serious-discussion

[thorn brook]

I guess like "projecting" up with some function, right? Like the varphi map?

[odd narwhal]

The varphi map is the chat

Chart

[light needle]

yeah you like, take the inverse of varphi map

and remember charts where homeos so this is doable

[thorn brook]

yeah okay I see I see

[light needle]

and you think of whatever the appropriate domain/ codomain is and all that stuff

[odd narwhal]

Is t an indeterminate here?

[light needle]

yeah

its the field of rational functions on C

[odd narwhal]

Also does this have to be true for every 2 charts for f to be considered holomorohic?

Ah ok

[light needle]

yeah any combination of chart should do this

any other questions?

[odd narwhal]

I'm good

[light needle]

nice!

so we are going to be focusing on the meromorphic functions now

which are very cool imo

so by M(X) i denote the meromomorphic functions f: X->C

[neat lintel]

Please

Help me

[light needle]

#❓how-to-get-help

[neat lintel]

I speak spanish

I have homework

[light needle]

read #❓how-to-get-help

[thorn brook]

liar

[light needle]

so right now I claim that M(X) is actually a field under function addition and multiplication

[neat lintel]

and my teacher don´t teach me from this

[light needle]

@cold needle help pls

[cold needle]

lmfao

[light needle]

but ok getting back to my train of thought

[cold needle]

please read #❓how-to-get-help and follow the instructions there.

[neat lintel]

ok

[light needle]

like intuitively that statement makes sense right

[thorn brook]

yeah I guess so

[light needle]

like you kind of have finite poles that you could cancel out and etc

The way to do this is cool but I wont go over it now

ill just tell yall the main idea

[last oxide]

john trying to be dami

[light needle]

so the riemann sphere, often denoted PC^1

is the one point compactification of C

the way we will think about this is that its just the sphere

and

let me draw this

we have the sphere with two charts

one is this one, where we are doing this stereographic projection onto C through the point at infinity

the other one is doing it through the point at the origin

does this make sense?

[thorn brook]

I don't really get this tbh. How do we do it through the origin?

oh, the same map?

[odd narwhal]

Just think of unfolding the sphere around the origin

[light needle]

yeah exactly

[thorn brook]

yeah okay then I get it lmao

[light needle]

and you can also visualize this as adding apoint at infinity to the complex plane

very roughly visualizing, its like

you know how you have a 2-disk and you identify the boundary you get a 2-sphere?

The point at infinity is like, you are saying the infinities in each direction is the same point

[thorn brook]

yeah okay I see

[light needle]

and its doing the same kind of thing

[odd narwhal]

It's actually a cool way to visualize a 3-sphere too. Just imagine our regular 3d space, but if you walk far enough in any direction you'll end up in the same spot

Not visualize cuz you can't do that but think about it at least

[light needle]

yep

but yeah so if you think about it now

if you have a meromorphic function from X to C

then it extends to a holo function from X to PC^1

because the poles are like, kind of continously sending you to infinity roughly speaking

but yeah so M(X) is a field and you prove it using this alternate way to think about mero functions

the + is function addition and the * is function product (not composition)

so now heres the really cool think

thing

lets say you have

a holo map f:Y->X

then this induces a map f*: M(X)-> M(Y)

and this induced map is actually also a field homomorphism!

ill let u figure out how this induced map works

its a good exercise while i get some water kek

[neat lintel]

[thorn brook]

[neat lintel]

M() is a contravariant functor

[odd narwhal]

Fuck terra I was just gonna say that

[neat lintel]

it doesn't count because i'm already familiar with this stuff to an extent

[odd narwhal]

I'm assuming it's just by composition? If g is in M(X) then g o f is in M(Y)? Supposing that the composition of a meromorphic function with a holomorphic function is meromorphic

[narrow rock]

tteppa

[neat lintel]

brofib

im taking this http://www.math.toronto.edu/mein/teaching/MAT1341_PoissonGeometry/Poisson8.pdf in the winter

should be cool

[light needle]

alright im back

yeah shin its just post composition

and do you see how this also a field homo

[narrow rock]

looks dope

[neat lintel]

poisson geometry

ok let me not interrupt john anymore

[narrow rock]

lie algebroids

[odd narwhal]

Yea

[thorn brook]

wait how is that?

[odd narwhal]

I think

[nimble shuttle]

fish geometry

[light needle]

right so for example

(g+g') o f = g o f +g' o f

and same for multiplication and all that stuff

the idea is post composition doesnt really change your structure

so good to move on?

[thorn brook]

but aren't you supposed to show that gf(x+y) = gf(x) + gf(y)?

or does this fact come from this?

[light needle]

so remember the operation on M(X) was

adding the functions

[thorn brook]

oh yeah right

[light needle]

and same for M(Y)

[thorn brook]

yeah okay I see now

[light needle]

nice! so

now we have an induced homo f*:M(X)->M(Y)

right

remember from field theory that all field homomorphisms are injective

so what we actually have is an embedding of M(X) into M(Y)

or in other words

we can consider M(Y) as a field extension of M(X)

so yeah we started of with holo functions in X and ended up with field extensions of M(X) which might give you a hint about the galois

so now we are gonna compute M

M(CP^1)

and this is kind of cool too

so take a meromorphic function, say f, on CP^1

now meromorphic functions have finitely many poles(not at infinity) of finite order each

[bronze pelican]

Meromorphic function

[light needle]

so what we can do is, multiply our f by a polynomial to get rid of these poles

and now what you have is a holomorphic function

and now what are holomorphic functions on the riemann spheres? well right out the taylor series

and you realize you will need to have only finitely many terms in it

otherwise you have an infinite order pole at infinity

so this means its a polynomial

and so f is a rational function

i.e M(CP^1) = C(t)

i kind of went over that quick

I will let yall absorb

so questions?

[nimble shuttle]

john nazi arc???

get it cause

poles

[blazing pawn]

Yes

[nimble shuttle]

laugh now

[blazing pawn]

laugh.wav

[cold needle]

[light needle]

ur a few years late unfort

[thorn brook]

hmm yeah I think I sort of get

[light needle]

wbu shin

[odd narwhal]

I think I'm good

[thorn brook]

this is me right now

[light needle]

nice

so really one way to study field extensions of C(t)

is to look into holomorphic maps into CP^1

let me give an example

[blazing pawn]

waiting for john to get inverse galoispilled

[light needle]

so we are gonna take the map from CP^1 -> CP^1

[blazing pawn]

my disaster explanation

[light needle]

thats just squaring

[odd narwhal]

Into CP? not from CP?

[light needle]

yeah its into CP

remember contravariant

[odd narwhal]

Ah right

Ye ye

[light needle]

right so sending z->z^2

now think about the induced map on C(t)

its sending the meromorphic function f(t) to f(t^2) right

bc post composition

so really this is the field extension

C(sqrt(t))/C(t)

i reallize using 2 CP^1 probably not best example too easy to confuse them

but yeah we will go with this

now I want you to observe something nice about this map

its almost a covering map right

like if you ignore the point at infinity and the origin in this case

then its a two sheeted cover right

(say yes when yall convinced urself of that)

[odd narwhal]

Can you define a 2 sheeted cover?

[blazing pawn]

fibers have cardinality 2

[light needle]

yeah, and im assuming you guys know what covers are from AT

which i remember u guys are studying

[blazing pawn]

if you think of the usual cover this means that if i have an open neighborhood U of x in our base space then there are two open neighborhoods, one for each point in the fiber, mapped homeomorphically onto U

[odd narwhal]

I haven't gotten to covers yet (rotman goes in a different order) but I know what they are more or less

[blazing pawn]

ie "two sheets" of U

[odd narwhal]

Gotcha

Alright

[thorn brook]

Hmm well I don't really see how that is a cover tho

like the map sending f(t) to f(t^2)?

[light needle]

thats the field homo

i meant like the CP^1->CP^1 squaring

[thorn brook]

oh lmao

[light needle]

ig imagine like an open ball on the sphere

[blazing pawn]

think in analogy with covers of the circle

which come from z |-> z^n in the finite sheet case

[thorn brook]

oh yeah okay I see now

[light needle]

yeah good example

[odd narwhal]

Oki

[light needle]

nice so this is kind of nice

[thorn brook]

Okidoki ✓

[light needle]

our this was just an example

but it turns out

that in general because of how strong complex analysis is

we have an equivalence of these branched coverings (ignore a few point basically and then its a covering) and a certain class of holomorphic maps

kek what i meant by that is how strong holo maps are ig

so the precise statement is like

all holomorphic maps into X who is proper (preimage of compact is compact) is also a branched covering

I dont wanna prove this rn so take my word for it lol

lets show the opposite side

a covering map p:Y-> X into riemann surface X

can be made into a holo map by choosing a complex structure on Y

good exercise, think about how

[thorn brook]

tbh I don't think I can lmao. It's getting late here and I'm getting tired

[light needle]

oh oof i see

wbu shin wanna give it a try

or shall i just spoil

[blazing pawn]

hint: covering maps give us a local relationship on an open cover of Y to an open cover of X

what local structure do we have on a riemann surface X?

[light needle]

(you there @odd narwhal )

[blazing pawn]

johnathan DS moment

[odd narwhal]

What do you mean by complex structure

[blazing pawn]

complex atlas

[odd narwhal]

Ah

Composing the charts on X with the homeomorphism from the open sets making up the fibres of the covering?

Something to that effect

[light needle]

yep basically

[blazing pawn]

Uh you need to be careful

because the complex atlas and the locally trivial sets covering Y need not be the same

but with a proper refinement yes

its not that monkaS just take intersections

[neat lintel]

Congrats on mod, Moth!

[light needle]

smh mothkaS moment

[blazing pawn]

Thanks Tess

:mothkaS:

[light needle]

but yeah so the point of all that was

[sly thistle]

@blazing pawn btw just congratulations on becoming a moderator

[light needle]

that branched coverings of our surface and proper holo maps into it are basically the same things

and rememember how we used holo maps to induce field extensions of M(X)

so chaining along

this means we can use branched coverings of X to induce field extensions of M(X)

[blazing pawn]

Fet_X moment

[thorn brook]

holy yeah that's kind of cool

[light needle]

and now we use the natural thing next

galois covering theory

[blazing pawn]

toki you have not seen the very cool part

but it is coming

its easier if you've seen finite etale covers before

and infinite galois theory

[light needle]

mothkaS

[sly thistle]

lol

MothkaS

[light needle]

right so let me gather my thoughts on how to do this

how much of the galois covering theory are u guys familiar with

[thorn brook]

I'm familiar with none lmao

[sly thistle]

none

[blazing pawn]

[odd narwhal]

Same

[light needle]

oh oof

alright lets go

[blazing pawn]

It might be a good idea t otake a break

[light needle]

yeah maybe

[odd narwhal]

Maybe we can continue this tmrw

[blazing pawn]

and for them to familiarize themselves with it first

[light needle]

yeah i have to tutor someone in 20 mins

sadge

[odd narwhal]

Oof

[sly thistle]

Nice

You’re a tutor?

[light needle]

indeed

[thorn brook]

yeah honestly I'm really tired (not from reading all of this but because it's getting late)

[sly thistle]

Sick

What do you tutor

[light needle]

yeah let it simmer kek and if yall are like, avalaible sometime tomorrow ill finish this talk

[odd narwhal]

Same it's 2:30 am

[light needle]

everything.

[odd narwhal]

I'm available any time pretty much

It's summer

[thorn brook]

holy crap lmao, it's not that late here

yeah same here

[odd narwhal]

Also I've been thinking of this problem all day and it's pretty draining

[thorn brook]

it's 01.36 here. I mean like not as late as ShiN

So we can continue tomorrow?

[light needle]

yep i will probably free at somepoint to finish this too

[odd narwhal]

Yee

[thorn brook]

Okay great! Thank you so much for the explanation and all that stuff, it was really interesting! Good luck with the tutoring, good night!

[odd narwhal]

Yea thanks!

[light needle]

nice, gn to both of u, sweet dreams (about covering spaces) and etc

[rare rose]

hello lets talk about benfords law implements if any one interested

[vagrant kestrel]

benfords law applies to nothing, change my mind

[astral marsh]

@velvet dagger @vagrant kestrel @jovial ember @hybrid zephyr @sharp mulch how common is it for a (long-running) college club to die

[vagrant kestrel]

reported

[astral marsh]

i was doing some research on the harvard anime club after i found that it seems their last post was from 2016

thats honestly kind of depressing

it just died

[sharp mulch]

[astral marsh]

and it was started in the 90s

[sharp mulch]

Anyways

Think of it as a Markov process

Each year, there is a small chance for it to die

Just via like

Human error/laziness

[astral marsh]

well yeah i mean it was apparently a rather small and casual club so like

[sharp mulch]

And after it dies, it takes a lot more effort to revive

[astral marsh]

in 2016 ig just a bunch of key members graduated

and there wasn't enough momentum left

[sharp mulch]

Yeah

[astral marsh]

pretty sad that it hasnt been revived for that long

like jeez

2016

[sharp mulch]

Harvard people are too rich for anime

[astral marsh]

lmao

[sharp mulch]

Cornell probably has a more active anime club

[astral marsh]

bro what cornell anime club's last events were in 2016 as well

holy

what happened in 2016

are we uncovering some sort of conspiracy

[bronze pelican]

Just revive it

[astral marsh]

4head

[bronze pelican]

Like seriously

[astral marsh]

also its not up to me lol its the harvard anime club

i was just snooping

[bronze pelican]

Oh

[astral marsh]

i mean honestly if that was the case for my school i actually would revive it

lord knows theres enough weebs here

[bronze pelican]

Yeah

[astral marsh]

i got my room assignment the other day and met my roommate, also a weeb

[bronze pelican]

[astral marsh]

but anyways its honestly kinda spooky that cornell and harvard anime clubs died in 2016

tf happened

[light needle]

me,

i happened

[bronze pelican]

Purge of anime in 2016

[astral marsh]

[bronze pelican]

Catastrophic event

Many weebs died

[astral marsh]

i swear if i find another northeast college with an anime club that died in 2016

theres actually legit gotta be something up

ok i was ACTUALLY sad when i saw the harvard club died but this just pisses me off

THEY are doing such a better job than my school

for one, their webpage is actually updated

and has details about plans to resume for fall 2021

[sharp mulch]

@deep mango now that you've been in Paris for an hour, do let Demmel and Holtz know if you want to postpone the meeting scheduled for tomo

[astral marsh]

over here i had to fuckin snoop and shit and find people and message them directly to try to find out whats goin on this fall

and the website hasnt been updated for like 1000 years

and then princeton's website NOT ONLY HAS A MUCH BETTER UI but it has a BETTER DRAWING, clearly lists all the eboard members, and not only STATES THAT THEY ARE PLANNING TO RESUME THIS FALL but also DETAILS WHAT EVENTS THEY PLAN TO KICK THE YEAR OFF WITH

like ffs how are there even weebs in nj

[bronze pelican]

Is this expected for clubs

[astral marsh]

wdym

is it? i dont know

[wild lantern]

Do big CS schools generally have stronger anime clubs?

[astral marsh]

all i know is that they're doing a much better job

[wild lantern]

It seems like they would..

[bronze pelican]

Arch just become president of anime club and lead the revolution

[wild lantern]

Not sure what other majors would work like that though.

[bronze pelican]

Eh my undergrads anime club was pretty weak

Idk why

[wild lantern]

What majors was your school known for?

[astral marsh]

like it honestly actually pisses me off because they seem like they care so much more

[bronze pelican]

CS is one of them

[astral marsh]

its so welcoming isnt it???

look atthe princeton page again

[bronze pelican]

Ig

[wild lantern]

I'm shocked and surprised at how your school failed to establish a strong anime club.

[astral marsh]

like if i actually were president at some point this is how i would want it to be

well first of all i would get the shitty UI updated for our page

[torn willow]

[bronze pelican]

Yeah they were sharing the same room as the smash club and that this small room in the basement

[wild lantern]

I feel like not many people in the math program at my school are very into anime.

[vagrant kestrel]

most clubs need a professor to vouch for them

I think you see the problem

[inner finch]

sussin my way down town

[wild lantern]

I feel like you could convince a prof who teaches japanese to do it possibly?

[bronze pelican]

Trust me there are

Secret weebs

Weebs in hiding

There always are

[deep mango]

Sure

Everything was fine

Made it to the connection 20 minutes before boarding

[astral marsh]

ok this is not fair though like actually

Some past special events we've held include karaoke nights, origami nights, pictionary, debates, and our biannual jeopardy competition and 24-hour anime marathon!

On-Campus Activities are set to resume Fall 2021, and we've got some HUGE plans for our campus comeback. We hope you'll all be able to join us for what is set to be a brilliant year!```

why is the princeton anime club so well-run

[deep mango]

The one time I went to berkeley anime club some guy pulled me over to a table and taught me riichi mahjong from scratch

[astral marsh]

🤔

[deep mango]

It was terrifying

[astral marsh]

@deep mango

im done

princeton just has the better anime club in every single way

[ancient flame]

how many of y'all have a good understanding of the subject matter of all of the channels in this server?

[blazing pawn]

Why would u want to join an anime club

people in anime cliubs have bad taste

[leaden torrent]

define "good understanding"

[light needle]

Anime is the bad taste.

[blazing pawn]

no the bad taste is not obsessively watching everything produced by random directors from the 80s and 90s

also liking anime for straight people

Ok let me correct that liking anime for straight guys

[ancient flame]

@leaden torrent im sure you do

well the definition is arbitrary

but

like you could have a discussion with someone about this

or teach them about that area of math

[leaden torrent]

i could not discuss any of #numerical-analysis or #advanced-probability or #dynamical-systems with any confidence

[ancient flame]

I see

[leaden torrent]

and my knowledge of analysis is early grad at best

[light needle]

I couldn’t discuss any of the help channels

[ancient flame]

LOL

[toxic schooner]

i cant even discuss all of pre uni channels

[wild lantern]

I can't discuss

[toxic schooner]

[wild lantern]

I guess I can discuss some things. Pre university stuff is fine except I forget tons of stuff I shouldn't.

[brave hollow]

I can't even discuss #chill

[ancient flame]

lmao

[wild lantern]

Early university is hit or miss since I haven't taken stuff like complex vars yet and I'm trash at basic statistics.

I'm also not super far into undergrad courses in general though.

[ancient flame]

I could def discuss the pre u ones (except competition math) as well as calculus, I could do decently with multivar, lin alg, discrete math, proofs/logic, and elem number theory, and im currently learning some topology

so I've unlocked 10 channels

plus math pedagogy since im a tutor

[light needle]

but can u discuss #help-0

thats the hardest one

[wild lantern]

In comparison to a normal person off the street you know quite a lot of math if you think about it.

[pale orchid]

"average joe life" copypasta moment

[wild lantern]

Average joe copypasta?

[ancient flame]

yeah lol I would hope so since I've spent the last year and a half intently studying various areas of math

[brave hollow]

Average Joe mama ,
(I had to do it)

[ancient flame]

gg

[pale orchid]

The reason your dad is so disappointed is that he asks himself, "Who wants to raise a son who say yo instaid of hi and always take the lazt way?" instead of studying math. Math produces so many gems and visionaries because it is definitively hard, and has the hardest problems known to man, so men who consistently push themselves to solve adverse problems, will attain a generalizable ability to develop creative solutions to problems with ease as oppose to only dealing with the problems of a regular joe life, e.g. working at target and going to the local community college; people who have been through it develop street smarts and learn how to solve street problems, but you can only see so many street problems, there are thousands of math related problems in physics engineering and many other disciplines it is pure beauty! In fact, beautiful enough for him to ask you how that degree is coming like 3 times a month!

[wild lantern]

[ancient flame]

The reason your dad is so disappointed is that he asks himself, "Who wants to raise a son who say yo instaid of hi and always take the lazt way?" instead of studying math. Math produces so many gems and visionaries because it is definitively hard, and has the hardest problems known to man, so men who consistently push themselves to solve adverse problems, will attain a generalizable ability to develop creative solutions to problems with ease as oppose to only dealing with the problems of a regular joe life, e.g. working at target and going to the local community college; people who have been through it develop street smarts and learn how to solve street problems, but you can only see so many street problems, there are thousands of math related problems in physics engineering and many other disciplines it is pure beauty! In fact, beautiful enough for him to ask you how that degree is coming like 3 times a month!

[wild lantern]

Lmao

[brave hollow]

Combine this with the gem copypasta

[toxic schooner]

one of the best copypasta i have seen, ngl

[pale orchid]

the funnier part was that some random person agreed unironically

"I don't know the exact context of the above message, but I agree with many things in the message. Pure Mathematics in some sense, is only one of the few fields where there is certainty and we can get closest to truth, it is amazing how even things which a high schooler can understand like "Can every even number(>2) can be written as a sum of two primes?" is open and is extremely difficult. Rigour in pure mathematics is the highest, and in some sense deals with things in it's perfect form. And in the process of proving so, some get closer to their self actualized version in some sense in my opinion.""

[toxic schooner]

[limpid venture]

This does not change the fact that in Australia there are 48 million Kangaroos and in Uruguay there are 3,457,380 inhabitants. So if the Kangaroos decide to invade Uruguay, each Uruguayan will have to fight 14 kangaroos.

[devout nacelle]

🦘

[proven hornet]

kangaroos solo

[cold needle]

slimejesus

[devout nacelle]

Slimrhesus

[cold needle]

yes

[astral marsh]

Slimreeses

[cold needle]

Slime

[astral marsh]

I haven't had a reeses cup in a while

The candy

I can imagine eating one right now though

We've talked about this before, namely, discussing the differing extents of how we visualize stuff but also mentally simulate other senses

For me when I imagine eating the reeses cup I'm seeing it, I can imagine the taste, the texture

Not sure if that's different for anyone else, I mean, aphantasia is a thing right but idk about for instance the extent to which one's capacity to imagine taste or texture would vary

[hollow jackal]

my imagination is pretty shallow. it's clear to me what i'm imagining but it's nowhere near the real thing

[cold needle]

comedy

i can keep going

it's ridiculous

[sharp mulch]

...

[cold needle]

this is fun

i don't want to bully ange too much though

still you must appreciate my creativity

[pale orchid]

hmm

i have to say the 32 char limitation is a harsh one

[cold needle]

yeah its hard

yeah its hard

otherwise you could string many words togehter

[pale orchid]

"outback steakhouse" already meets all the requirements

also jack in the box

[cold needle]

lmfao

[pale orchid]

you had sullied me first and i was like i thought i made a funny

[nimble shuttle]

emptiness of fading midnight...

[pale orchid]

king of the burgers

[cold needle]

yeah 😔

[pale orchid]

fullness of waxing lunchtime

[sharp mulch]

Maybe in a bit I'll return to Chinese poetry

[cold needle]

yes

[pale orchid]

Eventual Return to Chinese Poetry

[cold needle]

this was a mistake

now there are several people with the ange nickname style

this is gonna be pain

[odd narwhal]

👀

[cold needle]

😭 WHAT

MORE

😭

[torn willow]

Hi

[modest rune]

only those who have read the prophecy will know which is the real ange

[sharp mulch]

Metal this is entirely your fault

[odd narwhal]

^

[cold needle]

yeah this is a rip

Influence of the Local Server Moderator

[pale orchid]

regretful influence of the moderator

[cold needle]

Considerable Regret.

[pale orchid]

considerable delay of tteppa

[odd narwhal]

what's tteppa

[pure sun]

[neat lintel]

hi

[pale orchid]

[odd narwhal]

yea I know

[torn willow]

Hi

[odd narwhal]

but like

why the p

[neat lintel]

my name was tterra but in russian once

[torn willow]

Yes

[odd narwhal]

who's responsible for the p

ah

[pale orchid]

you don't know the letter pho?

[neat lintel]

or it was greek

[cold needle]

LMAO drake

[neat lintel]

same thing

[cold needle]

fsdjkghlsdf

[odd narwhal]

lmao

[cold needle]

this is getting out of hand

[odd narwhal]

yea r in russian is just r isn't it

[odd narwhal]

I love pho, my fav vietnamese dish

[neat lintel]

p

[cold needle]

p

that thang bleedin p

wocky slush

[odd narwhal]

ah wait

right

[pale orchid]

smh

metal has caused the End of Ange's Whole Career

[cold needle]

lmfao

[narrow rock]

tteppa

[neat lintel]

lie derivative of the lie derivative

[sharp mulch]

Second Lie derivative

You know

Like second derivatives

[neat lintel]

idk sounds hard

[odd narwhal]

Sophus Lie was a mistake

[neat lintel]

the best part is

it's always zero

[rich cloud]

Is there a channel on this server where type theory would be on topic?

[modest rune]

#foundations

[untold sapphire]

#category-theory

👀

[blazing pawn]

Chuuni names

[sharp mulch]

I wonder who's fault this is

[pale orchid]

chuunitenar

[cold needle]

[light needle]

btw i have 2 hrs free now @odd narwhal @Tokidoki

rip fail

[odd narwhal]

Cool

[light needle]

how do i ping toki lmao

[odd narwhal]

It doesn't let you ping offline people on mobile sometimes

For whatever reason

[light needle]

ok yes get on here kek

[sharp mulch]

@tokidoki

[odd narwhal]

@thorn brook

[sharp mulch]

@thorn brook

[light needle]

https://discordapp.com/channels/268882317391429632/849776666161971240/872963057536618558

link to yesterdays convo to review or w/e

until toki gets here, he was online like a sec ago

[odd narwhal]

Meme review

[light needle]

oh he heas the studying role lmao

[odd narwhal]

Oof

[sharp mulch]

Lol

[zealous raven]

@opal linden ping

[opal linden]

[light needle]

ok he is gonna be here in a few mins

[opal linden]

that's 6

[light needle]

kek

[thorn brook]

ohhh lmao you guys were trying to ping me here

I'm too powerful for the pings, nice try 😎

[sharp mulch]

@thorn brook

[thorn brook]

NOOO

MY POWER

GONE!!!

[deep mango]

[astral marsh]

@fervent flame

[bronze pelican]

@noble lotus How is the SMALL REU project with Miller going?

[noble lotus]

Great!!!

Very very fun stuff

Proved a thingy

[bronze pelican]

Could you describe what your project was about ?

[noble lotus]

Yeah

[toxic schooner]

#❓how-to-get-help

[bronze pelican]

What was it about?

[noble lotus]

Sooooo

I was on like 4 projects

[bronze pelican]

[noble lotus]

Zeckendorf games, random matrix theory, erdos angles problems, and irreducible sets

And they all have different feels

And like

I will have like 6 papers with me as coauthor

But I worked most on zeck stuff

[bronze pelican]

which one was number theory

[noble lotus]

All of them and none of them

[bronze pelican]

[noble lotus]

Well erdos is definitely not number theory

[bronze pelican]

Did you do L function stuff with the random matrix theory

project

[noble lotus]

Nah

Fuck l functions

[bronze pelican]

🥲

[noble lotus]

L functions group spends all their time like calculating sums and bounding stuff which like

Good for them some of my best friends are on the project sounds neat

But is just not my kind of math

[bronze pelican]

sounds about right

Which one was your favorite project

[noble lotus]

Zeckendorf

was very baller

so like a Zeckendorf decomposition of a number is a way of writing it as a sum of non-adjacent fibonacci numbers

these are unique and always exist

and there's a particular game you can play called the Zeckendorf Game

which decomposes an integer as you play it

[bronze pelican]

I like dont get whats the motivation for considering this game

[noble lotus]

and it's known that the second player has a winning strategy

[noble lotus]

why not?

I never know how to answer this question

it's because it's cool

[bronze pelican]

It always felt random

[noble lotus]

always? Do you know about this stuff?

[bronze pelican]

not much

[noble lotus]

I mean it is kinda random

so is considering special weird ensemble number 5000 in RMT

¯_(ツ)_/¯

the methods are cool

so anyway

our Zeck group defined a similar game for base phi decompositions, which is where you write your number as a sum of non-adjacent powers of phi

and we proved a few neat things

[bronze pelican]

phi as in golden ration phi?

[noble lotus]

ye

[bronze pelican]

[noble lotus]

(1) The longest game on n tokens terminates in Theta(n^2) time
(2) The game is played on a tape, and the longest the tape needs to be is like Theta(2n)
(3) A slight generalization of the game to graphs is PSPACE-Complete
(4) We can generalize (1)-(3) to dominating roots of Non-Increasing Positive Linear Recurrences, aka NIPLRS
(5) The number of summands in a base phi decomposition of a number n in [L_i, L_{i + 1}] (lucas numbers) converges to a gaussian as i goes to infinity

The proofs of (1) and (2) especially in the general case for (4)

are like

surprisingly nontrivial

and for (5) I didn't work on that as much but

one of my colleagues essentially proved a new Central Limit Theorem

[bronze pelican]

do not google NIPLRS

[noble lotus]

[noble lotus]

PLRS is actually a common acronym in the field

[bronze pelican]

Your project sounds cool

[noble lotus]

I mean Zeck is like my main project and it's getting a lower bound of 3 papers

4 if you count conference proceedings paper for (1) and (2) seperately from the journal paper for (4)

and 5 if Hamming Distances gets enough by the end to write something good

and it's just like very very neat

and the methods are dope as shit

monovariants, foreknowledge proofs, some algebraic number theory to get (4), and this like weird bound iteration process I came up with to match coefficients on dominating terms

getting the dominating term coefficients to match is actually something I can't do in the general case

that is like

very frustrating bc it should be doable with some more work but ran out of time

guess that's for Future Work

¯_(ツ)_/¯

there's some cool results in other stuff to

we proved one of Neil Sloane's open conjectures about lunar numbers

[bronze pelican]

Watching the numberphile video rn

[noble lotus]

Lunar numbers are also related to like additive number theory /combinatorics too so it’s not just like

Rec math

Altho the two areas barely talk

[bronze pelican]

ahah

[bronze pelican]

[primal lion]

@cunning elbow

[hollow jackal]

i know it's impossible to answer this at this time, but when will math research plateau?

just looking for opinions from more qualified/experienced people

[ancient flame]

I don't think it ever will

more geniuses will come up with new ideas and potentially new fields in math that will have to be thoroughly researched

[inner finch]

geniuses like me

[ancient flame]

no

you can't even count correctly

[inner finch]

define counting correctly

[ancient flame]

the act involving correct counts

[inner finch]

define the

[ancient flame]

a word used to point forward to a following qualifying or defining clause or phrase

[inner finch]

define

[icy forge]

oh no

mirza broke

[ancient flame]

||
||

[devout nacelle]

Mirza existential crisis arc

Right after Mirza existential quantifier arc

[ancient flame]

look at my lizard

she so cute

[devout nacelle]

🐲

Nice

[inner finch]

lizzar

[hollow jackal]

he already got all your valuables

[inner finch]

d

e

[hollow jackal]

you just caught him mid escape

[ancient flame]

her*

[hollow jackal]

she*

[ancient flame]

gg

[hollow jackal]

wp

[inner finch]

lizzaerfd

[ancient flame]

mirza has gone bonkers

mriazra

[inner finch]

mrrri

magnetic resonance imaging za

[cold needle]

mizza

[inner finch]

mriza

[toxic schooner]

pizza

[cold needle]

mriazma

im hungry now

for pizza

oog

in other news friends my summer semester is coming to a close soon and i only have one more final exam left to work on due tomorrow at midnight

kind of hyped to get it over with

a proper break is needed

[toxic schooner]

[timid spindle]

why do startegy based games have mathematics as research option for ranged weapons ?

[untold sapphire]

you need some dynamics to develop ballistic weapons

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

[timid spindle]

idk it should be named physics.
math should be only allowed in creative mode.
too damn dangerous 🙂

[timid spindle]

now I am just staring at the points go weeeeee over and over

[brave hollow]

I bet black will win

[thorn brook]

How much free time does a undergrad in the first year have?

Like approximately

A lot or absolutely none

[timid spindle]

a lot/2

and it decreases rapidly

[devout nacelle]

Depends

[autumn raft]

dang

[thorn brook]

Because exams and stuff?

[wraith trail]

Depends what major for sure

[devout nacelle]

Assignments/exams, studying on your own

[thorn brook]

let's say bsc in math

[devout nacelle]

Yeah, major/selection of courses, and most importantly how you respond to them matters a lot

[wraith trail]

And depends where u start too as in college credit etc

[devout nacelle]

For example you're the kind who'd probably devote a lot of time to learning beyond the class as well I'd wager

[thorn brook]

well that's the thing. I really want to continue doing stuff that I'm doing now, but I don't know if I will have the time

[devout nacelle]

But standalone, first year at uni isn't generally supposed to weigh you down, especially if you already have a hang of working/learning on your own

[wraith trail]

Also depends on how active u wanna be in college too (sports working out clubs…)

[devout nacelle]

You should have enough time imo

[thorn brook]

yeah okay got it. Thank you!

[wraith trail]

And definitely how many credits ur taking

[thorn brook]

yeah I think that the credit system here is different idk

but I will be taking like 5 courses

or 4

[cold needle]

i made it so i didnt have a lot of free time (mistake)

[thorn brook]

crap, that doesn't sound nice...

[wraith trail]

I had a good bit last year, this year might not. I’m taking 18 credits (6 classes)

And on top of that I’m already in like 5-6 clubs two bands and I work out and gotta prepare for internship interviews

[thorn brook]

I think that I will be taking 15.5, which isn't a lot, right?

[wraith trail]

No 15 is average

[thorn brook]

ah okay great

Thank you!

[wraith trail]

They want u to do 15 a semester to graduate on time most of the time

[vestal river]

Does anyone know where I can find a copy of Evan Chen’s EGMO it looks like it’s out of stock everywhere also it’s a bit pricey

[blazing pawn]

im surprised its not free online?

[vestal river]

Oh maybe it is I’ll check more sorry

[primal lion]

try libgen

[primal lion]

it is legal!!!!!!!

totally not illegal

[deep mango]

jon sully does not represent the views of this server

[nimble shuttle]

it's true

but I am a Law-Abiding Citizen

[deep mango]

i could find a reason to get you locked away for life.

[cold needle]

we do not endorse piracy

[blazing pawn]

Don't post links to pirated materials or endorse piracy here

[neat lintel]

“We don’t endorse helping people save money by not needing to fork over egregious amounts to enormous capital giants”

You realize it’s in essence file sharing?

It’s not stealing if someone bought and uploaded it for others to share

[blazing pawn]

Its not a moral thing its just against discord TOS lmfao

[neat lintel]

So it would seem

Very well slime

[slim meadow]

Imagine letting a 12 yr old mod ur server lmao

[latent forge]

Ageist Propaganda

[cold needle]

zoph is right

the sooner this server removes mod as moth the sooner we will return to our former glory

[sharp mulch]

Mod as moth

[cold needle]

fuck

its 5pm ok

i am not okay at this hour

i have no excuse.

[bronze pelican]

I endorse piracy

[cold needle]

I endorse banning u

[sharp mulch]

[cold needle]

honk thonk

ok back to packing my things

oog

[inner finch]

i endorse deez nuts

[hollow ginkgo]

Solution: start a competitor to Discord.

[blazing pawn]

Owned

[azure kettle]

based

[grim token]

@crystal stone

Moon bears

I have great news

I convinced me mum that Cal CC is decent as f

It's the best backup plan

[sharp mulch]

Lol

[crystal stone]

congrats!!

it's just so cheap

and you can even take uni courses while at CC

[grim token]

Yeah Im really happy

It's like the pressure is taken off

I can actually learn because I want to now

It's weird to explain but yeah

[vivid halo]

I mean certainly do it if it's a final backup plan

most community colleges are quite bad compared to other colleges and universities

[grim token]

My HS GPA is scuffed nGroupoid

[vivid halo]

Ah, there you go

[grim token]

So I have no choice

[vivid halo]

I'm assuming you did not get in elsewhere?

[crystal stone]

I don't think this is accurate in California for lower division courses

[grim token]

I didn't apply yet

But I have 3.6 and 4.9 gpa's

[vivid halo]

that seems perfectly fine

[grim token]

So not good enough for the top, but if I can transfer through CC

[vivid halo]

for something better than a community college

[grim token]

I can get there

[vivid halo]

I mean you can also transfer from not a CC lol

[grim token]

it's not as easy

[sharp mulch]

Most undergrads at UCs start upper division courses their second year

[vivid halo]

I'm just saying the plan of "start at CC and transfer to a top school" is a lot more risky than you might realize

[crystal stone]

You can also do this while attending a CC

at a UC or CSU

What's more is the class you take is at a CC prices

[blazing pawn]

a 3.6 is fine

[crystal stone]

You just need instructor permission

[blazing pawn]

[crystal stone]

For Berkeley, UCLA, Irvine, SD, and SB

The rate of transfer is a lot higher than you'd think for math

For private colleges it's harder to transfer in

But USC has been accepting a lot of CC transfers lately

[grim token]

Im looking at your website Moon Bear

https://www.universityofcalifornia.edu/infocenter/transfers-major

And IM trying to find a CC with good applied math acceptance

[blazing pawn]

this seems kind of silly just because like

you should probably talk to your counselor if you have one

You're not in the kind of position where strong state schools are inaccessible to you because you have a 3.6

[grim token]

Nothing is guaranteed for me tho

[vivid halo]

Apply anyways

[grim token]

I mean forget my overall

[blazing pawn]

Nothing is guaranteed for anyone

[grim token]

I had like 3.0 freshman year

they see that

[blazing pawn]

Thats why you see where you get in and then make decisions

[grim token]

and I am immediately rejected

[vivid halo]

Honestly settling for a CC because of a reasonable GPA is moronic

[blazing pawn]

Didnt we literally have this conversation where people pointed out to you that upward trends are actually viewed favorably

[grim token]

Idk

yeah but I was thinking that

[blazing pawn]

No one is going to autoreject you because of a 3.0 in freshman year

[grim token]

I guess

[vivid halo]

Seriously reconsider

[blazing pawn]

No you dont "guess" this is a fact lmfao

[bronze pelican]

Reject yourself before admissions can reject you

[grim token]

but still I am making a good backup plan

[bronze pelican]

That's the way

[vivid halo]

Okay it’s only a backup plan if you’re seriously applying to other state schools

[blazing pawn]

some schools dont even look at freshmen year gpa

[vivid halo]

I hope you are doing this too

[grim token]

I am applying to Cal Poly and UIUC

but thoseare ugh

[vivid halo]

Alright solid, apply to more

[blazing pawn]

UIUC is great for math

[vivid halo]

Also yea what

[blazing pawn]

Hurb

[grim token]

idk

[vivid halo]

UIUC is great

[blazing pawn]

we LITERALLY also had this conversation

[grim token]

I KNOW

[vivid halo]

Apply to more schools like this

[grim token]

ok I will have to think of some

[vivid halo]

Fight to go somewhere that isn’t a CC unless you have a really compelling reason to do so

[grim token]

maybe I can find a top school and do early decision

[crystal stone]

California CC's are free

[grim token]

yeah

[vivid halo]

Apply to like 12+ places idk

[crystal stone]

I really think CC is the way to go

[vivid halo]

I really disagree

And this is coming from someone that went to a CC for free

[grim token]

it would be very bad if I get stuck at CC

like I don't get transfer acceptance

that would be horrible

[vivid halo]

I don’t regret it but I also don’t think it was the right decision

[grim token]

I would die on the spot

[vivid halo]

You will, it’s easy to transfer

It’s just like

[blazing pawn]

Why not apply and see your finaid and then make the decision

[vivid halo]

Something that puts you at a massive disadvantage

[grim token]

yeah

[vivid halo]

Absolutely huge disadvantage

[grim token]

wdyM?

im scares

[vivid halo]

You are effectively giving up two years that you can have at a respectable department and building connections there

[grim token]

scared

yeah ur right

[vivid halo]

Unless you’re genuinely like mathematically disabled and can’t gain benefit from anything other than the base classes

Then this is a huge disadvantage

[grim token]

i rly wanted to go to UCB and UCSD

I guess I have to look elsewhere

but its tough

to find good options

[vivid halo]

Do you have plans for grad school?

[grim token]

Yeah I want to do it

[vivid halo]

Yea so like

Go somewhere like UIUC or whatever

And then you can work up later

[blazing pawn]

UCs dont even look at freshmen year GPA

[grim token]

yeah

[grim token]

let me check my soph gpa

[blazing pawn]

I just think ur massively overestimating the negatives of having a 3.0 in freshman year

and a 3.6 overall

[vivid halo]

The main issue is that especially if you have some idea of wanting to do mathematics, CC will just not give you the right environment for you to thrive, end of story

The main issue is that you are then facing a huge uphill battle to get the proper environment and advisors and so on that creates a good graduate application

[grim token]

hmm

yeah I see

[crystal stone]

I think this is relatively inaccurate

there are plenty of CCs with good math environments

[deep mango]

my perception of all the CC students I RAd was that they were all super hard working and self-sufficient, but at times that wasn't enough for the amount of catch-up they needed to do especially in terms of research and grad classes for PhD applications. e.g. one physics transfer who i RAd had an extremely rough first semester because she had to do so much right away and didn't have time to adjust to berkeley rigor.

[grim token]

ra?

[vivid halo]

lol which ones

[deep mango]

while it is totally possible for CC to lead into math well and to produce a well-rounded, healthy PhD student, it takes a lot of really dedicated work in those last 2 years of undergrad.

[grim token]

yes

[vivid halo]

I went to one with a good math environment and even that was very anemic

[deep mango]

resident advisor (in dorms)

[crystal stone]

Fullerton College, Orange Coast College, Santa Monica College

all have solid math programs

Prof. Dana at Fullerton actually has students do seminars

Moreover, while you're at CC you can take UC or CSU courses at CC prices

Even in math

[vivid halo]

okay then that might be okay

I still don't think it's worth settling for unless you have better reasons

[crystal stone]

At Orange Coast College we had proof based math in the calculus sequence and up

[deep mango]

i mean this is totally different depending on the CC you go to, but i agree california CCs near UC's are probably quite good

[crystal stone]

Ending on Spivak's calc on manifolds

[grim token]

how do I see which schools are good in Applied math? I dont know what ranking to. look at anymore

[deep mango]

like CCs near me here in NJ are.... never gonna teach you anything besides strang-level linear algebra.

[leaden torrent]

dont look at rankings, look at faculty lists

[grim token]

What about faculty lists?

[deep mango]

for undergrad???

[crystal stone]

The linear algebra I had at CC was combined with differential equations, and we had to prove rank nullity on exam, had to prove independence of eigenvectors given that eigenvalues are unique

[grim token]

Like teacher publications?

[leaden torrent]

oh

[vivid halo]

not even just like

[crystal stone]

So if you look around, you can find a solid program

It's mainly be word of mouth

[leaden torrent]

for undergrad thats too much

[vivid halo]

look through who is there, look through what they do, if they run student seminars or whatever

[leaden torrent]

just look at course offerings then\

[vivid halo]

for undergrad you don't have to be as thorough with this and things like course offerings or coarse ranking are probably more indicative

[deep mango]

i don't think this experience is representative of the typical "good CC" outside CA.

[grim token]

So I should disregard ranking?

[leaden torrent]

how much applied math do they offer? how much dyn sys? etc

[vivid halo]

but it's still working looking through

ranking matters a little more for undergrad

[crystal stone]

But if you're in California, and you look around for a decent CC

It's very good

[blazing pawn]

are cali CCs free for non cali residents

i doubt it

[deep mango]

this is correct

[vivid halo]

but still look for what courses they offer, who is there, what kinds of things they offer

[deep mango]

i will often judge the quality of a math undergrad program by their course requirements and elective offerings

this isn't a perfect way to look at it of course

[leaden torrent]

also check how their programs are structured, 500 applied math courses wont do you much good if you can only take 2 of them due to all your electives

[grim token]

What is "Academic Decathlon GPA" ?

[deep mango]

but at least it tells you you have the opportunity to dive deep into a subject you like and to develop breadth elsewhere, which is what's most important.

[deep mango]

keeping in mind that some schools are a lot more flexible with this stuff than they look to be on paper (and some are not)

[blazing pawn]

MIT moment

[grim token]

Idk I fking give up on univeristy of california

its impossible for out of state

[blazing pawn]

Why

Some UCs have better OOS acceptance rates than in state

[grim token]

You need to be perfect to be the 1% of out of state

[blazing pawn]

Lol

[grim token]

not UCSD

[deep mango]

you really don't

i mean

maybe now for some reason

but i was absolutely not perfect

[grim token]

My gpa without freshman year is 3.769

[deep mango]

covid was really weird and idk how that affects things

[grim token]

Is that what UC will see?

[deep mango]

they will calculate what they want to calculate to perform a """holistic""" review

[blazing pawn]

UC in San Diego admitted 51% of its out-of-state applicants compared to the 26% of California residents who applied that were granted admission. The numbers look similar at UC Santa Barbara, with 29% of applicants admitted being California residents and 47% coming from out of state.Nov 15, 2018

Again not true

[deep mango]

tbf

[grim token]

Bruh what

[blazing pawn]

those students probably skew stronger but still

[grim token]

I have an app that tells me these things

[deep mango]

the people applying to UCSD oos

[blazing pawn]

Its absolutely not remotely 1%

[deep mango]

are gonna be on average better

[grim token]

UCSD has like 3% our of state

[blazing pawn]

That is absolutely not true

[deep mango]

yeah that's not true

[grim token]

yeah im taking this into account as well

[deep mango]

berkeley OOS my year was like

10% or something

[blazing pawn]

this app is clearly bad

[grim token]

thats still difficult man

I have decent EC and decent attributes/story too tho

that's my main ticket

if I can get these esssays good

but it sucks that its so hard

for OOS

[blazing pawn]

I know people with GPAs equivalent to a 3.6 that got in

[grim token]

rly?

[deep mango]

idk like

[blazing pawn]

urs is probably higher because freshmen year is ignored

[deep mango]

berkeley and ucla are also very expensive for OOS

even though i loved going to berkeley