#serious-discussion
1 messages · Page 185 of 1
this is a general discussion channel :p
i clicked on it and you and sharp were sending messages at discussion 1 pace
plus outsider
what I'm actually confused about is why Sharp posted the image here
when all of us were already in discussion 1
Outsider doesn't visit discussion often, but is in discussion 2 a lot more
see doesn't it seem like discussion 1
that should've been your first sign that smth was amiss
well i'm sorry for not knowing that
apology accepted
I clicked this one by mistake

I see
goober
anything can be discussy if you force it to look like one
case in point: Syrex's channels
hi i'm a depther
Depth...
hi
I'm a shallower
it's been years since I've seen anything of this game
you're an owl, so you fly
We've been over this, I'm not actually an owl.
Well I do, because if I attempt to fly I will break at least a few of my limbs
I don’t remember what it is
And I could do with keeping them all intact
Oh right i remember that
this is still the most omnious thing I've seen all week
I'm gonna have to think about this some more
Real
hii
hi
hii
Cursed
it's a cool paper
It’s nifty, but also super cursed the bounds and such involved
yea but that's sort of how it goes sometimes
I can’t say much when I say “O(f) for some f such that for all sufficiently small \eps we have g(\eps) = \sum f^n(\eps) converges and g -> 0 as \eps does”
(assume all transactions are monitored and everything knows the scheme purpose, you also get some transaction fee from all the transactions that occur)
Suppose you sell a piece of paper for 1 dollar.
Your first friend buys it for 31 dollars and sells it for 61
your second friend buys it for 61 and sells it for 91
your third friend buys it for 91 and sells it for 121...
now imagine other people do the same transaction and the final price of the paper becomes a total of 300 dollars.
Now the person who monitored the transactions and sold the piece of paper got a enough transaction fees so that they could buy the 300 dollars (i think its like 18-20% off each transaction) from the last person and so that all 20 people made money and the owner either breaks even or makes a little profit of his own.
where is the flaw in this?
more cursed bounds in another paper:
Abyssal
Oh interesting to see fibonacci pop up naturally.
there’s nothing more beautiful than a complexity bound /hj
zigzag
As sets of ordered pairs
Are there problems with saying they are equivalent sets, I think they are
I broigjt it up with a friend today
Upon further inspection I cant think of any problem with representing Rn as the cartesian product of R1 n times
Cus we consider n-dimensional intervals to be just the cartesian product of the n 1-dimensional intervals
it is
thats what Rⁿ is
Good
I would consider the cartesian product as exactly that -- and anyway any other sensible definition of it can be identified through a bijection
Glad im not going crayzee
He was confused at converting vectors to points i guess
Like thinking of R2 as a set of vectors
If you consider each vector as an orderer pair its not a problem
Ignore this ramble if it seems silly cus only I knlw the details of the covo I had
Cool
I have once seen someone say that the elements of R^2 look like (a.b) while the elements of R x R look like ((a),(b)), but I agree with you here
it can be identified anyways - so why bother?
lmao
hm but RxR would be (a,b) right surely its just the set with first and second member in R
OH
U saying 1-tuple vs a number
(1) vs 1
Hmm
Idk Im just calling the thing (a) in higher!s representation of the set RxR a 1-tuple.
But its sort of a dumb concept
yeah i’m sort of responding to highers original message anyways
Cus the point of tuples is order
since 1-tuples are sort of not defined in the first place
I will restate that it was not my definition 
maybe (a) is the singleton containing the singleton containing a
I find defining R x R that way to be a waste of time
Whats a singleton is that an insult towards maths students
(Bad joke sorry)
I know i can look it up
is there a map from singletons to simpletons?
😔
there’s probably a map the other way
higher did you see my burger post
what should I get mapped to :kekehands:
burger
borgar
just because i wanted to
learn a bit more how linux works yk
i learned a few cool things
fair enough
nice
I don't know anything about operating systems 
you need to learn
i went from partitioning my disk 3 times to setting up xorg and getting a gui up and running (though maybe i should just leave it as a command line because i’m not even gonna do anything with a gui anyways)
on that laptop
it can be useful if you're working with data or just for programming (learning to set up and use gnu/Linux I mean

it’s the first time i got excited about computer stuff in a long while tbh
also i learned about the reisub system request thing
which was funny
yeah tinkering with Linux is fun
huh I had no idea about this 
gnu/linux 
idt my arch system has froze that bad
and if it did I'd probably just hard reboot 
someone told me today about it, i think it’s useful for me because i’m on a low power laptop running a billion processes on ubuntu 
oh I see
i also learned that there’s a used parts shop that gets old lab parts like every week, so i’m gonna go and see if i can get parts to build shit with
exciting stuff
or just generally workspace stuff
like they just have everything like furniture and sometimes cool shit
oh that's very cool
so i’m gonna go when they’re open, like maybe tuesday
a friend of mine has a huge like 50kg oscilloscope from the 60s 
used to belong to our undergrsds physics lab
maybe we have the same friend lol
i have a roommate who got an oscilloscope from a thrift store
housemate*
(you could interpret that as him being my roommate and getting the housemate from the thrift store, which is also acceptable)
"I use Linux as my operating system," I state proudly to the unkempt, bearded man. He swivels around in his desk chair with a devilish gleam in his eyes, ready to mansplain with extreme precision. "Actually", he says with a grin, "Linux is just the kernel. You use GNU+Linux!' I don't miss a beat and reply with a smirk, "I use Alpine, a distro that doesn't include the GNU coreutils, or any other GNU code. It's Linux, but it's not GNU+Linux."
The smile quickly drops from the man's face. His body begins convulsing and he foams at the mouth and drops to the floor with a sickly thud. As he writhes around he screams "I-IT WAS COMPILED WITH GCC! THAT MEANS IT'S STILL GNU!" Coolly, I reply "If windows was compiled with gcc, would that make it GNU?" I interrupt his response with "-and work is being made on the kernel to make it more compiler-agnostic. Even you were correct, you wont be for long."
With a sickly wheeze, the last of the man's life is ejected from his body. He lies on the floor, cold and limp. I've womansplained him to death.
Probably a long shot, but does anyone happen to know julia and could give me a hand?
It's probably a pretty simple fix, but I'm super new to julia and have no idea where I've gone wrong.
try chatgpt
niceee
LPL
Nah, chatgpt can't fix it annoyingly lol

I started learning Julia a while ago but am decent at debugging
can't know whether we're of help if you don't ask your question though
also try #computing-software ?
Ah true, thanks. I didn't see there was a computer software channel.
I might chuck my q in there
@open flower
Hey it just occured to me after you closed the question, if you replace that 1 on the diagonal by 0. the argument for C should work and the rest of the question didn't rely on that fact so it remains correct 👀
!nogpt
Please do not trust ChatGPT or similar AI tools for mathematical tasks, as they often generate output which "sounds correct" but has numerous factual or logical errors. Use of these AI tools to answer other people's help questions is strictly against server rules (see #rules).
(finally, a joke)
🤓
I was literally writing the non-NSFW words until I read what was written below
i only saw the nsfw words
I resisted my intrusive thoughts
maybe i should do that more
Damn. You shouldn't show the answer below
I mean.... it was just an example for secret
I didn't think people would actually be interested in solving it
Well, you need to think hard to come up with the words that is not NSFW
<@&268886789983436800>
damn
- ||boots||
- ||fandom||
- ||funk||
- ||pints||
- ||purse||
- ||sax||
I demand being judged as correct
I like your answers
I would give you 6/6 if I could
i can only think of one thing for 4
die
That post wasn't appropriate for here
Don't post sexually referential content please
hello
I'm new, from Hong Kong and I am studying course for us preparing for calculus 🙂
I'm in year 1
hey there! welcome to mathcord! 
good luck with your calculus course!
just a heads up: if you want to ask calculus related questions, you can either open a help channel (see #❓how-to-get-help ) or you can post your questions to #calculus 
hope your studies go well no matter where you end up studying in future
||your profile screams 巴士迷 to me, btw||
Guise
Is the definition of a subcollection, that. If F is a collectiom of sets, and G is a subcollection of F, then all sets in G must be a subset of some set in F
Cus im wondering if every set in G has to be exactly the same as a set in F
Like {1,2} only subsets are of form {1} and {2} obviously empty set aseell and itself
But for {{1,2},{3,4}} is {{1},{2}} a subcollection basically
For use in proving Lindelöf covering theorem
I got a countable set of n-balls that are all a subset of at least one set in a collection F so is the set of n-balls a subcollection of F by definiton
That's not a definition I'm used to, to me "G is a subcollection of F" means "G is a subset of F"
A collection of sets is just a set of sets, except a lot of people use the word "collection" to avoid having to use the word "set" all the time.
Especially once you start talking about sets of sets of sets
So I wouldn't consider {{1},{2}} to be a subcollection of {{1,2},{3,4}}
{{1,2}} would be a subcollection
The book might use a different defintion of subcollection.
does anyone know where i can get some chemistry help 😎💯🔥😭✌️
Hii does anyone know how to decrypt letters with no key
These are letters For each word
Nydx-oiia-djwqqwru
It’s in response to this riddle “I am a slippery fellow, what did I lose?”
But the Lindelof covering theorem uses subcollection in the sense in which I used it.
If G is a collection of open sets which covers a subset S of R^n, then there exists a countable subcollection F (i.e. every set in F also belongs to G) which covers S.
my course is an 1+3 degree course
year 1 is only general education on precalculus atm
like functions and those things
what is the Lindelöf covering theorem? 
I've never heard of this before
@fresh comet this
oh I see
In more general phrasing, R^n has the Lindelof property (which is basically a weaker version of compactness; with "countable" instead of "finite")
but R^n is 2nd countable
and 2nd countability implies the Lindelof property by default
no?
Which helps a lot in having the Lindelof property, yes.
But historically the Lindelof theorem predates the notion of second-countability
I see
Just like the Bolzano-Weierstrass theorem predates the notion of compactness
Yes, 2nd countability implies Lindelof (but Lindelof does not imply second-countability)
I am aware
hmm, there was a question I asked a while ago but didn't get any answers
is there a characterization for 2nd countability?
Maybe Im just misunderstanding the proof
really? they definitely have calculus in DSE, M1 and M2
A funny way to make a Lindelof that isn't second-countable is to take an arbitrary non-second countable space, add a new point {x} and make the new open sets be the original ones + the whole space
I have seen that Lindelof + 1st countable + separable is still not enough to imply 2nd countability... so what does?
I took Compulsory Part only
:((
ohhhhhhh I see
@neat lintel @old oak do you two know of any conditions? 
Not me, sorry
or do I have to resort to finding a countable basis
I don't do much in the way of non-metric topology, and a metric space is second-countable if and only if it's separable.
You have a countable set of n-balls which covers a set, and you also have an open covering F of the set, so assign each n-ball to one member of F and you get a countable subcollection of F, this is proper reasoning right
metric spaces are interesting
2nd countablility, the Lindelof property, and separability are all equivalent
compactness maybe? no idea
Yep, metric spaces are very decent.
And perfectly normal.

Apostol introduced metric spaces next
I don't think this'll work 
Excited for those
Example of compact space which isn't even first-countable

not compactness alone I mean
but thx
I’ll give nitro to anyone who can help decrypt some letters
I wonder if 1st countability + separability + compactness is enough to imply 2nd countability
@north topaz https://en.wikipedia.org/wiki/Normal_space
All metric spaces (and hence all metrizable spaces) are perfectly normal Hausdorff;
oh right that's what normal means in topology
It's an excellent joke
do not sully me you owl 
I did
you're the same age as a lot of my profs then
but maybe that says more about me than you
a lot of people told me my humor is like that of a dad or uncle
and I don't even know what to make of it
do you like stupid puns
I found in pi-base that being weakly Lindelof and having a sigma-locally finite base implies 2nd countability
I do!
this is not direct at you btw Bequi
A community database of topological theorems and spaces, with powerful search and automated proof deduction.
I think the takeaway is that second-countability doesn't have a great alternative characterization.
thank you
It's just "has a countable base"
Also second countable implies having a sigma-locally finite base
So weakly Lindelof and having a sigma-locally finite base is equivalent to Second countable
In particular weakly lindelof is weaker than lindelof
So you could also just say
Lindelof + having a sigma-locally finite base is equivalent to Second countable
So you just need to add sigma-locally finite base to this (and can remove some of them and weaken lindelofness)
I wonder if any subject comes close to point set topology in terms of how many named properties there are.

This reminds me of something but I don't know if I can find it
For the avoidance of doubt, I quite like point set topology
I wonder how many terms fields like logic have
Even though most of my work is in the tame world of metrizable spaces
I might believe group theory?
I remember seeing a theorem spanning several pages about a massive amount of topological properties that are equivalent under some conditions
Each line a property

my goodness
Ergodic theory has like 7 versions of mixing, but I think that's the only weirdly excessive moment
do you have a source for where I can read about this?
I'm curious now
perhaps morbidly so
I might be able to find it if I try to find it
it's no problem if you can't
I feel like ergodic theory isn't super heavy on jargon
I'm just intrigued
I think Dami has shared some 4 page long differential geometry theorem he saw in a book or something lol
Is the statement of the theorem 4 pages long?
Yeah, I think so too; I also started thinking of joinings, but the various types of joinings are distint classes rather than a collection of almost-the-same-but-subtly-different properties with an intricate web of implications
is this the one where there was like 30 equivalent conditions?
I think that was a dynamics book, actually
So there's a lot of named joinings but they're not a blur
The following thirty-one statements dreamed up by the utterly deranged
That said, my recent paper at one point establishes that a certain triple of elements satisfies a list of properties labelled (a)-(n)
So maybe I shouldn't throw stones
But at least it's a highly technical auxiliary lemma rather than a main theorem
And I can blame that madness on my co-author, since he came up with the lemma.
The key to success

next time I fail smth, I'll blame someone else instead
surely nothing will go wrong
I mean, it was accepted for publication, so there's not that much blame to be shifted.
In fact putting in stuff like that is a good way to avoid rejection, because some reviewers will just glaze over and not verify each line too carefully.
"it's so complicated, it must be true"
I was just messing around :p
I didn't actually mean it haha
I know!
What the actual fuck
That looks like some shit id see on Ancient Aliens or some shit
Thirty one statements is masochist work
Proof: these are all trivial
can anyone help me understand POTENTIAL DIFFERENCE? (high school level)
I'll give Federer credit: it seems like he actually bothers to prove a lot of these in detail
the next 20 or so pages are just filled with the proof of this theorem
randomly stumbled upon in the mathematics section at my uni’s natural sciences library
VIVE LA FRANCE !
😭
published in 1960
quite a politically heated time
probably not a joke
still very weird to come across while i was looking for another book
namely:
Forall discrete thoughts there exists an induction proof
Rota in particular writes very interesting essays
introduction of the titular essay
...which is just two and a half pages long
Rota has written both Discrete Thoughts and Indiscrete Thoughts?
What's the difference?
indiscrete is 13 years later, different set of essays
latter seems also to be exclusively rota, while discrete also contains ones by kac and by schwarz
WOOOPS i can't arithmetiv
I've read about half of indiscrete, and there are some interesting anecdotes there, but I've gotten to the part where he starts ranting on philosophy and math, and I just got too bored to continue
9 years later
haha i get that
maybe I should pick up discrete thoughts
Hiii good thanks, you? 🥰
if i stumble upon something particularily interesting (and if i remember) i can ping you with it if you like
Yes please! 🙏
reminds me of this
might be useful in certain context but was happily intruiged by the relationships
this is my favorite kind of theorem lol
That is minuscle compared to the one I mentioned
Unfortunately I think it'd take me literal hours to try to find it
is there anyone good in linear algebra that could perhaps help me been struggling with the same question for over an hour
OK, but that's just alternative characterizations of compactness in a metric space
Not a jumble of 31 facts
yeah i never saw that long of a list yet
usually the equivalences are pretty tame
one may wonder how many of the 31 is actually useful 
It's very dangerous to raise the issue of usefulness in higher mathematics.
If you think too hard, the answer always turns out to be "none of it"
yeah its mostly that sometimes a certain charachterization is so usefull
that the original actual definition is pretty obsolete
im trying to remember a good example
okay idk if this even counts as a charachterization lol but the weak* topology
its just pointwise convergence of linear functionals
while its defined as a topology generated by certain semi-norms initially
from Rota's essay simply titled Ulam:
Mathematics is a cruel profession. Solving a mathematical problem is for most mathematicians an ardous and lengthy process which may take years, even a lifetime. The final conquest of the truth comes, if ever, inevitably tinged with disillusion, soured by the realization of the ultimate irrelevance of all intellectual endeavor.
his writing in general seem to be very much put on edge, while amusing it's also a bit tiresome
don't sweat it
I don't need to know, I was just curious haha
Average day in algebraic geometry land
how do I get picture posting permissions 🥺
you need the Active role, at the very least
what math class in college covers taking Gradients of Matrices?
ah I see
like it gives calc3 vibes + linear algebra squashed together
but I swear none of those classes covered gradients of matrices
Vector calculus
Idk what calc 4 covers
Cor example calc 3 here covers algebraic geometry
Just depends on the institution
got it
in the traditional sense in North America, calc 4 corresponds to vector calculus yes (typically calc 1 = review of precalc/limits/differentiation, calc 2 = integrals/series, calc 3 = multivariable, calc 4 = vector calculus)
hhhh diffrential geometry vu

Epsilon deltas or algebraic projective varieties
Choose your poison
my calc course: both
so swag
You talk about algebraic geometry in your calc course?
We talked about algebraic de rham cohomology yes
algebraic project varieties
etc
Conic sections
Sheaves
A weed out class btw
I wish I had such courses at my university
Well, that is true, I agree
agreed
(Thank you capitalism)

a class that's used to weed people people out of the program
real analysis is often a candidate
okay yeah that class is metric topology here
there's a few too many weed out courses for my liking here
A class designed to be difficult on purpose to fail people
idk I get the impression that any hard class is called "weedout" by the students
i know a person who is on his 4th attempt
this is a fair assessment
but I think a class with a 50+% drop out rate is too much to just be considered "hard"
esp if it's coupled with bad prof reviews
sometimes its just the students fault but sometimes it's genuinely the professor is a bad teacher
I get the point some uni courses are just a crap experience
Especially when you have "calc 3" and what you actually do is a combination of baby calc 3/differential geometry and heavy algebraic geometry
the 4th year complex analysis course here went from 30 to 5 students last year 
and it was filled with bright UGs and grad students
for things like real analysis or topology, previous courses should ideally build up to it
I'm not quite sure what happened there
Deltoid would be sad about this
like don't just teach calc or discrete math or whatever but make sure students learn proofs and abstract thinking along the way
students can defo recognize hard classes but good professors, like we had lagrangian mechanics with low pass rates but rarely will people call it the professors fault cause the man does his absolute best at explaining a difficult topic
the problem is, this is a matter of pedagogy and not syllabus content so it's hard to write it down lol
Weed out classes are a thing. It's not really just "difficult for students" or a skill issue
and sometimes the class is too easy you dont feel satisfied haha
yes, I would've called my linear algebra classes hard but good classes
group theory moment
this is also true
All of linear algebra
Real analysis after the famous weeding out class
At least real analysis was not bad. I found out that I love analysis that moment
Even though it was another weed out class and everyone was destroyed


You gotta net it out
Take something easy like graph theory with a weed out class to cope

that depends on the graph theory class
there is definitely some difficult graph theory, especially at the advanced level
Graph theory for mathematicians
We had graph theory for computer scientists (weed out class)
Bruh my entire yeargroup at uni cut from 100+ to ~30 after 1 year (not even hard stuff) 💀
like diestel book type of graph theory would not be the easiest class imo
fun af
but needs effort
I definitely liked applying algebraic topology to graph theory
So many black magic that I love
Algebraic topology was already a "love at first sight" field

imo the combinatorics part of graph theory is hella fun on its own too
i think my favorite type of proofs are regarding hamiltonian paths
International mathematics olympiad imo
its so fun
for some reason, combinatorics is always the MVP of hard math classes
It's really fun yeah but also very frustrating
I need to learn a bit of measure theory and functional analysis
I learned a bit from my number theory textbooks but I feel like I still have some gap to fill in
yeah those are the gateway to good analysis
especially on the probability or operator theory end
the fun applied stuff needs some dank banach space analysis
probability 
which was a bit difficult for me initially too
yeah those are fun, the dank part is like when you start to discuss differentiation on banach spaces
it opens up a lot of fun shit in optimization and dynamics
which in turn opens up the fun PDE stuff
outside the theory
well you only really need a couple spaces
you can usually move between them by a process called interpolation
so you can afford the ristriction
what's interpolation
is it like moving to another space with the cost of some restrictions
for L^p spaces its basically asking what happens between L^p and L^q
if you are L^p and L^q are you in L^r for p<r<q
f: L^p -> L^q?
oh
Interesting
Soo many analysis stuff I don't know yet

yeah its literally just asking what happens between your spaces
the only issue with interpolation is that its quite technical
so it tends to scare people off lol
technicality moment
that's the same thing with like
Analytic continuation
The idea is beautiful but the technical details are annoying
Especially when you have a weird function
ouf yeah, i dont even remember the details just the main idea
i should probably revisit it in rudin
im at the point where i dont encounter enough CA that i get tempted to avoid it
real
the most i end up using it is in spectral shit
but that doesn't require that much CA
I find myself doing a lot of CA
spectral theory is amazing
The hidden world of linear algebra
depends on the field, the things i study happen a lot in R or vector spaces over R/C
which you dont need to know the depth of CA to do
like i had to use a fair bit of it in FA tbf
When the problem reduces to cauchy residue or rouche: satisfaction level ^^^^^
morera, study of space of holomorphic functions, distributions definitely neef CA
but then it faded away
morera 
There is still some stuff I don't know in CA
It's mostly geometric stuff
Complex manifolds
I don't really encounter them so I don't care much
But they look interesting
the geometry is cool af but for me personally the maximum principle is one of the coolest shit tbh 
REAL
its like one of those things that you learn but only after a bit realize how insanely powerful it is
Yeah this is really true
instead my ca class focused on residue , roche and complex integration 🛏️
I initially thought it was just whatever
Well to be fair these are important as well
Did you guys do transformations?
Riemann mappings, mobius transformations etc
I'm realizing now how useful they can be
yeah like i think its fair to include those but its definitely sleeper topics, nah i dont think we did too much of it
it was like the usual power series/differentiation/cauchy reimann, maximum principle, analytic continuity , comformal mapping, integration + residue + rouche
the average ca class
the professor was a fan of rudins RCA for a couple topics
so its what i ended up using as well
hence didnt get to see much of the geometry
and "fun number theory stuff"
wow that's so sad
altho im seeing them while studying harmonic analysis in the form of learning about p adics
geometric stuff get fun when you look at complex manifolds and cursed stuff like "contour integration in C^n"
and for number theory, <enter analytic number theory>
nice
yeah i heard CA in higher dimensions is cool af, but thats a sea i wont touch for a while lmao
usually i try to find a onlinr course, not cause i want a course
but cause it lists prerequisites
or previous classes
and thats usually my assesment
the pain of prereqs
if i know the prereqs ile find a book and dig in
having a solid foundation definitely help
nothing beats the feeling
of being interested in a topic
and seeing you know all whats required to study it

welp, its getting late so ile be taking my leave, good talk 
cya have a nice day
Im so cooked with something bout geometry 😔 i made a help ticket lets see if I can finally solve it
Its in #1277771466405970021
Guys how do I understand the WHY'S to algebra so I can actually understand what Im doing in class instead of following random steps and then getting stuck when the step didn't work
or I can't apply that step to another problem
A lot of it is just reading your book and doing a lot of exercises from it.
Math is based on this thing called the axiomatic method
We make a bunch of assumptions called axioms, we see what things follow logically from them.
To do this you have to know "the rules of the game"
As far as what things you're assuming and how you can combine those things to infer new things.
Most of the calculations and stuff you do in algebra are meant to be short toy examples to help illustrate some idea easily within this kind of framework.
one thing that might help is explaining each step in your own words -- if you're unsure about why we do a certain thing or what is done in some step you can ask teachers or people here
I mean I think I understand why we do some stuff, I understand doing what you do to one side to the other, I understand how and why clearing fractions works. I just get incredibly stuck when I see slightly new stuff
Algebra is killing me right now and the worst part is 50% of my errors are extremely dumb mistakes out of simply having a poor working memory
I see, okay I guess I just need to grind more
What derivada said is pretty relevant as far as clearing up misunderstandings and confusions go.
If you're not understanding a problem or a part of your book it's good to ask somebody more knowledgable than you about it to help clear up the issue.
Alright understood, thank you guys!
What is it like having a mu alpha theta chapter at your highschool? I'm thinking of asking my school to open one up. What's it like? Do you guys like it?
,,\mu\alpha\theta
רי-ית
רי-ית
$\mu\alpha\theta\eta\mu\alpha\tau\iota\kappa\alpha$
רי-ית
Hi guys I would like to prepare for the harvard exam, and in the section of theory groups recommend these books, I'm reading the dummit and Foote, but the book that says the theory of representation I have not understood much that other books recommended to serve as a complement please :D
two common recommendations are Serre's "Linear Representations of Finite Groups" and Fulton & Harris "Representation Theory". I prefer the latter though it's a bit harder in terms of prerequisites I think
One of my classes next semester will be about non-archimedian fields and subsequently berkovich spaces/geometry. This is a completely new field to me and it doesn't seem like there are even that many publications about it, do any of you have some (free) material to check out before going into the class?
One of my classes next semester will be about non-archimedian fields and subsequently berkovich spaces/geometry. This is a completely new field to me and it doesn't seem like there are even that many publications about it, do any of you have some (free) material to check out before going into the class?
the nlab article lists a few references, so why not check those: https://ncatlab.org/nlab/show/Berkovich+space#references
personally i would just email the lecturer
i have no idea what berkovich spaces are, but non-archimedian fields are very commonly studied, so there will be plenty of material for that at least
looking at this article though, seems like such a class would have to assume strong background in AG and non-archimedian fields already...
!help
To ask for mathematics help on this server, please open your own help channel or help thread. See #❓how-to-get-help for instructions.
HELO
I wasnt asking for help
Wanted to see how you guys solve it
Lol
(I already have solutions)
Rational roots test
whoa
james with a decent ass bed time?
during the summer??
impossible
is james in eu?
Four integer ones?
HELO
That's very impressive
Ok I'll just show it ngl
the coefficients are symmetric, so we know that the map x -> 1/x maps roots to roots
a trick is to divide by x^2 and then you get a quadratic in x+1/x
It doesn’t have any integer roots
By rational root test, they’d have to be +-1, but neither work
why do we multiply the permutations of independent events together?
Wait dont tell me I wrote the wrong one down
Yep wrote down the wrong one
Its over
See you in the grave
or minor trials of a major experiment that is done successively (successively again sorta mean theres dependency so doesnt this kinda makes it recursive?)
is it solely to associate the empirical observations with an operator that best explains the magnitude of the outcomes?
am i stuck in the specificality of things here and overlooking the generality?
atleast in terms of the objects i chose to explain my situation (which means i couldve framed my question in a much cleaner way?)
<@&286206848099549185>
nevermind its an insanely stupid question

treated it as some kind of unshakeable formula
where i couldve just replaced it with repeated addition which would mean i am changing the meaning i was previously internally associating with operands even though they may appear the same(?) symbolically
down to the preferred way of counting perhaps
multiplication has a distributive property unlike additon
so
its like
2×2×2
can go like
(1+1)×(1+1)×(1+1)
why do i not get those child-like kicks thinking about math as i used to
@psychiatrists
surprised we dont have a dedicated team of psychiatrists to this server like we have of helpers
why do we need though?
QED
Meaty's alt
What-
can you elaborate what you mean?
left as an exercise for the reader
i am numb, sorry / thank you
i wonder if this is even the basis of all
Meaty's alt
Meaty salt
Me a ty salt (I am a salt that is used to thank you)
Mea ty salt
That's salty...
Can somebody recommend a set of tools/software they are using for their math studies (see some more details below), like a math tech stack. I would be curious to exchange info and maybe discover some new useful tools.
These points would be interesting:
-software for taking hand-written (digital/on tablet) notes for math-heavy studies
-tools used for math studies in general (e.g. wolfram alpha, matematica, desmos, geogebra)
-tools/software for network learning: creating thematic summaries for different branches of mathematics (e.g. calculus, discerete mathematics, complex analysis); the main goal here would be to be able to interlink different theorems & effectively capture how different advanced concepts relate
I would appreciate any input or help
Latex
I just started learning Python a bit ago and x = x+1
And a = b doesnt mean b = a has been quite an interesting experience
TeX can be handwritten?
In programming "=" sign is an entirely different thing
It is an assignment operator
Yeah I know it's just a weird adjustment
Understand why they'd do that though
Isn't there an actual equals operator or smth like ==
Yeah, == is comparison operator like = in math
Why JavaScript is always different from the rest of the world 😔
because everyone uses it so they can do whatever they please
Indeed
has anyone had success using ai generated quizzes
i tried using gizmo a while back and the outputs were well...
stunningly bad; they would have done better just seperating the front and back sides by the question marks
Honestly it’s hit or miss with ai atp
I’ve used chat gpt for geography and it was awful
but for science quizzes it’s tolerable
!nogpt
Please do not trust ChatGPT or similar AI tools for mathematical tasks, as they often generate output which "sounds correct" but has numerous factual or logical errors. Use of these AI tools to answer other people's help questions is strictly against server rules (see #rules).

honestly im kind of surprised this isn't something you can just solve with some fine tuning
like on the spectrum of "basic manipulation of text" to "the most impressive thing ive seen current LLMs regularly be able to do", "take some notes and generate a quiz out of it" seems much closer to the former
Huh
μαθηματικα
Что
maybe you could try RAG -- the idea is that you can give a set of documents to an LLM that supports this, and they'll answer based on it or even citing these sources
idk if there's an easy to use version of that online I've only tried this running locally on a friends' server
hey does anyone know a data scientist/analyst or is one?
huh? what exactly were you thinking of?
like give different types of "notes" -> "question" relations to the LLM?
I know some data analysis tools and know people currently working in datasci
yes kinda
you just upload documents and the model uses them
That's great! I'm researching on what careers I want to pursue in the future. I've heard that ds and ai is the next big thing in IT and it'll be booming for the next 10 years or so. I'm not sure if I want to get into that field tho. I'm considering it because of the job stability, high payment, interdisciplinary learning as well. Can you give me any knowledge about that career?
I know that I'm not that interested in coding as well and ds does require a lot of coding right?
there are a lot of graphical tools for data analysis and visualization, most people aren't using Python all the time
it is true that it'll likely be in demand for the coming years, all our devices are constantly producing data and someone can go and make sense of it
it is also a interdisciplinary field as you say since "data science" just refers to a set of applied statistics tools, paradigms and conceptual frameworks that can be applied to problems in any other area, whether it is medical sciences or business analytics or etc.
I have a liking in math and economics, and don't want to waste it. But I'm just fearful of coding and also the layoffs occurs currently. Do you think the layoffs would increase more in the coming years?
well we kind of are looking at a possible global recession as we speak
people with good technical background and networking skills will get hired regardless so if it's something you like and you can combine e.g. what you know of economics with these skills you'll be fine
and about fear of coding, best I could suggest is to take your time with it and learn slowly, ideally also with a purpose in mind like realizing a specific project or just completing courses etc
is this what chatgpt does when you upload large documents?
I graduated with a CS degree months ago, I had internships too, still unemployed 😄
Don't major in CS
Yes it will increase. Everyone is majoring in CS nowadays, AI is popping off too.
nah, if you can major in CS and be a competent enough person I say do it
Thank you for your advice! I've also been considering finance or fintech, but I'm not sure if I'm interested in it. Do you have any advice on how I can find my interest in pursuing a certain career
yes the job market is saturated, yes it's a trendy major, then just stand out from the crowd
maybe try delving into a project regarding that
like in algorithmic trading
the other day I was reading about that lol, check these repositories out
https://github.com/nickmccullum/algorithmic-trading-python
https://github.com/quantopian/zipline
and about this, there's no-code platforms for just about anything these days
check out e.g. https://www.tableau.com and https://www.knime.com/ for data in particular
what degree would be best to get into these variety of fields? Nowadays people are doing cs or ds, engineering. Basically getting into IT. I've seen that it has a higher pay salary and much better benefits as well. But I'm not sure if I'm really interested in pursuing that. I'd like the benefits that IT has though.
What are you doing instead? How did you decide to major cs?
one common path I see is to major in something related to what you want to do and then either get a cert or a MSc in data science
for instance you could major economics and while you're at that figure out how to get certified in data science or data analysis
Are there any requirements for Msc in ds? Like a certain bachelors?
usually they'll want something related but anything in the sciences or any quantitative field is good
I know a sociologist who's currently getting a degree in datasci lol
it's usually not a "hard" or exclusive requirement
Hello, I'm using the hiset program and I've made good progress. I'm planning on going to trade school, (most likely plumbing) so I want to have a good grasp of the math required, and I'm also genuinely curious. I have a quick decimal question. When using long division for decimals, the divisor must be a whole number. How exactly can you tell whether it's already a whole number or not?
But if comparing this to a person who did a btech in ds and ai, who would get a ds job easier? Certifications don't have much value compared to a degree right?
Alright thanks!
it depends a lot on the candidate and employer, one employer might value the value of a technical degree more but another (and this is usually the case:) will value a wider diversity of skills and qualifications which might be given by majoring in something different and then applying you current knowledge to that
???
No major in CS if you feel like it
@stone garnet don't let other people discourage you
ah I see alright!
I don't want to regret a decision at all
If you like computer stuff then I don't see a problem with CS
Closer CS moment

If u are scared of trying hard to stand out
Well my only advice is to talk with a lot of people
"Domain Expansion" your network

You could like make a project about algebraic geometry
Yapp about it in ur resume or something
There are a lot of subfields inside CS. One sub-field might get saluted but other sub-fields aren't
The best field is web development /j
No, web dev is sh*t
F*ck JS 
My trauma from learning JS has still not recovered yet
===
Same
Ok so this is going to be controversial. We should let ai be our government. Now I know most people's immediate reaction is what your insane. Have you never seen insert ai dystopia media. Thing is until very recently media regarding ai has been based off humans experience with more powerful humans. You know the whole sufficiently advanced tech looks like magic deal. Now modern llms are essentially just really fancy matrix multiplication machines that lack anything we would call a consciousness or intention. So much so that we can apply pretty rock solid restrictions to what they can and can't output(yes there are loopholes). As such saying they would turn life into a dystopia out of some sort of malicious intent is a bit of a stretch. On top of that nobody has ever actually tried this sort of thing so again we don't have any historical precident for ai turning anything into a dystopia aside from maybe short form generated slop which is actually more of a human caused problem. I would argue that since llm are really good for drawing conclusion and looking for patterns in gargantuan datasets this makes then perfect for running a government other qualities aside which I will talk about next. Those other qualities can really all be put under the umbrella of not being conscious nor human. That is to say an llm is generally incorruptible in the conventional monetary sense, not subject to emotion, makes as rational as possible outputs always, and just all around doesn't have any of the flaws human politicians do. Since an llm is capable of understanding well language it could make a decision in a hypothetical ai government and in real time monitor the impacts of that decision sourced from more conventional statistics and the testimonies of those affected were it could very quickly figure out what each person's experience with that decision has in common giving it a pathway to adjust that decision if neccesary.
my eyes glazed over after controversial
Yuh lfg.
going for the block
lmao
I would call it the commie block bc ai would be perfect at resolving the issues with communism like corrupt high level authoritarian officials or the issue of balanced resource distribution.
Also it would be very much so democratic in that it would be looking for people's feedback basically always.
Of course this all will never happen because unlike an ai humans are far to attached to preconceived notions of what things will be or are like.
🥱
you could start by making a discord bot moderator/admin and having a server that's run entirely by AI
start small, prove it works at a small scale for starters
dont @ me
that would be a fun experiment, but also you should then do like 1000 such servers for a proper trial
That's essentially just a text recognition task tho. It doesn't really have any governing tasks and i doubt discord administration would be too keen on the idea. Otherwise something like this yeah.
yeah I'm just trying to keep them busy and get them outta here lmao
ideally some run by AI and some by humans in a double-blind experiment
Say something on the naughty word vector space and here's a ban for you.
entirely fair
wdym "discord adminstration" or "just text recognition"
anyone can make a server, and social communication on this dinky app is just a small fry compared to managing an entire nation
got a long way to go
get to work, baby steps
Discord doesn't typically let large servers stay up without a mod team. By just text recognition I mean there isn't a whole lot to discord moderation aside from looking for people saying stuff they shouldn't and then banning or suspending them. I suppose you let such an ai run discord server set the rules and structure of the server itself which would be a bit more interesting. Otherwise good idea imma see how I can implement it.
If you want to run a nation, you gotta convince way more than just discord staff of its viability
Channel structure, roles and role colors, perms
emoji and stickers
It of course even gets to decide its own policies
Like banning anyone who mentions vinegar
Finally!
Vinegar is only acceptable on chips
WHAT
I WILL DIE ON THIS HILL
sub this'
<@&268886789983436800> plz, this person has been warned
i dont like it, I only like the benefits it can give such as job stability and high pay
I never heard about that, how can I make a project relating to that?
💀
salty much
it has nothing to do with that
some things I just don't want to see
if it's against the rules then i'll just ping mods and get on with my life
False
Isn't there a version of JS called that
Inspired after BrainF*k
It's still JS but uses only 6 operators i think
6* characters
I am just saying from my experience. But I think it is pretty tough to follow CS if you don't like it and this can also be said to every field out there. I have seen some people go into CS just because of the hype in the media that says it is high pay or job opportunities. Those people feel bored after some courses about CS and then drop out after 1 or 2 years. So if you follow CS because of high pay and job stability then that motivation needs to be strong enough to keep you going.
But who knows maybe you will like it when you learn more about it
Bad job prospects will definitely drag you down if money is your sole motivation
^^^^ It's tough to stand out when you don't like the material and the people you're going up against like the material
Even though money is important in this world but I think you are going to feel "empty" about your job sooner or later. I heard some people drop their current jobs and then go to college or university to follow their passion. I would rather do a lower-paid job but it is the thing I love than a high-pay job but I hate it.
This doesn't apply to people who love making money, tho 
i love making money
If any of you think any kind of academic credential will make you any sort of “real” money working for someone else in today’s world, you may want to reconsider.
Well, making money is a valid reason to live for

by having money
wait but you are missing the point, closer is asserting the thing that closer said
like it’s not a misunderstanding
about whether the two statements are the same
then my response is simply claim invalidated 
or by managing without money, that is, after all, possible
it’s tough even when you do like the material. Doing it without that, either gotta truly love money more than anything or be a masochist probably.
that said, it’s very rewarding if you do end up finding some literature that you really vibe with and that fills the role you need
problem is finding that can be a lot of work
but ime it pays off in the long run
They are
I very much want to make money to live.
i don’t want to but don’t really have much choice in the matter, i’ve found starving is bearable but not exactly comfortable

You could say I kind of scammed people to get my first job
Well not really scamming but more like connections stuff
you worked in sales?
Like I know a lot of people that are way more talented than me and still are unemployed
I agree. I’d rather live in a world where we don’t have to slave away so many hours a day just to survive. But this isn’t an option so I just picked the want out of the options available.
No
Valid
Connection is an important thing these days 😔
It's unfair and not a skill issue if you don't know how to do it
It's mostly luck
I don't necessarily like making money even tho I do get paid a lot of money
You could say it's Stockholm syndrome
I do love my job tho
I just hate the money part of it

Well, if you love your job then money is just a bonus
must be nice to have any social capabilities 
to me even just saying "hello" seems a wholly insurmountable task
you are wrong. academic credentials are rarely a sufficient condition, but almost always a necessary one.
People around me aren't even willing to engage in a convo
i am very much willing to, but very much struggling to
If you want to have a convo you need to give them some money or something else that's materialistic
whar
Even though my social skill is sh*t but I can still say hello 😎
amazibg
But after that, I don't know what to say. Doing CS too much will make you forget how to communicate with humans
Valid
dw you're off to a good start just keep at it 
But I might need to communicate with recruiters or I will be unemployed so better training for that fateful day 
Okay I kind of posted something in #1021175428326633542 that wasn't actually school related and I'm realizing no-one's gonna read it like this
System.out.println("so true");
System.exit(0);
#1278386823831355434 message
This should be enough to hook a few people lmao
I think its my best line this week
its more of just general math discussion and not just asking for like math problem help
you don't need to exit assuming that the line there is at the end of main :3
!noadvert
Please do not advertise your help channel or thread in other parts of the server. There are many people who need help, so advertising can quickly turn into spam.
Wasn't sure if it counted as an advert, sorry
just wanted to move it to a discussion channel instead or something
Linking any help channel is always considered as such
AFAIK
Fair
just saying I doubt anyone in here is any more familiar with the intricacies of bullshitting and exploiting summation notation to write programs
And a really suspicious caption
What mod should we ping
<@&268886789983436800>
dealt with
i love that so many of AMS-published books are freely available at the internet archive 
on a whole other note...
Did one die too young and the other live too long?
😭
— Weil, btw
Why does he say that about them?
Anyone have hector Lomeli or John Osborn?
guys, i'm studying accounting and i want to learn financial mathematics from basic. so can anyone recommend me book or some course on youtube?
This is usually how you’d phrase what you mean in standard English
What I wrote means exactly what you formalized, in this language called standard English
alright, in any case I think it's a relevant point to make that education is still essentially required to get any sort of good paying position
Very true though- especially today: when it seems like you need a masters just to earn minimum wage
funnily enough, CS is one of the fields where this is not true. at least if by academic credentials you mean a college degree
It’s mostly true.
The opportunities for CS without a college degree are really closing.
There are some exceptions. But most people who make it today without a college degree. It’s because they’re really cracked and started super early and already proven themselves (that they really don’t need a degree to do what they do).
That is not a viable thing to expect for most people. And regulations aside I suspect a similar thing would be true for some other disciplines.
I heard opportunities for CS with college degrees is also not great
It is not
So I dunno, maybe one can get hired without credentials on the next boom
Even with the degree. Getting an actual CS job is a horrible grind.
Yeah I heard CS job market is insane rn
No. It’s only gonna get worse from here on. The field is really getting oversaturated.
I mean boom and pop cycle of about 20 years long, by the way
After some time, people might get disinterested.
There’s enough opportunities that you probably can get a job if you outgrind everyone or are just better.
But if you aren’t one of those, gotta get really lucky. (and still have good enough skill to make good on that luck)
True
I’m developing a love for math simply out of the beauty that is algebra 🥺
Ngl I feel bad for my bf rn
The same thing happened with me.
Yessssss
Algebra is so pretty
Analysis is so pretty
that's why i like it
analysis is dirty, messy.... for REAL mathematicians
gotta dig your fingernails in
^ propaganda sold to you by algebraists
i know someone who has that diagram on a t-shirt
What do you think of my banner
Holy based suremark
a few years ago, they wore it to an algebra lecture (some intro to groups I think) when the prof drew that diagram, and the prof burst out laughing
And it’s not advanced algebra, it’s intermediate algebra in community college (never paid attention or cared for high school algebra or math in general) and decided this semester I wanted to be a better student and actually study. Not only am I starting to like because oh my gosh, did you know if you study and do problems you get better?????!!! + just seeing how algebra simply works and can applied to a wide range of problems and watching each operation unfold is the purest form of pleasure
Sorry we are not brainwashed as you are 
(Don't take it srsly I'm mostly joking btw)
i am personally not a diagram enjoyer, but i respect those who are
filters are gonna be the death of me rn
Same
(they're so annoying, this is why nets are nicer)
true
even better, deal with first countable spaces only so that you can just take sequences and be done with all the shenanigans (geometry gang rise up)
I really love the maximal principle in CA
My question is, why get into CS at all at this point given you’ll likely never exceed AI if you aren’t already advanced or proficient in the field. The work likely will become obsolete.
oh that's preposterous



