#serious-discussion
1 messages · Page 316 of 1

Lego 1×1
Welcome to the server @grim yacht
@cold forge affine variaties are cool 🙂
took some time to get wrap my head around all the sheaves stuff
they are cool!
yeah like honestly they should be taught in elementary school
real
tbh if math was taught at a faster pace (and not 12 years to get to basic calculus) it is very possible to reach advanced things
I will need some help with cat theory xD
I think Milne just assumes that everyone who reads his AG notes knows cat theory
it is good to be familiar with universal properties and limits and colimits
yep I can see that
when the definition of a stalk is basically a colimit
could you actually do this
lol no
and when you have the intuition of colimits it really just makes sense that it works this way
hi nG
howdy
category theory probably
ig so
not great! but better than the last few days I guess
dont we all..
yeah I feel mostly better now guh
what intuiton are you talking about?
had horrible horrible lack of sleep earlier in the week and then made up for it by bedrotting for a few days
then had pretty bad migraine yesterday
but doing okay today
feeling very disorganized with the preprints I'm trying to finish guh
oh i got my first preprint recently
well the stalk of x can be thought of as the set of functions of the sheaf defined on some neighborhood of x, where two functions are identified whenever they agree locally at x, that is, on some neighborhood of x.
this is exactly what a direct limit does
that was the definition
well that's the construction of a colimit, at least
though not really its universal property
oo whats it about
it's still wild to me that you can do reasonable geometry with prestacks (no gluing conditions whatsoever, just functors)
some stuff i did in my undergrad about bootstrapping QM
oh nice
no but that behavior is the intuition to have for direct limits
ig i like the intuition from coends
since they provide a "polymorphic" version of $\exists$
Pseudo (Cat theory #1 Fan)
which is essentially what you want - there exists an open neighbourhood of x with a function defined on that neighbourhood
yeah
the identification is just built into the categorical def of "there exists"
you're basically doing $\int^{x \in U} F(U)$ after all
Pseudo (Cat theory #1 Fan)
which you can read as $\exists x \in U . F(U)$
Pseudo (Cat theory #1 Fan)
gotta be honest i know basically nothing about coends
lol yeah I also never properly learned coends
to me they're a really pretty idea
yeah they are quite nice
ends and coends provide categorifications of $\forall$ and $\exists$
Pseudo (Cat theory #1 Fan)
but with naturality built-in
they just don't come up often enough for me to remember a lot of the details around them
other than like, Day convolution as a special case
there are lots of categorical definitions that can be written as "forall blah, a morphism from foo to bar such that this diagram commutes"
ends let you just read the "forall" part of that statement and write it as an end
the naturality follows automatically from the definition of the end
yes this is what depedent products/dependent coproducts are for, and I guess you can write these in terms of ends/coends
mhm
they also appeared in yoneda's phd thesis
so they've been around for a very long time
I have got a lot of mileage out of this dictionary for representation theory
interesting
i actually know more about the HoTT side of this table than the rep theory side
it's neat how (co)induced representations can be viewed as dependent (co)products like this
that is quite cool
and that this gives you all the adjunction properties for free
yeah i guess the nice thing about classifying spaces is that they let you view representations in a "fibred" way
so you can apply all these techniques from dependent type theory
this is very similar (identical in content) to how people these days think about representation theory in terms of 6-functor formalism
do you guys know etale cohomology? how much prerequisites are there for it?
as opposed to viewing them in an "indexed" way with a functor out of BG
yes I know lots about this
i know nothing about this
the prereq is basically AG at the level of Hartshorne (chapters 2 and 3 especially)
like as long as you are comfortable with schemes and sheaf cohomology
etale cohomology is usually the first time you learn how to deal with sheaf cohomology for more general sites rather than for topological spaces
oh interesting
understanding some of the content about curves from Hartshorne chapter 4 is useful especially once you get around to the first real computations of etale cohomology for curves
ok so I have a lot to learn
yeah haha
actually there is a class on sheaf cohomology starting soon in my uni
I will try to get notes from there
nice nice
i've heard some stuff about sheaf cohomology
measuring the failure of local solutions to glue to a global one?
my previous advisor taught a really nice course on etale cohomology and the Weil conjectures you can find all the recordings here https://www.daniellitt.com/tale-cohomology
yeah typically this is defined in terms of derived functors of global sections
if you're dealing with sheaves of Abelian groups or modules or whatever yeah
mhm
if you have a sheaf of Abelian groups A on a space X then H^0(X,A) is global sections
yeah
if you have a short exact sequence of sheaves of Abelian groups 0->A_1->A_2->A_3->0 on a space X then global sections doesn't preserve this exact sequence
mhm
so I need AG up to sheaf cohomology
but I really have no experience with homology/cohomology
its from alg top right?
you get 0->H^0(X,A_1)->H^0(X,A_2)->H^0(X,A_3) but not 0->H^0(X,A_1)->H^0(X,A_2)->H^0(X,A_3)->0 in general
hm why does the last part fail
well the failure is measured by H^1(X,A_1)
in general you get a long exact sequence
0->H^0(X,A_1)->H^0(X,A_2)->H^0(X,A_3)->H^1(X,A_1)->H^1(X,A_2)->H^1(X,A_3)->H^2(X,A_1)...
oh it's what you said before, namely obstructions to gluing local sections to global sections
A_2(X) -> A_3(X)
hm...
i guess i'd need to work through a concrete example to see this#
but i can black-box it for now
usually the motivating example is the complex logarithm on C-{0}
is it weird this reminds me of mayer-vietoris
you can always find local sections for the logarithm, but you run into issues gluing these to a global section because of monodromy
not at all, they come from the same idea
ok gotcha
ah sure sure
i guess my issue with not knowing the formalism is that sheaves are all about "gluing compatible local sections to a global one"
so a priori it's not obvious to me what is actually meant by "failure of local sections gluing to a global one"
yeah I guess the main point is that sheaf cohomology is what is actually measuring this failure
like classes in H^1(X,A_1) are obstructions to this sort of local to global construction for global sections
i see
same can be said in higher degrees
so it's somehow measuring the inability to choose a bunch of compatible local sections?
yeah
fascinating
like in the logarithm example, you have a nontrivial obstruction coming from monodromy around 0
and that really does see some nontrivial topological fact about C-{0}, that it is not simply connected
honestly i feel like this makes "homology is indicator functions for algebraic structures" make even more sense to me
when you apply sheaf cohomology to very specific kinds of sheaves (locally constant sheaves) then this recovers the usual constructions of singular (co)homology
but it applies to other kinds of sheaves as well
it also applies to sheaves defined not just on topological spaces, but defined on more general Grothendieck topologies
yeah that makes sense
i guess the main thing is trying to find an analog of the "global sections" functor?
on a more generic site
sure
my initial guess would be $\int_U F(U)$ or something
Pseudo (Cat theory #1 Fan)
well usually it's like
global sections is usually just coming from a terminal object
right, which the end would recover
but what if your site doesn't have a terminal object?
or do i not need to worry about that
I can't think of so many examples where one has to worry about this haha
like for etale cohomology the site in question is the "small etale site" of a scheme X
objects of that site are etale morphisms of schemes Y->X
morphisms are commutative triangles as one would have in a slice category
mhm
terminal object is the identity X->X
makes sense
i have a doubt
in almost any reasonable example I can think of you're always dealing with some category with a distinguished collection of "covering families" including the terminal object and closed under pullback
the etale topology is finer than the usual Zariski topology
Zariski covering families are etale covering families but you have more etale covering families which are not Zariski covering families
the closest analog in the setting of smooth manifolds would be the local diffeomorphism site
-# idk what etale covers are @.@
that's fine it's not so relevant
you can think of etale morphisms of schemes as similar to local diffeomorphisms of smooth manifolds
Part 1: Presheaves and sheaves. Sheaf associated with a presheaf. Direct and inverse image. Locally ringed spaces. The category of O_X Modules.
Part 2: Schemes. Quasi-coherent modules. Closed sub-schemes. Products. Separated schemes. Cech cohomology of affine schemes.
If time permits, we will also discuss topics among the following:
Survey of derived functors. Sheaf cohomology. Flabby sheaves. Soft sheaves and application of de Rham cohomology on smooth manifolds. Introduction to spectral sequences. The spectral sequence associated with Cech cohomology. Theorems of Leray and Cartan and application to the cohomology of separated schemes.
A few books:
Bosch - Algebraic geometry and commutative algebra (second edition)
Wedhorn - Manifolds, Sheaves, and cohomology
Gortz, Wedhorn - Algebraic geometry I: Schemes (second edition)
@vivid halo this is the syllabus for that course
does this sound good to you?
mhm
this is decent as a preparation for etale cohomology yeah
ooo the book by Bosch is beautiful
as in like aesthetically pretty
good to know
But I will stick to milne for now
I am slowly learning names of authors
The cover?
I haven't tried it
it has some nice pictures too
I learned yesterday (and will continue today) how Galois groups correspond to deck transformations
Last time I stopped at taking 2 copies of C and doing some quirky branching stuff to make sense of field automorphisms
thats related to the fundamental group of an affine scheme right
yea etale fundamental groups
whats the overarching idea of "etale" stuff
@latent edge how much combi do you need to know for rep theory?
how are people doin?
0

mhm mhm
I have been getting filter-pilled today
filters
Based
based based based
fr fr
Anyways back to

What kind of rep theory?
modular groups and lie groups and algebras
Still vague
I'll pose a more proper question in a bit, I have a pset to finish for pr*bability

hey TT, higher
sob
I have to juggle 4 problem sets in the next week
they don't seem that bad, but I'll probably need a few dozen hours combined to finish them all
half of which might be from my numerical methods assignment alone 
Yoo
Hi
It seems a lot more quiet here

discussion 2 is the middle child
which channel is the youngest child? 

Dude this is so much more peaceful than #discussion , that place is insane
Yeah
Never that non in-person interaction could give me social anxiety
💔
True dude🙏
we love #serious-discussion 
There is a place that is even better than here
this is my first year at the University of Washington I cant handle college difficulty, rigor, the stress of midterms, finals, labs, the cost of $5000 tuition, etc. college isnt meant for me is there any other path for me?
Better than This, what could possibly be that?
A secret club that you’ll soon have access to 
i have a timed assingment on statistics if i start it would someone mind helping me out 🙂
Ahhhhh wait I kinda get it now, can't wait to be there! ||Initially I thought you meant #「the-obsidian-twink-jesus」 ||
Hello chat ( ' u')//
@rancid cave can you tell me what was so funny that it made you go "lol" here
none taken, but i was curious if there was anything in specific that made you laugh shortly after i asked not to be called "sir".
chill out
eh?
She's pretty chill from the past week i've seen
so the problem might be on you
?
i mean yeah im not really in any sort of explosive state rn lmao
💤

<@&268886789983436800> 
Hi,miss Ann
Yes, please do you have any pre algebra book recommendations?(for a beginner)
no
you might have better luck in#book-recommendations
but if you really wanted to grab my attention you... could have simply said one message
My bad🙏
like, saying just this:
@Ann hi, do you have any pre-algebra book recs for a beginner?
feels less awkward than:
- getting reply-pinged on a random msg
- you saying just hello
- me needing to react before youve even gone down to business
Thanks ♥️
I'll watch out next time🙏
euler did formal power series and exponentiation on the algebraic structure known as the wheel?
idk here’s the reference for the extract from euler if you want to contextualize it:
this (excellent) book btw is luboš nový’s origins of modern algebra
Jens are you studying mathematical history? You always post historical stuff and I never asked
um well i spend quite some time reading math history 
maybe i should look into whether i could try study it officially
but idk if i actually want that
Fuckkkkkkkkkthis life
i haven't been revising my stuff for all of my summer holidays and forgot all 7 modules
I have abstract algebra lectures tomorrow would u recommend learning the stuff i forgot like calc 1 and 2, probability statistics 1 etc or should i only re learn Linear algebra?
Would u say its a waste of time to re learn my other modules i dont have enough time for the others so im wondering if only re learning linear algebra is fine
(ik this is discussion and less math focused but i need helpppppppp) 😭😭😭
like, doing a masters in math history might be possible 
Some1 help me out 🥹
What do you think¿
Euler would be a frequent flyer in #crank-discussion if he were alive today
I do want to learn a bit about math history
Do you have a book recommendation?

well what sorts of maths are you interested in ? 
I wouldn't imagine you'd need any of that for abs alg lectures, linear algebra might be good cause you may be able to draw parallels but if this is your first brush with abs alg then it's fine to go without prior knowledge (learning how to frame proofs however will help, which you'd learn in this course anyways)
Im not knowledgeable at all in math history, i just wanna start somewhere to see a bit of everything and then see what part im the most interested it
Or maybe not a book but something else
A podcast or a video would do too for a start
Abel died of tubercolosis when he hit his 30s just a few days before getting a univeristy position
almost all of my math history comes from like textbooks which have those little boxes mentioning the mathematicians/scientists 😭
I was reading this abs alg text and there was section on lagrange and abel, very cool
a lot of it is surprisingly tragic though
He died when he was 26 nevermind
...
Thank you, ill try what you said because no way do i have enough time to re learn 7 whole modules 😭
- new ones
yeah but don't forget to spend some time everyday revising all of that cause the courses up ahead might require some preliminary knowledge/preliminary knowledge will help
Yea thanks im kinda annoyed at myself for doing 0 revision 💀
It's okay it happens fr
I have uni from 9am to fucking 6
Ts pmo sm
I have so many lectures(i cant skip them too or else my parents will off me themselves)
😭ts isnt fair my brother comes home way sooner than me
<@&268886789983436800> suicide joke
general histories of mathematics, will probably always fail to represent the sheer multitude of modern mathematics, but stillwell’s concise mathematics and its history offers a lovely selection of topics 

Please don't joke about stuff like this, I think you may be unaware of how it can affect people
I'm going to remove this message in a moment
Oh oops sorry
Thank you for being understanding
Ty, turns out the small uni library has it too
Hi! Is this the right place to ask for some feedback on a short math article (blog post) I wrote?
if u want sure

https://cosmin-stefan.com/article/konig
Nice, here it is
I can't provide u a specific feedback on this bc I have never studied set theory 
u got some interesting projects btw
Thanks 😅
If anyone wants to take a look, I would love some feedback 
hi everyone! Would smn mock interview me for quantitive trading. I can also mock interview you! Would be super greatf! Just dm me : )
Welcome to the server @neat lintel
،
it's cool it's completely normal to forget most of the material, it's a sign for you to review your study methods and to know what material was more important.
anyhow, there's not much review you can do to prepare for abstract algebra, it's a completely new subject. You can skim the textbook if you want.
Ohh ok i just thought abstract alg would be a continuation from linear alg
Guess not
Anyone writing exams today, tomorrow, next month.. Any other day or month
Good luck and all the best
I'm writing my midterm today at 8am 
All the best bro
thanks bro
You welcome

Good luck Akira
Ok 

thanks though
today's midterm should be easy but im sleepy asf

You've got this
@lofty forge BBMath has received his role, you're next :))
it went alright i think
it took me forever to find something in word
so annoying
it is lol
prof gave me a lab report and i have to do that shit using word document


Good luck with your report 👍

its finished 
i have to prepare for next one

Congratulation BBMaths!! I sure do hope so :)
Good luck 🍀🤞
@umbral grottohow ya doin?
what
yeah, you can post your problems here
if you get any questions
math-related for sure
._.
why that face 😭

Not really
lalalalalalalalalalalalalalaalal
i just cant get you outta my head
girl your loving is all i think about
every night
and every day
just to be there in your arms
fair
im fine wbu bella !!
i do physics wbu
and solved some of doubts like hw doubts of a guy called don
School
why are there several discussion channels?
Lots of discussion
fr
Have you seen #discussion ?!
Precisely, and some of us like a more sedate experience
same
But wait, what stops them from coming here and pretty much making this place twitter too, like they can come here at any time, so why don't they, maybe some insane psychology is at work
Oh so you say I should positively influence discussion two too?
Hii

It's just not active enough for them to actually get in on it, plus this place usually has more thought out conversations which discourages most people
Yeah true, the lack of activity is what stops them IG
the contrast is nice though, cause it's essentially made this channel a sort of safe haven cause literally everyone is up there discussion so you can actually talk about things more productively here
I think discussion will remain like the dumpster fire it is because now it's sort of engraved that whatever's happening up there right now is the norm, no matter what measures are taken
the off topic channel in the physics server however feels more tightknit and under control (might be because they ban at sight), not that it doesn't have it's weird moments but it isn't as active and jumpy as discussion
I think it's also cause most people get a little intimidated because like there's actual on topic convos happening
that being said discussion is fine but there's just a little bit of entropy that makes it uncomfortable
I like both channels
#discussion for its chaos, and #serious-discussion for its calm :p
we gotta have a bit of both in life sometimes 
Well, some of us do
guys guess what
@wheat iris
What?
Doing some leetcode to try to get slightly less rusty at coding, wrote a solution I felt proud of, used a stack and hashmap and all of that good DSA nonsense
35% for time and memory 
why leetcode?;3
wanna get a job in coding? 
Possibly, I’ve been talking with some quant people and I have a coding test coming up and I’ve basically not done any for 2 years lol
I think I’m still probably going to go for academia but I’ll give it a bash
do not pay attention to the %s lmfao
exceptionally useless
just make sure your big O time and space are optimal (often there is a tradeoff, understand these)
the %s vary widely depending on how warm the testbench is, cache optimizations, language, etc
sometimes when im bored i farm for best % by js running the same solution over and over again
theres a very large variation
That is actually true I ran it a few times and did manage to get 100% one of the time, and I guess that makes sense when we’re talking about code running in like single digit milliseconds
This is actually one thing I don’t really understand, I’ve never taken CS coding courses and none of my scientific programming courses ever cared about writing good code, I really have no idea how you’re supposed to balance memory and time complexity
I’m guessing it’s very much a “it depends” based on the problem and use case but yeah 
I can pretty much work out time complexity too but I’ve really got no idea about space complexity
if youre populating a list that isnt your output chances are youve got linear space complexity
otherwise youre probably constant space complexity
Ts is a good heuristic
but js reason about how many objects you're keeping around at any given instant
it literally is depends
the general strat is optimize for time complexity
but do be aware of the space complexity you have
for interviews
for the real world, please refer to your specific situation, hardware, constraints, and use case
also be aware of how data structures are implemented in your language of choice
That's a map? Ok is it a tree map or hash map?
That list supports appending elements to the end? Ok so then you should know that doesn't run in O(1) time, it runs in O(1) amortizedtime. Can you explain that?
etc etc
I do wish I had taken a DSA course in my UG but I should also really just learn this stuff a bit more carefully on my own time it shouldn’t be so bad
The amortised thing is just like “it’s usually not worst case” though right? Like on average it’s O(1)
Thx
Yes
Hi
Welcome to the server @late compass
Ty
u dont always analyze big O
technically
expected
amortized is a bit conceptually different than average, it means the average cost of batch jobs.
it's not average in the meaning of probability
@worn walrus did u manage solve the problem at the end?
yeah !
happy to hear 🙂

is anyone here going to Thailand WMTC 25

the formula for average depends on probability. And I think amortized does mean this in the CS sense of it.
I have never heard it as something which only applies to batch jobs, either. It's without respect to whether the runs are ran as a batch or in sequence.
it's just the average of all cases, yeah. Usually approximated.
You need to be mindful of what you're actually averaging over though. If you have a hashtable that is less than half full, then insertion is gonna be O(1) no matter what you're inserting. And if the hash table is close to capacity and needs to be reallocated, then insertion is gonna be O(n). But if you're inserting n elements in a row, then this is gonna take O(n) on average, so I guess it's a different average than averaging across the values of a single input. So saying hashtable insertion is amortized O(1) is slightly different than saying that for example quicksort is O(n log(n)) on average
what if you have a bad hash function and the keys are clustered
I don't think this is true. If you have a hash table that is less than half full - let's say 49% - and you're hashing the exact same value repeatedly, and let's say it hashes to the first position in the hash table, and all the current entries are in the first half of the table, you're gonna be running on a time complexity of O(n) where n is the number of entries in the table on every insert.
it do matter what you're inserting. And what the current table looks like.
Hmm okay, bad example, but take appending to a list for example. If the length is less than the capacity, then appending is guaranteed O(1), otherwise it's O(n). So the point is that it doesn't depend on the input, it depends on the state of the data structure, i.e. how many appends you have done
p.s. I should be clear in my counterexample I am also taking collision resolution algorithm to be linear probing
could be redundant hashing instead, or something crazy complex like rooting trees where keys map to
(crazy complex is an overstatement ik)
(I mean list as in an autogrowing array, like a vector in Rust or C++)
capacity of what?
The length of the backing array
When the length exceeds the capacity, you need to reallocate
you're saying a hash map implemented as an array and you'd expect* append to be a common operation?
No, forget the hashmap. I'm talking about a list, also called a vector in Rust
probably shouldn't use any language-specific terms here, keep it abstract. I got you though. I'm just wondering what exactly capacity means for a linked list.
I guess if it's backing a hash table then it makes sense
but obviously resizing a linked list opens up way more fluid hash table design
Dynamic array is the term I'm looking for: https://en.m.wikipedia.org/wiki/Dynamic_array
I don't usually think of them being backed by a linked list though, because it is the average case constant access time on a balanced table for getting values for a given key that tends to be the entire reason you would use a hash table in the first place
I'm not talking about linked list, and I'm still not talking about hash maps
sure, ok. I got it.
at capacity, an insertion into an array implementation of a hash table would need to resize the array.
you're not wrong there.
I don't think you can just talk about an array in a meaningful way in the context we have here though because we are talking about specific operations
if it's not a hash map, and it's not a linked list, maybe you don't ever even need to handle resizing the subject of your considerations.
who knows? yeah, an array is an array. Dynamic arrays allow cheap insertion / deletion.
(up to their actual maximum ofc)
No idea what you're talking about. My point is that amortized analysis is not about averaging over the possible values of a single input, it's about averaging over a sequence of operations. And the example I gave was appending to a dynamic array
dude
firstly, this is just wrong
this side point should've been your made point
this was not your point
I thought we got past that and were discussing different ways to implement hash tables wrt to specific operations
I guess I'm saying we've got a major assymmetric understanding here
Okay, sorry, I think we talked past each other 😅
this is just not quite right. If you read what I said, you'd see I did understand you.
anyways yeah I think I talked past you
actually I'm being an ass, yeah, we talked past eachother
my bad too
I agree with this 100%. I also agree with your earlier point that you need to be aware that average case analysis is not necessarily meaningful without a clear idea of specific cases.
Yep, for hash maps I guess you need to average in two different ways: an insertion can be O(n) either if the hash function gives a lot of collisions, or if the table is close to capacity and needs to be resized. But for a reasonable hash function across multiple insertions it's gonna O(1) on average
yeah definitely
unless your input is 1 identical thing that is always the input!!!!
then you need to discover the god hash
an unreasonable hash function in the sense that it transcends our understanding of numbers and functions
given an unreasonable input like that. But at that point I guess the choice of data structure itself would become the unreasonable thing.

I mostly meant that there's a concept of average complexity and amortized complexity and they're a bit different
it can be a gotcha question
Yep, this was what I was trying to highlight too. For example, you wouldn't say quicksort is amortized O(n log(n))
well
its cheap when you use doubling for resizing
if you dont then its kinda shit
arent there arguments about like what scale factor is best for this
2 is easy and simple to do but not everything use a factor of 2
iirc python resizes using n => n + (n >> 3) which is about a scale factor of 1.125
yeah thats just one implementation
fibonacci numbers are also an interesting choice
you can use other scale factors
same way you can use diff pivot choices for quicksort / quickselect
my favorite is random pivot
the average time per insertion is a/(a-1) if your scale factor is a but also the amount of wasted memory is n*a-O(1)
lmao
making quicksort non-deterministic
but also yes it is still deterministic
that makes the average time per insertion 1+phi
<@&286206848099549185>. hello this is a long shot but I am really struggling with APA formatting and citation and I know this is only for math questions but I’ve tried multiple other platforms and nothing has helped are you able to help.
well you usually analyze expected w quicksort
because worst case is quadratic
and randomized pivots have good expected case performance
ye
you could also do median of medians
what do you think of algorithms that basically rely on randomness in order to be fast
like imagine if you were given 2 arbitrary polynomials and you wanted to check if they're equal
mm yeah i see
its just that theyre really hard to analyze
you could try to expand them both with distributive property (taking a long time), or evaluate them at randomly chosen inputs in modular arithmetic (posisbly a lot faster)
do u know about Schwarz-Zippel Lemma , it states that if the polynomial P−Q is truly non-zero (meaning P and Q are not equal) the probability that this single random evaluation happens to land on a "root" and incorrectly yield zero is extremely low, specifically bounded by d/|S|
(where d is the degree and ∣S∣ is the size of the set). by choosing a "large enough" set S this probability of error is pushed down to a negligible level
https://en.wikipedia.org/wiki/Schwartz–Zippel_lemma
ah interesting
S is just the number of points you wanna test ig?
or the set of the points whatever
formally S is finite subset of the field over which the polynomial is defined when testing a multivariate polynomial P(x1,x2....xn) test involves selecting a random point r = (r1,r2...rn)
from the n dimensional space defined by the Cartesian product S..S×⋯×S (often denoted S^n)
oh
i kinda understand ig
just multidimensional polynomials are a bit strange to me
same lol
Looks pog
sybau
what the heck was that?
two pieced of shit floating in the air performing SHM?
i can see why you were timed out
💀
Martyr
lmfaoooo
Hello everyone, would anyone here like to be my advisor for publishing an article on commutative algebra?
Ask a professor in your university
Unfortunately, no one studies commutative algebra.
Lol
Algebraic number theory or algebraic geometry?
Or even just algebra
Its still better than asking on discord
There are only professors who work in dynamic systems.
Algebraic Geometry
hello , anyone here did their phd , dissertation in PDE????
If in Lie symmetries
I'm finishing my degree, but I did it with an EDP applying Lie symmetry theory.
Hello guys does anyone know comp sci serves that help like this math one
there is a compsci server in #old-network
that one is barely active
there's the programmer's hangout u might need look at
The amount of singular reaction this message got deserves it to be pinned
its just very easy to farm reactions in discussy 2 because it gets like 10 messages a day
Don't let Yassine, Deltoid, nG or manifold know
hi
The Real Reason nGroupoid Lost Honourable . . .
selfreacted too close to the sun
Mods dont want you to know ts
it was a series of gamer moments that led to it
Leading up to one massive self react
Deltoid :3
mrr
kon
Gamer moments, lmfao
has anyone worked with xcursor before and/or knows the standard names for cursor files
hii
What is Mathematics, really?
Yes.



mathematics is what mathematicians do
Agreed.
I hope you found the answer satisfying.
What are Mathematicians, really?
people who do mathematics
I hope you found the answer satisfying.
Hardly.
It's just a part of life kiddo.
🫂
:_ )
What is 6 times 9?
Result:
42
well there you have it
that's the question & answer to the life the universe and everything so hopefully that's satisfactory
Maybe you're not supposed to.
Maybe you trying to understand what life means is what keeps you away from living it to the fullest.
Maybe you just need to let go; and go on to do great things.
that is quite the euphemism 
Result:
42
☠️☠️☠️🗿🗿🗿 TUFF BOIIIII 😂😂🫱🫱
thank you harpz
thanks much help
🙏
owlsider
Good morning 😭
It seems unlikely
It does seem that way doesn't it?
If nothing else, it is currently afternoon where I'm sitting
Well right now for me it's 08:33am, where are you sitting?
I believe you
Where are you sitting?
good night
In my home office
I meant country wise and time wise?
Ok
Poland
Nice
Let me guess, you're in Europe?
Anyway, the point of this was to say I'm pretty much dying.
Huh
?

perhaps
He must be very lucky to have a gf like you
I'm a boy 
Means you Gay
Yes 
Ooo
look funny
is some one hear

tudududoo poin poin poin
<@&268886789983436800> advert
pls can enyone help me i have homwork for tumorow
bros on /gamemode spectator
! help
To ask for mathematics help on this server, please open your own help channel or help thread. See #❓how-to-get-help for instructions.
!noadvert
Please do not advertise your help channel or thread in other parts of the server. There are many people who need help, so advertising can quickly turn into spam.
Any tron nerds get tickets to the tron aries double feature? (Ik this is a math server BUT im crowdsourcing my nerd areas rn)
Question: What are your interests?
That movie looks kinda cool. I think I’ll get into Tron if it ends up being good
Welcome to the server @distant cedar
Thank you
hi
sleeping
happy friday! I have a training at hospital today and im so eepy 
Has there ever been an instance where all 50 help channels were being used?
It’s all over the place tbh. 

Thinking, but it's like double edged
hello
yes, usually during the end of a semester when everyone is cramming for exams
oh dear god.
I’m assuming the occupied factoid is used a lot during those times
hello?
@wispy bramble i see you got the helpful tag
Yeah I got it
grats
hi!
what is that
That's a hi, by a person who watches anime.
how do i factor x squared minus 11x plus 28
I need two numders
But I have to turn in my homewokr tomorrow
i dont like math its my least favorite subject..
I hate my math rn, as well
are you also doing fractions
No
Adding fractions?
No, I am in high school
Oh wow...
Do they teach you the biggest number there
Because my teacher says infinity isnt a number
and im like "I dont belive you" but she dont care
A number that is larger than any given number, approaches infinity.
A number that is smaller than any given number, approaches minus infinity.
This is the limited knowledge that I have of infinity.
it’s not part of the real or complex numbers
but there are number systems where it actually does exist
there’s usually more than one though
infinity is a concept that can refer to several different mathematical things, some of which are numbers and some aren't
hello
what if we had a diffrent algebra where positive*positive = negative ?
what would negative * negative be
positive
My idea is basically:
(+)(+)=(-)
(-)(-)=(+)
(+)(-)=(+)
(-)(+)=(-)
so multiplication is not commutative
That would just be -1 * the sign of the second number.
Yeah, and imaginary numbers no longer exist, also exponents now feature a (-1)^n
2^3=-8 under this new Algebra
e^x -> e^x*(-1)^x
however ln(-1) wouldn't be defined

let's do a simple calculation
0
= 0*1
= (1-1)*1
= 1*1 + -1*1
= -1 + -1
= -2
this only uses very basic rules of arithmetic
so basically, any system in which this idea for a multiplication operation works must either
- be really awful and break some fundamental assumptions about algebra
- satisfy the equation 2 = 0
the second option is not so bad - a lot of "number systems" in more advanced mathematics actually satisfy 0=2 (look up the "integers mod 2" for a common example)
but if you slightly rearrange the equation you see that what you've done is show 1 = -1, so your system of multiplying signs is trivial because negatives and positives are the same
What do you do when someone says they hate math? Sometimes I want to explain a discovery I have made, but people say it's all gibbrish to them.
lock them in a room with math and shock them if they don't do it, until they learn to enjoy doing math
(i need this)
hi
hi
hi
hru?
what r u doing?
Hi everyone! 👋
I’m excited to be part of this group. I run a small YouTube channel called Erl_Studies , where I share study tips, vlogs, and helpful resources for students. I’d love for you to check it out if it interests you! No pressure at all—just thought I’d share something I enjoy creating. 😊
Here’s the link: [https://youtube.com/@snehankitaarandive?si=DbYUHLISTRVslpAB]
Thanks for letting me be part of this community! 💛
nothing
say a number below 1 and 20
Char 2 gang rises again
0
ق،
That's good
You'll be doing plenty of it
Tell them that school fails to teach math in an productive way. Our school system is old and doesn't help make the learning experience fun or enjoyable.
It is pretty good I'll admit
WHAT HAPPENED

nitro scam
Ew. Scems 


what happend to ur pet demon
He’s angry with me
won’t stop calling me names
He keeps talking about the fitnessgram pacer test 
whats that
He keeps saying it’s a multi-stage fitness test where participants run back and forth across a 20-meter space at a progressively faster pace, guided by audio cues but idk
he won’t stop talking about it
oh i get it now
ya
fucking Gerald 
can’t. He’ll make a 1 micrometer puddle all over my house.
ur colour changed
oh mines diffrent
gg

so if ur active that means ur color change
yes.
u should have access #「the-obsidian-twink-jesus」 now
smells unemployement it jus joke and im also unemployed
LOL
I took one yesterday. He stared at me the entire time.
didn’t make a peep
oh
mines sleeps
cause i beat the shi out
You have a pet demon? Any advice?
when it anger or controller jus ignore or beat the shi out
I want to but he spawns water that doesn’t have surface tension
my pet name is black monster
Mine is Gerald
i see
*you have to bold it or he gets angry
yes
if he get too angry he controol me
if he gets too angry he despawns for a lil bit
which is good but he also likes to cast the anxiety spell onto me
oh k so what u feed him
EXACTLY 3 and a half carrots. No more and no less

k man catch u later
Adios pepe man
im not surprised i got a 100 on that midterm 

Congrats
thank you 
@royal tangle #help-5 message yes, that is it
hi

What's happening here? What's the last cool thing you've done? (you as in the person reading this)
Reading this message 🙂
Ngl, that is pretty cool.
I've beaten the final boss of Hades 2 (well, one of them) on empowered mode
Now working towards the other final boss
hey it’s another one of my kind!
Wassup Bro
You a major in math rn ?
that’s all over the place tbh
so is that a yes 😂
Cool cool cool. I've never played it though but seems like you're enjoying it
I am! Hades 1 was a great game, and the sequel improves on it in most ways
its 3:14 for me right now, pi oclock lol
Such a shame the French Revolution got derailed before they really got going with decimal time
i will buy it
i swear
hades 1 was too good
It was!
community reference?
I will say that I found the overarching story of Hades 2 less engrossing, mostly because of the higher stakes.
i root for 100 days in the year
But everything else is heaps better than Hades 1
They went with 360, and 5 extra: https://en.wikipedia.org/wiki/French_Republican_calendar
The French Republican calendar (French: calendrier républicain français), also commonly called the French Revolutionary calendar (calendrier révolutionnaire français), was a calendar created and implemented during the French Revolution and used by the French government for about 12 years from late 1793 to 1805, and for 18 days by the Paris C...
And the republican calendar did get implemented and was officially used for a while until Bonaparte rolled it back
they did try some stuff lol
But they were also planning to implement decimal time: https://en.wikipedia.org/wiki/Decimal_time
Decimal time is the representation of the time of day using units which are decimally related. This term is often used specifically to refer to the French Republican calendar time system used in France from 1794 to 1800, during the French Revolution, which divided the day into 10 decimal hours, each decimal hour into 100 decimal minutes and each...
Some clocks and watches even got made, but then Thermidor happened and everything got put on hold and eventually scrapped
did they change up the months or just rename them?
They had to change them up, since it was 12 months of 30 days each
With 5 "supernumerary days"
demon days
Sort of, they were basically an extended feast in honour of the revolution
i know they replaced [st something] days with seasonal veggies
which tbh
would be a good thing today
bc idk seasonal veggies
Yeah, every day was dedicated to something, the way in the Catholic church every day is dedicated to a patron saint.
But instead of saints they went with vegetables
ye
Well, "they", it was mostly one guy's pet project
I mean, the revolution as such certainly wasn't one guy's pet project
But I believe the thing with the patron veggies and the weird names of the months was almost entirely this guy: https://en.wikipedia.org/wiki/Fabre_d'Églantine
Philippe François Nazaire Fabre d'Églantine (French pronunciation: [filip fʁɑ̃swa nazɛːʁ fabʁ deɡlɑ̃tin]; 28 July 1750 – 5 April 1794), commonly known as Fabre d'Églantine, was a French actor, dramatist, poet, and politician of the French Revolution.
He is best known for having invented the names of the months in the French Republ...
(this is what they're called in ancient egypt iirc)
oh okay
i mean
just renaming stuff isn't huge
i mean it is now bc computer programs
but instoring a made up cult is lmao
January 1 is such an arbitrary date, the only thing it has going for it is that it's close to periapsis
The calendar wasn't really to do with the cult, it was a separate thing
The French revolution also instituted the metric system, which was a huge and lasting accomplishment
The calendar was also part of this rationalization drive, to have the months be of equal length and more easily divisible
hence what you said about it not having time to implement decimal time
Yep, eventually they had to dedicate all their focus on staying in power and alive, mostly with limited effect.
they also tried having decimal time
And once the radical phase ended, the Directory also focused mostly on keeping things going and themselves in power, reforms were mostly on hold until the Consulate/Empire
yes that's what outsider has been saying lmao
😭
yeah
I'm a teacher, I'm used to people not paying attention to what I say
i mean specifically decimal hours, minutes, and seconds
Yep, I have been saying that as well: #serious-discussion message
wasn't the directory like a mercantile dicatorship
so they didn't care much about progress did they
just money
oh i didn't scroll back up that far 😭
you must also be used to people being late to class

Just staying in power and alive, really. Moneywise it's complicated, since for instance they really screwed over their banker friends (which is why it was so easy to get them deposed and replaced with Bonaparte)
You can keep an unpopular and useless government going quite long if you have the army and the money, but those both went to Bonaparte
my teeachers always barely covered that part because it's probably not as "interesting" as the other parts before and after that
bythat i mean
less epic
oh ye we know that
Well yeah, it's fair to say that the exciting phase mostly ends with Thermidor, until of course Napoleon's own coup and subsequent wars
Oh yes, but I mean the Napoleonic wars are their own thing
But yeah, it got started in 1792 and basically kept going until 1815
there's so much to learn about that part of history
Interesting times, to be sure
Not as such, although my BF is a historian, and as for the French revolution I mostly got interested because of Mike Duncan's podcast: https://open.spotify.com/show/05lvdf9T77KE6y4gyMGEsD
His series on the French Revolution is a great listen
I mean, so are his series on the other revolutions
Excellent choice
ok nvm bank app is down i cn't pay
meow
Herro people
hi
Hey
Ling Gang Guli Guli Guliii Watcha Ching Lang Guuu Ling Gang Guuu
meow
you are so right
meow meow








