#serious-discussion
1 messages · Page 63 of 1
yun emoji
My first choice was mid as well
Why do you take coffee then?
this is what coffee does to me
Milk >>>>>>>>>>>>>>>>> Coffee
alcohol >>
it is time to attempt sleep AGAIN
Drugs >
Good night
good night to u too
good night blo, rest well
have a nice sleep
omgggggggggg so cuteeeee
night night bloey
i kinda forgot
milk amazing
good night
what about tea? 
real cat
Earl Grey is great
Earl grey be da best
agreed
Imaginary doggy
I drink more tea than milk somehow.. chinese tea are normally bland but I fine them alright
taiwanese tea too
but tea from my country is a big no
too sweet
So condensed milk in strong tea
what about milk tea
can I ask a bot for example if something like this is true ?
$2A\left(A-B\right)-B\left(A-B\right)=\left(A-B\right)\left(2A-B\right)$
forin
for non-commutative things you can only factor (A-B) to the right
do you mean like this ?
$2A\left(A-B\right)-B\left(A-B\right)=\left(2A-B\right)\left(A-B\right)$
forin
yes
okayy tnx got it
shame a bot cant check if that statment is true
it would be sick if we had a tool that check your math solution line by line and it tells you where you messed up
like virtual teacher
but I guess AI will do that soon so no point in building it now
sup
$ a $
https://tenor.com/view/twerk-dribbling-basketball-gif-15929795 can someone tell me the physics of this?
why?
man's got a donk
out of curiosity, how does one obtain the "ℌonorable" role?
i think you're nominated by other honorables.
I was probably given this honor for establishing a reputation for long and sometimes informative rants about category theory
interesting, what about the helpful role? do they give that role to people who help only in the help channels or in any channel?
ah ok, thx 🙂
So where did the first honorable come from?
about categories
What kinda categories
think of sets but like way more comprehensive
in general, category consists of a collection objects (elements) and arrows/morphisms that relate from one object to another, you can think of morphisms as 'mappings'.

these objects can be anything pertaining to a specific category
example is the category of sets (Sets) which have sets as objects and functions as morphisms
theres also the category of groups, rings, vector spaces, topological spaces etc etc

the main motivation is that
if you study enough math you'll see the same constructions pop up over and over in different contexts
and the proofs of certain properties of these constructions (and this is with some handwaving) are all the same after you change around some adjectives
so category theory is one way (idk if there are other ways but I doubt there aren't other ways) of talking about arbitrary elements and morphisms between these elements and characterizing these constructions
abstraction 
It's a branch of math which tries to study things, not in terms of their inherent properties, but by the relationships they have with other things. It abstracts away from caring about the particular details of the thing itself and tries to understand it better by understanding all similar things of that kind, and how they relate to each other all at once. Idk maybe a good analogy is like, most mathematicians study one species of object. Like you have some biologists who study fish, and some who study dogs, and others who study parrots. The category theorist perspective is like, thinking about fish and dogs and parrots all at the same time, and asking about relationships between fish and relationships between dogs and asking how those relationships are similar and what they have in common. Like two fish can relate to each other by sexual reproduction, and two dogs can also relate to each other by sexual relationship, so there's some structural similarities between the fish ecosystem and the dog ecosystem.
"it's not about who you are. it's about who you know"
proof: yoneda lemma
I'm stealing this
anyone know how wolframalpha and music albums go together 
reminds me of this video
While the concept of infinity may seem mysterious, mathematicians have developed processes to reason the strange properties of infinity. Mathematician Emily Riehl has been challenged to explain infinity to 5 different people; a child, a teen, a college student, a grad student, and an expert.
Director: Maya Dangerfield
Producer: Wendi Jonass...
still hilarious that this exists
shush slurp

uu
Is there any situation where integration doesnt work and you have to use Simpsons rule or rectangle rule?
"mathematician explains homotopy type theory in 5 levels of difficulty" when
fr like they had emily riehl and didn't have her talk about HoTT? travesty
does riehl know any hott
i will confess i know literally nothing about her research lmfao
i just know that she wrote the category book
i am a terrible academic
but i thought she did infty cat stuff
not hott
yes
i'm still working through the HoTT book
but as i understand it infty categories have deep connections to HoTT (as they relate to infty groupoids?)
she also has tons of lectures on YT talking about HoTT if ur curious
Speaker: Emily Riehl, Johns Hopkins University
Date: October 18th, 2022
Abstract: http://www.fields.utoronto.ca/talks/How-I-became-seduced-univalent-foundations
Part of the "2022 Fields Medal Symposium: Akshay Venkatesh": http://www.fields.utoronto.ca/activities/22-23/fieldsmedalsym
At its current state of the art, ∞-category theory is challenging to explain even to specialists in closely related mathematical areas. Nevertheless, historical experience suggests that in, say, a century’s time, we will routinely teach this material to undergraduates. This talk describes one dream about how this might come about — under the ass...
ic
my knowledge on this is literally "skimmed half of lurie's first book and that's it"
i wonder how youd explain hott to a grade schooler
explaining types doesnt seem hard, in some ways theyre more natural than sets
"tags" you apply to things
(i mean, even D students in intro programming know what an int is)
but the "ho" part of hott seems like... a bit more of a leap lmfao
you can give some vagueries about how types are related sure
but you need a lot of details to make that... well, homotopical
rather than a description that can apply to any system that permits prepositions on types lmfao
like at the very least youd have to explain like, equivalences to get across the univalence axiom right?
i feel like even types would be hard to communicate, cause you have to get across uniqueness in an intuitive way
I'd tell them homotopy makes a coffee mug equivalent to a donut.
And the point of HoTT is to make this kind of homotopy equivalence rigorous. One reason for doing this is that advanced physics such as string theory needs to deal with homotopy a lot, and when problems are formulated in HoTT they look much more obvious. So it's like a conceptual aid (which is what category theory does, for the adult mathematicians listening)
The distinction between sets and types is, imho, the distinction between starting with things and putting them in collections, versus describing "game rules" and then looking at everything that follows from it. You can see these as the inside vs the outside view. Then HoTT is the observation that when you take the outside view, there's no point in distinguishing things that look the same. But things can look the same in multiple ways, so suddenly "being the same" is more than just a yes-or-no thing.
I finally understood the C++ perfect forwarding
It's all because the value semantics of expressions & declarations
When you declare a function that accepts a, lets say, r-value reference type, like void uwu(std::string&& nya), after that nya gets out of the scope of the argument list(the parenthesis), it becomes a glvalue reference type, so to have it back to its original value semantics, you need to forward it
Yep, and with a universal reference, you need to know the deduced type to determine whether it should be an lvalue or rvalue when passing it along
any one want to play with me a chess click here now pls https://lichess.org/j8YvLlP3
Join the challenge or watch the game here.
But a universal references only happens when the argument type is T&& where T is a generic, right?
I guess one could write a requires clause to overload the set, and deduce whether it's a lvalue or rvalue, like:
template<class T> requires std::is_lvalue_reference_v<T> void uwu(T&& meow){}
template<class T> requires std::is_rvalue_reference_v<T> void uwu(T&& meow){}
That's correct
My C++ terminology is rusty, perhaps I'm mixing up perfect forwarding with something else, by the way
omg yes
What are pre requisites to differential geometry 🤔
if it is "classical" differential geometry in the sense of curves and surfaces in R³ in the style of Manfredo.
Then pretty much just linear algebra and some multivariable calculus
if you want to get deeper than that
Which is doing differential geometry on more general smooth manifolds (e.g riemannian geometry, symplectic geometry, poisson geometry, G-structures...)
then you need some point-set topology, analysis and also some knowledge of smooth manifolds.
I think.
John Lee's "Introduction to Topological Manifolds" and his book "Introduction to Smooth Manifolds" are the way to go for point-set topology and smooth manifold theory.
he also has a book on riemannian geometry
How about introduction to manifolds by L. Tu
this is the kind of explanation that makes a lot of sense to the mathematically minded but i fear is a bit too much of an abstraction for the layman
particularly the stuff on equivalences
like how do things "look the same" without "being the same"
i guess you could introduce like, modular arithmetic as the classic learner's example
It is pretty much the same as John Lee's book on smooh manifolds
except shorter
Oo aiight
i do agree that if you have a bit of mathematical maturity then the motivation behind hott is easy enough to communicate
Sounds more beginner friendly
since john lee assumes some knowledge of covering spaces and π_1 in a few sections
while Tu does not even touch that
Tu also talks about quotient maps from scratch in his book
while Lee already assumes the reader knows this stuff
there are a few other differences here and there
like the way i think of hott is that "it's a system where we study objects by what they are 'tagged' as rather than what set they 'belong' to, and the thing that makes it homotopical (well, univalent) is that there is no distinction between 'good' and 'evil'"
and then uh
magic magic somehow abstract homotopy stuff comes into the picture
in ways beyond the nuking-a-mosquito that it is for normal equivalence relation stuff
I don't get the analogy with good and evil there
do you know what good/evil mean in a categorical sense
"evil" means that we care about equality instead of equivalence
in univalent foundations, equality is equivalence
the classic example of an "evil" question is "how many objects does [x category] have"
never heard of that before lmao
didn't know category theorists also cared about ethics 
(as opposed to objects up to equivalence, which is a meaningful question)
Damn category theory sneaking up from nowhere
(though still not usually THAT useful lmao)
good/evil is a bit more broad than this
its really about like, "layers" of equivalence (in the sense of presentations)
but the basest layer is equality vs direct equivalence, and thats the one the univalence axiom cares about
(though i think the univalence axiom is like giga-strong and actually generalizes? i dont know the details but i heard something to that gist)
say something evil and clerk will come for you
something
nlab gives this example:
For instance, a category can be presented by a simplicial set (the nerve of a corresponding strict category, see there), but isomorphism of simplicial sets is much finer than equivalences of their corresponding categories. It is generally a mistake to mix up these two levels and, for instance, assign to a category properties that are shared only by some of the simplicial sets representing it, say, by distinguishing between isomorphic objects. This breaks the equivalence invariance.
anyway the univalence axiom says that equality is equivalence
so "something is a duck iff it acts and quacks like a duck"
2+2=5 change my mind
ngl i remember it too
that's what i remember from her personality, that's why
That's not me
Someone with the same roles and username and tag and id impersonated me
imma leave this server
umu
they must be jealous
i remeber seeing a video of someone gaslighting chatgpt into accepting 2+2 =5
!help
Please read #❓how-to-get-help
did u retake a year
why do i feel like i am always like an last option for some of my friends, they never want to be in a voice call with just me and them only if its 2+ people they want me to join. Often i can talk about something and ask them a question and they will just like be quiet and if i ask like again like "what do you think?" they will go like "what did you say?" and the issue isnt that i dont speak loud enough or i speak unclearly its just that they almost never wanna listen to me, please help
relatable
I feel like I'm the last choice for everyone as well. like only talked to If nobody else will. like the bare bottom
I guess it's just because I have the least interesting personality imaginable
id talk to u before @woven whale
lol thanks
same
But why do i feel like that
id talk to you before @neat frost
how does someone achieve the status of having a personality

False
Have better personality
thanks nikola tesla
Are you a programmer
not professionally but i know a bit
Do you know how to do python
What a way to end such a high quality discussion 
I mean
I don't think that sufficiently captures the "Ho" part either lmfao
Like, isn't homotopy about detecting holes or some shit?
Need there not be a topological space?
Types are infinity groupoids, which you can turn into a simplical set, then a topological space
basically a homotopy type is a topological space modulo homotopy equivalence shenanigans but possibly blown up formally
there's a reason i specified abstract homotopy theory
hott is not geometric
at least not moreso than any other formalism
You can, however, internally get notions of infinity groupoids and such and internal equivalences with some hypotheses about monads existing
It’s not really possible. Just do maths instead. Don’t waste your time
did someone just ping me here
literally the message right before yours
Bruh look ⬆️
The part that makes it "Ho" is the intensional equality (and also univalence & functional extensionality which gives an equivalence with equivalences/homotopies and relevant paths)
So if (x =_A y) is paths x->y in A, then we also have for p, q: (x =_A y) the type (p =_(x =_A y) q) of homotopies p=>q among paths x->y
oh wait
@bright hill
huh
His discord froze i think
discord can be weird with caching but i havent seen it straight up ignore messages before
i found it
try ctrl + r i guess?
yeah
Bruh how did it go from the last one to this?
yep thats what im doing rn
More like random glitch
uniqueness of identity proofs moment
Namington's explanation is correct I believe, though the good/evil branding is a tad odd
I am here for the record
I'm just trying to process what you wrote 
oh yeah replies are just weird sometimes
If you know infinity groupoids you know how a specific homotopy type looks
though the pi, sigma things can have weird nuances to them
they really are 
but infinity groupoids are basically equivalent to topological spaces
as if topological spaces are docile
(very imprecise statement here but you can imagine why considering every single topological space& continuous function at once is spooky)
infinity groupoids are just simplicial sets satisfying some fairly explicit conditions
yeah as one presentation
still scary but it's not as bad as you might think
Anyone know any good ways of representing 4 dimensional graphs?
This statement ranges from immediately obvious to unproven conjecture depending on your definition
But it's the same intuition regardless
Think paths in topological spaces
Sorry I meant graphs with 4 variables
Yh
uhh one common way, especially if one of your variables is periodic, is with colours
The infinity groupoids I referenced above in the internal statement are opetope-flavored btw so it's a cursed one
(or if your variable isnt periodic, consider a parametrization that makes it so)
its the complex sine function
oh god
then yeah thats sufficiently periodic that such an approach works
this is a mathematica help forum but
oh yeah
the principles apply
comical sets
haha
Path induction is mf hilarious
for complex plots its also common to just
plot the real part and imaginary part
on the same 2d plane
this is what wolframalpha does for example
and then use some other axis, such as time or colour, to vary wrt the other dimension
(obviously varying time means you'll get an animation, not a still)
this is the proof btw, except for one line that says "Yeah the identity monad satisfies these conditions"
lmao
Before I was plotting the real and imaginary outputs along w the real part of the input and was varying the imaginary part of the input
I feel like I lost information though
This looks horrible, but remember that this is hott so you can wish away equivalences
So e0, e1 are the identity

Context
Translation for the non enlightened: it's horrible but it's basically just a formal worse version of saying you've got a basic type X_0 and X_n+1 is trees of points in X_n decorated by n+1 paths
i.e. how do you stitch paths together
- a way to stitch them together
unimportant 
we literally do not care about it except for the singleton point, trees with some bundle projecting onto them, and bundle versions of these two
(Also if you want an actual proper explanation in relation to some concept lemme know)
Hehe, I most likely don't have enough mathematical maturity
Also not quite related, but I've seen ones built out of globular pasting diagrams (apparently equivalent to Dyck words of excess 0 in the type approach) interestingly enough too, one which slapped globular operad algebras on top to get a sort of range between strong and weak ω-categories at once
I'll let you know once I've done some AT tho 
Neither do I, but type theory is funny like that because it doesn't have to make sense it just has to typecheck
Lmfaoo
lmao
I also almost emailed the author about the infinity category composition not type checking until I realized the fibrant condition being moved up a level didn't screw it up
X_1 (1-cells) indeed loses a property, but that hurts nullary composition
n+1 not n moment
actual brain damage on my part
there is a time in my life where I cared much more about this stuff and I could go on about different models of higher categories and how different models are good for different things
but now they're just simplicial sets to me 🙂
went on to care about bigger things
yeah idk tbh they're all equivalent probably
I don't care about the interrelations, I just care if it's reasonable to say things apply elsewhere
not any worse than using a conjectural category
These type based ones are interesting for practical concerns though since a strictly unital and associative one built on globular pasting diagrams has decidable equality
How does type checking work in type theory
which is clearly pretty nice compared to HoTT having contractible types with ultra giga uncountable number of points
nG idk if you care but the opetope trees are the bane of my existence in HoTT for precisely this homotopical unfolding
because we just get like a bundle of trees 
If your function has the correct typing on output, it works gg
I couldn't give any sort of technical explanation on how it works in implementation of Agda, etc
but recall an inhabitant of P can be regarded as a proof of P as a proposition
And if your function is defined everywhere (continuously) and has the right outputs, then it's an inhabitant of the relevant function type
Even if it doesn't seem right, you can get some wacky induction done that's forced to work because of this
cool lol
Ok so is type conversion not a thing in type theory
this is so far from the math I care about these days
I assume it wouldn't be
not really but functions can still be evaluated
what cringe math are you into these days
D-modules in positive characteristic
So, What's wrong with thinking things as (object,type) pairs
have fun with that
it isn't
kinda
but obviously "object" doesn't really mean much
So why do you need category theory for type theory if you can just do that
it's nice, I am studying differential equations over some very simple rings 
K theory of the integers
Idk anything on that so I can't offer anything interesting in conversation
Not that you have to be an expert to talk about something, but if you have no idea what's going on it's not much of a dialogue
my professors dealing with this cursed article be like
(nobody studies this here)
lmao who pushed you into this then
nobody
I mean this is why I stopped caring about category theory at some point
yeah
it's fun to have topics that actually connect to other areas of math easily
But I'm not exactly interested in rings and such
bummer
ordered algebraic things are cool though
like developing integration in po-groups
there's apparently a kinda oldish book on po-semigroup valued measures 
sounds terrible
it is
But remember that they all look finite even if not archimedean because they're still group elements

But this like immediately proves results about like banach spaces or something
because riesz rep
(or analogue thereof)

you can basically get a topological group out of these orders too
but rings are sussier I think

as per usual
Functions f:T->X, measures m: Σ -> Y, a bilinear-y multiplication XxY->Z, gets you integration partial function (M_m(X, Z), Σ) -> Z
why?
I have no idea why you'd do this to yourself
yeah nor do I
this is why I study things that are like
much more easily motivated

But ring multiplication in lattice ordered rings isn't strong enough for that multiplication
I think
I'd have to double check but it doesn't play nice with order continuity iirc
okay lol
The motivation for this: there was none given 
but it's still nifty
Obviously could say things about general ordered integration things, might be able to say things about vNA?

me
I am still idiot undergrad so who knows, maybe I'll see the light of applicable math
or see the applications of these things
I mean the stuff you're talking about is quite far from what a lot of people care about
you seem to dislike rings, but this is where so many actual applications lie
idk you should have a more open mind to more standard stuff
yeah non-commutative rings are a little hard to think about
commutative rings are better
there's a lot you can say about them
non-noetherian 
or about certain classes of them
yeah there's a lot you can say
and commutative ones are clearly nicer and useful for AG
yeah
like in my case a lot of D-modules in char p is literally just thinking about differential operators on a polynomial ring like F_p[x]
I've also seen them used in proof trees in reference to some reduced versions of linear logic
so something very very concrete
Interesting
I have doodoo brain tho
Not very good at math unfortunately
Just kinda think silly infinity categories are nifty 
Nifty is a nifty word
Might get more into measures who knows

Topology is probably just straight out since I struggle with it
basically order-centric version of studying rings of functions 
there's a lot of things which are just based on rings of functions
also interestingly the type based approaches are pretty concrete in a sense by necessity because of this kinda thing. Maybe I'm just dumb for thinking it's more concrete than topology
what does any of this mean
why is topology in algebra
Well I mean functions valued in a ring are usually structured from that
what in particular is odd though?
((i just know neither enough algebra or topology to understand it))
same
How should I prepare for AMC 12 and AIME qual as a Sophomore with no history in competitive math? In Algebra 2, taking Pre-Calculus over the summer.
Do the problems from previous years ig
When I took them there was like 15-20 years or something of problems posted online with worked solutions
the day apple releases a touchscreen M3 macbook air is the day they finally corner the market
as of now it's still awkward to not able to write / draw on a macbook
Also macos runs on the M1 & M2 chips which are arm64 based, so the change should be trivial
do ipads need to run Mac os though. seems like apple is the type of company to prefer people not have their users be able to do anything. ipad is a lot more restricted than a Mac and I imagine apple rather keep people there if they can
letting ipads run Mac would allow users to download software from websites, ruining their monopoly in the app store.
then also it causes people to not need a Mac as much if there ipad can already do everything.
when looking at apple you can't think at all about what customers would like, it's all about what makes apple the most money
You think Microsoft and Red Hat ain't doing that on their respective operating systems?
Data mining is lucrative smh my head
vewo awake at 0340
Woof
i was playing skribbl with ryc and friends
pls help me with decimal
Ok thanks.
Yes, the news is that Apple is working on touchscreen Macs. Which is why I paid attention
Haven't seen a more aptly-named mathematical concept than confusion matrices
True positive rate = True positives / (true positives + false negatives)
There are like 10+ metrics tied to confusion matrices
my main issue lies in that "false negative" means something that is originally negative and you falsely thought it was positive, not something that was originally positive and you falsely thought it was negative
just seems completely backwards to me
sounds confusing
It isn't as long as you know why you are prioritising one over the others
hopefully it'll become more intuitive going forward
I work on real problems faced by businesses. It became intuitive for me starting from that point. I am pretty sure it will for you as well as long as you get the chance to apply it.
it's not really my area but I'm taking an elective on machine learning so I'm not completely clueless about it, I'm probably not gonna get a chance to apply it :(
Have you heard of Kaggle? You can still solve problems there related to ML if you want. Nobody needs to give you a chance.
yeah I just mean in terms of prioritizing it over my other projects etc
my main area is computer architecture so I try to take electives in different topics so I know what the computational requirements of other people are
for example I took an elective on bioinformatics and even though that's not really something I wish to work on, the string matching and motif finding algorithms are very interesting and stand to be accelerated with hardware.
AI accelerators are kinda huge in computer architecture right now so I want to get a good understanding of machine learning for that
@neat frost I rediscovered the best movie ever
we have to watch mean girls together
this is so cringe hahahahaha
all I remember from mean girls is that one scene where she goes "ThE LiMiT DoEsn'T ExISt"
such a staple of modern HS cinematography
I can't believe I forgot this shit existed
Lmfaoo
I'm down to watch it

I'll drag ryc and stuff into it
we can do it over the weekend
(with COMPLETELY legal means, mind you)
I prefer piracy
And afterward we can watch prince of Egypt
PoE


UwU rycie bycie
Watching PoE togedderrr
UwU rycie bycie
I will not watch poe together
I will not watch mean girls together. I already saw mean girls
Fuck you yes you will you little twat
Never
I sent DarQ a very funny clip from mean girls though
HEADPHONES RECOMMENDED
This is a scene from the 2004 Paramount film "Mean Girls" in which Cady tricks Regina into saying what Regina really thinks about Karen and Gretchen on the phone, while Karen and Gretchen are listening on the other line.
No copyright infringement intended.
I could watch this a thousand times and it would make me laugh every time
Keh keh im sick
the other two mathematics servers look pretty sus
DarQ turning into a middle aged man moment
the other girl should have gotten that right easily
not sure why she said the limit was one when there was a zero in the denominator
im convinced she read the bottom as sin^2(x) and the expression on top as log(1 - x) - cos x rather than log(1 - x) - sin x
mentally swapped all the sin and cos terms somehow
cant lie it'd have taken me a good minute or two longer than cady did if put on the spot like that lol
hfffffffffghhhhjj
How do you guys find enjoyment in an easy class with a lot of busy work
I imagine a lot of it is letting go of ego and trying to find where you can improve despite the difficulty
I don't, I'd swap my econ/risk management classes with a bunch of easy exercises/paper work for a math class any time
I was hooked up on the exercises in the control theory class because they were genuinely interesting and not as easy, but now I'm feeling like I'm wasting my own time
Not sure about an easy class but I have a lot of hobbies that helps satiate my boredom with easy work
I guess I try to finish all of this easy work in a day or two so that I don't have to come back to it ever again, or even if I do then I have very little to fix/add
You could use the taylor series ig
Add enough terms to you get precision of 4 decimal places
HUH
Surely you can recall the taylor expansion for e^x from memory? o .o
Brother i am in the 3rd week of college
First semester college algebra
I have no idea who this person named taylor is
hey buddies what are your POVs about existence of perfect cuboid
then are you sure you're not supposed to use a calculator?
but also #❓how-to-get-help
My POV is at a computer screen right now, wbu?
No calculators, No calculators, No calculators, No calculators, No calculators, No calculators, No calculators, No calculators, No calculators, No calculators,
It has been repeated
in class
while he reads
from 14 year old
pirated power point notes
that he
calls his own
Didn't you take calc in hs?
no
Ah
Well I can't think of any other way of computing e to the negative 2 without a calculator
Unless
Hmm.. maybe u could compute 1/(2.78)(2.78) by hand
Doesn't look very tough
,calc 1/((2.78)*(78))
Result:
0.0046116952591773
,calc e
Result:
2.718281828459
Maybe use 2.7182 instead
Pardon my inability to correctly recall the digit at the second decimal place of e earlier.
Uh are you able to type in e^(-2)?
yeah I mean 1/(2.7182)(2.7182) doesn't sound terrible
no calculators is just goofy though
idk what doing that problem by hand is supposed to teach you
ig it might help with getting more comfortable with e but it's a pretty roundabout way to do it
Dumb wasting time calculating it since that's not really the point of the course
You've usually mastered basic arithmetic operations before going into calculus
i can see your mom with some black guys. mmmhhh.... NVM
Why are you peeking? That's a crime bro
just leave it buddy...
i just want to know about perfect cuboid
coz i just found its solution.....
hello
Hi
do you know vectors?
?
Yes he's a very good friend of mine
I know him very well
no i mean the chapter
Sorry i don't know any guy who goes by the name "the chapter"
Maybe try asking in #math-discussion ?
ok thanks
Or #❓how-to-get-help idk
I think you should be the one to leave before someone calls the cops
loool this made me exhale
yeah
try khan academy
Xddd
Tf is khan academy?
🐟
🐟
I wonder if there's anyone here who's done the Putman exam
i like turtles
Geometric derivation of a depressed cubic solution. Thanks Gerolamo Cardano for solving this many a years ago lol
https://youtu.be/2XbFT1hWT_k
Geometrically deriving the Depressed Cubic Equation.
@untold sapphire 
Yes
It is not me though
We got a few sus individuals
yes
But uh, I don’t think I’m capable of a PhD program currently
Ok. Well you have time. Are you doing a bachelor's degree in math currently
Yep
or is your major something else
Math major
The infinity 2 case is already troublesome ofc
And (infinity, 1) still should have more work I think
Infinity n should work in a similar fashion to n=2 though
still thinking about this paper?
Ok. I am going to go to bed as i have a work in the morning. good luck
Good luck with that one lol
Ah shit, now math has become so advanced that now you need to know a bit of psychology as well
Yeah Cubic has never been the same after losing the love of his life Quadratic. Thankfully their daughter Linear is still around to help out with the baby Constant. Hopefully this geometry can help add some foundation to their lives.
@brisk smelt not here man
Sry brother
discussion 2 has slow mode? 
hu
Math makes me 
love this sticker
Falling Backwards reference?
Same
hello, where can I post a signal processing problem? I have an exercise and I want to verify my result.
who wants a coffee candy
same 😭
Ooh I love coffee candy
The little espresso flavored suckers
coffee candy is yum, this one was plain coffee flavour still so good
yes
candy
What are some conditionally convergent series that aren’t the alternate harmonic series
sin(n)/n
(-1)^n a_n, where a_n -> 0?
Depending on how complicated it is, maybe #linear-algebra or #modeling ?
There's not really a dedicated place for it
If you want to ask about Fourier transforms then #odes-and-pdes is probably also a good place
Uhhh how? Certainly you don't learn Fourier transforms in a normal secondary school
I meant like where sum(a_n) wouldn’t converge but the alternate one would
How can I find my help room that has been closed already ? Need to revisit some answers
i just want to say
that i looked up that quote in your bio
and i just now learned
that the respondents in that supreme court docket about the onion
the entirety of the onions amicus brief is a great read
were from parma
argument I is my personal favorite part
do not advertise your help channel
why is this server so dead
It’s like the opposite normally. Go to the neuroscience discord if you want to see a dead discord.
Not enough
It's not good to be counting hours lol
the chinese will take over the world
So ironic neuro discord is brain dead lmao
every academic discord is dead other than maths and politics(this is less of an academic server and more of a shitpost server)
how
"this is less of an academic server and more of a shitpost server"
Have you looked in the university or advanced mathematics channels
Does anyone know what book teach me how to take gradient of a multivariable real valued function written in matrix form?
such book doesn't exist
you can read something like Boyd's convex optimization to get a better hang of the standard functions like linear, affine, quadratic, etc and how to differentiate them
Wait I'm confused
Isn't what LilYee is asking just like
A multivariable calculus book?
What I mean is for example a quadratic function written in matrix form: f(x) = a + transpose(b) *x + transpose(x)Cx
certainly knowing that will help, but I figured it only solved the simplest questions for me
If the functions is written normally, I can take gradient. But its written in matrix
On thing in principle you could do is to convert to coordinate form. So write x = (x_1,...,x_n)
for this specific function you can just write it as a sum and take partial derivative
Well, b^Tx = \sum_{i=1}^n b_i x_i
Yeah but i was wondering is there proof on how to find gradient on the whole matrix notation thing
I think this chapter is quite comprehensive
https://www.cambridge.org/core/books/abs/matrix-analysis-and-applications/matrix-differential/4EA2DCF09BEF6346B6B7687D2DC02227
if you know what each partial looks like then you know what gradient looks like
It's very common for such books to just list results than to comment anything though
I want to know what book instruct me how to do the above
Without breaking the matrix notation down and take partial derivative normally
you can just use the properties of the scalar product
Why not?
Cuz Im paranoid and its too much work
ohh wow, but its not holocaust deniers or nazi supporters, unlike politics server
$\frac{d}{dt} c^T(t)c(t) = \frac{d}{dt}(c(t), c(t)) = (\nabla c(t), c(t)) + (c(t), \nabla c(t))$
So LilYee, for what it's worth once you go into coordinates to compute the gradient, well now you know the gradient and can write it back in vector form, and take it as a known fact. That said, you can use properties of functions to avoid it
Transparent_Elemental
that server is a whole weird thing
there's generally no reason not to learn how to take partial derivatives of complicated functions, it actually helps differentiating more complicated functions without relying on some "rules"
Where is this from? I only learned basic calculus 3
Right. I just wanted to know if there is a compact way to do these things cuz when there are many variables it looks messy
well now you know more, I didn't know that either at some point
that's why I'm saying that what you're asking for doesn't exist, there's simply too much nuance
might as well try to prove it by writing the components of these vectors and taking the derivative
child labor
the problem with "compact" notation is that you have to respect the order heavily as the things you're working with do not commute in general, for example the derivative of x^T C x is generally (C+C^T)x and not 2Cx if we don't assume C is symmetric
Ok
Its just a simple quadratic function
k
you mean child labour is the reason for that?
make sense i gr
LilYee: in this case one thing you can do to dodge going to coordinates is to write down directional derivatives
i have a whole lot of information but can't share it publically
atleast not on this server
i am amazed to read you wrote the chinese might take over this world
i think they have already taken most of it
they are also very hard working and very diligent they can take over very easily
yea. that, Exactly! thats why
nice
wtf is going on here
chinese to take over this world haha
Wait how the fuck did I miss this
This gives off borderline conspiracy vibes. And given that you were first inclined to attribute China's success primarily to child labor this combination starts to feel more like having a bone to pick with China on principle of the matter
While child labor in China at least at one point was, and likely still is, a problem, in context you give off the vibe as caring about that as a means to an end of going after China which isn't the way to play it
Agree with the sloth
Use plastic hammer
(Probably made in China)
Techno you seem to have a habit of trying to dictate to me when you decide something's banworthy
But frankly I have my eyes
I will use my own judgment to decide this sorta thing
2-adics be like
1/2-adics when
piadics
i am a 2 addict
Dyadic 
youtube comments are the greatest. i read comments on almost all videos, 100%fun from video, and another 100% from comments, = 200% fun
Just a suggestion as always the final decision is yours as the holder of the plastic hammer... sometimes it's a joke lmao
I HATE DISCRETE MATH, ITS JUST NORMAL MATH BUT WITH RNG
Ironically, discrete rng is easier to understand
im just mad chatgpt cant do my homework anymore
It being able to do your homework was a mistake
Because well chatGPT's goal is to sound authentic, not being correct
discrete rngroupoid
Is there anyone at U of Chicago here?
Daminark
Used to be, not anymore
I don't think we have any current UoC students
ah
Maybe he'll still have access though
university of ryc when
university of math discord
I am an undergrad there
Oh finally someone! Would you be willing to take some pictures/scans of a document in the library that can't be found anywhere else? It's a math article in an old discontinued journal and it seems that this libraey is one of the few places in the world that has it. I'd be very grateful if you were 
I think if you're in a U.S. institution, then you might have access to interlibrary loan. Basically, you can ask for material from another institution through your library.
I am in fact not in the US (I'm french) and I have already graduated from my uni anyway, I only have minimal access to its resources now
If you can't that's ok, I think I can try to ask directly the library thanks to an online form. Though the form isn't really meant for that as far as I gathered so I don't know how they might respond or how long it would take for them to answer.
you can DM me the details of the doc and I will try to request it
Starting a university would be really fun

Laplace expansion
there is, using row operations
Thank you!
That my friend, is hell
What the Hell
Even Laplace expansion isn't the worst if you immediately start with the last row
How am i supposed to remember any of this
More you do it the more used to it you get
you could convert it to an upper/lower triangular matrix and just keep track of the row operations iirc
@neat lintel
though that's probably what josemom meant

Gm
is that Arithmetic progression ?
I have no idea, it's the math for finding the determinate of a 5x5 matrix
oh
Is it possible to solve for x here?
Yeah ofcourse
How
factoring
Factor x out
Swap the side of equation might make it more familiar to you
!help
Please read #❓how-to-get-help
im looking at perturbations to an equilibrium solution of a 50 dimensional ODE
some components of the 50 dimensional solution oscillate
what would one expect the jacobian's eigenvalues/evectors to look like?
if there's oscillation
There are complex eigenvalues
i get some really tiny complex parts for the eigenvalues
when i compute them
on the order of 10^{-19}
- there's a few evals that are negative, order 10^{-2}
- mostly positive real evals, order 10^{-17}
- a few complex evals, with both real and complex part order between 10^{-17} and 10^{-19}
what does that mean?
and also when i plot the graphs, most components converge except a few that oscillate
so im just confused
So the adelic Poisson summation etc and the adelic language do make thing interesting and easify understanding of Hecke original contribution to analytic continuation of Hecke L function. But what's with the K theory angle of talking about special values of L function. Does K theory angle really helps much in number theory stuff?
Your jacobian is singular and a lot of the effects could be simply due to poor calculation accuracy due to singularity
Is it really a non-zero eigenvalue when we're talking order ^-17
Even if you ask e. g. python to compute sqroot(-1) it'll produce a non-zero real part on the order of ^-17
Looks like a polynomial to me
You shouldn't
substitute in y=e^x
then when you have y, you can solve for x as x=log(y)
I got it
thanks!
Question 11
Why I cannot using this way to solve A?
The answer say A=3.67
You're trying to take a log of a value which is already measured on the log scale
I got it already
https://www.youtube.com/watch?v=41HIXtBElH4&ab_channel=MichaelParloff who else thinks allegro molto is overrated? Allegretto is far better
00:00 Largo
05:07 Allegro molto
08:12 Allegretto
12:36 Largo
17:43 Largo
1st violin: Eugene Drucker
2nd violin: Philip Setzer
Viola: Lawrence Dutton
Cello: Paul Watson
This performance of Dmitri Shostakovich’s 8th String Quartet in C minor, Op. 110, by the Emerson String Quartet took place on December 16, 2018 on Parlance Chamber Concerts at ...
i love shostakovich's quartets
can someone help me on help-22 please?
No part of that quartet is overrated.
if anyone can help me dm rq its geometry 10th grade math TY if you can
#❓how-to-get-help your chances to get help are better
If 100 cats exist, and 75 of them have orange shoes on. 3 of the cats run into the street and get hit by a bus. What are the chances that 2/3 cats have orange shoes on
Now I want to see 75 kitties with orange shoes on
Are some of them just sitting in a giant boot
Please read #❓how-to-get-help
Learning math is such a slow process for me
that I run outta copium sometimes 
How do you guys deal with your own progress seeming slow to yourself 

No but seriously though, how do you guys deal with it
I mean I get rationally that learning math is not a easy or quick process, and I shouldn't dwell too much on that. But it still is demotivating, from time to time, how little I skills and knowledge I have after putting in a certain amount of effort.
Again though, if I think about it rationally, I think I have improved a lot in both skills and knowledge over the past year
I hate that math is a competition
It is not
I hate that public schooling and standardized testing and limited seats in college and limited jobs has made the act of learning math culturally associated with competition
Ah okay then yes
I hate it for everything
yeah i can agree with that i guess
i'm very glad that the system is different in my country
well limited jobs are still a thing of course but well that's inevitable
Therapy
how does therapy solve this global-scale norm?
It doesn't. I go to therapy because Im sad lol
I hate life being a competition 
- a competitive person
This is what I think about all the time
now i think about it, i dont hate it that much, was just meming. Sorry 
competition is only good when you win
Check your privilege

my issue about exams/tests is less the competition, but more that they fail to assess what they're designed to assess more often than not
And due to this, encourage certain unnecessary/useless/sometimes downright bad skills
I enjoyed contests as a kid won medals and certificates some interschool
Like what
Fair
Is it better to be able to half-ass a question in 30 mins, or need a day to fully answer?
Speed is still important tho
That depends on context
Time is money
When it comes to research mathematics... idk about that.
Like if you're doing research, that translates to more research output
It would be wrong to say speed is totally irrelevant
but I don't think it should be prioritised over quality
But sometimes they prioritise it too much
I agree
which exams kinda encourage you to do
Like doing tons of easy questions in a short period
So what are alternatives to exams....projects maybe
projects 
I'd say stick with exams
like I have no idea how many times I had to factorize a simple quadratic in class
Well that's actually useful for stamina
im not proposing something better over exams, no, its just how it is
What could be better is a personal evaluation
But that's logistically impossible, and inherently biased/flawed
You can obviously change the exam format to make it better
everyone be like rating themselves straight As to get into top unis frfr
i mean personally by someone else who is qualified to do so 
Could be happening as we chat lmao
meritocracy is false. The number one marketable skill is inherited wealth. We should honestly do away with exams and grades
teacher's pets be like
we should but there's no better alternative for now is there?
This be partly true but not entirely some do rise up from lower economic classes
I'm not proposing some change. I'm frustrated that school is shit.
Inherited wealth is not a skill
Exactly
school is shit, yes, but not like we have anything better now do we? So we have no choice but to s u c k i t u p
I'm out of school. I don't need to suck anything up. I can just complain now

wdym? Imagine not being able to choose which family yr born into man
If it's "shit" and there's nothing better, every goddamn thing is shit so your metrics are wrong. "Shit" would mean below average
skullissue
democracy is shit along with all other systems that ppl have come up with so far 
You say everything is shit implies metric is wrong? It isn't a metric pal it's a human emotion in reaction to life being frustrating and shitty.
society is kinda bad in quite a few ways but welp just live with it till it gets better 1 day
i wouldnt hold your breath.
indeed
1000 years in the future we will determine it all by brain scanners trust ™️
since you cannot change it (probably), it is better to try change yourself so its less so
And compromise yourself and your ideals to fit an unjust and inequitable system lmao
you dont have to mold yourself to the system
Im out of school. What is there for me to improve for myself? School sucks and I wanna complain
u can simply accept certain parts of it and avoid actively warring with it (internally)
like if u cant change it, theres not much good that will come out of complaining about it
What system ru referring to
The one we live in rn
unconstructive criticism is just a waste of your own time
Social strata differences in capital
https://en.wikipedia.org/wiki/Hopf_fibration#Geometry_and_applications wtf am I looking at
In the mathematical field of differential topology, the Hopf fibration (also known as the Hopf bundle or Hopf map) describes a 3-sphere (a hypersphere in four-dimensional space) in terms of circles and an ordinary sphere. Discovered by Heinz Hopf in 1931, it is an influential early example of a fiber bundle. Technically, Hopf found a many-to-one...
No it's also a waste of other ppls time as well
How do you propose to fix that
Very stoic...such admire
I am not proposing a fix I am complaining that it sucks







