#serious-discussion
1 messages · Page 524 of 1
like this formula was just created and then held as a reference point
no one was ever able to prove that this is real to me
until today, when i saw this marvellous thing
this is... kind of circular? it implicitly assumes you can differentiate complex trigonometric functions
which the power series definition ensures you can do, yes, but if you havee that definition then you can just take the sum directly
the power series one was always sus to me
how
with infinite sums you end up having wierd things that are untrue like
1 + 2+ 3 + .. == -1/12
because nonsense like that is possible to bring about with infinite sums
a proof that doesnt rely on it makes me feel like its more rigorous
use of power series in a proof is perfectly rigorous so long as you use them appropriately
you don't get nonsense as long as the series is convergent
absolutely convergent, in fact
indeed
algebra is BULLSHIT because i take the square root of (-1)² = 1² and get -1 = 1
for e^z = 1 + z + z^2/2! + etc.
here how do you prove that z^n/n! tends to 0 for any z
this proof uses ℝ but the argument is the same for ℂ
somewhat more direct: just use the root test lmao
here how do you prove that z^n/n! tends to 0 for any z
also fyi: this is not sufficient to prove their sum converges.
it doesn't work for the harmonic series, for example
the proof using real analysis makes it more clear due to some inequality rules that make it akin to a geometric series, which converge if < 1
hola, slurp

Where’ve you been?

finals and ib and ap exams
fuck offffff im so tireddd
Tf is ib tho 
I have been stuck
on a single Euclidean geometry problem for almost 4 hours
and I can't even get bailed out by #❓how-to-get-help this time because it's a take home final

this is for my topics in geometry class
covering topics from the basic (differential geometry) to the agonizingly advanced (Euclidean geometry)
like we only spent the first 2 weeks on Euclidean geo before moving on to more advanced stuff
it's just differential geometry with R = 0
but there's a question about it on the final
that I'm pretty sure would be suitable to ask highschoolers
and I cannot for the life of me figure it out
I might just look up the answer in Elements 
the prof said consulting that book would be fine, but I'd also feel bad doing so since the book would likely just have a complete proof
it's a final
it's do or fuckin die
you use every scummy underhanded tactic for every single measly mark
you kill a man for an extra 3 points
no mercy
I feel like I can probably figure it out on my own
besides I just moved back from college and I'd probably have to dig through my stuff for a few minutes to find my copy of Elements
Heh
ok I think I've almost solved it

it's funny. I don't think it was actually a hard problem, I just had no idea how to approach it
I have no real intuition for what steps to take
Me in discrete math
see discrete math I can do
on the bright side I honestly feel less hopeless with geometry now
despite struggling with what is arguably a hs geo problem for almost 5 hours
that is me
you do model theory wew?
you think I've got the foggiest idea what a circle theorem is
anyways euclidean geo is starting to feel less like something I'm hopelessly bad at and more like something I'm inexperienced at
what is fluids
fluid dynamics
its funny because all of math is also geometry
it's honestly been sorta fun
aka my favourite area of maths
which leads me to deduce geometry = model theory
can you send the problem after your final
ping me when you do
wait did you solve it already
not yet
is it cheating to send and not get help on it
but I think I finally have the right approach
i just wanna see it
but it’s physics
geometry \subset model theory
physics \subset matth
I mean it doesn't really matter in the scheme of things
it's applied maths ;)
physics = math confirmed
like the prof would literally never know
wait
this inclusion is strict
physics subset math
😕
physics makes observations using experiments
why isnt agriculture considered math
and I think in the long run it's probably a good experience to spend hours struggling over a problem and getting nowhere
we have fields, sheaves, etc...
crop "circles"
I'll likely be doing that a lot this summer in my REU
trust me loch, we’ll get there eventually
if its take home maybe take a walk
and give it some time off
whats reu
research experience for undergrads
niceee
I got a really nice one
I'm not going to dox myself which exactly
cool
I think it might have some geometry in it?
or like one of the projects is maybe geometry
but I'll probably be able to avoid that part
hopefully
well congrats 🥳
I mean it's really just euclidean geo that I have the hardest time with
if I can put coordinates on it then it's less hard as it is just annoying
say what you want about Euclidean geo, at least it doesn't have trig functions and integrals
hmm yea i guess
I'm taking a break and then coming back to it after dinner
I
gl buddy
will post the problem on Monday after I submit the exam
if you dont like trig functions and integrals, you are going to have a bad time at some point...
react to this message if you want me to ping you when I do
REOs
Research experience for overgrads
I'm an overgrad
is it easy to get undergrad research
I'm over it
it's hard but doable
almost all unis offer programs, as for how competitive they are idk
Supergrad
i’m predoc
subgrad
you need to apply to a bunch of programs and get lucky
just like a PhD
imagine applying for a phd 
I'm crying
but the sense I get is that if you're the kind of person that would succeed in one of the programs and you apply to a bunch then you'll probably get something
isnt that the whole
i'm a pre-pre-postdoc
lemme appply to 10 10% acceptance unis and get into atleast 1
I'm a Perfected Ultra Instinct grad
this is literally what you do for research positions lol
W
you gotta do a shotgun approach
i guess
lucky im in highschool
and just approach members of my local uni for jobs <333
i mean this is what you do when applying for most things
me applying for janitorial positions at every engineering firm in the world
i think they subcontract
I have no fuckin clue what that means 
they dont employ janitorial staff themselves
they pay a company to take care of that
wew janitor tbh
I'm going up
cause your brain is small
going up to wat
oh roasted omg roasted
the moon
how will you recover wew
recover from what
where
what
i did not mean it
huh
wew blurry vision tbh
wha
You can get the exceptional automorphism of S_6 by constructing an exotic embedding S_5 -> S_6
The usual way to construct the exotic embedding S_5 -> S_6 is by thinking about Sylow 5-subgroups of S_5
ok I kind of get this embedding
But I have another way
very peculiar
go on?
Consider the complete graph on 5 verticies regularly embedded in the torus
How many ways are there to color the 5 faces of this map with 5 distinct colors?
I claim there are 6 ways
I think I see where you're going with this
Now I have a set of 5 elements: the colors
And a set of 6 elements: the colored maps
Any permutation of the set of 5 colors induces a permutation of the set of 6 colored maps
This is an exotic embedding S_5 -> S_6
◉◡◉
matches up with each of the conjugate subgroups that are acted on in S_6 being cyclic order 5
Wdym
That's really cool yamin
is there a branch of maths that studies sequences/series or does that sort of go into analysis
that's def analysis
People would call that "hard analysis" usually
Thats not exactly what hard analysis is
But the vibes are right
Tao wrote a very good blogpost on it
But the main difference is that hard analysis is all about quantitative estimates while soft analysis is all about inclusions / implications
So functional analytic methods usually offer the latter
And increasingly people are caring more about the former
Certainly
But there are subfields of analysis where the standard toolkits are very "hard" (like analytic number theory)
And subfields where the standard toolkits are very soft (like pdes)
So e.g. right now there is a program where people are taking it upon themselves to quantify lots of known PDE estimates, since there are increasingly many hard methods which can take advantage of stuff like the actual size of constants in an asymptotic bound.
LOL
tfw pigeonhole your way around the non-existence of angle-side-side
one of these triangles must be congruent so I'm good
Hello everyone I am studying for act what math should I master before taking the test?
Maybe find a study guide?
And try some practice tests
When I took it there was nothing super hard, the challenge was just you had to go super quick
yea I just missed out on alot of math classes in my earlier years of HS so I dont know how to do much math
Then it sounds like you have a lot to review
I'm not sure if there's anything we can give you that a study guide or a (few) practice test(s) can't
I can’t chose between abstract or anal
Gotta chose one
Abstract algebra is more fun
do it
why you gotta choose
is there any structure with a sort of specialized inclusion (like subgroups, subfields, etc) that also has the property that if A is included in B then the automorphism group of B is a subgroup of A
both have their fun moments and their "oh my god I fucking hate this" moments
both are required in a math degree
both can be studied simultaneously
I plan to major in electrical engineering I just do math because I have no other hobbies 
This is a property of fields but is there any other structures with this
do I have every white role in the server
No
oh true
I am tutoring my sister in calculus 2.
my condolences
I used to have the chess role then it disappeared.
I should get rid of my irrelevant roles
can I have banach_alg_hermitian_involution
I can give you back the chess role plegasus
Also I hate when I have too many roles. Similar to how I hate when I am in too many servers.

I am only in two servers right now.
im in 7
I only use 2 basically
I can't handle more than 3 for some reason.
now im in 5
lol.
2 are for legit math communities
Not legit but
Like
Professional
One was my old secret hitler group which hasnt been active for a long time
Sigh
what?
Secret hitler is a board game
!
Its like mafia
oh, lol add that next time.
You cant lie in chess
ryc is a nazi!!!!
I suck but its fun.
my elo is 154
“I’m gonna attack his queen don’t tell him” - GM Ben Finegold
Im also horrid at chess
Ryc you want a game of chess?
Annoying thing in chess right now is dealing with enemies knight.
I play Minecraft but dont tell my parents they think I have a job
I thought you did have a job
I do
I haven't played minecraft since highschool.
We had a minecraft server here
aren't you in highschool gmod.
lol
I made an abelian grape vineyard
well technically I finished but my graduation isn't for another 2ish weeks
All I do in minecraft is blow shit up.
Lol
All I do is speedrun and make computers
I pvp in minecraft
And bed waurz once in a blue moon
I play good games like terraria instead
congrats. I am guessing your majoring in maths.
btw this is a quote from a youtuber
no im majoring in business
Sounds boring af.
maybe a math minor but I feel like a CS/info science minor would be more useful
business is cool as fuck
Info science
Hi anamono
What are you drinking
Oh its Saturday
You went to a party
What did you drink at the party
Wait it was Saturday yesterday?
ive had
so far
a screwdriver
a shot of pink whitney
a shot of vodka
a jello cup
a shot of sake
i am intact
Got damn
ok now im mixing fireball w some berry soda
not bad
tastes like hot tamales
shot of malibu
i am stull at the party :D
Nice
I haven't drank ever
My uncle came over and left it on the table. So I drank it. Tasted horrible.
Lol
but it's crazy now that I'm over 21 realizing it would be entirely legal
yeah.
It tastes better with practice
I almost had my first ever drink a week ago
there was a big end of semester event on campus and there was free beer
I was offered a mug
Probably shit beer
Too be honest all I am going to try is wine.
I just know there’s a big chance I’ll become a big alcoholic if I ever drink
So I’m never touching alcohol except as a way to clean stuff
there was a hard cider too
yeah this somewhat concerns me
Tfw For external use only
scotch is wonderful
I think I'll probably be fine
Yeah
I don't think it almost ever looks like "had one drink -> becomes an alcoholic" but you should do whatever makes you happy and comfortable so ofc its fine to never bother
oh yeah ryc I liked your latex talk. It cleared up a few things and from now on using overleaf for doing exercises.
Thanks!
ryc what's the best whiskey/scotch you've had
I appreciate you watching it
Something my uncle brought to a family gathering, idk what it was unfortunately
lmao the game of thrones edition?
It was very nice, but i dont have enough experience to really know how to compare it
It makes a lot of sense that my uncle would get game of thrones whiskey
I should have started looking with that in mind
hahaha
im so gone
need 2 pace myself
only 9
i can still drop that ass tho
but i will adhere to my moral code
like no inappropriate contact

are you drunk
perfect time for doing math
in the discord channel?
heh had some spare dollars from my grandparents
really nice
just now I was meditating on whether to spend a bunch of money on the springer sale or not
all of these interest me and are on discount rn
Hmm so maybe a good way of thinking about it is
If you're concluding that an operator is bounded because of the closed graph theorem
That's soft
If you're concluding that an operator is bounded because you bounded it
That's hard
Is it just me, or are they allowing complimentary downloads of their books?
what is a quarter inch smaller than 3.46 inches
I only have two of that.
Also where did you get that nice copy of Hoffman and kunze. My looks terrible.
Look at that nice specular reflection. That a brand new copy you have there.
it was at a large bookstore place
i live in korea so i doubt you can go there
but
yeah it’s my first time even seeing books like these in an actual store in korea
there's a recent-ish edition of H-K, might be that one
also looks like it's paperback?
most stores only had random books that looked like they were from the 18 th century or stewart’s calculus
yeah
it was the only one they had
only dummit and foote was hardcover
unfortunate but i gotta make do with what’s there ig
Physical copies of math books are so expensive
One can simply get them in the totally legal way 
rudin 
if you need any help with rudin, please feel free to ping me
I won't guarantee I'd be helpful
but at least we can mold together 
mold 
gotta set their expectations right lmao

i can hop in to mold together as well

rudin has a lot of resources and solutions
thats the good thing about it
bad thing about it is that it is old as f**k
and very unforgiving
I'm pretty sure all advanced texts aren't that different
it's not impossibly hard
not as self study but accompanied with resources like lecture vids
idk man
i wont want anyone learning analysis for the first time to jump into rudin
I'm using Lang/Abbott
especially if they havent done much proofs
they seem to be pretty accessible
lang has an analysis book?
yes
apostols book is also amazing
it has full solutions
written by shakarchi
no

SS?
its sold separetly
oh ok lol

but if it has solutions from the people from SS?
making it not a good choice for first learners
thats amazing
popular book writers
who wrote 3 books on analysis
iirc

4 books
from my colleagues: depends on the professor
the professor in my university teaches the whole book in 1 semester

and another professor teaches real analysis in 1 year
so technically fourier is harder in my school
Oh
I was super confused what the Nazi police had to do with anything 

wha
The Schutzstaffel (SS; also stylized as ᛋᛋ with Armanen runes; German pronunciation: [ˈʃʊtsˌʃtafl̩] (listen); "Protection Squadron") was a major paramilitary organization under Adolf Hitler and the Nazi Party in Nazi Germany, and later throughout German-occupied Europe during World War II.
It began with a small guard unit known as the Saal-Schut...

Lmao
I heard the same word yesterday
is rudin a must read in analysis
or can you just read other books like zorich/lang/tao and move on?
it's not a must read lol
there are a lot of different analysis books; you can read whatever fits you best
for bragging right? yes
for anything else? not rlly
oh ok
most book in intro mentions analysis in level of rudin as prerequisites
so I thought that the rigor in the level of rudin was mandatory
Other books can be just as rigorous
They just name rudin probably because its one of the most well known and established RA books
rudin is well known so it's a good benchmark
doesn't mean you can't get the same understanding from elsewhere
I have heard from ppl here that Apostol and Abbott is good so you can try those out with Rudin and see which you like the best i guess
Does anyone else use homework sets on course webpages to decide which problems to do when studying a topic from a book?
For example: https://www.math.tamu.edu/~ken.dykema/Teaching/608/
I find it really hard to search for assigned problems for a given book though
And I don't really know what problems to choose otherwise and I don't want to just do every single problem
would anyone be able to help me in help channel 2?
smth about shitty college student beer tho
it’s shit natty light or smth but still tastes kinda good cos ur w people
🤨
dont gimme that
Question : What else do we explore in ML save for decision trees?
save for decision trees?
What is that supposed to mean
Other than decision trees?
yeah
Are u talking to me?
yeah

decision tree are like one of the least exciting parts of ML
isn't there a bunch of theory behind constructing trees?
Gotta realize, I'm a goddamn rookie in ML. . . .I got a good grade in intro, but I'm learning like. . . . 5 different technologies right now, and I'm trying to stoke myself up for ML.
"besides decision trees" is what it means....
like isn't it one of the main ML algorithms
yes
Well, what are some of the MORE exciting parts? I'd like to know!
basically a form of nonlinear regression
a myriad of things
yeah there's a lotta models
I find generative models particularly interesting
but they're kinda technically to get into first hand
Ooooh, sounds cool. Wat dat?
neural networks, various forms of regression, nearest neighbors and their variants, etc.
have you ever heard of thispersondoesntexist?
I remember neural networks now! I got introduced to that via mar.io.
Yeah!
I wonder if the website is still up
Ml algos other decision trees
The main ML algorithms excluding deep learning are :
Support vector machines
K means clustering
well, all of those faces were gotten from a generative model
Well I'm definitely looking on wikipedia for what a generative model is now.
The last two are modifications to decision trees
And are the main algorithms in ML
lmao
In deep learning neutral networks and many artitectures of them
like some for sequence
Some for images
Some style transfer
Etc
I couldn't understand what's so funny in that 
And all we're doing with this shit is selling stuff and manipulating ads???
Yes they are but ML algorithms are also necessary
Deep learning is used when we have more data
Which now we do
Because of advancement of tech
Not only reccomendations they generally don't use deep learning
They use k means clustering or knn
Probably
Hmmm. . .I see!
for example, it's almost always better to NOT use nn for tabular data
bruh
I'm not sure about that
it probably depends
Question : for ML to be effective, you need to typically feed it samples, right? Is this true for only decision trees? Or does this generally apply across the board for ML?
Answer (1 of 25): TL;DR: The main takeaway is that you should adopt a pragmatic approach. Specifically, start by considering the expected data availability for the next six months, say, and then build a recommender accordingly. Your choice of algorithms should fit your data constraints and of cou...
Look here to get insite if u want
Don't ignore ML algorithms topic modelling still uses LDA which is not DL
but you don't need data for reinforcement learning for example
That's true
But in general
When u have tabular data
Which not many columns
Try Ml algos
Deep learning neural networks overfit many times from my observation
In such cases
note the age of these answers
that's what I said #serious-discussion message
Oh i confused the too many nos

U mean they are old????
Ig the standard way for recomendation engines
Which I learnes
Is singluar value decomposition
we had transformers in only 2017 and those are game changers
Damn!!!
it was found in nature duh
anyways, we digressed a bit too long
@neat lintel if you want to get motivated about learning ML you can watch a documentary or something
nowadays, ML is ubiquitous
Way I see it, small businesses need it to survive in a world of big ones.
When we have that, THEN its ubiquitous.
you hardly can do anything on the internet without interacting with some ML algorithm
That honestly says more about the agencies who own the most web space than it does ML.
I mean doesn't Amazon have 60% of the web under its control?
eh
through AWS?
that's kinda irrelevant
its not. . . .
they own the servers
Like at all. . ..
but not what runs in them
Ask Jeff Bezos or his replacement.
if the big guys are using ML they're probably using it for good reason, don't you think?
besides, ML doesn't only have applications in the industry
Well if u won the server then u kinda can control the website
Even if a bit
Sure, but what I mean to say is that the BIG guys are ubiquitous.
ML ? Eh, not exactly.
Its a tool used by the ubiquitous and used by them a lot, but its not used by the populace.
Google is ubiquitous because its used by the populace. As is Amazon and Walmart.
Anyways, that's my ted talk. Gonna find that documentary after Coursera and meditating.
ml is ubiquitous, you just often don’t notice it
True
that's like saying code isn't ubiquitous coz not everyone codes
that's what I'm saying
true, but irrelevant
Its not ubiquitous though. . . .To comptuer scientists its ubiquitous, to businesses in tech its definitely ubiquitous.
But code isn't everywhere. . .
Dude what
do you live under a rock
Is code on a farm?
Is code in a gym?
How did u just sent that message
farmers use ml to control inventory
It nowadays is
look at their plants
Dude, what???
control sprinklers
Ur literally talking to me
gym membership systems use code
everyone interacts with physics daily but not everyone is isaac newton
does that mean physics isn't ubiquitous in our lives?
Alright, guess you're right.
Lmfao programming most useless thing in today’s society
true!
Delete discord then?
Thank you!
this is a hunting and gathering society anyways tbh
It's a creation of code
hello slurp 
I don’t see how you got from point A to point B
perhaps today i shall find an elk!
Discord is just a bunch of code
Seevers
Anamono i hope your head is okay this morning
Good morning!
it is very good
And developers work
i got home safe and am not hungover
Sharkpog

just a bit sleepy
So…? I hope you understand why that’s a shitty argument
Im jealous
look at these cats they had!
When the mod cusses
so cute
Cute
Cuteness overloaded
I feed on attention!
oops
pi creature yes
hello ryc 
Hi darth guappi
3b1bs pi creatures
Hi ptyamin
God fucking dammit ryc
Oh ab was here too. Hi ab
I’m gonna go get blo’s attention then
Who cussed?
wut
i see no cuss words

Wait what
if i did, i would tell my mom immediately
Cussing is a-okie here, why are you commenting on it
What's this
a statement
Oh shit a bunch of messages just loaded for me. Wow
The second word 
again if i saw a cuss word i would tell my mother
I'm sorry for ignoring you shuri
please forgive me
yet i do not see any

Time to bring the cuss detector I trained
@long matrix uwu
I thought the person u tagged left the server
She is still there 
Didn't knew it
shuri is a he
Oh ok ok mb
I dont plan to
Ok I feel like bots don’t like me.
who plans for their death? lmao
Another person with active role.
Depressed people

Plegasus has a capitalized P again
Who wants to commit suicide
shit you're right
those people
I was deciding which I liked more.
People make wills and funeral plans and stuff
People got so pissy when I changed ryc to RYC
cringe
lowercase username superiority
if u change it back to RYC i will give u smth to be uppercase abt
ure not even capital u tryna be like NYC or summn nah fam u shittin bru
Im changing it to RYC
dont :(
nooOoOoOO
It's very aesthetic
RyC

I had this for a bit to imitate ShiN
its clunky out of place and ugly
Also ryu what the hell does you name say?
ryc = ryu
and shin in turn was imitating me
The longer version.
Ryc
ryu like that one character
I hope you weren’t referring to me when you said “Shuri”
There's another active ryu on this server
ok Ryc is just bad
If you were, I’m blocking you.
from that fighter platformer
it's objectively bad
No no no no I wasnt
don't use Ryc
Good.
Ran Yakumo's Chalkboard
shuri gets a blue_heart from me
Ran yakumo is a mathematician/physicist from the Touhou games
slurp is just shuri at home
a side ref
Oh I see thank you.
But it was more of a backronym
The point was to be ryc
My name was supposed to be the name of the winged horse. But I misspelled it.

pegasus like the beyblade
My parents mispelled my middle name, they mixed up a standard name with the spelling of a word
So my middle name is a word
And I really like that
I don't have a middle name 
???????????????
i have two i will give you one
It's a much better word than the name was a name
shuri 

Don't make me explain this or slurp might block me
what's it gonna be?
You know what I think I switch back to lower case for my name. So I can be an analyst.
Lol
dar yao q

unironically, it has a ring to it
@long matrix hi uwu
it does dont it

I like the lowercase p
you, gomez, cocat, c^2, potato, well not Antole, deriva something, washingtonbear, etc
True
poor quantum 
deriva shawarma
trolled
@limber thunder hi deriva something
oh i could go for a shawarma rn
Finally he stopped simping for Wew
I also would like shawarma
it was ironic simping 

the middle east really knows how to do food

Can we bring back Kanga Gang.
No never
no
no please
why do users of this discord server have a knack for bad dead jokes
what was kanga gang again
You have been here longer than me quantum.
Kanga gang was... uhhh
the horse died
Chmonkey kind of
stop
Umm
chmolumbia baby
mathematics server lore 
Blo.. why would you do this to me…..
no continue please 
its ok shuri has purple name now
i miss hangovers
A prolific server user said something lascivious about kanga from the winnie the pooh franchise
i am dizzy
my pooh personality test
chmonkey yes
Well cya, I got work and lazy weekend is over.
And developed it into a fanclub, which spread to people who did not know what fanclub they were joining
lowmath user challenge : dont mindlessly join the bandwagon
:bruh:
why isnt anyone joining the bandwagon of blo strawberry huh??
Then I guess it turned into a mafia, and then fell apart due to internal conflict
i don’t change my nickname ❤️
uderstadable
uwu
then this bastard RYC has no excuse

