I think they meant "general public" as acedemia.
#serious-discussion
stiff aurora
surreal sapphire
i heard of one case where academia discovered something and it was later revealed that the NSA already knew about this x years
but i dont think this is common
stiff aurora
I mean I can think of differential cryptanalysis (from the post) and RSA
surreal sapphire
there are a lot of good researchers nowadays and most of them dont work for the NSA (or are even american)
pearl moth
more so in recent years, as well
the US had outsized influence in the decades after WW2 but that has increasingly not been the case as european centers of excellence recovered from the depredations of the war
surreal sapphire
also south asia
pearl moth
as well as various centers outside of both europe and america became more respectable
(bloody fingers not behaving)
stiff aurora
Also Loch are you our resident ECC expert?... if so is this true:
The mathematics behind Elliptic Curves are not well understood
We have no proof that elliptic curves are inherently strong
pearl moth
there are certainly unanswered questions related to elliptic curves, answers t owhich might potentially give someone who knew them a competitive advantage in this area
surreal sapphire
elliptic curves are still being researched
pearl moth
but i think it's unlikely that the NSA is sitting on any such gems
surreal sapphire
we dont have a proof that anything is inherently strong
also ECC is rather wide
there is the classical approach via the group law and the more modern approach via isogenies
the latter isnt understood very well at all, its only being researched for 20 years
this is one reason why NIST decided against it
(there is no other post-quantum protocol based on elliptic curves)
stiff aurora
Don't we have proof some are strong by the whole NP, NP-Hard stuff? Or I guess thats a bad indicator for strength.
surreal sapphire
with most things we use its no one knows
complexity theory isnt well understood either i think
pearl moth
there's plenty of unanswered questions there too, yeah
fervent pebble
hey loch what was that massive book you recommended for cryptography again?
linear algebra
surreal sapphire
good question, its really just a vibe
"we tried for 20 years and didnt find any major flaw so its probably fine"
fervent pebble
yeah, but it's still well understood
surreal sapphire
i would also say linear algebra is well understood fwiw
sick kite
pearl moth
it is unlikel that someone will pop up and announce some result that undermines our broad understanding of linear algebra
surreal sapphire
hey loch what was that massive book you recommended for cryptography again?
if its a math "book", probably https://www.math.auckland.ac.nz/~sgal018/crypto-book/main.pdf
fervent pebble
yee that was it tyty
surreal sapphire
ye also there arent many articles published on linear algebra or euclidean geometry
pearl moth
there are likely more articles on the history of euclidean geometry published in any year than there are on euclidean geometry itself
surreal sapphire
oh sorry by linear algebra i meant the finite dimensional case
pearl moth
there are definitely things to research in infinite-dimensional linear algebra
fervent pebble
elliptic curves are hard to understand
pearl moth
they're so wobbly
bronze pelican
They're donuts
pearl moth
so strong so brave
fervent pebble
for now 😭
surreal sapphire
"we tried for 20 years to break this but couldnt"
also you have to mention that NP-hardness doesnt suffice for the needs of cryptography
you need problems that are hard on average
and with many NP-hard problems you dont have this
im not sure if average complexity is even researched in complexity theory
but in cryptography its mostly "we assume this problem is hard because we tried to break it for a while and couldnt"
sometimes there are more mathematical reasons to suspect something is generally hard
pearl moth
this reminds me of the ongoing effort to find efficient multiplication algorithms
fervent pebble
wasn't karatsuba's proved to be the most efficient?
pearl moth
no, it's been proven not the most efficient
schoenhage-strassen is more efficient in the limit case and practically for cases involving more than 10,000 digits
fervent pebble
huh
pearl moth
and Harvey-van der Hoeven is categorically faster, being flat out O(n log n)
but that's only from last year, and people are still poking at it
karatsuba remains practically faster for digit counts between about 1000 and between 10,000 and 40,000 depending on hardware
gmp has seven (iirc) different algorithms it selects from depending on the size of the problem, including some that are specifically for "unbalanced" multiplications
hollow sundial
@reef carbon moving here. i disagree that i in any way yelled at them
that you consider all PDFs not made by yourself to be infested with viruses by default
Obviously not. e.g. co-workers, friends, etc.
reef carbon
you told them off for daring to upload their problem in the form of a PDF and not an image.
reef carbon
this reads as telling them off to me.
but i guess this is grounds for you to publicly accuse me of defamation of character.
could be grounds for you to publicly accuse me of defamation of character.
hollow sundial
"defamation of character" is also an exaggeration. i haven't said anything about you
reef carbon
i said you HAD THE ABILITY TO present this as such.
neat lintel
Calm down.
reef carbon
i am calm.
hollow sundial
what's the point in presenting hypotheticals? i have the ability to type a lot of things.
reef carbon
the point is that you demonstrated that something i said about you is false
which is like, Bad or something, or so i would think
tall badge
@reef carbon @hollow sundial this convo seems like it belongs in a dm
reef carbon
i have nothing more to say anyway
neat lintel
I sometimes read internet comments as meaner as it's meant to. Just because I'm in a bad head space.
hollow sundial
i'm perfectly content with being accused of being too harsh or yelling at people. more often than not, other people are right. just not in this case.
alright i'm done too
neat lintel
Just assume the best intention from the other party.
hollow sundial
<@183668144404037632> <@261933205387477002> this convo seems like it belongs in ...
thanks for chiming in
tall badge
for future reference, pls raise personal concerns in dms
hollow sundial
differential equations
what's the closest university to you that has a good math program? they usually give templates
neat lintel
what's the closest university to you that has a good math program? they usually ...
they do?
like do i just ask them to give me their template on maths(pure)
neat lintel
https://math.berkeley.edu/programs/undergraduate/major/pure
coool thanks
hollow sundial
but yea i think real analysis and abstract algebra would be first after differential equations. some universities have an "intro to proof" class since it's such a big leap from calculations to proofs.
neat lintel
hmmm do they not start with proofs?
hollow sundial
i think real analysis and abstract algebra just assume you understand proofs very well already
coming up with contrapositives, logical equivalents, proof by contradiction, etc.
errant ridge
that's probably why most people don't do well in their first pass of real anal
at least from what I've heard
hollow sundial
yea i went through the class and it was good for me
also makes people get a flavor for the rest of math and see if they want to change majors before wasting too much time
https://math.mit.edu/classes/proofsiap/ seems pretty good
the first half is all i learned since i was on the quarter system
errant ridge
proofs and basic real anal should be introduced in highschool tbh so that the can get a taste of it earlier
hollow sundial
ancient flame
this sounds like a fun and interesting course
ancient flame
reposting bc nobody gave a shit
bright locust
I wonder how intentional it is
Internet troll level
ancient flame
lmao
junior stump
fun fact here
fervent pebble
huh
that number feels low to me
although ig unique solutions is a pretty big limiter
velvet dagger
I mean
20 digits, 9^{81} is 77 digits
And then keep in mind that we're putting a bunch of heavy simultaneous constraints
wooden flax
yeah
fervent pebble
hmmm
put that way it sounds much more reasonable
i don't think i fully get how 'heavy' the constraints are
velvet dagger
Well within one 3x3 box
If you could have any sequence of numbers
9^9
And then instead it's 9!
0.09% of possibilities
Let's do a more precise estimate
If each 3x3 box can contain any permutation of 1-9
Number of digits is 9*log_{10}(9!)
Which is about 50
But now we're requiring on top of that that every row and column is a permutation of 1-9
So if the total number of sudoku puzzles is the square root of the number of "sudoku puzzles but we're not requiring anything on rows/columns", that goes down to 25 digits
This is 22
So this feels aight to me
(I didn't have any intuition for coming up with the square root number I just noticed it's approximately double the number of digits)
uncut socket
@sonic steeple -3
uncut socket
Opps can't math
sonic steeple
uncut socket
I meant -2
low relic
whos good at word problems
cold needle
do you need help on some problems?
uncut socket
do you need help on some problems?
They opened their own channel
neat lintel
proofs and basic real anal should be introduced in highschool tbh so that the ca...
yess
late geode
Real anal.
arctic grove
lament flicker
can you write the set of complex numbers in this way?
R[i]/(i^2+1)
frigid narwhal
For anyone who has done the Australian Maths Competition what did you think of it
For reference I have done but want to here other peoples opinions on it
scenic narwhal
can you write the set of complex numbers in this way?
R[i]/(i^2+1)
Yes usually that's the definition
lament flicker
nice
vivid halo
right, R[i]/(i^2+1) is adjoining the roots of i^2+1 to R
the two roots, say i and -i, are algebraically indistinguishable
so you get a symmetry which is complex conjugation
neat lintel
<:sotrue:826971355542192148>
Anal.
arctic grove
we all love anal
cold needle
anak
cold needle
suly
neat lintel
we all love anal
Yes!
wooden flax
smh i still need to read complex anal
lunar spear
You what?
pine ledge
we all love anal
As in?
pine ledge
to do some good anal
Could've worked that better
wooden flax
real or complex
arctic grove
and i dont think i have the time to also do anal since i am not done with entrance exams yet
😭
i would love to do it a lil later if u dont mind
wooden flax
r u from india?
arctic grove
yes
wooden flax
i would love to do it a lil later if u dont mind
o yea definitely
wooden flax
arctic grove
but im giving it just in case
wooden flax
rip
arctic grove
indian institute of science education and research
wooden flax
sounds fancy
wooden flax
so like ivy league in us?
wooden flax
its kinda like the best u can get here
better than iit?
arctic grove
its ivy league for people who want to do pure science
wooden flax
ohh ok
arctic grove
better than iit?
usually there isnt a direct comparison
but for science yes
wooden flax
i see
vast surge
we all love anal
The math server certainly is something.
pine ledge
The math server certainly is something.
Math server is fun
deep mango
bright hill
<:sully:651816820122189834>
hehehe
hello ryc
@deep mango would you say fun anal is more fun than intro anal?
deep mango
Yes
bright hill
bright hill
yee
it's like
nothing is new but you gotta painstakingly prove every seemingly obvious fact
so it's no fun and all the pain
deep mango
I thought compactness was fun
That was about it
Seeing why Taylor's theorem is true was fun
hollow sundial
I thought compactness was fun
compactness is only fun outside of R^n
hollow sundial
sequential compactness is the way to go
cold needle
being able to pass between sequential and open sets notions for things is good
hollow sundial
although proving sequential compactness and the topological definition are equivalent is a bitch
bright hill
sequential compactness is the way to go
sequential compactness is every sequence got a convergent sub sequence?
hollow sundial
this proves one direction
just looking at that i want to vomit on my munkres book
no wait that's a 3rd kind of compactness
hollow sundial
topology is too ball heavy for me
neat frost
My balls… are heavy….
neat frost
Wewcome
rose dock
My balls… are heavy….
I can help with that
hollow sundial
drain the ||cubes||
wooden flax
The math server certainly is something.
i mean it just feels good to do hard things in anal
if you know what i mean
wooden flax
how do you pronounce wew
in my head i think
wheeeu where the final u is the u in like stupid
wooden flax
like woo?
echo fox
something like view
deep mango
although proving sequential compactness and the topological definition are equiv...
Thats the sort of argument I think is cool
deep mango
compactness was fun?
Yeah
hollow sundial
i agree that argument is cool. it's just a complete bitch
deep mango
Proof that [0, 1] is compact by splitting into two intervals and picking the one which requires infinitely many open sets on it, and repeating this until one interval is small enough to fit in one of the open sets
Is cool
It's like finding a path down an infinite binary tree
hollow sundial
Final Exam: Prove [0, 1] is compact
Ryc: Merge sort :lel:
hollow sundial
i agree that argument is cool. it's just a complete bitch
completeness bitch
FTFMe
deep mango
Though you might not discuss that in intro analysis
hollow sundial
i definitely didn't learn that
deep mango
I think I learned it in my graduate analysis class
leaden sage
@hollow sundial its compact because its using brackets and none of the arguments are infinity
frozen merlin
I'm still not convinced [0, 1] is compact whereas (0, 1) isn't
(0,1) is homeo to R, does that still seem compact?
wicked ore
Compactness is formally defined as a space that includes brackets when you write it down, and also no infinity symbol
static loom
here i thought it meant every open cover has a finite subcover
wicked ore
Only a fool
frail lagoon
Every space is compact as infinite objects don't exist
vast surge
here i thought it meant every open cover has a finite subcover
Compact is defined to be closed and bounded.
leaden sage
@woeful oxide like electrical circuits?
woeful oxide
yeah
leaden sage
theres a good amount of resources for the basics online, or at libraries
static loom
Compact is defined to be closed and bounded.
I prefer to define compactness to mean sequetially compact
woeful oxide
theres a good amount of resources for the basics online, or at libraries
Pls help me I can't find any
I want someone to help me with physics really
I wanna learn and I'm enthuasiatic
My exams are really soon after 3 days
I have to study electricity and magnetisim
leaden sage
woeful oxide
And I have to solve circuit problems
leaden sage
storm sage
proof that [0,1] is compact: bounded closed interval
bright hill
(0,1) is homeo to R, does that still seem compact?
ok, so (0, 1) is homeo to R but [0, 1] isn't?
storm sage
yeah
cold needle
which part of that is so 
storm sage
Compactness is formally defined as a space that includes brackets when you write...
[-1,2] \ [1,2] \ [-1,0] is compact 😎
bright hill
which part of that is so <:starebleak:911875700489871380>
when I imagine (0,1) being homeomorphic to R I imagine (0, 1) being stretched to cover R
I don't intuitively get why we can't do that for [0, 1] as well
cold needle
it has to do this continuously
vast surge
I don't intuitively get why we can't do that for [0, 1] as well
Where are the boundary points mapped to when we do this?
cold needle
so a continuous map is one where the preimage of open sets is open
but preimage of (a,\infty) is ???
vast surge
so at infinity I assume
Right, but infinity isn't a real number. So as a map to R this isn't even well-defined.
cold needle
||not open in subspace topology||
storm sage
so at infinity I assume
R unioned with infinity (the set of extended real numbers) is compact
cold needle
oo
storm sage
so if you stretch out the boundaries of [0, 1] to infinity, then it actually stays compact
:)
cold needle
vast surge
There are compact spaces that contain R. For instance, the circle.
cold needle
ignore me lol i had a Moment
vast surge
Anyway, perhaps the way to think of compact is "things that behave like closed intervals and points"
storm sage
terrence tao has a good explanation
bright hill
how tf do you picture every cover got a finite subcover
bright hill
terrence tao has a good explanation
hm?
bright hill
where
vast surge
how tf do you picture every cover got a finite subcover
Imagine you have infinitely many blankets and then you remove some
You want to cover your space with blankets that you put on top of it. But, however you do that, you want to then be able to remove all but a finite number without removing all the blankets.
Like, literally think of something in R^2 covered in blankets if you want to visualize it
static loom
how tf do you picture every cover got a finite subcover
it also might help to see compactness used in a proof. the simplest example I can think of is proving a function that's continuous on a compact set is uniformly continuous. Roughly you just imagine at every point it's continuous you can place an open ball centered there, then this forms your proverbial infinite open cover. But since it's compact, it actually has a finite subcover, and so you then go on to end up proving it's uniformly continuous.
cold needle
i like that theorem a lot its so cute
bright hill
it also might help to see compactness used in a proof. the simplest example I ca...
I did see compactness in proofs
cold needle
it really captures the "finiteness" that comes from compactness that my prof likes to talk about
bright hill
I think I just need to get used to it?
celest pulsar
Here is another way to think about it but it is not using open covers and it only works in metric spaces (for example it works in R)
Like if you take a finite set and consider a sequence on it, at least one point must be obtained infinitely often by the sequence
Now if you replace the finite set by an infinite set, this is clearly not true anymore
Because you can have a sequence that visits each point once
But with compact sets, you can get the next best thing
For any sequence, you can find a point that is approximated arbitrarily closely by the sequence infinitely often
tall badge
it really captures the "finiteness" that comes from compactness that my prof lik...
the idea of 'smol wrt topo' is already captured in the finite subcover part of being compact
cold needle
ah yea dats true
ig i mean more like
another example of the finiteness feelings
or maybe like in context/use
tall badge
this theorem is like smolness in action
tall badge
anytime u extract finite subcover
tall badge
ig I just don't have an intuitive feel for compactness, is what I'm trying to sa...
as per above, compact expresses being 'smol' wrt a topology by letting u extract finite subcovers
arctic grove
The math server certainly is something.
Indeed
velvet dagger
this theorem is like smolness in action
:0
arctic grove
ok, so (0, 1) is homeo to R but [0, 1] isn't?
Im sorry what
leaden torrent
and [0, 1] certainly isnt homeomorphic since like
what do you map the endpoints to
arctic grove
I thought u could map them somewhere in between, but Ig that won't be a homeomorphism then
deep mango
That would not be continuous
There isnt even a continuous surjection from [0, 1] to R
arctic grove
There isnt even a continuous surjection from [0, 1] to R
hmmm
simply because of the endpoints yeah?
peak tide
continuous functions map compact sets to compact sets; [0,1] is compact but R is not. truth hurts
brittle socket
Hmm what are these r's that appeared
arctic grove
continuous functions map compact sets to compact sets; [0,1] is compact but R is...
😭
lunar spear
Hmm what are these r's that appeared
letters
brittle socket
letters
Ah yes, the floor is made of floor
Im asking what are they supposed to represent since i didn't have them in the collection of variables i defined
median zinc
Hmm what are these r's that appeared
Is this sage or sympy?
brittle socket
Sage
median zinc
Well it could be some constants/real numbers
brittle socket
On a side note, setting up sage was an absolute pain
brittle socket
Well it could be some constants/real numbers
Hmm
median zinc
They are real-valued parameters.
https://ask.sagemath.org/question/52904/what-does-r-in-an-answer-mean/
woeful oxide
Guys
brittle socket
They are real-valued parameters.
https://ask.sagemath.org/question/52904/what-do...
But since i asked sage to solve the equation, why didn't it just tell me what those real numbers are instead of just telling me they're some real numbers without specifying
median zinc
They are families of solutions, do you know what this means?
brittle socket
Yeah i know what are families
I get what it meant
But is there a way to let sage like compute one of the answers from that family of solutions
Like just for the fun of it
Or like express the solution in terms of x,y,z,a,b,c
median zinc
There's probably some substitution you can force it, I'm not sure
brittle socket
I see
Anyways thanks haha
: )
Tried to google for an answer just now but didn't find this one for some reason
Or i was just being blind lol
neat lintel
GUYS./
I need a REALLY good Algebra / Trig book.
One of my BIGGEST Obstacles to self-studying calc are the holes in my algebra.
Is there a book that is the Algebra/ Trig equivalent to Spivak's calculus?
errant ridge
do it!
prime plover
There is serg lang's basic mathmatics, which is supposed to cover high school math
up to pre calc
i tried reading it once when i was in your situation
neat lintel
no
storm sage
khan academy is pretty good I think
storm sage
matrices and determinants are precalc..?
first time I got taught that was linear algebra
huh
that sounds like a typical first semester linear algebra class
that's so strange
you don't need matrices for anything until linear algebra, why teach it before calculus
tf
your high school is advanced LOL
a good deal of high schools don't even teach calc ii
yeah I don't think there's any reason to teach them in a precalc class
trig identities and stuff are important though
clear parcel
I also learned matrices early too in school just like how to multiply them etc did help when I went to linear algebra and manipulating them was nothing new
calm sigil
ive just read about length contraction and im curious
does it mean if we had the millennium falcon and flew at 1.5 times light speed, great distances in space would seem to only be 2/3 what measures made on earth say they are?
fringe needle
ive just read about length contraction and im curious
does it mean if we had the...
Can’t travel at 1.5 times light speed
At least not with matter
calm sigil
Can’t travel at 1.5 times light speed
hypothetically
fringe needle
There is no hypothetically
clear parcel
Also things would appear 2/3 smaller before you get to 1x the speed of light
calm sigil
well millennium falcon also doesnt physically exist but thats not the point
fringe needle
It is the point
calm sigil
Also things would appear 2/3 smaller before you get to 1x the speed of light
whys that
fringe needle
Cause you’re trying to apply a theory to something it doesn’t cover
We can’t reasonably answer your question because it’s against the laws of physics
calm sigil
imagine a little
clear parcel
well because length is equal to proper length divided by gamma and gamma is always bigger than 1 you only need gamma to be 3/2 then your length is 2/3 the proper length
fringe needle
imagine a little
But then what are you learning
I can give you a bullshit answer of you want
But like
It brings absolutely nothing
calm sigil
well because length is equal to proper length divided by gamma and gamma is alwa...
i see
fringe needle
It’s like asking: if I apply the perfect gas law to a viscous fluid with heat transfer what do I get
fringe needle
It’s like asking: if I apply the perfect gas law to a viscous fluid with heat tr...
The model just doesn’t apply
calm sigil
that says nothing to me idk chemistry
fringe needle
If I let electricity flow in a non conductor
What happens
It’s a non question
Okay that’s a pretty shit example tbf
But I hope you get my point
It wasn’t a stupid question don’t get me wrong, just founded on a misunderstanding but the idea of the question was fine
fringe needle
not misunderstanding just expanding on the idea
No see this is where I disagree
fringe needle
“If time stops how do I apply the law of physics to find the speed of a moving car” is in analogy to your question
It doesn’t make sense
Why am I so shit at generating one good analogy 😂
calm sigil
moving a bit of information 1400 kilometers instantly also doesnt make sense and they did that in 2017
fringe needle
The point is if you want to find out what happens in a scenario that physics doesn’t currently follow, don’t try to just extend an already existing theory naively
The only way you’ll be able to deal with those scenarios is by building a new theory that refutes the old one
And you sure as hell aren’t going to do that on a discord server
clear parcel
something I wondered is if the universe could have 2 separate electromagnetic fields with two different speeds of light, then what would happen? What if there was an infinite number each with different speeds and we experience the average? I read a QED book by Feynman once and talked to my professor about it and he said photons don’t really have a speed. It’s more like an interval that a photon is detected from one place to another. This interval can actually take any magnitude, but it averages to the speed of light. Idk how accurate that is but that’s what I understand @calm sigil
clear parcel
I think it is something we have to measure we don’t have a theoretical way to predict what the speed of light will be
take that with a grain of salt lmao
calm sigil
leaden sage
its already different through different mediums; I would assume a similar situation is the only way that would be able to make sense
leaden sage
but how do you take the average of an infinite number of speeds
symmetric infinity around an identity, or something
calm sigil
symmetric infinity around an identity, or something
idk what that is
and neither does google lol
leaden sage
do you think we could say that 0 is the average of all reals? if the bounds are + and - infinity? or also we could say its something similar to an average
fringe needle
There’s certainly a sense in which you can say it
Take a the limit of the averages of compact disks as the radius increases
But the question always remains: is your definition worthwhile
In this case, saying 0 is the average of real numbers in this sense has a few caveats
For example: why pick a limit of compact disks of increasing size? Why not just compact sets?
But now you run into a problem because the average becomes ill defined, ie the limit doesn’t exist
Thought experiments and questions are great, but often times they are not questions that are answered by the current theory and unless you build your own framework for the things you say to start making sense and be of use, the questions are best left as an after thought
That doesn’t mean you should stop asking them though
leaden sage
its physics so you'd just wait for the experiments, I suppose
fringe needle
Yeah in physics you have the added luxury of experiments
storm sage
do you think we could say that 0 is the average of all reals? if the bounds are ...
if you translate the reals over by some amount c though you get the set of reals again, but the average has moved to c
so it's reasonable to say that the reals do not have any middle point
viscid pecan
Wdym
tender tulip
I keep asking this but I wonder if anyone has any idea, it's kinda complex and more discussion worthy but
From what I've seen
Every (complex) function that satisfies y'' = L(y), and by integration and differentiation, y'^2 = L(y) where L is a complex polynomial [regardless of initial conditions] is perioidic
either singularly periodic or doubly periodic
Is there any good explanation for this
Along with that, many often have addition theorems
The exponential, elliptic, and tangential functions are all examples
storm sage
this sounds like harmonic analysis
tender tulip
this sounds like harmonic analysis
idk how that would help
unless you use reimann cauchy which is even worse
static loom
I guess there are some edge cases to consider as exceptions, idk if they can be pushed into worse examples
like when L(y) is a constant we have solutions that are quadratics which aren't periodic (well, assuming I have the right idea of periodic as you do)
storm sage
Wdym
I just mean that the real numbers are invariant under translation, so I'm not sure if the notion of an average of all real numbers is useful
tender tulip
like when L(y) is a constant we have solutions that are quadratics which aren't ...
fair enough, didn't think of that
if it's a nonconstant polynomial
static loom
does this disrupt any solution because if you have a solution, you can always add a quadratic with a bit of scaling to it to get another solution I think
or maybe not idk
tender tulip
it's weird
static loom
when you say periodic what do you mean specifically, there's some line in the complex plane where it's periodic I assume
tender tulip
specially when you consider elliptic curves and how their group law's addition correlates in some way with their function
tender tulip
when you say periodic what do you mean specifically, there's some line in the co...
yeah
static loom
I think maybe it's worth fleshing out in a bit more detail so we have our hands on it, let's assume $L(y)$ is some fixed polynomial, then $y''=L(y)$ can be turned into $\dv{y'}{y}y'=L(y)$ and so $$\int y' dy' = \int L(y) dy$$ and then a bit of manipulation makes it for some other arbitrary polynomial $M$, $$y'^2 = M(y)$$ and so we can now end up looking at this $$\int \frac{dy}{\sqrt{M(y)}} = t+C$$
fathom swallowBOT
Merosity
static loom
I don't know how useful that is but trying to flesh this out a bit to make sure I'm actually on the same page as you because I've not fully realized my psychic abilities
leaden sage
@storm sage that's also where the identity aspect might be useful though
tender tulip
**Merosity**
rational function.
it's an elliptic integral
but only for degree 3 and 4
static loom
I think there may be an addition theorem to prove from this
if I were you I would attempt to go through the proof for arctan, or any other one, then try to see if you can mimic/alter it to work for this general case
tender tulip
here's why it's difficult
static loom
you might have to think in terms of defining a kind of function and inverse etc to get the job done
static loom
M is the result of integrating a polynomial
tender tulip
First you need to consider a branch cut for x^1/2
static loom
if its degree is less than 1 that's just a constant
tender tulip
M is the result of integrating a polynomial
<2
SO here's the issues
- Branch cut for the square root
- Branch cuts for the inverse function
@static loom I don't really know how to work with branch cuts well
Lets assume M(x) is inseperable
static loom
well sounds like you have a motivation to learn now
tender tulip
then 1/M(x) has n many differing simple poles
how can we connect these poles with a branch cut for sqrt(x) in a way we can make a contour around them
Working with that seems messy as FUCK
static loom
well the most obvious thing I see without thinking too hard in terms of reverse engineering a solution is since the integral ended up being t, we can think of it as s+t = (s+t) with the first being two integrals, one going to s, one going to t, then the right integral is to s+t
tender tulip
idk where the t comes from
static loom
I just derived it earlier
static loom
**Merosity**
$y'^2=M(y)$ gets us $\dv{y}{t} = \sqrt{M(y)}$ so we end up just in the simplest case at $$\int_0^t \frac{dy}{\sqrt{M(y)}} = \int_0^t ds$$ $$\int_0^t \frac{dy}{\sqrt{M(y)}} = t$$
fathom swallowBOT
Merosity
tender tulip
oh yea, nvm
static loom
$$\int_0^t \frac{dy}{\sqrt{M(y)}}+\int_0^s \frac{dy}{\sqrt{M(y)}} = \int_0^{s+t} \frac{dy}{\sqrt{M(y)}}$$
fathom swallowBOT
Merosity
static loom
of course if you're doing a contour integral in the complex plane you need to consider more but
tender tulip
of course if you're doing a contour integral in the complex plane you need to co...
Cant intersect a branch cut, must wind around the contours, etc.
sqrt(x) also needs to slice the domain
static loom
a polynomial only has finitely many roots so this is true between any two real roots along the real line
so long as it's not got a pole at 0
but I'm just saying start small and work up
tender tulip
I tried starting with a quadratic.
static loom
if I were you I would attempt to go through the proof for arctan, or any other o...
like I said earlier here
tender tulip
Here's what I came up with
y'^2 = y^2 + by + c, y(A) = B
well M(y) = (y - u)(y- v)
so we know our two poles are u and v
our branch cut either traces a line between u and v as points, or traces a line outward to infinity and back
so lets assume the branch cut connects them
Actually let me draw it out
@static loom Yeah
Essentially, if the y lies in the half of the plane with (0,0), we just integrate infinetismally close to the midpoint of the poles and then back to y
otherwise, we integrate infinitesimally close to the midpoint and then AROUND one of the poles to infinitesimally close to the other side and then to the y
but idk how we'd do this with like, 3 poles, or four
neat lintel
i tried reading it once when i was in your situation
You were in my situation? Graduated and trying to self-study calc? So this can be done. WOOT.
neat lintel
If you took the US equivalent of algebra 2, pre-calculus is not necessary.
prime plover
You were in my situation? Graduated and trying to self-study calc? So this can b...
Yes. I self studied much of my math, throughout my degree. I am a slow learner and so I wanted to get a headstart during the breaks. I self studied real analysis and abstract algebra as well
It's not as efficient as taking classes, usually
brittle socket
Yes. I self studied much of my math, throughout my degree. I am a slow learner a...
charred mortar
Tbh I learn better from books than lectures myself
prime plover
thats exactly what i look like, but without the huge smile
neat lintel
It's not as efficient as taking classes, usually
I would disagree with this in the sense that book content is often more advanced than lecture content
prime plover
I think it depends on my lecturer and it depends on the person. It's depending on many variables!
charred mortar
Yeah in general it can vary widely
prime plover
Yes books are a huge time commitment for me since it covers way more than a class
brittle socket
Self study the whole of undergrad like moth
charred mortar
Honestly yes
neat lintel
Self study the whole of undergrad like moth <:sotrue:826971355542192148>
If you sleep 4 hours a day and delete social media, ‘tis plausible
prime plover
Like, i read terrance tao's analysis volume 1 for example, it took a loong time. Did most of the problems in it. When i came back the next year the real analysis classes were really easy tho
charred mortar
Still seems plausible tbh with a reasonable schedule
brittle socket
If you sleep 4 hours a day and delete social media, ‘tis plausible
Moth somehow knows / knew algebraic geometry in hs
neat lintel
Like, i read terrance tao's analysis volume 1 for example, it took a loong time...
Introductory real analysis or graduate?
prime plover
the one inbetween those
charred mortar
Moth is still a giga outlier in any case
prime plover
senior undergrad
charred mortar
But self-studying most of an undergrad course in math seems doable enough I think
neat lintel
Moth somehow knows / knew algebraic geometry in hs
You can work up to algebraic geometry in a few months of specialized work Linear Algebra and Calculus (with proofs) ——> Abstract Algebra —-> Algebraic Geometry
prime plover
i took a class on measure theory in grad...i havnt gone past that though. It was really tough even with all the self study!
neat lintel
I have to get around to learning measure theory
charred mortar
You probably could get to basic alg geo like that yeah
But Moth knows all the other stuff proper
neat lintel
Oh
prime plover
Anyway like i said, i learn at a very slow pace. I don't understand why people think "it takes X amount of time to learn" can be some sort of objective statement
brittle socket
Yeah moth is an absolute beast
charred mortar
Yeah learning pace varies widely too
neat lintel
Advanced alg geo in hs is OP
prime plover
who is moth? are they are on this discord?
brittle socket
A moderator who has become a reserve moderator
Could still ban our asses 
This is what moth looks like btw
prime plover
btw on the topic of "learning better by reading books". That's been true of some of my classes. One of them was literally just reading from the book. So I didn't see the point in classes because it's just the same except not allowing me to go at my own pace. The only thing i got out of it was being able to ask questions when i was stuck.
It made me seriously question why I was even at uni
brittle socket
To get a piece of paper 
prime plover
Would prefer to just use crayon and write "legit math degree" on it
brittle socket
prime plover
The class was functional analysis. We read about half of Kreyszig. Good book. Also found it strange that the proffessor would recommend us to read super advanced books on PDE's every other week haha
brittle socket
Taylor's book on PDEs
errant ridge
neat lintel
sick burrow
This is what moth looks like btw
actually this is what moth looks like
wooden flax
What does the term 'unbroken string' mean?
leaden torrent
context?
wooden flax
oh wait i think i figured it out after being confused for half an hour
i think it means a sequence with every term being nonzero
this was from a proof in a paper i was reading
neat lintel
hey whats ur guys opinion on the 4th dimension
slow obsidian
ratio
alpine kindle
hey whats ur guys opinion on the 4th dimension
nth dimension is better
neat lintel
hey whats ur guys opinion on the 4th dimension
it's weird. a lot of weird stuff happens topologically
slow obsidian
thats rude
neat lintel
when u rlly think about it you could literally move in a new direction
slow obsidian
i will be informing the admins of the server plus my mother
neat lintel
like turn in a new angle allowing you to move through a new unit of measurement along the w axis
guys im onto something really
alpine kindle
when u rlly think about it you could literally move in a new direction
ok
now think of n dimensions
neat lintel
i tried
alpine kindle
you can move in n-3 extra directions
alpine kindle
yeah
neat lintel
so basically yeah
slow obsidian
ok so is God 4D or 5D
slow obsidian
we cant see god because we can only see 3D and below
ancient flame
ok so is God 4D or 5D
0D
neat lintel
whats ur opinion on the grandfather paradox
slow obsidian
dude why did u come to this channel to belittle my beliefs again
neat lintel
can i time travel back to when my parents get together asking for a friend
slow obsidian
this is literally targeted harassment
alpine kindle
whats ur opinion on the grandfather paradox
how are you suggesting time travel works
neat lintel
can i time travel back to when my parents get together asking for a friend
damn L
slow obsidian
oh so bullying is what we do here
slow obsidian
honestly extremely disappointed, i wanted to join a community with like minded individuals
but im greeted with this disgusting behavior
ancient flame
wait no
slow obsidian
im ending my life. GGWP
honest veldt
Evil, this is a math discord, not a religion one, come back
deep mango
honest veldt
Sit your bottom down
deep mango
Please stop bait trolling
ancient flame
sorry
deep mango
Not you
honest veldt
Let me tell you a story evil
ancient flame
oh
slow obsidian
hello my son is dead what did u do to him
ancient flame
bruh
honest veldt
One time, a man met a lion in the forest
slow obsidian
my son just wanted to know if god was 4D or 5D
honest veldt
Uh I mean jungle
slow obsidian
and u killed him.
neat lintel
i almost got to have a fun discussion about 4 manifolds, but the highschoolers came in. oh, if only there was a place to do so!
sleek wing
dude why did u come to this channel to belittle my beliefs again
your "beliefs" show that you have no understanding of what a dimension is
ancient flame
@neat lintel #❓how-to-get-help
neat lintel
okay guys please back to the 4th dimension like i am really curious
honest veldt
the man asked the lion "Just how did you become the king of the jungle? "
slow obsidian
okay guys please back to the 4th dimension like i am really curious
ratio
honest veldt
You know what the lion said?
ancient flame
what does the fox say
honest veldt
never ask what the fox says
neat lintel
<@456226577798135808> <#488120190538743810>
@ancient flame i understand interpreting tone may be difficult through text
slow obsidian
oh fuck its not like my mom to ratio people i broke character
ancient flame
LOL
ancient flame
tteppa is my dad
honest veldt
Tterra are you looking for adoption
neat lintel
i dislike and do not want children
slow obsidian
your "beliefs" show that you have no understanding of what a dimension is
thats rude btw bro
ancient flame
fuck kids
honest veldt
This is heartbreaking
slow obsidian
we can all understand dimensions no need to get personal
sleek wing
I don't particularly care
ancient flame
I hate them
honest veldt
kids are nice
sleek wing
(1, 2, 3)
3d
(1,2,3,4)
4d
ancient flame
kids are devils
honest veldt
I just don't want them because I'm a teenager, I wanna live my own life first
sleek wing
very spooky
neat lintel
(1, 2, 3)
3d
(1,2,3,4)
4d
thanks we all know this bro we are in a maths server
like
..
we know this pls
slow obsidian
pls bro
honest veldt
wew kinda true doe
ancient flame
wew kinda cute doe
sleek wing
wew kinda cute doe
then what is with the schizo-posting earli-AAAAAAAAAAAAAAAAAA
honest veldt
melody I think you're looking for more of a physics discussion than a maths one
ancient flame
LOL
neat lintel
melody I think you're looking for more of a physics discussion than a maths one
you think so?
neat lintel
melody I think you're looking for more of a physics discussion than a maths one
ggs roasted
gg leaving the server
thanks guys
honest veldt
Yeah, maths people aren't too interested in 4D representing time or whatever, as far as I know
neat lintel
melody I think you're looking for more of a physics discussion than a maths one
i'd say the question still fits here, but it's just being shat up by highschoolers trying to troll and what not
ancient flame
hey im not a high schooler anymore
slow obsidian
i bet u guys would instantly be better at valorant than melody
honest veldt
i'd say the question still fits here, but it's just being shat up by highschoole...
I see, I see
sleek wing
hey im not a high schooler anymore
same
honest veldt
It could start a discussion about manifolds yeah, let's do that
ancient flame
sleek wing
https://youtu.be/0ca4miMMaCE
mods ban
ancient flame
LOL
honest veldt
Sick sick sick
neat lintel
i've already lost interest in talking about manifolds, i don't need highschooler #1 and highschooler #2 and first year #1 spamming about video games and god whilst doing so
ancient flame
I just put my shirt on backwards
slow obsidian
whats a manifold
ancient flame
opposite of a womanifold
slow obsidian
still not helping
honest veldt
it's a thing that locally looks like another familiar thing
ancient flame
isn't it like the generalization of a surface in n dimensions
neat lintel
do you guys wanna hear a good math pickup line
honest veldt
yeah
slow obsidian
elaborate
alpine kindle
n-3 extra
consider the 3d translation vectors representing the 3 usual "directions" $$\mqty(1\0\0), \mqty(0\1\0), \mqty(0\0\1)$$
if you move up to $n>3$ dimensions you get equivalents of those translations plus $n-3$ more: $$\mqty(0\0\0\1\0\ \vdots),\mqty(0\0\0\0\1\ \vdots)\cdots$$
neat lintel
why am i tryna understand this stuff
fathom swallowBOT
ally 🌈
ancient flame
sure melody
neat lintel
@honest veldt i know you like adding numbers… could you please add yours to my contacts?
ancient flame
YO
honest veldt
<@305064722225692674> i know you like adding numbers… could you please add yours...
Smooth. As. Butter
Let's move
slow obsidian
oaDSKaskasD
neat lintel
u nerds are welcome
sleek wing
do you guys wanna hear a good math pickup line
WOMEN! DATE ME!!!!!!
ancient flame
LOL
slow obsidian
consider the 3d translation vectors representing the 3 usual "directions" $$\mqt...
i appreciate the response, no idea what u said tho unfortunately
ancient flame
@sleek wing no more countries?
honest veldt
Can vouch, wew is kinda attractive
sleek wing
WOMEN! DATE ME!!!!!!
jk I would never actually say this in real life
ancient flame
wew is so hot
sleek wing
I would say "MEN! DATE ME!!!!!!!!!"
ancient flame
I think tterra gave up
sleek wing
meow
ancient flame
woof
slow obsidian
ive been in this server for at least 10 minutes and i dont have the very cool ppl role
is this a bug?
honest veldt
Kinda weird behavior
ancient flame
bc L
honest veldt
Suspicious activity
sleek wing
Kinda weird behavior
positively freakazoidal
honest veldt
alpine kindle
a better maths related pickup line is the abstract of a paper you have written
if they don't walk away then you probably have a chance
alpine kindle
I would say "MEN! DATE ME!!!!!!!!!"
wew you have a girlfriend
slow obsidian
I was gonna say something but
all good bro no ones paying attention
sleek wing
don't SPOIL IT ally
neat lintel
consider the 3d translation vectors representing the 3 usual "directions" $$\mqt...
so hot
alpine kindle
lmao
neat lintel
ally ure so hot
sleek wing
all good bro no ones paying attention
the child quips
neat lintel
tell me more
alpine kindle
ally ure so hot
how old are you
neat lintel
i am 21
slow obsidian
the child quips
thats personal
alpine kindle
I'm 16
neat lintel
ggs
neat lintel
LMAOO
sleek wing
*personnel
slow obsidian
DISCORD MOD LOOKIN ASS @neat lintel
deep mango
sleek wing
children in chat
sleek wing
it's fine
i would advise against hitting on random internet people
@ancient flame
ancient flame
???
deep mango
Owned
slow obsidian
please no memes in general thank u
alpine kindle
wew i like the pfp
sleek wing
thanks I made it myself
slow obsidian
aite ggs
sleek wing
imagine being
alpine kindle
thanks I made it myself
the pure intensity of that gaze is unparalleled
sleek wing
I wanted to use my dream one but it took too long so I gave up
alpine kindle
Grow up fellas. Get real tonite
why would i get real when i could get p-adic
sleek wing
pear-addic
alpine kindle
complex analysis more like fake analysis lmao gottem 🤣 🤣 🤣
honest veldt
😂 🤣 😂 🤣 😂 🤣 😂 🤣
sleek wing
feeling like making a joke album EP under the name DJ Qwertyuiop
honest veldt
Extending the common qwerty, I enjoy
alpine kindle
feeling like making a joke album EP under the name DJ Qwertyuiop
call yourself matrix man
cold needle
QWERT YUIOP
honest veldt
Very intellectually stimulating
alpine kindle
yes
sleek wing
qwertz
sleek wing
nether qwertz
alpine kindle
azerty master race
sleek wing
sure, hop on the maths discord serv- oh wait
honest veldt
I used to spend all day on minecraft a few years ago, I was kinda cracked
Oh....... White name.....
sleek wing
I had a 11 bedwaurz winstreak
honest veldt
I was reached like level 122 in bedwars then sold my account
alpine kindle
Oh....... White name.....
i swear they just archived the channel
honest veldt
Is it actually gone?
sleek wing
honest veldt
Bedwars is kinda zased
sleek wing
Is it actually gone?
no it is actually #help-37
honest veldt
I used to play with parties all day but eventually I realized my error
Playing only 3s or 4s with randoms is so much better, I somehow maintained a good win rate like that
Let them defend, go do yo thang
sleek wing
I had a squad of lads
honest veldt
no it is actually <#908076667224854568>
let's game.
sleek wing
I am not playing hypixel
alpine kindle
at 8 past midnight
honest veldt
Yeah no I don't even know how to run minecraft on this arch crap, I might have to boot up my old pc that only works when put on its side
I cannot play at this time
sleek wing
they call me the tsar bomba
alpine kindle
Yeah no I don't even know how to run minecraft on this arch crap, I might have t...
there's literally a version of Minecraft java for linux
sleek wing
there's literally a version of Minecraft java for linux
yeah "bitch edition version 6.9" 🤣
alpine kindle
you don't even need to wine or anything
sleek wing
Actually factually? I don't have to do that stupid wine crap?
red or white
honest veldt
white wine is called milk, get real
deep mango
Rose
honest veldt
Red gentleman
sleek wing
kingly take as is to be expected
honest veldt
You can't make white wine, because white grapes don't exist
sleek wing
southener
honest veldt
I drink mango juice box
sleek wing
if you're not dealing crack by 16 you're a southener
honest veldt
if you're not making your way up the ranks of the underground mob at 15, you're not going places in life
alpine kindle
if you're not dealing crack by 16 you're a southener
wew you weren't dealing crack at 16 you were doing matrix multiplication
honest veldt
same thing
sleek wing
if you're not making your way up the ranks of the underground mob at 15, you're ...
underground mob call that cave spider spawner
deep mango
Mango
alpine kindle
same thing
dealing crack is not the same as doing crack
deep mango
Undeground mob call that kanga gang
honest veldt
call me the mob grinder cause I spawn some shit
have you tried that hypixel skyblock wew
neat lintel
Go play monster hunter, nerd.
sleek wing
jesse did you remember to light up the inside of the mob spawner
deep mango
have you tried that hypixel skyblock wew
@delicate mulch
neat lintel
Hey Strad, Shinzo Abe asked me to send you this: https://www.youtube.com/watch?v=DhtEKCqmvU4&ab_channel=DavieAK
honest veldt
Go play monster hunter, nerd.
I tried it recently actually, freedom unite I think
Kinda moving
deep mango
u have been summoned
honest veldt
Tox. I need to speak with you.
neat lintel
I tried it recently actually, freedom unite I think
freedom unite? Bro, Rise came out and its the bees knees.
honest veldt
My man, I have nothing but this lowly psp to make do with, I've gotta go
Well, actually a psvita but I emulate psp on it cause it's better
alpine kindle
Hey Strad, Shinzo Abe asked me to send you this: https://www.youtube.com/watch?v...
off the meds is such a good band
neat lintel
Yeah, ngl. . .
honest veldt
Hey Strad, Shinzo Abe asked me to send you this: https://www.youtube.com/watch?v...
Sick. Hideo Kojima asked me to send you this: https://youtu.be/_FOESVW8ndU
neat lintel
If one good thing came out of Morbius? It's me finding this band.
neat lintel
Sick. Hideo Kojima asked me to send you this: https://youtu.be/_FOESVW8ndU
PFHAHAHAHAHAHAH
You know, it's honestly funny. . . .Taking out Shinzo Abe sounds like something a.) Kojima would do b.) do in one of his games if he ever thought of it.
honest veldt
I can't believe this accusation is a real thing lmao, what's happening
neat lintel
Well, it's honestly been a thing for awhile.
I don't remember where this company got their data from : But basically, this firm in the UKs job is to raise engagement for their clients by any means necessary.
Which means, you guessed it : Fake news and propaganda.
https://twitter.com/i/status/1545857338929827840 Also, this is the most hilarious thing I've ever seen.
honest veldt
Which means, you guessed it : Fake news and propaganda.
Ahhhh..... That's just great, isn't it
I love media
delicate mulch
<@474349617212030988>
didn't have to out me like this
delicate mulch
that applies to many people here, I fail to see your point
neat lintel
um so back to the 4th dimension thing
is a 4th dimensional organism able to travel through time, walk through physical objects, create endless space, and read minds?
brittle socket
brittle socket
neat lintel
you might get a better response than asking the discord server populated by third (and less) dimensional organisms
😔 sigh
neat lintel
um so back to the 4th dimension thing
is a 4th dimensional organism able to trav...
. . . .Fresh out of high school, huh?
Got your anime pfp ready to stomp everyone with your "factual and logical" mind?
Gonna tell us how economics work too?
are u ok