and this is also the age that schizophrenia will in most cases develop if you are likely to get it
#serious-discussion
surreal sapphire
latent forge
my family has history of mental health with dementia
latent forge
40s
vivid halo
oh hmmm
latent forge
not 70s
vivid halo
yike
vivid halo
surreal sapphire
me with a family history of schizophrenia 
latent forge
but i luckily am not addicted to alcohol
eh i guess its worthwhile to have a bad trip once
because it gives you more perspective and makes you more cautious in future
vivid halo
idk if it's necessarily worthwhile
it can be
definitely not something to like
seek out
vivid halo
oh yea the dissociatives are a really weird class
too bad they're all like
really bad for brain
latent forge
yea
vivid halo
latent forge
and you know its bad when it happens too
but cant do much about it
thats assuming you are self awwre enough to notice
vivid halo
I've only had one dissociative experience which was taking too much cough medicine while I probably had COVID
not enough to have a full on robotrip but enough to have that like
really weird fever dream state and not be able to sleep
latent forge
thats funny that you mention fever dream
when I was young I got scarlet fever for 3 days
probably top 1 worst experience in my life
my most recent bad trip is a close 3rd
becsuse disassociating is the worst feeling if you arent comfortable
blazing pawn
Imagine needing drugs to dissociate and have a waking fever dream
I would just constantly be sick enough that this happens 
latent forge
just by existing?
leaden torrent
what about drugs that make you more productive at math
like penicillin
latent forge
bruh moment
blazing pawn
No i had a 104.5 degree fever 
vivid halo
aaaa
latent forge
oh yikes
vivid halo
moth don't die
blazing pawn
Its gone now nG 
surreal sapphire
me, a european, thinking this is degrees celsius at first
latent forge
ye lol
leaden torrent
how tf do you survive 107
latent forge
i went to ER
leaden torrent
what the shit
latent forge
i had scarlet fever
blazing pawn
Its survivable if you drop it fast enough nami
vivid halo
blazing pawn
you dont start sustaining brain damage until 107.6
crystal stone
Surprised you didn't have serious dmg to your organs
pale orchid
i had that too, but i didn't get that bad a fever
latent forge
and peaked to 107
pale orchid
stayed around 40°C
latent forge
all during christmas
vivid halo
115 degrees: On July 10, 1980, 52-year-old Willie Jones of Atlanta was admitted to the hospital with heatstroke and a temperature of 115 degrees Fahrenheit. He spent 24 days in the hospital and survived.
latent forge
ahh
blazing pawn
i dont remember what my peak was exactly
crystal stone
wait is that the guy
blazing pawn
maybe i will ask my mom
crystal stone
With serious brain damage
latent forge
ask your mom
vivid halo
how do you survive that lmfao
latent forge
boil an egg on ya bois head
blazing pawn
I have like yearly illnesses/fevers pretty much i think my immune system is just weak
latent forge
that explains why you are good at math 
blazing pawn
cosmic balance
latent forge
yearly illnesses improve mental longevity
cold needle
Wht
latent forge
✅
pale orchid
chronic illness is super strongly correlated to depression
latent forge
idk sounds like a term though
blazing pawn
i dont have chronic illness i just get a cold or flu every year
cold needle
oh
latent forge
is just pseudoscience
latent forge
disassociating rn?
pale orchid
Thessociating
blazing pawn
Childhood-onset cluster headache is an excruciatingly painful and distressing condition.
latent forge
are those like frequent migranes?
blazing pawn
No not really
latent forge
when i was in elementary school id have to leave class twice a week because of trash headaches
i couldnt be in class because the lights were too bright for no reason
latent forge
false, im convinced every other kid has super resistence to lights
blazing pawn
I think for me part of it is probably that my parents were just older when they had me
pale orchid
my salad was caesarean
blazing pawn
which tends to correlate with these things
blazing pawn
My dad had me when he was 53
latent forge
ive always found it hilarious when i find out my friends have moms that are 60 or 70
odd narwhal
dam
latent forge
LOL
odd narwhal
dayum
latent forge
bruh ur not even 20
odd narwhal
my grandma is like 75
blazing pawn
The game was rigged from the start
odd narwhal
wtf
blazing pawn
I dont have any living grandparents 
odd narwhal
ur grandparents had kids young
pale orchid
between a moth and a hard place
blazing pawn
🦋
latent forge
birth after menopause
odd narwhal
immaculate conception
untold sapphire
what a nice thing to say
i think moth is immaculate too.
completely unvarnished
cold needle
bubble
sullen valley
are u there metal
hollow drift
.-.
cold needle
hmm
neat lintel
cold needle
toxic schooner
pale orchid
oo of the golden g
crystal stone
spicy?
cold needle
spicy meatball integral
thorn brook
toxic schooner
oo of the golden g
atomic cypress
Post worst integral you know with elementary solution.
inner finch
lmao
jovial ember
$\int_{me}^{ur mom} swag(x)dx = \pi$
fathom swallowBOT
Chmonkey
inner finch
swag 😎
vivid halo
swag
inner finch
swaggin
jovial ember
Swag 
austere stratus
i have a question about exact differentiation, where can I post it?
not sure whether it should go under calculus or multivar calc and diffeq
neat lintel
probably #multivariable-calculus
deep mango
It's a surface integral over a closed surface
The circle means closed
There is no curve
mint patio
So the region of integration is implicit since the surface is closed?
Kind of like triple integrals
deep mango
Yeah, just over the whole surface
mint patio
Yup okay
deep mango
Yeah
mint patio
Nice cool would I understand the proof if I were to read it lmao
deep mango
Idk but this formula has a good intuition
mint patio
Oh wait yes it does
deep mango
The left hand side is "Amount of F that is leaving the surface"
The right hand side is "total F being created within the surface" (divergence = amount coming out of the point)
So it says "the amount that leaves a surface is exactly the amount that is created inside the surface"
mint patio
What if the divergence is negative?
deep mango
Or in more precise terms "the flux of a vector field out of a surface is the total divergence of the vector field inside the surface"
Those are sinks, i.e. where the "stuff" following the vector field is being destroyed
So if you have total negative divergence in the surface
Stuff has to be going in
(it could go out in some places, but the net effect has to be inward)
And then you can imagine the vector field being tangent to the surface at every point, so that it's spinning around the surface. Then the dot product between F and dS is 0, since dS is the normal vector.
And then nothing leaves or enters the surface, so the total divergence must be 0 (maybe there are sources and sinks, but they balance out)
So the proof for things like this is usually "split into little pieces, see that in each little piece amount created = amount leaving"
mint patio
Gah man I am learning all this stuff way too fast it sucks
crystal stone
Eh just learn the computation tricks
A deeper understanding will come with more experience
mint patio
I have to relearn all my intuition for where the flux formula using surface integrals comes from
Yeah you're right, I'll have to be patient. I'm gonna bet that this kind of stuff will appear more once I get further into my engineering courses
But in context
Thank you for explaining by the way Ryc
deep mango
By what?
Yes the best situation here is charges
Fluids dont create out of thin air
They are divergence-free
(divergence 0)
Well unless they are compressible
cold needle
magnetic dipoles
deep mango
Divergence = how much is being created or destroyed at a point
Like if your divergence is positive, then the vector field is pushing more stuff out at that point than it is taking into that point
cold needle
some terminology i heard is like
you have "sources" and "sinks"
source is outwards stuff
deep mango
The vector field is gay and would like you to accept it for who it is
deep mango
Yes sure
Here like
Vector fields represent the velocities of objects right
So if you have the derivatives of the velocities
Those represent acceleration
Divergence positive says "stuff is accelerating positively in every direction"
Or at least
It's accelerating more than its decelerating in other directions
So then if stuff is accelerating away
It is getting less and less dense
Spreading out
mellow moon
They are divergence-free
tell this to people who are lookin at Compressible Navier-Stokes
(jk)
deep mango
Well this is the sense in which you could consider divergence in a fluid, spreading out (or compression)
And then you can see why the total compression is the amount you're stuffing into your container right
For yohan
Or I guess I should say the total rate of compression is the total rate at which you are shoving stuff in
sick burrow
When did peope start calling eryc eryc
mint patio
I do not like this
deep mango
When did peope start calling eryc eryc
It's just him. It's just the vicious mobster.
mint patio
The triple integrals seem so much easier to evaluate
mint patio
Did you see what I said about PDEs earlier? :3
mint patio
Yesss I'm excited
What kind of triple integral set up would you have for something like a cube?
sick burrow
It's just him. It's just the vicious mobster.
ok eryc
deep mango
For any prism the bounds of the integral are just the bounds of the prism on each axis
But for non prism things the triple integral is bad
Sometimes the surface integral ends up being easier, e.g. with a sphere
Then F dot dS is just F dot (x, y, z) dwhatever
mint patio
How is the surface integral of a sphere easier O.o
Bounds for a sphere are easy in spherical coordinates
I know you can convert the surface integral to spherical as well but the actual process for doing a surface integral is a lot more involved
neat lintel
How is the surface integral of a sphere easier O.o
Surface integral over a sphere is easy as pi. Area element is $\dd{\phi}\dd{\theta}r^2\sin\theta$; integrate over, you get $\int^{2\pi}0\dd{\phi}\int^1{-1}\dd{\cos\theta}r^2=4\pi r^2$.
fathom swallowBOT
Tesseract
deep mango
True, bounda for a sphere are easy in spherical coords for triple integrals
leaden torrent
do you mean to get the degree (+ pass the bar) or get hired?
latent forge
whenever you are considered the profession, so when you get the job i guess
like i wont be a mathematician until i get paid as such
im thinking lawyer is easier because i think it is less time wise
but in reality im not sure
deep mango
i suppose i am a mathematician 
inner finch
dildara dildara mere dil mai tera jalsa raha
latent forge
no ryc
phd students dont count
imo
even though they should
but its not like you can drop being a phd student and pick up another job as “mathematician” , right?
like med students cant drop out of med school and be considered doctors, even though they dont get paid to be in med school
thats my point sorta
majority people dont consider you a doctor unless you are working as one
if you drop out of phd you cant become mathematician until after you break that hurdle
crystal stone
Hrm?
What is your definition of mathematician? Having a PhD?
So what of Freeman Dyson?
Do you have to be employed to be considered a mathematician
Or can you just work on mathematics
If wikipedia is anything to go by
"A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change."
deep mango
Dr. Virgil...
nimble shuttle
that's Doctor Vergil to you.
deep mango
that's Doctor *Vergil* to you.
Oopsie~
nimble shuttle
nya~
inner finch
umu
proven bridge
Any computer engineers open for an interview for my activity for my uni?
waxen stump
do you all, know a book or material, with good questions, that will make me learn Calculus fast?
deep mango
Khan Academy has tons of calculus videos and questions for free. You can also use 3blue1brown's "essence of calculus" youtube videos for conceptual learning.
halcyon basin
do you all, know a book or material, with good questions, that will make me lear...
learning is more about compounding interest than fast
you learn something one day, connect it to something else, come back to it again at a later day
otherwise your just learning to do quizzes
waxen stump
interesting description.
waxen stump
otherwise your just learning to do quizzes
You've summarized something else I want to do, I want to try to learn functions (advanced) along with calculus (mostly limits) in same time, my intention is to assimilate one thing to another somehow
waxen stump
Oh sorry, I translated literally hahaha, but what I wanted to say, I wanna learn f(x) - I know it but I am bad in the graphics, and Calculus 1 (limits at least) together @surreal sapphire @craggy gust
steep trellis
if I'm given a critical point of a multivariable function, but not given any sort of interval or constraint, then the only conclusion I can logically draw is that we can't tell if this critical point is maximum or minimum?
Even when I find that the Hessian matrix at this point is positive definite (or negative), I can not conclude that it's max or min if I don't have a constraint on the function right?
sick burrow
Oh sorry, I translated literally hahaha, but what I wanted to say, I wanna learn...
What does it mean to "learn f(x)"
halcyon basin
I feel like mathematicians must have a little bit of masochism. Like i can understand easy math being peaceful and serene, but high level stuff is painful. its like the brain equivalent of trying to bench 200 ibs when your max was 150
steel sorrel
True
But often times the hardest problems are the ones with the most elegant solutions
waxen stump
@sick burrow Where I live they call it Affine Function and Quadratic Function, I don't know what they call in English usually.
cold needle
in english they will call the affine function as linear equation
waxen stump
lol confusion
trim stratus
Is representation theory more of a framework applied to groups/algebras/etc... or is it more of an independent theory
And please don't go on some rant about how it's naive to try to classify mathematical topics as belonging to X field or Y field.
surreal sapphire
every time you study an object X and you have some nice map that turns it into a vector space, say F(X) then this is also a representation of Aut(X)
so the representation theory of Aut(X) gives you a tool to study F(X) and in turn X
trim stratus
Got it, thanks a ton
surreal sapphire
what i was trying to say is that its a pretty powerful idea
trim stratus
I can tell. I try to categorize the textbooks available in my Google Drive to a fairly agreeable extent
but sometimes it can be extremely difficult
like distinctions between differential topology and geometry
especially when the title of the book is "differential topology and geometry"
😐
trim stratus
😂
That's fair
Diff top seems cool but I'm still too smoov brain to study it
my silly ass hasn't studied multivariable calculus yet ;___;
Oop time to go take my midterm peace
blazing pawn
good luck
steep trellis
Anyone have recommendation on problem solving? A way to develop an aptitude regarding solving problems and such?
sick burrow
my silly ass hasn't studied multivariable calculus yet ;___;
How are you asking about representation theory if you don't know multi what
trim stratus
good luck <:nozoomi:651816986837254148>
Thankfully it was really easy
Intro class so I think I got most of the points
trim stratus
How are you asking about representation theory if you don't know multi what
I don't really care about prerequisites.
sick burrow
I mean
trim stratus
Admittedly, I have trouble learning all that I want to, but I can still learn a ton without cracking open books.
Two days ago I wanted to read on an intro to QFT for mathematicians and I couldn't make it past the second page, but I learned about the Dirac delta function, its integral, a measure based on it, and also what the (compact) support of a function is 😌
sick burrow
Prerequisites are generally there for a reason
trim stratus
Of course, but I don't need to know about the Jacobian matrix to talk about a group acting on a vector space
sick burrow
Like you definitely can skip them sometimes
sick burrow
Of course, but I don't need to know about the Jacobian matrix to talk about a gr...
I mean yes but it helps to build mathematical maturity
trim stratus
I fully agree
sick burrow
Multi can be a bit of a joke though
trim stratus
I think it'd be great to learn, since I want to study all things with the tag "differential" or "manifold"
but I just can't be bothered to go through all of the wordiness and long lectures
I wanna just see the formulas I need and work through a few problems so I can call it a day and move on
intro calculus is so painfully boring
sick burrow
Yeah
I thankfully was able to skip calc 1 and 2 through self study but I needed to take multi
Took it at a local community college. The class was a joke
trim stratus
LMAO
sick burrow
Didn't even get to any of the interesting stuff
trim stratus
I want to take an honors class that follows a text like Calculus on Manifolds
kill two birds with one stone
sick burrow
Acutely there were a few cool things
sick burrow
I mean the gradient was interesting and optimization in multiple dimensions was cool
Don't remember all of it but I remember if being interesting
I mean tbh
The material was all good
The pace was just in the neighborhood of 3-4 times too slow
trim stratus
That's real nice
You could probably supplement it with Munkres' analysis on manifolds and probably get a bit more enjoyment out of it
I'll probably have to do that to avoid total boredom
trim stratus
I don't want to take multi but I go to an undergrad only college
so there aren't too many more classes to take
sick burrow
You could probably supplement it with Munkres' analysis on manifolds and probabl...
Here's the thing though
I dislike all things calculus
trim stratus
ack ;___;
sick burrow
I don't want to take multi but I go to an undergrad only college
Oh I also go to an undergrad only school
trim stratus
I heard, a long time ago, from someone in this server, that their analysis professor was an algebraist, and so all of their continuity/differentiability definitions were completely algebraic/categorical (as best as I remember)
maybe you'd fit well into this class 😌
sick burrow
But I've been able to get a lot of reading courses
surreal sapphire
my analysis prof was also an algebraist 🤔
trim stratus
But I've been able to get a lot of reading courses
Solid, solid
trim stratus
my analysis prof was also an algebraist 🤔
Anything special about your course? 😂
surreal sapphire
well, analysis 1 and 2, analysis 3 not
sick burrow
Did a year long course on set theory last year
surreal sapphire
he did a lot of complex analysis stuff
it was a nice class because inverted classroom
trim stratus
Analysis 3? Are we talking measure theory?
surreal sapphire
yeah mostly
trim stratus
he did a lot of complex analysis stuff
Oh sounds fun
trim stratus
Did a year long course on set theory last year
Axiomatic?
sick burrow
Yeah
trim stratus
yeah mostly
Tried to learn it but for the love of me I can't understand the definitions
sick burrow
Ended with the proof of the consistency of GCH with ZFC
surreal sapphire
analysis 3 is intro measure theory and some analysis on manifolds
sick burrow
Really the proof of GCH+C from ZF
trim stratus
Ended with the proof of the consistency of GCH with ZFC
Pretty neat. I've only gotten a very small introduction
surreal sapphire
haha ye
trim stratus
analysis 3 is intro measure theory and some analysis on manifolds
Gotcha
surreal sapphire
i had this probability class that also did measure theory
sick burrow
Well that was second semester
surreal sapphire
but the prof did it super, super general
sick burrow
The first semester was a mathematical logic course
And then I asked the prof to continue as a reading course
surreal sapphire
(i dropped that class)
trim stratus
AFK for a moment, sadly
trim stratus
but the prof did it super, super general
Gotcha
sick burrow
First semester ended with definition of satisfaction/formal proof and the soundness and compactness theorems
trim stratus
And then I asked the prof to continue as a reading course
Oh that's really neat
trim stratus
First semester ended with definition of satisfaction/formal proof and the soundn...
Neat
Unfortunately I'm only in my first semester at uni, and all I'm doing are calc II, and intro logic
sick burrow
f
trim stratus
my logic class is a philosophy class 🙄
sick burrow
Ah yes phil logic
I feel your pain because I took cs 101 my first semester
But they were dumb and insisting on using a bad language so they could teach functional programming or whatever
trim stratus
(i dropped that class)
Only measure I can work with is the "Lebesgue integral on the Dirac delta measure" ;___;
sick burrow
And the entire class was literally just
trim stratus
I only remember the Wiki 😌 but it's a neat little measure: f(a)
trim stratus
But they were dumb and insisting on using a bad language so they could teach fun...
Bruh moment
sick burrow
It was literally just
Recursion 101
I just zoned out in the lectures and wrote snake for fun
Then the prof couldn't assign snake as a final project since I had already written it
trim stratus
LMAO
I wanna do one of those "topics" classes where you just select something with a professor or whatever
I'd have a real brief runthrough of multivar, linear alg, and just dive into diff geo
I think that'd be fun 🥰
there's a really nice text out there by Guillemin, I believe, that runs from basic linear algebra to differential forms
would've kept reading but I get distracted by all things, as usual
sick burrow
I wanna do one of those "topics" classes where you just select something with a ...
I'm kinda doing that with alg top now
Like there isn't really a syllabus to the class
It's just "learn alg top"
trim stratus
😂
sick burrow
And we talk about how we want to cover things
Like what order and stuff
It's literally just me and the professor
trim stratus
That's neat
all of my experience with AT has just been "here's what this thing does" and "here are some examples"
Like how the fundamental group of R is trivial... couldn't prove it to you for my life though 😂
sick burrow
Fundamental group of R is easy
trim stratus
Yeah but I stoopid
sick burrow
There's an explicit retract of every path via a straight line homotopy
trim stratus
ahh null homotopy
trim stratus
I know that it's intuitively 'cause every loop is contractible but I can't do the rigorous proof
trim stratus
Just H(x,t) = t x_0+ (1-t)f(x)
Gotcha :D
sick burrow
The interesting proof is fundamental group of a circle
The intuition is clear but it takes a bit of work to make it rigorous
trim stratus
Speaking of that
I read something that didn't really resolve an issue it pointed out
and it made me kinda mad :/
odd narwhal
Fund group of R is easy because it's convex
But yea you use what gamma said to prove every convex set is contractible
trim stratus
Solid
Where do you guys stand on the Hatcher vs. Bredon argument 😌
or is there another book y'all like more
sick burrow
Brendon?
trim stratus
No n
trim stratus
Bredon has a book called "Topology and Geometry" which provides an introduction to all of the same things, but takes the context of differentiable manifolds
the rigor buffs like Bredon, and the intuition buffs prefer Hatcher, from what I can tell
sick burrow
It definitely requires you to fill in the details in basically every proof but the broad strokes are good
Seems like it's a text that does best supplemented by other sources or a professor
trim stratus
Yeah I agree there
I like this one though
For obvious reasons I don't actually study from this book, but I've read some and it's really nice
Anyway, I'll be on my way. It was good chatting math with you guys today. 👋 I'll be on later, perhaps.
Have fun with your alg top topics class 😌
waxen stump
Friends, how to stop procrastination?
deep mango
do thing
sick burrow
This server certainly can have
waxen stump
I procrastinate in math.
sick burrow
Some ahem strong opinions on Hatcher
waxen stump
lol
what study methods do you all use for math?
I usually copy in notebook or a paper, the theory
brave hollow
Some *ahem* strong opinions on Hatcher
oh thats it then how do I read about this man jacking himself?
waxen stump
idk if this is the best method.
sick burrow
what study methods do you all use for math?
try to brute force my way through via intuition
Then have imposter syndrome when I inevitably fail
waxen stump
hahahahaahhahahah
sick burrow
"Are you telling me that I can't skim a textbook without taking notes and still learn the material? Insane"
"I must just not be good at math/oh fuck this is all I've been doing I understand nothing and am a fraud"
sick burrow
I'm still so bad at taking notes
This is the first semester I've actually managed to take proper notes
And that's only for one class
And if isn't math
But I'll be dammed if I'm not proud of my feminist theory notes
waxen stump
In beggining, my notes were a bible.
brave hollow
written by multiple people?
waxen stump
nope, but it was in Greek or Aramaic (my beatiful letter shape when I was noob) and so much pages.
odd narwhal
or is there another book y'all like more
I really like rotman
trim stratus
I heard that anything written by Rotman is a gem
odd narwhal
It's more rigorous than hatcher and less visual but still leaves you to fill in small details for proofs which I think keeps you sharp
trim stratus
Was going to read his algebra text but I much prefer Aluffi so that I can get the categorical treatment right away
odd narwhal
I love his writing style but it's not for everyone
I think it's perfect for a first course in AT tho
leaden torrent
my priors
trim stratus
Appreciated, I'll give Rotman a shot before I commit to Bredon 😌
odd narwhal
Tho he does go in a bit of a different order first doing homology and only later returning to covering spaces
trim stratus
No worries, homology sounds cooler than covering spaces
in plain English that means that I have never seen any discussion of covering spaces
odd narwhal
Lol
trim stratus
Thanks for the recommendation
odd narwhal
Np
sick burrow
No worries, homology sounds cooler than covering spaces
Covering spaces are cool
trim stratus
Prove your claim 😌
meager sonnet
Covering space theory is pretty much necessary for homotopy and in that way it motivates homology
Homology being an abelianisation of homotopy in some sense
So big deal
trim stratus
gotcha
bronze pelican
halcyon basin
I just do multiple problems
see what I am missing
look up how it works
practice a bunch more
rinse and repeat
The only downside to this method is if a problem is one ive never seen before im fucked
deep mango
the virgin problem soolver
deep mango
the chad youtube math video watcher
halcyon basin
But I just do it because Im not gonna understand how a rational function works
or why we use logarith,s
what are logarithms
why they work
doing math can be peaceful
learning math is horrendously boring for me
Ive stared at walls for 40 mins and that was less painful for my brain
sick burrow
she doesn't need to tell you
Wait Ultra is a girl?
meager sonnet
ultra goes by any pronouns iirc
sick burrow
crystal stone
the chad youtube math video watcher
some of those youtube videos are good
but most are bad
hot cloud
organic chemistry tutor? 😳
hidden bone
i feel im approaching proofs wrong
exotic frost
questions related to theory of computation go in which channel ?
crystal stone
organic chemistry tutor? 😳
🤮
latent forge
@crystal stone how do you force 6 hours of sleep and then feel rested
alpine beacon
Consider this sentence: "7 in base 2 is 3 1s/1's/ones"
Which of the slashed expressions is more conventional?
pale orchid
probably either ones or 111
pale orchid
one of my supervisors once told me of the "rule of thumb" in which numbers up to ten are written in letters
idk how much truth there is to that
alpine beacon
The number of digits is actually variable. Sorry I didn't clarify that
pale orchid
then you're better off writing the generic tuple, aren't you?
alpine beacon
Thinking about it, "1's" reminds me of the possessive s in English so I will ignore it
What's that?
pale orchid
or rather the definition of a number in a given base
$\sum_{n=0}^N a_n 2^n$ with $a_n \in {0,1}$
fathom swallowBOT
19eddy4
alpine beacon
I see
pale orchid
i missed some backslashes for the {} but yeah
alpine beacon
My goal is simpler though. I want to express something like:
a(n) in base 2 is n+2 1s and n 0s
That is:
11
1110
111100
alpine beacon
It's this sequence in base 2: https://oeis.org/A171499
crystal stone
Much better math YouTube content
pale orchid
ok, a specific one. what you wrote is ok then.
crystal stone
Is available
Professor Leonard
Khan Academy has good modules
Can you not hear?
rip
narrow rock
sup moonbears
rare pond
Sup moonbears
narrow rock
5 
crystal stone
Fuck you Berg
rare pond
😦
narrow rock
do more rec letters help
rare pond
Is 5 the max
crystal stone
My two extra letters talk about my math Ed adventures
narrow rock
there is no max for some places I think
jovial ember
Sending 69 Rec letters (my mom wrote them)
crystal stone
Is 5 the max
Yes
narrow rock
a lot of kids were born in 2000
jovial ember
And those kids suck at math
crystal stone
Berg ask the old man for a letter
jovial ember
Cuz they’re 2000 babies
crystal stone
Submit 5
rare pond
@crystal stone that seems excessive, did he write you one
jovial ember
département
crystal stone
It auto corrected to French
narrow rock
département
crystal stone
Sue me
rare pond
Frénch?
rapid folio
Most robot like is right at the beginning "The notion of family is very important, it seems. "
thorn brook
yo this is so sussy. My prof writes that if I have a vector orthogonal to a plane then the orthogonal component of that vector is zero. Isn't that wrong?
I'm so confused
pale orchid
in a basis formed by vectors on a hyperplane and the normal to that hyperplane, that is true
thorn brook
oh yeah right
pale orchid
you usually just group those up and take the sum of all the appropriately weighted vectors on the hyperplane, and then you take the direction of the normal vector
from the point of view of the normal vector, the normal is the "parallel component" and the other stuff is the "orthogonal component"
from the point of view of the hyperplane it's backwards
thorn brook
yee right, that's always where I get stuff wrong lmao
thorn brook
yeah okay I see now. Thanks for clarifying! 
eager crescent
In early 2021, the Hanson Robotics company announced that they would start the production of hundreds of robots with Artificial Intelligence like Sophia, to help fight Covid-19.
I fail to see the cause and effect relationship
crystal stream
```In early 2021, the Hanson Robotics company announced that they would start th...
kind of like how every robot ever is used for "search and rescue"
latent forge
kind of like how every robot ever is used for "search and rescue"
go further
idk what ur insinuating
manic sequoia
I don’t understand trig identities
near mulch
I don’t understand trig identities
DW you just have to learn most of them
And get used to using them
But the ones like cos(π/2-x) are easy to find geometrically
vague lion
I don’t understand trig identities
you can get a lot of them by just visualising the graphs
mint patio
do we have taylor series/polynomial expansion for multivariable functions?
well ig why couldn't we right 
mint patio
would it just be like sum_i and sum_n corresponding to the different variables?
mint patio
one way to prove it is to reduce to the 1 variable case
wdym?
cold needle
multivariable taylor series
i had to compute those by hand up to like the 3rd or 4th degree and i was exhausted... i am weak..
cold needle
mixed terms...
mint patio
tyt 
neat lintel
yeah ok so like
pale orchid
the one i see pop up most often is this formulation, just up to 2nd order
for optimization with newton methods
inner finch
i had to compute those by hand up to like the 3rd or 4th degree and i was exhaus...
lol pain
mint patio
Is that T for transpose?
pale orchid
yes
neat lintel
let's say you have a $C^1$ (for simplicity of presentation) function $f \colon \bR^n \to \bR$, and you only know taylor's theorem for functions $\bR \to \bR$. what you can do is consider $g(t) = f(tx)$, for $t \in \bR$. now this is a thing you can use taylor's theorem on: $$g(t) = g(0) + tg'(0) + R(t, x)$$ for some $R(t, x)$ such that $R(t,x)/t \to 0$ as $t \to 0$. (this guy actually does depend on $x$, good to keep in mind.) if we do the computations and what not it comes out to $$f(tx) = f(0) + t\sum_i\frac{\partial f}{\partial x^i}(0)x^i + R(t, x).$$ if you set $t = 1$, $$f(x) = f(0) + \sum_i\frac{\partial f}{\partial x^i}(0)x^i + R(1, x).$$ does $R(1, x)/|x| \to 0$ as $x \to 0$?
fathom swallowBOT
TTerra
mint patio
What is the D for here? Derivative yeah but I don't see multiple variables
pale orchid
and Df(a) and D^2f(a) are the so-called jacobian and hessian, respectively
mint patio
holy fuck tterra
neat lintel
that's what i mean by reducing to the 1-variable case
mint patio
and Df(a) and D^2f(a) are the so-called jacobian and hessian, respectively
ahhh duh I'm dumb
ok let me read all that
neat lintel
you're basically looking at f restricted to a line through the origin and x
i blame any errors on my 5 hours of sleep
neat lintel
holy fuck tterra
i've typed longer
anyways, if you get explicit formulas for the remainder R(t, x), then you also get formulas for the remainder in higher dimensions by taking t = 1
such as the integral form or the MVT looking form (?)
i just didnt wanna write out anything explicit for R lol
if you wanna do the expansion around a different point, say a, then take g(t) = f(a + t(x - a))
mint patio
If the domain of f is R^n then how come you only write f(x) instead of f(x_1, x_2, ..., x_n) or something?
neat lintel
x is (x_1, ..., x_n) lol
too lazy to write out the full thing or make my x's bold
also i think i wrote x^i for x_i there
that's common in DG but i guess i should let you know
this is why they dont let geometers explain things
mint patio
okok got it :p
so it's the original function value (at center) + sum of all partials for each variable (evaluated at center) + some remainder term?
so partial wrt x_1 + partial wrt x_2 + partial wrt x_3 + partial wrt x_4 ... all evaluated where we centered the series
neat lintel
dont forget to multiply each of those partials by x_i
but yeah, that's the first order taylor's theorem
mint patio
just x_i? wouldn't it actually be x^i this time?
mint patio
like exponent x^i not indexed x_i
fathom swallowBOT
TTerra
neat lintel
that's better
mint patio
I know I know, but why shouldn't it be x^i? Because this looks really similar to a singlevariable Taylor series except in a normal Taylor series the x is taken to the power of the order of the derivative
neat lintel
the exponents start to show up for the higher order terms
neat lintel
yea sorry if the notation was confusing
mint patio
Wait so it's this messy for each order?!?!
pale orchid
the sum is over the components of the vector x
there's a new sum for each order of derivative
steep mountain
this would take a while to compute
mint patio
So you take each order of partial for each component
So first partial for x_1
then second partial for x_2
then third partial for x_3
...
And multiply those all by their respective component to the power of whatever order series we're looking for
(partials evaluated at center)
rare frigate
Does anyone know what GCSE is?
neat lintel
if you learn a bit of multi index notation you can write the higher order taylor formulas rather nicely
pale orchid
cuz now each one of the terms in the sum has to be differentiated w.r.t. all of the x_i
rare frigate
If I can do these sort of questions should I move on to calculus?
pale orchid
i'll be honest, i'm not sure i can do that myself by now
rare frigate
K
neat lintel
this is just tedium
mint patio
That's crazy lol, is this covered in a standard MVC textbook?
mint patio
cuz now each one of the terms in the sum has to be differentiated w.r.t. all of ...
wait this makes me think I'm misunderstanding something
rare frigate
I’m 15 still trying to master algebra
neat lintel
taylor's theorem? i know folland's advanced calculus covers it, that's a pretty good mvc book
rare frigate
Can anyone give me algebra tips?
neat lintel
in fact the explanation i gave follows that book
mint patio
So for any single component we're summing the partials wrt every variable for that one component?
pale orchid
i'll use vectors to make my case
say you have $f(\boldsymbol{x})$, where $\boldsymbol{x}$ is a vector of variables
fathom swallowBOT
19eddy4
pale orchid
the first derivatives can be collected into the gradient vector $\nabla f(\boldsymbol{x}) = \begin{bmatrix} \partial f(\boldsymbol{x}) / \partial x_1 \\ \partial f(\boldsymbol{x}) / \partial x_2 \\ \vdots \\ \partial f(\boldsymbol{x}) / \partial x_n \end{bmatrix}$
fathom swallowBOT
19eddy4
pale orchid
the second derivative is gonna be a matrix
the third will be a ??? with 3 indices
and so on
mint patio
the third will be a ??? with 3 indices
tensor? 🥴
idk anything about tensors
I just heard the phrase "mAtRiX oF mAtRiXeS"
pale orchid
you can call it that if you want, since it's gonna act as a transformation on other stuff
otherwise, following tteppa's construction, the first order term is a sum, the second order term will have a double sum, then triple, etc
so you can einstein notation your way out of it if you like
steep mountain
is there a good explanation for this in some book or paper? im intrigued
pale orchid
just wikipedia taylor's theorem or taylor series
mint patio
Let f(\boldsymbol{x}) = f(x_1, x_2, x_3, x_4)$
So the Taylor series (centered around the origin) is
$f(0, 0, 0, 0) + \frac{\partial f}{\partial x_1}(0)x_1 + \frac{\partial f}{\partial x_2}(0)x_2 ...$?
pale orchid
thorn brook
you forgot to put $ at the top
mint patio
thank u toki
fathom swallowBOT
feather
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
thorn brook
lmao
mint patio
OH duh omg
pale orchid
the partial ders are R^n -> R
mint patio
yup
Oh wait
and then for the second order
Would it be like
(excuse the latex gore coming up...)
pale orchid
preemptive
mint patio
holy fuck I think I get it (hf at how ugly it is not at u edd LMAO)
this is disgusting
typing it out
be patient ty sorry to everyone who has to see this
neat lintel
no such thing as latex gore to a geometer
mint patio
i
neat lintel
it's all bloody
mint patio
dont know
how to write it out
but I get it
let me write it out without partial symbols
and just use f_x
LMAO
neat lintel
oh my god i want to do more riemannian geometry but i also am desperately clinging onto the last fragments of sanity i have
pale orchid
mint patio
Let f(x, y, z) = some weird shit
Taylor series around 0 is
$f(\boldsymbol{0}) + f_x(\boldsymbol{0})x + f_y(\boldsymbol{0})y + f_z(\boldsymbol{0})z + f_{xx}(\boldsymbol{0})x^2 + f_{yy}(\boldsymbol{0})y^2 + f_{zz}(\boldsymbol{0})z^2 + f_{xy}(\boldsymbol{0})xy + f_{xz}(\boldsymbol{0})xz + f_{yz}(\boldsymbol{0})yz ...$
fathom swallowBOT
feather
neat lintel
lol
it is messy
there's a reason i didn't wanna do more than first order
and you're discovering it
mint patio
well ty both for your time
do you have to like
do some shit w this for multivariable analysis
omg wait
pale orchid
i've used up to 2nd order
neat lintel
yeah but you do actually useful mathematics
pale orchid
cuz dat newton
mint patio
@cold needle AND YOU SAID YOU HAD TO DO THIRD OR FOURTH ORDER?!?!?!?!?!?
pale orchid
useful mathematics
mint patio
someone get metal a therapist
neat lintel
let me go look back at my old mvc homework and see what the worst i had to do was
cold needle
neat lintel
i remember some nasty ones
pale orchid
i have something i was working on just today
neat lintel
i just committed a complex analysis crime
cold needle
lot of derivatives
pale orchid
debating on which poison to drink
matricized tensors
or hide the pain with 6 index einstein notation
and then doing newton methods on that
neat lintel
these were the only problems where i actually had to write anything out
mint patio
HAH
pale orchid
find the based 3rd-order taylor poly
mint patio
Okay wait yeah what is the remainder term though
omg nvm
I gotta stop
and get back to my work
LOL
neat lintel
it wasnt even graded
mint patio
ty all goodbye I m studying for physics possibly bleaching my eyes
pale orchid
if ur doing physics
neat lintel
do rg
pale orchid
this'll show up all the time
imagine doing measurements at the lab and not computing the propagated error with a 1st order multivar taylor
neat lintel
SHUT UP! SHUT THE FUCK UP! STOP FUCKING EMAILING ME ABOUT GRAD SCHOOL!!!!
leaden torrent
neat lintel
OH MY GOD oh my god please
pale orchid
end their whole career
cold needle
holy_shit_2.txt
vague lion
just mark it as spam
neat lintel
every single email i get from my university is spam
vague lion
i'm not seeing the problem
neat lintel
they all go into my student email and ive blocked them from my personal emails
neat lintel
i must attack the roots of the problem and get rid of the university completely.
else they will come back
vague lion
true!
steep mountain
i had to compute those by hand up to like the 3rd or 4th degree and i was exhaus...
just out of curiosity how much paper did that take
cold needle
half a page or so
mint patio
you write with an atomic pen ?
rancid meadow
fuck GradSchool
vague lion
half a page or so
a3? a2?
neat lintel
fuck GradSchool
steep mountain
gonna attempt to reach 7th order for 3 vars 
laughs in masochism
neat lintel
cold needle
i will die
neat lintel
indeed
we all do
well, most of us
reading r/uoft subreddit and learning people are losing marks for shit like writing commas instead of and
truly a wonderful place to do a mathematics undergraduate
im so glad none of my classes have TAs
mint patio
is tors torsion?
neat lintel
i honestly should have dropped out after my second year, it's only been downhill since then
rancid meadow
yeah its the torsion group of G
cold needle
this is so cringe
neat lintel
uoft math TAs are all sharing some kind of fucking drug
steep mountain
i honestly should have dropped out after my second year, it's only been downhill...
what level you at rn
rancid meadow
this is what happens when you hire undergrad TAs whos highest level of mathematics is literally the most basic group theory course this school offers
surreal sapphire
i am starting to think that im too lenient as a TA
neat lintel
what level you at rn <:hmmCat:831508801646755850>
senioritis
mint patio
dude I think my school does that jesse
rancid meadow
to be clear I am also one of these TAs
mint patio
my diffeqs ta is incompetent
rancid meadow
but theres a difference between being strict and being stupid
mint patio
he looks dead inside so idk maybe life's just hard but dude makes mistakes every ha;f second that we're correcting
rancid meadow
lmao
surreal sapphire
lucky to have great class lmao
neat lintel
my topology TA in 2nd year was good. my RG TA in 3rd year was good. these are the only good comments i can make
surreal sapphire
i will do a mistake and nobody will even ask me about it
steep mountain
i didnt even know thats a thing
neat lintel
jesse do you want to write mean and hateful emails to the math department with me
could be fun
rancid meadow
i have nothing to complain ab out besides my group theory grading
even the topology guy has been fair
neat lintel
im never taking a class with more than 30 people ever again
rancid meadow
i think my topololgy has < 15 people
neat lintel
topololgy
neat lintel
surreal sapphire
but in general small classes are better
steep mountain
my freshmen classes had 500+ each
good thing 20% passed the year 
neat lintel
the best class i've ever taken was a ~15 person intro to russian course
rancid meadow
i actually dont know how many ppl dropped the top course
surreal sapphire
i TAd a class with ~250 people
neat lintel
my condolences
surreal sapphire
we graded the exam in one day
rancid meadow
just shove all the TAs in a room and get it done in a f ew hrs
surreal sapphire
yeah
its hell
and its not fair
you can feel your brain being drained after a while
and you start to treat later exams differently
steep mountain
best thing about big classes is to see a class average of 15/100 and feel superior even tho the class is basic analysis
rancid meadow
so smooth.
rancid meadow
woah i just realized i never set my external monitor to 120hz
for my laptop not my pc cuz i only type tex on here so neve rnoticed
steep mountain
now you can never go back without noticing congrats
rare frigate
is one ohm = 1V/1A
mint patio
cold needle
The definition is Insanity is doing the exact same thing over and over expecting shit to change. from ur pfp
why would you post again expecting a different response
rare frigate
Because there is different people
Plus I did get an answer in the first time I asked
steep mountain
limber perch
when the jokes write themselves
steep mountain
inner finch
he definition is Insanity is doing the exact same thing over and over expecting shit to change
i literally answered you 
literal nightmare server
latent forge
you are stuck in the wild
what math are you going to use in a year to inproce your life
mint patio
math actively shortens your life
when we grow a year older (+1 yrs) that's one year closer to dying
so just adding 1 to ur age means ur closer to dying
addition is mathematics
boom.
swift sinew
My brain immediately forgets anything that ends with “boom.”
brave hollow
thats how bombs work, they kill you
crystal stone
@rare pond
gentle bay
My brain immediately forgets anything that ends with “boom.”
I remember anything which ends with a boom.
peak halo
any PSAT tips?
jovial ember
PSAT more like pretty shitty assessment test