me alone again ;-;

[zealous garden]

Hey

[long matrix]

darq needy arc

[zealous garden]

You mentioned Spivak

Calculus on Manifolds

I've not read spivak

But i like Calculus and manifolds

[deep mango]

Yayyyyy!

[deep mango]

yay!!!! probability reading group!

[bright hill]

I'd be definitely down for a reading group tbh

[deep mango]

I don't know what book one should use

[bright hill]

One that uses measure theory

[deep mango]

Well

If only you knew some measure theory!

[bright hill]

Easy

[dapper badge]

measure theory

[bright hill]

I'll learn both in tendem

[dapper badge]

i should properly learn measure theory

lets learn it together darq

[brittle socket]

Hi rice boi

[zealous garden]

LETS DO IT

[deep mango]

hello grass

[zealous garden]

I also need probability and measure theory

[bright hill]

Wanna do folland?

(just to spite the royden fanboys)

[deep mango]

booo

[dapper badge]

what do you suggest ryc

[deep mango]

Folland

:)

[dapper badge]

let me check it out

[bright hill]

Lol

[flat harbor]

i liked reading folland

[bright hill]

Why boo then?

[deep mango]

cause it's not probability!

[bright hill]

It's measure theory tho!

[deep mango]

Whatever

[bright hill]

It's a prereq!

[dapper badge]

folland looks cool i guess

i don't really know what i'm supposed to be looking for

[deep mango]

You can kind of do a concise run at measure theory for probability, but it's healthier to learn measure theory properly

[dapper badge]

but if ryc suggests it and bloe liked it, then surely it's good

[flat harbor]

after folland u can read fremlins many books with me

[deep mango]

folland's perspective is probably best for someone with your interests, his "sequel" book is abstract harmonic analysis after all (which has a lot of algebra and rep theory)

[bright hill]

det told me i could learn both at the same time

So like

[dapper badge]

i'll probably be taking harmonic analysis sometime so this would be good preparation

[bright hill]

The two would compliment each other or w/e lel

[deep mango]

sort of

depends on the book

the book i used was Varadhan, which would probably be a lot to use without a good picture of measure theory

but that's a hard book

I just don't know what other measure theoretic probability books are popular

[bright hill]

I kinda don't want my next book to be hard

I've had a run with hard books lmao

I should prolly break that habit

[dapper badge]

books don't seem to get any easier

[bright hill]

But i seem to have been choosing the notoriously hardest text whenever i wanna read about a certain topic

[dapper badge]

fair

i kinda just feel my way around until I find something that feels the most comfortable to read

[deep mango]

folland is not the notoriously hardest text

it's a little more chill iirc

[dapper badge]

and it definitely helps to have a mentor or someone to guide you when reading

[deep mango]

i think halmos measure theory is the notorious one

folland is also nice because it ties things into basic functional analysis

[bright hill]

And papa rudin?

[deep mango]

yes

that books a meme though

[bright hill]

But that's not measure theory focuses tho, right?

[deep mango]

halmos is actually like, a bible

[deep mango]

it's measure theoretic real and complex analysis

omg nuclear throne is so hype

it's been so long

[bright hill]

ic

[bright hill]

One more reason to do folland when I get around to it

Btw, ryc, do you think I should be focusing on a single book at a time?

Coz i don't think that's what most students do

But that's what I've been doing since I started doing math lmfao

[zealous garden]

I'm interested in this opinion

[deep mango]

That's fine

2 at a time might be good too just so that you can go somewhere else when you get stuck

it's not like you "should" do that though. whatever helps you to internalize the material is fine

[bright hill]

I see

I would've asked you about your study routine but i really need to sleep now ;-;

or at least try

[zealous garden]

Well I don't need to sleep yet

Ryc how do you study

And how have you in the past

What are some things you tried that didn't work out for you

[deep mango]

took classes

[deep mango]

took classes

[deep mango]

read books

[brittle socket]

lmao

[brittle socket]

In what ways did it not work out

[wicked jackal]

Reading books is so much more fun than listening to people talking

[bright hill]

(couldn't sleep btw)

:)))

[deep mango]

boring

[brittle socket]

[zealous garden]

LMFAO

That's funny

[onyx pagoda]

even math books??

[zealous garden]

Books are actually one of the better ways for me to learn historically

In fact, the trick in the past has been to go to a class, and ignore the lecture while I read an unrelated textbook

[gusty star]

Is there any difference, typically, between discussion-1 and discussion-2?

[zealous garden]

Discussion 2 is kinda like overflow

Discussy gets hectic

Or occupied with one too many trails of conversation already

[static loom]

I actually muted #discussion for the past year or so because it's bad, but recently unmuted it the other day

now I will be remuting the channel

[zealous garden]

Good decision

[gusty star]

Because you just witnessed the 0/0 debacle?

[static loom]

it's basically the entry point for all the riff raff and is just people talking over each other because of it, impossible to have any quality convo there

[static loom]

no, but the fact that it was something else bad doesn't surprise me

[gusty star]

I mean I just learned the definition of condensed set in discussion 1

[static loom]

oh what's the definition

[gusty star]

sheaf on the pro-etale site of spec(k) for k algebraically closed

[static loom]

ok

what's that mean

[gusty star]

Which part?

[static loom]

what's the difference between etale and pro-etale

[gusty star]

That's the first thing I asked!

[static loom]

I know

I read it when it happened lol

[gusty star]

oh

[static loom]

but didn't see the response

and now that I've muted the channel I can't go back

[gusty star]

He only explained what it means for the affine setting

namely you take filtered limits of etale morphisms Spec(A_i)-->Spec(B) in Sch/Spec(B)

[static loom]

well you can always ask him again in #algebraic-geometry or wherever else later if you wanna talk more

[static loom]

that's a response to that but with considerable delay

[gusty star]

I see

Anyway, I was happy enough with the affine definition, since B = k here

[deep mango]

nonmath books are far better than math books...

[gusty star]

And the functor of points formalism tells us that you only need to know the value of h_X on the affines

[deep mango]

i like fiction

[gusty star]

So the affine version should be sufficient for our needs

[deep mango]

math is enjoyable when i'm talking with people about it or trying to solve problems. not when i'm reading encyclopedia entries about dubiously motivated objects

[static loom]

yeah, sounds reasonable to me

[gusty star]

I've yet to see a dubiously motivated object

In the literature, at least

[deep mango]

you and i very clearly have different definitions of dubiously motivated

you're into category theory / alg geo after all

i have very concrete mathematical tastes

ofc i respect other styles, but books have never been for me

[static loom]

explain why your favorite projective variety isn't dubiously motivated ||and don't talk about fermat's last theorem please||

[onyx pagoda]

so you're more of a lecture guy than a book guy. Perfect opportunity for a course-recommendations channel

[gusty star]

Define concrete?

[deep mango]

physical

is a better word

[static loom]

if we have to define it, we're already too far gone 🥹

[gusty star]

dubious "in a way that arouses suspicion, distrust, or uncertainty."

Does this encapsulate what you're meaning?

[zealous garden]

I like things I can pretend I'm able to visualize

[deep mango]

yes, it's an exaggeration but there are elements of distrust to it

[gusty star]

Hmm

[zealous garden]

Like anything with geometry in the name

Or more than 3 dimensions

[gusty star]

moer than?

[deep mango]

as far as i understand, that was being discussed

[gusty star]

are abelian categories too esoteric for you(r tastes)? @deep mango

[deep mango]

anyway, yes, i'm definitely more of a lecture guy than a books guy (and more than either a 1-1 conversation guy)

or small group convos person

like, reading groups make books palatable to me

i want to talk about misunderstandings or examples and work them out along the way with people

[zealous garden]

Yes

[gusty star]

like 10000000000 dimensional things?

[zealous garden]

The problem with that many dimensions is you have to give me a reason to care about that specific number of dimensions but sure

[gusty star]

You can pretend to visualise things that are that high dimensional hmmmm

[zealous garden]

I usually think more between 4-8

[gusty star]

can you pretend to visualise 808,017,424,794,512,875,886,459,904,961,710,757,005,754,368,000,000,000 dimensional things

[static loom]

im pretending rn

[zealous garden]

I'm done

[gusty star]

holy shit

[zealous garden]

That was cool

[static loom]

wow its big in my mind thats for sure

[gusty star]

did you see the monster in there?

[zealous garden]

I've never seen a millionfold rotation before

[static loom]

i only see polynomials

[gusty star]

did the monster give you some specially brewed moonshine?

[static loom]

im seeing a decently better approximation of sine in there than x

[gusty star]

lmao

[onyx pagoda]

cool

[bright hill]

Truer words have never been uttered

Also, learning the basics of stuff that look cool is kinda fun

[onyx pagoda]

learning + human interaction ftw