#serious-discussion

1 messages · Page 316 of 1

tight copper
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oh

junior veldt
grim yacht
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Lego 1×1

warm umbra
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Welcome to the server @grim yacht

atomic seal
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@cold forge affine variaties are cool 🙂

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took some time to get wrap my head around all the sheaves stuff

cold forge
#

they are cool!

cold forge
atomic seal
#

real

cold forge
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just like category theory

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thats the important stuff

atomic seal
#

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

atomic seal
#

I think Milne just assumes that everyone who reads his AG notes knows cat theory

cold forge
#

it is good to be familiar with universal properties and limits and colimits

atomic seal
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when the definition of a stalk is basically a colimit

junior veldt
vivid halo
#

lol no

cold forge
junior veldt
#

hi nG

vivid halo
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howdy

junior veldt
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hru doing

atomic seal
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what summoned you two?

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"cat theory"?

cold forge
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category theory probably

junior veldt
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ig so

vivid halo
junior veldt
#

hope you feel even better soon

cold forge
vivid halo
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yeah I feel mostly better now guh

atomic seal
vivid halo
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had horrible horrible lack of sleep earlier in the week and then made up for it by bedrotting for a few days

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then had pretty bad migraine yesterday

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but doing okay today

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feeling very disorganized with the preprints I'm trying to finish guh

junior veldt
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oh i got my first preprint recently

cold forge
# atomic seal what intuiton are you talking about?

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

junior veldt
#

well that's the construction of a colimit, at least

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though not really its universal property

cold forge
vivid halo
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it's still wild to me that you can do reasonable geometry with prestacks (no gluing conditions whatsoever, just functors)

junior veldt
vivid halo
#

oh nice

cold forge
junior veldt
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ig i like the intuition from coends

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since they provide a "polymorphic" version of $\exists$

fathom swallowBOT
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Pseudo (Cat theory #1 Fan)

junior veldt
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which is essentially what you want - there exists an open neighbourhood of x with a function defined on that neighbourhood

cold forge
#

yeah

junior veldt
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the identification is just built into the categorical def of "there exists"

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you're basically doing $\int^{x \in U} F(U)$ after all

fathom swallowBOT
#

Pseudo (Cat theory #1 Fan)

junior veldt
#

which you can read as $\exists x \in U . F(U)$

fathom swallowBOT
#

Pseudo (Cat theory #1 Fan)

cold forge
#

gotta be honest i know basically nothing about coends

vivid halo
#

lol yeah I also never properly learned coends

junior veldt
#

to me they're a really pretty idea

vivid halo
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yeah they are quite nice

cold forge
#

only thing i know is "category theory integral"

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lmao

junior veldt
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ends and coends provide categorifications of $\forall$ and $\exists$

fathom swallowBOT
#

Pseudo (Cat theory #1 Fan)

junior veldt
#

but with naturality built-in

vivid halo
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they just don't come up often enough for me to remember a lot of the details around them

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other than like, Day convolution as a special case

junior veldt
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there are lots of categorical definitions that can be written as "forall blah, a morphism from foo to bar such that this diagram commutes"

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ends let you just read the "forall" part of that statement and write it as an end

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the naturality follows automatically from the definition of the end

vivid halo
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yes this is what depedent products/dependent coproducts are for, and I guess you can write these in terms of ends/coends

junior veldt
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mhm

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they also appeared in yoneda's phd thesis

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so they've been around for a very long time

vivid halo
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I have got a lot of mileage out of this dictionary for representation theory

junior veldt
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interesting

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i actually know more about the HoTT side of this table than the rep theory side

vivid halo
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it's neat how (co)induced representations can be viewed as dependent (co)products like this

junior veldt
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that is quite cool

vivid halo
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and that this gives you all the adjunction properties for free

junior veldt
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yeah i guess the nice thing about classifying spaces is that they let you view representations in a "fibred" way

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so you can apply all these techniques from dependent type theory

vivid halo
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this is very similar (identical in content) to how people these days think about representation theory in terms of 6-functor formalism

atomic seal
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do you guys know etale cohomology? how much prerequisites are there for it?

junior veldt
vivid halo
junior veldt
vivid halo
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the prereq is basically AG at the level of Hartshorne (chapters 2 and 3 especially)

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like as long as you are comfortable with schemes and sheaf cohomology

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etale cohomology is usually the first time you learn how to deal with sheaf cohomology for more general sites rather than for topological spaces

junior veldt
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oh interesting

vivid halo
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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

atomic seal
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ok so I have a lot to learn

vivid halo
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yeah haha

atomic seal
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actually there is a class on sheaf cohomology starting soon in my uni

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I will try to get notes from there

vivid halo
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nice nice

junior veldt
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i've heard some stuff about sheaf cohomology

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measuring the failure of local solutions to glue to a global one?

vivid halo
vivid halo
junior veldt
#

interesting

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so it's a notion from abelian categories?

vivid halo
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if you're dealing with sheaves of Abelian groups or modules or whatever yeah

junior veldt
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mhm

vivid halo
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if you have a sheaf of Abelian groups A on a space X then H^0(X,A) is global sections

junior veldt
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oh ok

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is that just A(X)

vivid halo
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yeah

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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

junior veldt
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mhm

atomic seal
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but I really have no experience with homology/cohomology

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its from alg top right?

vivid halo
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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

junior veldt
vivid halo
junior veldt
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oh i mean more conceptually like

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why would i expect the last part to fail

vivid halo
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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)...

junior veldt
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it's a failure of surjectivity of the map X(A_2) -> X(A_3) right

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uh wait

vivid halo
junior veldt
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A_2(X) -> A_3(X)

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hm...

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i guess i'd need to work through a concrete example to see this#

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but i can black-box it for now

vivid halo
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usually the motivating example is the complex logarithm on C-{0}

junior veldt
vivid halo
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you can always find local sections for the logarithm, but you run into issues gluing these to a global section because of monodromy

vivid halo
junior veldt
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ok gotcha

junior veldt
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i guess my issue with not knowing the formalism is that sheaves are all about "gluing compatible local sections to a global one"

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so a priori it's not obvious to me what is actually meant by "failure of local sections gluing to a global one"

vivid halo
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yeah I guess the main point is that sheaf cohomology is what is actually measuring this failure

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like classes in H^1(X,A_1) are obstructions to this sort of local to global construction for global sections

junior veldt
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i see

vivid halo
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same can be said in higher degrees

junior veldt
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so it's somehow measuring the inability to choose a bunch of compatible local sections?

vivid halo
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yeah

junior veldt
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fascinating

vivid halo
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like in the logarithm example, you have a nontrivial obstruction coming from monodromy around 0

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and that really does see some nontrivial topological fact about C-{0}, that it is not simply connected

junior veldt
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honestly i feel like this makes "homology is indicator functions for algebraic structures" make even more sense to me

vivid halo
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when you apply sheaf cohomology to very specific kinds of sheaves (locally constant sheaves) then this recovers the usual constructions of singular (co)homology

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but it applies to other kinds of sheaves as well

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it also applies to sheaves defined not just on topological spaces, but defined on more general Grothendieck topologies

junior veldt
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i guess the main thing is trying to find an analog of the "global sections" functor?

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on a more generic site

vivid halo
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sure

junior veldt
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my initial guess would be $\int_U F(U)$ or something

fathom swallowBOT
#

Pseudo (Cat theory #1 Fan)

vivid halo
#

well usually it's like

junior veldt
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where U ranges over the objects in your site

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but mb not

vivid halo
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global sections is usually just coming from a terminal object

junior veldt
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right, which the end would recover

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but what if your site doesn't have a terminal object?

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or do i not need to worry about that

vivid halo
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I can't think of so many examples where one has to worry about this haha

junior veldt
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ok cool

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i'll keep the end def in mind then

vivid halo
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like for etale cohomology the site in question is the "small etale site" of a scheme X

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objects of that site are etale morphisms of schemes Y->X

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morphisms are commutative triangles as one would have in a slice category

junior veldt
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mhm

vivid halo
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terminal object is the identity X->X

junior veldt
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makes sense

glossy sparrow
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i have a doubt

vivid halo
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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

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the etale topology is finer than the usual Zariski topology

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Zariski covering families are etale covering families but you have more etale covering families which are not Zariski covering families

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the closest analog in the setting of smooth manifolds would be the local diffeomorphism site

junior veldt
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-# idk what etale covers are @.@

vivid halo
#

that's fine it's not so relevant

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you can think of etale morphisms of schemes as similar to local diffeomorphisms of smooth manifolds

atomic seal
#

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

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does this sound good to you?

vivid halo
atomic seal
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Thanks

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Its starts in a month or so

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so I have some time to prepare

cold forge
#

as in like aesthetically pretty

atomic seal
#

But I will stick to milne for now

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I am slowly learning names of authors

latent edge
cold forge
#

idk why

latent edge
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I haven't tried it

cold forge
#

it has some nice pictures too

latent edge
#

I learned yesterday (and will continue today) how Galois groups correspond to deck transformations

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Last time I stopped at taking 2 copies of C and doing some quirky branching stuff to make sense of field automorphisms

cold forge
#

thats related to the fundamental group of an affine scheme right

latent edge
#

yea etale fundamental groups

cold forge
#

everything is etale..

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everywhere i go i see its name

latent edge
#

It's neat stuff

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Not sure why I was scared before

cold forge
#

whats the overarching idea of "etale" stuff

empty mirage
#

roingus 🥐 lisayay

true zinc
#

@latent edge how much combi do you need to know for rep theory?

empty mirage
#

roingus 🥐 lisayay

barren kettle
#

how are people doin?

junior veldt
#

!bnuuy

quasi jettyBOT
empty mirage
#

roingus not much

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cleaning

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watching egyptian tiger nut cake recipes

junior veldt
#

I have been getting filter-pilled today

empty mirage
#

Based

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based based based

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fr fr

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Anyways back to

junior veldt
latent edge
true zinc
latent edge
#

Still vague

true zinc
fresh comet
empty mirage
fresh comet
#

higher! lisayay

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gm TTeppa

true zinc
#

hey TT, higher

fresh comet
#

sob

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I have to juggle 4 problem sets in the next week

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they don't seem that bad, but I'll probably need a few dozen hours combined to finish them all

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half of which might be from my numerical methods assignment alone KEK

teal minnow
#

Yoo

obtuse grail
worldly horizon
#

It seems a lot more quiet here

grand helm
stray viper
#

discussion 2 is the middle child

fresh comet
#

which channel is the youngest child? catthimc

limber thunder
#

left completely alone, unattended

#

figuring out its own identity

fresh comet
lofty forge
#

Dude this is so much more peaceful than #discussion , that place is insane

gritty heath
#

Yeah

worldly horizon
#

💔

lofty forge
#

True dude🙏

misty oracle
raw narwhal
#

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?

lofty forge
misty oracle
wraith schooner
#

i have a timed assingment on statistics if i start it would someone mind helping me out 🙂

lofty forge
lavish roost
#

Hello chat ( ' u')//

reef carbon
#

@rancid cave can you tell me what was so funny that it made you go "lol" here

rancid cave
#

bruh

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i just like to laugh, no offense

reef carbon
novel tundra
#

chill out

reef carbon
#

eh?

rancid cave
#

so the problem might be on you

novel tundra
#

?

reef carbon
#

i mean yeah im not really in any sort of explosive state rn lmao

novel tundra
#

💤

jaunty ibex
fresh comet
#

<@&268886789983436800> pikathink

reef carbon
#

hello

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why did you reply to a random msg of mine thonk

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did you want something from me

kindred trellis
reef carbon
#

no

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but if you really wanted to grab my attention you... could have simply said one message

kindred trellis
#

My bad🙏

reef carbon
#

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
kindred trellis
vast wraith
#

this footnote (10) is wild

empty mirage
# vast wraith

euler did formal power series and exponentiation on the algebraic structure known as the wheel?

vast wraith
#

idk here’s the reference for the extract from euler if you want to contextualize it:

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this (excellent) book btw is luboš nový’s origins of modern algebra

vernal token
vast wraith
#

um well i spend quite some time reading math history bnuuy

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maybe i should look into whether i could try study it officially

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but idk if i actually want that

long patrol
#

Fuckkkkkkkkkthis life

night garden
#

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?

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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

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(ik this is discussion and less math focused but i need helpppppppp) 😭😭😭

vast wraith
night garden
#

Some1 help me out 🥹

long patrol
#

What do you think¿

icy heron
# vast wraith

Euler would be a frequent flyer in #crank-discussion if he were alive today

vivid quest
#

Do you have a book recommendation?

fresh comet
vast wraith
neat lintel
vivid quest
#

Or maybe not a book but something else

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A podcast or a video would do too for a start

neat lintel
#

Abel died of tubercolosis when he hit his 30s just a few days before getting a univeristy position

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almost all of my math history comes from like textbooks which have those little boxes mentioning the mathematicians/scientists 😭

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I was reading this abs alg text and there was section on lagrange and abel, very cool

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a lot of it is surprisingly tragic though

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He died when he was 26 nevermind

pseudo lotus
#

...

night garden
#
  • new ones
neat lintel
#

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

night garden
neat lintel
#

It's okay it happens fr

night garden
#

I have uni from 9am to fucking 6

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Ts pmo sm

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I have so many lectures(i cant skip them too or else my parents will off me themselves)

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😭ts isnt fair my brother comes home way sooner than me

true zinc
#

<@&268886789983436800> suicide joke

vast wraith
tame egret
mint canopy
#

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

night garden
#

Oh oops sorry

mint canopy
#

Thank you for being understanding

vivid quest
tall solar
#

Hi! Is this the right place to ask for some feedback on a short math article (blog post) I wrote?

tall solar
ocean harbor
#

I can't provide u a specific feedback on this bc I have never studied set theory catscream

#

u got some interesting projects btw

tall solar
#

Thanks 😅

tall solar
ocean harbor
neat lintel
#

hi everyone! Would smn mock interview me for quantitive trading. I can also mock interview you! Would be super greatf! Just dm me : )

warm umbra
#

Welcome to the server @neat lintel

long patrol
#

،

lavish kayak
#

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.

night garden
#

Guess not

buoyant magnet
#

Anyone writing exams today, tomorrow, next month.. Any other day or month

Good luck and all the best

ocean harbor
ocean harbor
#

thanks bro

buoyant magnet
#

You welcome

ocean harbor
ocean harbor
#

no need for it

tame egret
#

Ok catthumbsup

ocean harbor
ocean harbor
#

today's midterm should be easy but im sleepy asf

tame egret
#

kongouderp
You've got this

misty oracle
#

@lofty forge BBMath has received his role, you're next :))

ocean harbor
tame egret
#

Just hope for the best now:)

ocean harbor
#

so annoying

tame egret
#

I still don't know why people have to use word though

ocean harbor
#

bc its annoying

#

have u not used it before?

tame egret
#

It seems useless tbh

ocean harbor
#

it is lol

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prof gave me a lab report and i have to do that shit using word document

tame egret
ocean harbor
#

i got a 60 in my english class

#

i passed

tame egret
tame egret
ocean harbor
#

i have to prepare for next one

ocean harbor
lofty forge
tame egret
misty oracle
#

@umbral grottohow ya doin?

umbral grotto
misty oracle
#

if you get any questions

#

math-related for sure

umbral grotto
#

._.

misty oracle
#

why that face 😭

fresh comet
ocean harbor
#

ur pfp explains 👀

neat totem
#

Hotpocketology

#

They're a Hotpocketologist

tame egret
robust laurel
#

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

ocean harbor
gloomy briar
#

hey!

#

How is everyone?

left umbra
gloomy briar
#

Wyd today?

left umbra
#

and solved some of doubts like hw doubts of a guy called don

gloomy briar
toxic python
#

why are there several discussion channels?

zealous garden
#

Lots of discussion

vocal flint
old oak
toxic python
#

yes i have

#

quite a lot going on at the same time

old oak
#

Precisely, and some of us like a more sedate experience

toxic python
#

same

lofty forge
#

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

burnt ledge
#

nothing stops them

#

nevertheless they don't

merry plank
shy summit
#

Hii

tame egret
neat lintel
lofty forge
neat lintel
#

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

fresh comet
#

I like both channels

#

we gotta have a bit of both in life sometimes blobsatisfied

old oak
#

Well, some of us do

wheat iris
#

guys guess what

shadow palm
#

@wheat iris
What?

dark stone
glass peak
#

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 ecstasy

dark stone
glass peak
#

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

cinder zephyr
#

exceptionally useless

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just make sure your big O time and space are optimal (often there is a tradeoff, understand these)

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the %s vary widely depending on how warm the testbench is, cache optimizations, language, etc

burnt ledge
#

sometimes when im bored i farm for best % by js running the same solution over and over again

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theres a very large variation

glass peak
#

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

glass peak
#

I can pretty much work out time complexity too but I’ve really got no idea about space complexity

burnt ledge
#

if youre populating a list that isnt your output chances are youve got linear space complexity

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otherwise youre probably constant space complexity

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Ts is a good heuristic

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but js reason about how many objects you're keeping around at any given instant

cinder zephyr
#

the general strat is optimize for time complexity

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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?

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etc etc

glass peak
#

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)

neat lintel
late compass
#

Hi

warm umbra
#

Welcome to the server @late compass

late compass
#

Ty

twin flicker
#

technically

lavish kayak
#

it's not average in the meaning of probability

ocean harbor
#

@worn walrus did u manage solve the problem at the end?

fresh comet
ocean harbor
ocean harbor
spring raptor
sage canyon
#

is anyone here going to Thailand WMTC 25

ocean harbor
barren anchor
#

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.

barren anchor
icy heron
#

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

twin flicker
barren anchor
# icy heron You need to be mindful of what you're actually averaging over though. If you hav...

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.

icy heron
#

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

barren anchor
#

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)

icy heron
icy heron
#

The length of the backing array

#

When the length exceeds the capacity, you need to reallocate

barren anchor
#

you're saying a hash map implemented as an array and you'd expect* append to be a common operation?

icy heron
#

No, forget the hashmap. I'm talking about a list, also called a vector in Rust

barren anchor
#

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

icy heron
barren anchor
#

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

icy heron
#

I'm not talking about linked list, and I'm still not talking about hash maps

barren anchor
#

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)

icy heron
#

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

barren anchor
#

dude

barren anchor
barren anchor
barren anchor
#

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

icy heron
barren anchor
#

anyways yeah I think I talked past you

#

actually I'm being an ass, yeah, we talked past eachother

#

my bad too

barren anchor
icy heron
#

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

barren anchor
#

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.

fresh comet
lavish kayak
#

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

icy heron
twin flicker
#

its cheap when you use doubling for resizing

#

if you dont then its kinda shit

compact surge
#

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

twin flicker
compact surge
#

fibonacci numbers are also an interesting choice

twin flicker
#

you can use other scale factors

#

same way you can use diff pivot choices for quicksort / quickselect

#

my favorite is random pivot

compact surge
#

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

compact surge
versed token
#

<@&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.

twin flicker
#

because worst case is quadratic

#

and randomized pivots have good expected case performance

compact surge
#

ye

twin flicker
#

you could also do median of medians

compact surge
#

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

twin flicker
#

well i like monte carlo algos a lot

#

simulated annealing etc

compact surge
#

mm yeah i see

twin flicker
#

its just that theyre really hard to analyze

compact surge
loud tinsel
# compact surge what do you think of algorithms that basically rely on randomness in order to be...

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

compact surge
#

ah interesting

#

S is just the number of points you wanna test ig?

#

or the set of the points whatever

loud tinsel
# compact surge 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)

compact surge
#

oh

#

i kinda understand ig

#

just multidimensional polynomials are a bit strange to me

pliant creek
#

First time doin desmos

shell vigil
#

Looks pog

neat lintel
#

sybau

snow helm
#

back again from my latest timeout

snow helm
#

two pieced of shit floating in the air performing SHM?

brave flare
#

i can see why you were timed out

inner canopy
#

💀

inner canopy
thick zealot
#

Hello everyone, would anyone here like to be my advisor for publishing an article on commutative algebra?

gritty heath
#

Ask a professor in your university

thick zealot
merry plank
gritty heath
#

Or even just algebra
Its still better than asking on discord

thick zealot
#

There are only professors who work in dynamic systems.

Algebraic Geometry

junior tartan
#

hello , anyone here did their phd , dissertation in PDE????

thick zealot
#

I'm finishing my degree, but I did it with an EDP applying Lie symmetry theory.

rose geode
#

Hello guys does anyone know comp sci serves that help like this math one

ocean harbor
ocean harbor
fringe dirge
brave flare
#

its just very easy to farm reactions in discussy 2 because it gets like 10 messages a day

jaunty ibex
#

Don't let Yassine, Deltoid, nG or manifold know

latent edge
#

hi

limber thunder
#

self react should be insta ban

#

by means of bot

burnt ledge
#

selfreacted too close to the sun

#

Mods dont want you to know ts

limber thunder
burnt ledge
#

Leading up to one massive self react

solid yarrow
compact surge
#

mrr

compact surge
zealous garden
drifting dove
#

has anyone worked with xcursor before and/or knows the standard names for cursor files

drifting dove
#

standard found

pure rover
#

hii

mystic hill
#

What is Mathematics, really?

warm umbra
mystic hill
warm umbra
mystic hill
agile fiber
#

mathematics is what mathematicians do

warm umbra
#

Agreed.

warm umbra
mystic hill
#

What are Mathematicians, really?

agile fiber
#

people who do mathematics

warm umbra
mystic hill
warm umbra
mystic hill
#

!meaningoflife

#

: (

#

Life is such a ragebait concept

warm umbra
mystic hill
agile fiber
#

What is 6 times 9?

fathom swallowBOT
#

Result:

42
agile fiber
#

well there you have it

#

that's the question & answer to the life the universe and everything so hopefully that's satisfactory

mystic hill
#

I dont get it

#

^ life in a nutshell

warm umbra
#

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.

mystic hill
#

I see

#

I am satisfied

#

YSST is very wise.

hidden isle
burnt ledge
#

Texit whats six seven

#

,calc 6*7

fathom swallowBOT
#

Result:

42
burnt ledge
#

☠️☠️☠️🗿🗿🗿 TUFF BOIIIII 😂😂🫱🫱

hidden isle
loud tinsel
#

What is 6 times 9?

gloomy briar
#

Good morning 😭

old oak
#

It seems unlikely

gloomy briar
#

It does seem that way doesn't it?

old oak
#

If nothing else, it is currently afternoon where I'm sitting

gloomy briar
#

Well right now for me it's 08:33am, where are you sitting?

old oak
#

I believe you

gloomy briar
#

Where are you sitting?

hallow plume
old oak
#

In my home office

gloomy briar
gloomy briar
old oak
#

Poland

gloomy briar
#

Nice

gloomy briar
#

Anyway, the point of this was to say I'm pretty much dying.

sharp mulch
#

Huh

cunning iron
#

?

fresh comet
glossy tulip
#

Hi

#

Anyone here?

sharp mulch
#

perhaps

honest ridge
#

I'm making a bracelet for my boyfriend holoyay

#

Going to be a big surprise

glossy tulip
honest ridge
glossy tulip
#

Means you Gay

honest ridge
glossy tulip
#

Ooo

ripe sparrow
#

Hi

#

Bye

oblique garden
#

look funny

oblique garden
#

is some one hear

fresh comet
neat lintel
neat lintel
#

<@&268886789983436800> advert

sacred rivet
#

pls can enyone help me i have homwork for tumorow

mystic hill
quasi jettyBOT
quasi jettyBOT
arctic atlas
#

Any tron nerds get tickets to the tron aries double feature? (Ik this is a math server BUT im crowdsourcing my nerd areas rn)

long patrol
#

Question: What are your interests?

restive oar
warm umbra
#

Welcome to the server @distant cedar

distant cedar
#

Thank you

pure rover
#

hi

ocean harbor
#

happy friday! I have a training at hospital today and im so eepy SCyawn

worldly horizon
#

Has there ever been an instance where all 50 help channels were being used?

worldly horizon
fresh comet
lofty forge
cunning iron
#

hello

agile fiber
cunning iron
#

sorry

#

?

worldly horizon
cunning iron
#

hello?

worldly horizon
#

WHY DO YOU KEEP POSTING HELLO IN ALL OF THE DAMN DISCUSSION CHANNELS

rancid cave
#

@wispy bramble i see you got the helpful tag

wispy bramble
#

Yeah I got it

rancid cave
#

grats

fresh comet
#

hi!

honest wagon
#

what is that

atomic tapir
#

That's a hi, by a person who watches anime.

slow remnant
#

how do i factor x squared minus 11x plus 28

atomic tapir
#

You use the quadratic formula.

#

Also it is (x-4)(x-7)

slow remnant
atomic tapir
#

xsquared-4x-7x+28

#

x(x-4) -7(x-4)

#

(x-4)(x-7)

slow remnant
#

I need the numbers

#

x =-4 and -7?

atomic tapir
#

Think about it

#

I'm not giving you the answers directly

slow remnant
#

But I have to turn in my homewokr tomorrow

atomic tapir
#

Learn factorisation first

#

do factorisation questions

slow remnant
#

i dont like math its my least favorite subject..

atomic tapir
#

I hate my math rn, as well

slow remnant
#

are you also doing fractions

atomic tapir
#

No

slow remnant
#

Adding fractions?

atomic tapir
#

No, I am in high school

slow remnant
#

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

atomic tapir
#

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.

whole horizon
#

but there are number systems where it actually does exist

#

there’s usually more than one though

agile fiber
#

infinity is a concept that can refer to several different mathematical things, some of which are numbers and some aren't

woven relic
#

what if we had a diffrent algebra where positive*positive = negative ?

agile fiber
#

what would negative * negative be

woven relic
#

My idea is basically:

(+)(+)=(-)
(-)(-)=(+)
(+)(-)=(+)
(-)(+)=(-)

agile fiber
#

so multiplication is not commutative

atomic crypt
woven relic
#

2^3=-8 under this new Algebra

#

e^x -> e^x*(-1)^x

#

however ln(-1) wouldn't be defined

fresh comet
alpine kindle
#

this only uses very basic rules of arithmetic

#

so basically, any system in which this idea for a multiplication operation works must either

  1. be really awful and break some fundamental assumptions about algebra
  2. 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

valid hornet
#

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.

light gate
#

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)

pure rover
#

hi

warm lance
#

hi

honest wagon
#

hi

pure rover
honest wagon
#

what r u doing?

hazy sleet
#

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! 💛

pure rover
wraith seal
#

say a number below 1 and 20

broken roost
#

Hey

#

Why's 5-4=3

zealous garden
vivid quest
#

Idk why i love linear algebra so much

#

But i do

long patrol
#

ق،

gritty heath
#

You'll be doing plenty of it

ocean harbor
#

linear algebra is goated

#

<@&268886789983436800>

woven relic
zealous garden
worldly horizon
ocean harbor
ocean harbor
worldly horizon
ocean harbor
earnest grotto
worldly horizon
#

won’t stop calling me names

earnest grotto
#

ya he should

#

is he telling u to do stuff

worldly horizon
#

He keeps talking about the fitnessgram pacer test sadde

worldly horizon
#

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

worldly horizon
#

fucking Gerald angerysad

earnest grotto
#

yes

#

beat him

worldly horizon
#

can’t. He’ll make a 1 micrometer puddle all over my house.

ocean harbor
#

ur colour changed

earnest grotto
worldly horizon
#

HOLY SHIT

#

I GOT ACTIVE

ocean harbor
#

gg

worldly horizon
earnest grotto
#

so if ur active that means ur color change

worldly horizon
#

yes.

ocean harbor
earnest grotto
#

smells unemployement it jus joke and im also unemployed

ocean harbor
#

LOL

earnest grotto
#

when last time u took bath

#

i think that y u r pet calling u names

worldly horizon
#

didn’t make a peep

earnest grotto
#

mines sleeps

#

cause i beat the shi out

worldly horizon
#

You have a pet demon? Any advice?

earnest grotto
worldly horizon
earnest grotto
#

my pet name is black monster

worldly horizon
earnest grotto
#

i see

worldly horizon
#

*you have to bold it or he gets angry

earnest grotto
#

if he get too angry he controol me

worldly horizon
#

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

earnest grotto
#

oh k so what u feed him

worldly horizon
earnest grotto
#

mines want cats

#

for no reason

worldly horizon
earnest grotto
#

k man catch u later

worldly horizon
#

Adios pepe man

ocean harbor
ocean harbor
subtle vessel
unique terrace
#

hi

fresh comet
lunar ruin
#

What's happening here? What's the last cool thing you've done? (you as in the person reading this)

lunar ruin
#

Ngl, that is pretty cool.

old oak
#

Now working towards the other final boss

worldly horizon
candid stump
#

Wassup Bro

worldly horizon
#

welcome to the mathcord

#

fellow space being

candid stump
#

You a major in math rn ?

worldly horizon
candid stump
#

so is that a yes 😂

lunar ruin
old oak
#

I am! Hades 1 was a great game, and the sequel improves on it in most ways

woven relic
#

its 3:14 for me right now, pi oclock lol

old oak
#

Such a shame the French Revolution got derailed before they really got going with decimal time

vivid quest
#

i swear

#

hades 1 was too good

old oak
#

It was!

old oak
vivid quest
old oak
#

But everything else is heaps better than Hades 1

old oak
# vivid quest i root for 100 days in the year

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

vivid quest
#

they did try some stuff lol

old oak
#

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

vivid quest
#

did they change up the months or just rename them?

old oak
#

They had to change them up, since it was 12 months of 30 days each

#

With 5 "supernumerary days"

unborn meteor
old oak
#

Sort of, they were basically an extended feast in honour of the revolution

vivid quest
#

i know they replaced [st something] days with seasonal veggies

#

which tbh

#

would be a good thing today

#

bc idk seasonal veggies

old oak
#

But instead of saints they went with vegetables

vivid quest
#

ye

old oak
#

Well, "they", it was mostly one guy's pet project

vivid quest
#

unsure about that

#

bc yk

#

no anyway

#

the cult of the supreme being was funny

old oak
#

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...

unborn meteor
vivid quest
#

i mean

#

just renaming stuff isn't huge

unborn meteor
#

i mean it is now bc computer programs

vivid quest
#

but instoring a made up cult is lmao

unborn meteor
#

January 1 is such an arbitrary date, the only thing it has going for it is that it's close to periapsis

old oak
vivid quest
#

yes

#

i was just listing stuff

old oak
#

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

vivid quest
#

hence what you said about it not having time to implement decimal time

old oak
#

Yep, eventually they had to dedicate all their focus on staying in power and alive, mostly with limited effect.

unborn meteor
#

they also tried having decimal time

old oak
#

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

vivid quest
#

😭

unborn meteor
#

yeah

old oak
unborn meteor
#

i mean specifically decimal hours, minutes, and seconds

old oak
vivid quest
#

so they didn't care much about progress did they

#

just money

unborn meteor
#

oh i didn't scroll back up that far 😭

vivid quest
old oak
# vivid quest just money

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

vivid quest
#

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

old oak
vivid quest
#

the wars started with the revolution

#

not with napoleon

#

right?

old oak
#

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

vivid quest
#

there's so much to learn about that part of historynozoomi

old oak
#

Interesting times, to be sure

vivid quest
#

also

#

why do you know so much about that

#

interested in history?

#

study it?

old oak
#

His series on the French Revolution is a great listen

#

I mean, so are his series on the other revolutions

vivid quest
#

nice

#

ok imma buy hades 2

old oak
#

Excellent choice

vivid quest
#

ok nvm bank app is down i cn't payblobcry

loud tinsel
#

meow

worldly horizon
#

Herro people

naive grail
#

hi

obtuse grail
worldly horizon
loud tinsel
#

meow

naive grail
loud tinsel
#

meow meow