#serious-discussion

1 messages · Page 63 of 1

neat lintel
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Lick it before it falls

flat harbor
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yun emoji

long matrix
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shuwi would like to be injected with some life

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dead

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dead

somber musk
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My first choice was mid as well

long matrix
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dead

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this is what coffee does to me

neat lintel
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Why do you take coffee then?

flat harbor
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this is what coffee does to me

neat lintel
#

Milk >>>>>>>>>>>>>>>>> Coffee

flat harbor
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tbh i dont have a retort to this

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milk is just better

agile lantern
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alcohol >>

neat lintel
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Me with my fresh milk bottle^

flat harbor
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it is time to attempt sleep AGAIN

somber musk
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Drugs >

flat harbor
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its half past 2

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good nite chat good night shurichan good. night vero

somber musk
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Good night

flat harbor
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good night to u too

neat lintel
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good night blo, rest well

agile lantern
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have a nice sleep

long matrix
#

night night bloey

long matrix
snow panther
snow panther
warped flax
neat lintel
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nu

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milk is better

long matrix
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real cat

hasty leaf
manic ginkgo
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Earl grey be da best

warped flax
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agreed

hasty leaf
warped flax
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I drink more tea than milk somehow.. chinese tea are normally bland but I fine them alright

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taiwanese tea too

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but tea from my country is a big no

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too sweet

hasty leaf
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So condensed milk in strong tea

snow panther
hasty leaf
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Win

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Maybe Win Win

dusty copper
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can I ask a bot for example if something like this is true ?

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$2A\left(A-B\right)-B\left(A-B\right)=\left(A-B\right)\left(2A-B\right)$

river moon
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if you meant to say (2a-B), then yes

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though that also assumes commutativity

fathom swallowBOT
river moon
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for non-commutative things you can only factor (A-B) to the right

dusty copper
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$2A\left(A-B\right)-B\left(A-B\right)=\left(2A-B\right)\left(A-B\right)$

fathom swallowBOT
river moon
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yes

dusty copper
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okayy tnx got it

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shame a bot cant check if that statment is true

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it would be sick if we had a tool that check your math solution line by line and it tells you where you messed up

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like virtual teacher

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but I guess AI will do that soon so no point in building it now

errant herald
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sup

sour sable
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guys

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how do i tag a role

fresh forum
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$ a $

alpine wren
fading pulsar
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why?

silver stratus
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out of curiosity, how does one obtain the "ℌonorable" role?

untold sapphire
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i think you're nominated by other honorables.

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I was probably given this honor for establishing a reputation for long and sometimes informative rants about category theory

silver stratus
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interesting, what about the helpful role? do they give that role to people who help only in the help channels or in any channel?

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ah ok, thx 🙂

hollow ginkgo
tiny saddle
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Wtf is category theory

cunning compass
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about categories

tiny saddle
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What kinda categories

cunning compass
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think of sets but like way more comprehensive

tiny saddle
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Comprehensive in what way?

cunning compass
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in general, category consists of a collection objects (elements) and arrows/morphisms that relate from one object to another, you can think of morphisms as 'mappings'.

tiny saddle
cunning compass
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these objects can be anything pertaining to a specific category

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example is the category of sets (Sets) which have sets as objects and functions as morphisms

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theres also the category of groups, rings, vector spaces, topological spaces etc etc

tiny saddle
cinder zephyr
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if you study enough math you'll see the same constructions pop up over and over in different contexts

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and the proofs of certain properties of these constructions (and this is with some handwaving) are all the same after you change around some adjectives

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so category theory is one way (idk if there are other ways but I doubt there aren't other ways) of talking about arbitrary elements and morphisms between these elements and characterizing these constructions

cunning compass
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abstraction AWOOKEN

cunning compass
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😔

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i love integration tho

deep mango
untold sapphire
# tiny saddle Wtf is category theory

It's a branch of math which tries to study things, not in terms of their inherent properties, but by the relationships they have with other things. It abstracts away from caring about the particular details of the thing itself and tries to understand it better by understanding all similar things of that kind, and how they relate to each other all at once. Idk maybe a good analogy is like, most mathematicians study one species of object. Like you have some biologists who study fish, and some who study dogs, and others who study parrots. The category theorist perspective is like, thinking about fish and dogs and parrots all at the same time, and asking about relationships between fish and relationships between dogs and asking how those relationships are similar and what they have in common. Like two fish can relate to each other by sexual reproduction, and two dogs can also relate to each other by sexual relationship, so there's some structural similarities between the fish ecosystem and the dog ecosystem.

tall minnow
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"it's not about who you are. it's about who you know"

fleet oyster
cinder zephyr
calm sigil
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anyone know how wolframalpha and music albums go together Hmmm

tall minnow
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wolframalpha doesn't seem so smart nowadays

alpine kindle
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reminds me of this video

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still hilarious that this exists

neat frost
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That video hella scripted

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They should've brought actual actors instead of students

long matrix
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shush slurp

worn wolf
tepid seal
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uu

austere solar
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Is there any situation where integration doesnt work and you have to use Simpsons rule or rectangle rule?

leaden torrent
neat lintel
leaden torrent
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does riehl know any hott

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i will confess i know literally nothing about her research lmfao

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i just know that she wrote the category book

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i am a terrible academic

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but i thought she did infty cat stuff

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not hott

alpine kindle
neat lintel
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i'm still working through the HoTT book

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but as i understand it infty categories have deep connections to HoTT (as they relate to infty groupoids?)

alpine kindle
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there's like
an entire hott section at the end of her infty cat book

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i think

neat lintel
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she also has tons of lectures on YT talking about HoTT if ur curious

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Speaker: Emily Riehl, Johns Hopkins University
Date: October 18th, 2022
Abstract: http://www.fields.utoronto.ca/talks/How-I-became-seduced-univalent-foundations

Part of the "2022 Fields Medal Symposium: Akshay Venkatesh": http://www.fields.utoronto.ca/activities/22-23/fieldsmedalsym

▶ Play video

At its current state of the art, ∞-category theory is challenging to explain even to specialists in closely related mathematical areas. Nevertheless, historical experience suggests that in, say, a century’s time, we will routinely teach this material to undergraduates. This talk describes one dream about how this might come about — under the ass...

▶ Play video
leaden torrent
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ic

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my knowledge on this is literally "skimmed half of lurie's first book and that's it"

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i wonder how youd explain hott to a grade schooler

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explaining types doesnt seem hard, in some ways theyre more natural than sets

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"tags" you apply to things

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(i mean, even D students in intro programming know what an int is)

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but the "ho" part of hott seems like... a bit more of a leap lmfao

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you can give some vagueries about how types are related sure

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but you need a lot of details to make that... well, homotopical

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rather than a description that can apply to any system that permits prepositions on types lmfao

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like at the very least youd have to explain like, equivalences to get across the univalence axiom right?

neat lintel
tall minnow
# leaden torrent i wonder how youd explain hott to a grade schooler

I'd tell them homotopy makes a coffee mug equivalent to a donut.
And the point of HoTT is to make this kind of homotopy equivalence rigorous. One reason for doing this is that advanced physics such as string theory needs to deal with homotopy a lot, and when problems are formulated in HoTT they look much more obvious. So it's like a conceptual aid (which is what category theory does, for the adult mathematicians listening)

fervent zephyr
# leaden torrent i wonder how youd explain hott to a grade schooler

The distinction between sets and types is, imho, the distinction between starting with things and putting them in collections, versus describing "game rules" and then looking at everything that follows from it. You can see these as the inside vs the outside view. Then HoTT is the observation that when you take the outside view, there's no point in distinguishing things that look the same. But things can look the same in multiple ways, so suddenly "being the same" is more than just a yes-or-no thing.

neat lintel
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I finally understood the C++ perfect forwarding

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It's all because the value semantics of expressions & declarations

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When you declare a function that accepts a, lets say, r-value reference type, like void uwu(std::string&& nya), after that nya gets out of the scope of the argument list(the parenthesis), it becomes a glvalue reference type, so to have it back to its original value semantics, you need to forward it

fervent zephyr
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Yep, and with a universal reference, you need to know the deduced type to determine whether it should be an lvalue or rvalue when passing it along

tepid seal
neat lintel
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I guess one could write a requires clause to overload the set, and deduce whether it's a lvalue or rvalue, like:

template<class T> requires std::is_lvalue_reference_v<T> void uwu(T&& meow){}

template<class T> requires std::is_rvalue_reference_v<T> void uwu(T&& meow){}
fervent zephyr
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My C++ terminology is rusty, perhaps I'm mixing up perfect forwarding with something else, by the way

cunning compass
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What are pre requisites to differential geometry 🤔

fast ivy
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if it is "classical" differential geometry in the sense of curves and surfaces in R³ in the style of Manfredo.

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Then pretty much just linear algebra and some multivariable calculus

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if you want to get deeper than that

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Which is doing differential geometry on more general smooth manifolds (e.g riemannian geometry, symplectic geometry, poisson geometry, G-structures...)

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then you need some point-set topology, analysis and also some knowledge of smooth manifolds.

cunning compass
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Interesting

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Thanks

fast ivy
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I think.

John Lee's "Introduction to Topological Manifolds" and his book "Introduction to Smooth Manifolds" are the way to go for point-set topology and smooth manifold theory.

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he also has a book on riemannian geometry

cunning compass
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How about introduction to manifolds by L. Tu

leaden torrent
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particularly the stuff on equivalences

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like how do things "look the same" without "being the same"

eager reef
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right i forgot to mention pset top earlier

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my bad

leaden torrent
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i guess you could introduce like, modular arithmetic as the classic learner's example

fast ivy
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except shorter

cunning compass
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Oo aiight

fast ivy
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and somewhat easier to read

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requires a bit less of background too

leaden torrent
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i do agree that if you have a bit of mathematical maturity then the motivation behind hott is easy enough to communicate

cunning compass
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Sounds more beginner friendly

fast ivy
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since john lee assumes some knowledge of covering spaces and π_1 in a few sections

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while Tu does not even touch that

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Tu also talks about quotient maps from scratch in his book

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while Lee already assumes the reader knows this stuff

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there are a few other differences here and there

leaden torrent
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like the way i think of hott is that "it's a system where we study objects by what they are 'tagged' as rather than what set they 'belong' to, and the thing that makes it homotopical (well, univalent) is that there is no distinction between 'good' and 'evil'"

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and then uh

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magic magic somehow abstract homotopy stuff comes into the picture

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in ways beyond the nuking-a-mosquito that it is for normal equivalence relation stuff

fast ivy
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I don't get the analogy with good and evil there

leaden torrent
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do you know what good/evil mean in a categorical sense

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"evil" means that we care about equality instead of equivalence

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in univalent foundations, equality is equivalence

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the classic example of an "evil" question is "how many objects does [x category] have"

fast ivy
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didn't know category theorists also cared about ethics sotrue

leaden torrent
cunning compass
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Damn category theory sneaking up from nowhere

leaden torrent
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(though still not usually THAT useful lmao)

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good/evil is a bit more broad than this

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its really about like, "layers" of equivalence (in the sense of presentations)

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but the basest layer is equality vs direct equivalence, and thats the one the univalence axiom cares about

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(though i think the univalence axiom is like giga-strong and actually generalizes? i dont know the details but i heard something to that gist)

eager reef
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say something evil and clerk will come for you

still dome
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something

leaden torrent
#

nlab gives this example:

For instance, a category can be presented by a simplicial set (the nerve of a corresponding strict category, see there), but isomorphism of simplicial sets is much finer than equivalences of their corresponding categories. It is generally a mistake to mix up these two levels and, for instance, assign to a category properties that are shared only by some of the simplicial sets representing it, say, by distinguishing between isomorphic objects. This breaks the equivalence invariance.

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anyway the univalence axiom says that equality is equivalence

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so "something is a duck iff it acts and quacks like a duck"

silver stratus
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2+2=5 change my mind

neat lintel
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this (i actually spent time querying to find this, help)

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idk why i even remember it

long matrix
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ngl i remember it too

neat lintel
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that's what i remember from her personality, that's why

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That's not me

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Someone with the same roles and username and tag and id impersonated me

flint hound
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imma leave this server

long matrix
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they must be jealous

cunning compass
neat lintel
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i need help guys

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😦

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im in 6th grade

tight comet
quasi jettyBOT
long matrix
tight comet
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O wait

forest vapor
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i problem mathematics

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homework tommorow

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help please

high fern
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why do i feel like i am always like an last option for some of my friends, they never want to be in a voice call with just me and them only if its 2+ people they want me to join. Often i can talk about something and ask them a question and they will just like be quiet and if i ask like again like "what do you think?" they will go like "what did you say?" and the issue isnt that i dont speak loud enough or i speak unclearly its just that they almost never wanna listen to me, please help

neat lintel
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relatable

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I feel like I'm the last choice for everyone as well. like only talked to If nobody else will. like the bare bottom

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I guess it's just because I have the least interesting personality imaginable

long matrix
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id talk to u before @woven whale

neat lintel
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lol thanks

high fern
long matrix
neat lintel
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how does someone achieve the status of having a personality

fading pulsar
willow mulch
#

@humble crypt can u firend me

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friend

neat frost
trail tulip
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I've just forgor how to divide

winged lichen
neat lintel
#

thanks nikola tesla

winged lichen
neat lintel
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not professionally but i know a bit

winged lichen
#

Do you know how to do python

bright hill
bright hill
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I don't think that sufficiently captures the "Ho" part either lmfao

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Like, isn't homotopy about detecting holes or some shit?

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Need there not be a topological space?

fringe summit
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basically a homotopy type is a topological space modulo homotopy equivalence shenanigans but possibly blown up formally

leaden torrent
#

hott is not geometric

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at least not moreso than any other formalism

fringe summit
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You can, however, internally get notions of infinity groupoids and such and internal equivalences with some hypotheses about monads existing

hearty marsh
neat lintel
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did someone just ping me here

leaden torrent
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literally the message right before yours

hearty marsh
fringe summit
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The part that makes it "Ho" is the intensional equality (and also univalence & functional extensionality which gives an equivalence with equivalences/homotopies and relevant paths)

So if (x =_A y) is paths x->y in A, then we also have for p, q: (x =_A y) the type (p =_(x =_A y) q) of homotopies p=>q among paths x->y

neat lintel
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oh wait

fringe summit
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@bright hill

neat lintel
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think my thing glitched lol

leaden torrent
#

huh

hearty marsh
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His discord froze i think

leaden torrent
#

discord can be weird with caching but i havent seen it straight up ignore messages before

neat lintel
#

i found it

leaden torrent
#

try ctrl + r i guess?

neat lintel
#

yeah

hearty marsh
neat lintel
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its happened to me a few times

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mystery

neat lintel
hearty marsh
fringe summit
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Namington's explanation is correct I believe, though the good/evil branding is a tad odd

bright hill
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I'm just trying to process what you wrote openbleak

fringe summit
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oh yeah replies are just weird sometimes

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If you know infinity groupoids you know how a specific homotopy type looks

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though the pi, sigma things can have weird nuances to them

bright hill
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I dunno infinity groupoids sad

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Infty categories sound scawwy af sad

fringe summit
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they really are sad

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but infinity groupoids are basically equivalent to topological spaces

bright hill
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as if topological spaces are docile

fringe summit
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(very imprecise statement here but you can imagine why considering every single topological space& continuous function at once is spooky)

vivid halo
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infinity groupoids are just simplicial sets satisfying some fairly explicit conditions

fringe summit
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yeah as one presentation

vivid halo
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still scary but it's not as bad as you might think

neat lintel
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Anyone know any good ways of representing 4 dimensional graphs?

fringe summit
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But it's the same intuition regardless

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Think paths in topological spaces

leaden torrent
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what is the dimension of a graph

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like maximal degree?

neat lintel
#

Sorry I meant graphs with 4 variables

leaden torrent
#

oh you mean like

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a coordinate plane

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lmao

neat lintel
#

Yh

leaden torrent
#

uhh one common way, especially if one of your variables is periodic, is with colours

fringe summit
leaden torrent
#

(or if your variable isnt periodic, consider a parametrization that makes it so)

neat lintel
#

its the complex sine function

vivid halo
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oh god

fringe summit
#

Also the proof of it is mf comical

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because remember this is hott

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so it's like

leaden torrent
#

then yeah thats sufficiently periodic that such an approach works

fringe summit
#

Until you realize

leaden torrent
#

this is a mathematica help forum but

fringe summit
#

oh yeah

leaden torrent
#

the principles apply

vivid halo
#

comical sets
haha

fringe summit
leaden torrent
#

for complex plots its also common to just

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plot the real part and imaginary part

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on the same 2d plane

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this is what wolframalpha does for example

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and then use some other axis, such as time or colour, to vary wrt the other dimension

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(obviously varying time means you'll get an animation, not a still)

fringe summit
# vivid halo oh god

this is the proof btw, except for one line that says "Yeah the identity monad satisfies these conditions"

vivid halo
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lmao

neat lintel
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Before I was plotting the real and imaginary outputs along w the real part of the input and was varying the imaginary part of the input

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I feel like I lost information though

fringe summit
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This looks horrible, but remember that this is hott so you can wish away equivalences

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So e0, e1 are the identity

bright hill
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What the F is \mbb{M}?

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I am so lost kongouDerp

fringe summit
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Translation for the non enlightened: it's horrible but it's basically just a formal worse version of saying you've got a basic type X_0 and X_n+1 is trees of points in X_n decorated by n+1 paths

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i.e. how do you stitch paths together

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  • a way to stitch them together
fringe summit
#

we literally do not care about it except for the singleton point, trees with some bundle projecting onto them, and bundle versions of these two

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(Also if you want an actual proper explanation in relation to some concept lemme know)

bright hill
#

Hehe, I most likely don't have enough mathematical maturity

fringe summit
bright hill
#

I'll let you know once I've done some AT tho nozoomi

fringe summit
bright hill
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Lmfaoo

vivid halo
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lmao

fringe summit
#

I also almost emailed the author about the infinity category composition not type checking until I realized the fibrant condition being moved up a level didn't screw it up

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X_1 (1-cells) indeed loses a property, but that hurts nullary composition

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n+1 not n moment

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actual brain damage on my part

vivid halo
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there is a time in my life where I cared much more about this stuff and I could go on about different models of higher categories and how different models are good for different things

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but now they're just simplicial sets to me 🙂

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went on to care about bigger things

fringe summit
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yeah idk tbh they're all equivalent probably

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I don't care about the interrelations, I just care if it's reasonable to say things apply elsewhere

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opencry not any worse than using a conjectural category

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These type based ones are interesting for practical concerns though since a strictly unital and associative one built on globular pasting diagrams has decidable equality

torn willow
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How does type checking work in type theory

fringe summit
#

which is clearly pretty nice compared to HoTT having contractible types with ultra giga uncountable number of points

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nG idk if you care but the opetope trees are the bane of my existence in HoTT for precisely this homotopical unfolding

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because we just get like a bundle of trees bleakkekw

fringe summit
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I couldn't give any sort of technical explanation on how it works in implementation of Agda, etc

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but recall an inhabitant of P can be regarded as a proof of P as a proposition

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And if your function is defined everywhere (continuously) and has the right outputs, then it's an inhabitant of the relevant function type

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Even if it doesn't seem right, you can get some wacky induction done that's forced to work because of this

vivid halo
#

cool lol

torn willow
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Ok so is type conversion not a thing in type theory

vivid halo
#

this is so far from the math I care about these days

torn willow
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I assume it wouldn't be

fringe summit
fringe summit
vivid halo
#

D-modules in positive characteristic

fringe summit
#

yeah that's vile

torn willow
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So, What's wrong with thinking things as (object,type) pairs

fringe summit
#

have fun with that

fringe summit
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kinda

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but obviously "object" doesn't really mean much

torn willow
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So why do you need category theory for type theory if you can just do that

vivid halo
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it's nice, I am studying differential equations over some very simple rings nozoomi

fringe summit
#

K theory of the integers

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Idk anything on that so I can't offer anything interesting in conversation

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Not that you have to be an expert to talk about something, but if you have no idea what's going on it's not much of a dialogue

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my professors dealing with this cursed article be like

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(nobody studies this here)

torn willow
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lmao who pushed you into this then

fringe summit
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nobody

vivid halo
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I mean this is why I stopped caring about category theory at some point

fringe summit
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yeah

vivid halo
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it's fun to have topics that actually connect to other areas of math easily

fringe summit
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But I'm not exactly interested in rings and such

vivid halo
#

bummer

fringe summit
#

ordered algebraic things are cool though

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like developing integration in po-groups

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there's apparently a kinda oldish book on po-semigroup valued measures kekw

vivid halo
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sounds terrible

fringe summit
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it is

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But remember that they all look finite even if not archimedean because they're still group elements

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But this like immediately proves results about like banach spaces or something

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because riesz rep

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(or analogue thereof)

vivid halo
fringe summit
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you can basically get a topological group out of these orders too

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but rings are sussier I think

vivid halo
fringe summit
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as per usual

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Functions f:T->X, measures m: Σ -> Y, a bilinear-y multiplication XxY->Z, gets you integration partial function (M_m(X, Z), Σ) -> Z

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why?

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I have no idea why you'd do this to yourself

vivid halo
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yeah nor do I

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this is why I study things that are like

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much more easily motivated

fringe summit
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But ring multiplication in lattice ordered rings isn't strong enough for that multiplication

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I think

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I'd have to double check but it doesn't play nice with order continuity iirc

vivid halo
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okay lol

fringe summit
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The motivation for this: there was none given bleakkekw

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but it's still nifty

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Obviously could say things about general ordered integration things, might be able to say things about vNA?

vivid halo
fringe summit
#

me

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I am still idiot undergrad so who knows, maybe I'll see the light of applicable math

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or see the applications of these things

vivid halo
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I mean the stuff you're talking about is quite far from what a lot of people care about

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you seem to dislike rings, but this is where so many actual applications lie

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idk you should have a more open mind to more standard stuff

fringe summit
#

it is what it s

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non-commutative rings are spooky

vivid halo
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yeah non-commutative rings are a little hard to think about

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commutative rings are better

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there's a lot you can say about them

fringe summit
#

non-noetherian bleakcat

vivid halo
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or about certain classes of them

fringe summit
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yeah there's a lot you can say

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and commutative ones are clearly nicer and useful for AG

vivid halo
#

yeah

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like in my case a lot of D-modules in char p is literally just thinking about differential operators on a polynomial ring like F_p[x]

fringe summit
#

I've also seen them used in proof trees in reference to some reduced versions of linear logic

vivid halo
#

so something very very concrete

fringe summit
#

Interesting

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I have doodoo brain tho

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Not very good at math unfortunately

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Just kinda think silly infinity categories are nifty kekw

bright hill
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Nifty is a nifty word

fringe summit
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Might get more into measures who knows

bright hill
fringe summit
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Topology is probably just straight out since I struggle with it

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basically order-centric version of studying rings of functions KEK

#

there's a lot of things which are just based on rings of functions

fringe summit
stray kite
#

what does any of this mean
why is topology in algebra

fringe summit
#

Well I mean functions valued in a ring are usually structured from that

fringe summit
stray kite
#

((i just know neither enough algebra or topology to understand it))

fringe summit
#

same

stiff osprey
#

hi podge

#

its been ages since i've came by, i now have calculus again in uni time to dai

neat lintel
#

How should I prepare for AMC 12 and AIME qual as a Sophomore with no history in competitive math? In Algebra 2, taking Pre-Calculus over the summer.

fading pulsar
#

Do the problems from previous years ig

#

When I took them there was like 15-20 years or something of problems posted online with worked solutions

tall minnow
#

the day apple releases a touchscreen M3 macbook air is the day they finally corner the market

#

as of now it's still awkward to not able to write / draw on a macbook

neat lintel
#

Also macos runs on the M1 & M2 chips which are arm64 based, so the change should be trivial

#

do ipads need to run Mac os though. seems like apple is the type of company to prefer people not have their users be able to do anything. ipad is a lot more restricted than a Mac and I imagine apple rather keep people there if they can

#

letting ipads run Mac would allow users to download software from websites, ruining their monopoly in the app store.
then also it causes people to not need a Mac as much if there ipad can already do everything.
when looking at apple you can't think at all about what customers would like, it's all about what makes apple the most money

neat lintel
#

You think Microsoft and Red Hat ain't doing that on their respective operating systems?

#

Data mining is lucrative smh my head

long matrix
#

vewo awake at 0340

neat lintel
#

Same for you

#

I had to study for exams the next week

#

What's your excuse? uwu

hasty leaf
long matrix
stoic harbor
#

pls help me with decimal

woven whale
bronze seal
#

Ok thanks.

tall minnow
#

Yes, the news is that Apple is working on touchscreen Macs. Which is why I paid attention

coarse fiber
#

Haven't seen a more aptly-named mathematical concept than confusion matrices

#

True positive rate = True positives / (true positives + false negatives)

tight comet
#

There are like 10+ metrics tied to confusion matrices

coarse fiber
#

my main issue lies in that "false negative" means something that is originally negative and you falsely thought it was positive, not something that was originally positive and you falsely thought it was negative

#

just seems completely backwards to me

coarse fiber
hot tusk
coarse fiber
#

hopefully it'll become more intuitive going forward

hot tusk
coarse fiber
#

it's not really my area but I'm taking an elective on machine learning so I'm not completely clueless about it, I'm probably not gonna get a chance to apply it :(

hot tusk
coarse fiber
#

yeah I just mean in terms of prioritizing it over my other projects etc

#

my main area is computer architecture so I try to take electives in different topics so I know what the computational requirements of other people are

#

for example I took an elective on bioinformatics and even though that's not really something I wish to work on, the string matching and motif finding algorithms are very interesting and stand to be accelerated with hardware.

#

AI accelerators are kinda huge in computer architecture right now so I want to get a good understanding of machine learning for that

bright hill
#

@neat frost I rediscovered the best movie ever

#

we have to watch mean girls together

#

this is so cringe hahahahaha

#

all I remember from mean girls is that one scene where she goes "ThE LiMiT DoEsn'T ExISt"

#

such a staple of modern HS cinematography

#

I can't believe I forgot this shit existed

neat frost
#

I'm down to watch it

bright hill
#

I'll drag ryc and stuff into it

#

we can do it over the weekend

#

(with COMPLETELY legal means, mind you)

neat frost
#

And afterward we can watch prince of Egypt

bright hill
#

sure

#

:)

rocky shuttle
#

PoE

neat frost
#

toowoo

rocky shuttle
deep mango
neat frost
deep mango
#

What

#

I just closed discord to get back to work

neat frost
#

UwU rycie bycie

deep mango
#

I will not watch poe together

#

I will not watch mean girls together. I already saw mean girls

neat frost
deep mango
#

Never

#

I sent DarQ a very funny clip from mean girls though

#

I could watch this a thousand times and it would make me laugh every time

neat frost
fading moon
#

the other two mathematics servers look pretty sus

neat frost
odd copper
#

not sure why she said the limit was one when there was a zero in the denominator

odd brook
#

im convinced she read the bottom as sin^2(x) and the expression on top as log(1 - x) - cos x rather than log(1 - x) - sin x

#

mentally swapped all the sin and cos terms somehow

#

cant lie it'd have taken me a good minute or two longer than cady did if put on the spot like that lol

neat lintel
#

hfffffffffghhhhjj

willow gulch
#

How do you guys find enjoyment in an easy class with a lot of busy work

#

I imagine a lot of it is letting go of ego and trying to find where you can improve despite the difficulty

river moon
#

I don't, I'd swap my econ/risk management classes with a bunch of easy exercises/paper work for a math class any time

#

I was hooked up on the exercises in the control theory class because they were genuinely interesting and not as easy, but now I'm feeling like I'm wasting my own time

willow gulch
#

Yeah it can be pretty mind numbing

#

But I'm stuck with it opencry

hot tusk
river moon
#

I guess I try to finish all of this easy work in a day or two so that I don't have to come back to it ever again, or even if I do then I have very little to fix/addhmmCat

neat lintel
#

How do i figure this out 😭

#

long division? Any videos? WTF

neat lintel
#

😐 Aint no way my teacher thinks i can do this without a calculator

regal night
#

You could use the taylor series ig

#

Add enough terms to you get precision of 4 decimal places

neat lintel
#

HUH

regal night
#

Surely you can recall the taylor expansion for e^x from memory? o .o

neat lintel
#

Brother i am in the 3rd week of college

#

First semester college algebra

#

I have no idea who this person named taylor is

analog jetty
#

hey buddies what are your POVs about existence of perfect cuboid

cinder zephyr
neat lintel
neat lintel
#

No calculators, No calculators, No calculators, No calculators, No calculators, No calculators, No calculators, No calculators, No calculators, No calculators,

#

It has been repeated

#

in class

#

while he reads

#

from 14 year old

#

pirated power point notes

#

that he

#

calls his own

regal night
neat lintel
regal night
#

Ah

neat lintel
#

I am american brother

#

THey teach nothing

regal night
#

Well I can't think of any other way of computing e to the negative 2 without a calculator

#

Unless

#

Hmm.. maybe u could compute 1/(2.78)(2.78) by hand

#

Doesn't look very tough

#

,calc 1/((2.78)*(78))

fathom swallowBOT
#

Result:

0.0046116952591773
regal night
#

,calc e

fathom swallowBOT
#

Result:

2.718281828459
regal night
#

Maybe use 2.7182 instead

#

Pardon my inability to correctly recall the digit at the second decimal place of e earlier.

proud olive
willow gulch
#

yeah I mean 1/(2.7182)(2.7182) doesn't sound terrible

#

no calculators is just goofy though

#

idk what doing that problem by hand is supposed to teach you

#

ig it might help with getting more comfortable with e but it's a pretty roundabout way to do it

proud olive
#

Dumb wasting time calculating it since that's not really the point of the course

#

You've usually mastered basic arithmetic operations before going into calculus

analog jetty
neat lintel
analog jetty
proud olive
#

Probably multiple solutions

#

Or Infinite idk

gray prism
runic charm
#

hello

hasty leaf
#

Hi

runic charm
#

do you know vectors?

runic charm
proud olive
#

I know him very well

runic charm
proud olive
#

Sorry i don't know any guy who goes by the name "the chapter"

proud olive
neat lintel
neat lintel
hearty marsh
neat lintel
#

Someone Can explain me the trigonometria

#

Pls

long matrix
#

try khan academy

neat lintel
#

???

#

Tf is that

long matrix
neat lintel
#

Xddd

neat lintel
long matrix
#

g o o g l e

leaden torrent
#

they got a life

#

alas....

alpine kindle
#

sad

#

there are many cool people still here tho

neat lintel
#

I'm still here I didn't get a life

#

O sorry, u specified cool people, nvm

solar hawk
#

holy shiz

#

i didnt even read it but

#

🐟😭i cant stop

neat lintel
#

🐟

solar hawk
shell oar
#

I wonder if there's anyone here who's done the Putman exam

lethal mango
#

i like turtles

abstract lion
fringe summit
#

@untold sapphire bleakkekw

storm sage
#

It is not me though

fringe summit
#

We got a few sus individuals

untold sapphire
#

yes

fringe summit
#

But uh, I don’t think I’m capable of a PhD program currently

untold sapphire
#

Ok. Well you have time. Are you doing a bachelor's degree in math currently

fringe summit
#

Yep

untold sapphire
#

or is your major something else

fringe summit
#

Math major

#

The infinity 2 case is already troublesome ofc

#

And (infinity, 1) still should have more work I think

#

Infinity n should work in a similar fashion to n=2 though

untold sapphire
#

still thinking about this paper?

fringe summit
#

Yep

#

Though as a hobby project

#

Gonna ofc look at class work studies KEK

untold sapphire
#

Ok. I am going to go to bed as i have a work in the morning. good luck

fringe summit
#

Good luck with that one lol

shell oar
abstract lion
tall badge
#

@brisk smelt not here man

brisk smelt
bright hill
#

discussion 2 has slow mode? thonkzoom

cunning ether
#

hu

latent sage
#

Math makes me sadcat

worthy shell
regal night
white hamlet
untold igloo
#

hello, where can I post a signal processing problem? I have an exercise and I want to verify my result.

neat lintel
#

who wants a coffee candy

neat lintel
deep mango
#

The little espresso flavored suckers

neat lintel
deep mango
#

Yes!

#

Coffee flavor is so wonderful

neat lintel
#

yes

long matrix
#

candy

umbral forge
#

What are some conditionally convergent series that aren’t the alternate harmonic series

storm sage
#

There's not really a dedicated place for it

#

If you want to ask about Fourier transforms then #odes-and-pdes is probably also a good place

storm sage
#

Uhhh how? Certainly you don't learn Fourier transforms in a normal secondary school

umbral forge
fringe summit
#

Yeah that’s it

#

The uhhhh, Dirac test?

native viper
#

How can I find my help room that has been closed already ? Need to revisit some answers

leaden torrent
#

search yourself with discord search

teal lion
#

that i looked up that quote in your bio

#

and i just now learned

#

that the respondents in that supreme court docket about the onion

tall badge
#

the entirety of the onions amicus brief is a great read

teal lion
#

were from parma

tall badge
#

argument I is my personal favorite part

teal lion
#

like, i never knew it existed

#

parma, ohio that is

void tundra
#

do not advertise your help channel

neat lintel
#

NOOO why is this server so dead

deep fiber
#

It’s like the opposite normally. Go to the neuroscience discord if you want to see a dead discord.

rocky shuttle
#

Not enough

fading pulsar
#

It's not good to be counting hours lol

tranquil cairn
#

the chinese will take over the world

hasty leaf
tranquil cairn
neat lintel
brittle socket
tribal hemlock
#

Does anyone know what book teach me how to take gradient of a multivariable real valued function written in matrix form?

river moon
#

such book doesn't exist

#

you can read something like Boyd's convex optimization to get a better hang of the standard functions like linear, affine, quadratic, etc and how to differentiate them

velvet dagger
#

Wait I'm confused

#

Isn't what LilYee is asking just like

#

A multivariable calculus book?

tribal hemlock
#

What I mean is for example a quadratic function written in matrix form: f(x) = a + transpose(b) *x + transpose(x)Cx

river moon
#

certainly knowing that will help, but I figured it only solved the simplest questions for me

tribal hemlock
#

If the functions is written normally, I can take gradient. But its written in matrix

velvet dagger
#

On thing in principle you could do is to convert to coordinate form. So write x = (x_1,...,x_n)

river moon
#

for this specific function you can just write it as a sum and take partial derivative

velvet dagger
#

Well, b^Tx = \sum_{i=1}^n b_i x_i

tribal hemlock
tight comet
river moon
tight comet
#

It's very common for such books to just list results than to comment anything though

tribal hemlock
#

I want to know what book instruct me how to do the above

#

Without breaking the matrix notation down and take partial derivative normally

river moon
#

you can just use the properties of the scalar product

tribal hemlock
tranquil cairn
river moon
velvet dagger
#

So LilYee, for what it's worth once you go into coordinates to compute the gradient, well now you know the gradient and can write it back in vector form, and take it as a known fact. That said, you can use properties of functions to avoid it

fathom swallowBOT
#

Transparent_Elemental

tranquil cairn
#

that server is a whole weird thing

river moon
#

there's generally no reason not to learn how to take partial derivatives of complicated functions, it actually helps differentiating more complicated functions without relying on some "rules"

tribal hemlock
tribal hemlock
river moon
#

that's why I'm saying that what you're asking for doesn't exist, there's simply too much nuance

#

might as well try to prove it by writing the components of these vectors and taking the derivative

tranquil cairn
river moon
#

the problem with "compact" notation is that you have to respect the order heavily as the things you're working with do not commute in general, for example the derivative of x^T C x is generally (C+C^T)x and not 2Cx if we don't assume C is symmetric

tribal hemlock
#

Its just a simple quadratic function

torpid marsh
#

k

neat lintel
#

make sense i gr

velvet dagger
#

LilYee: in this case one thing you can do to dodge going to coordinates is to write down directional derivatives

tranquil cairn
#

atleast not on this server

neat lintel
#

i think they have already taken most of it

#

they are also very hard working and very diligent they can take over very easily

tranquil cairn
#

yea. that, Exactly! thats why

neat lintel
#

nice

woven whale
#

wtf is going on here

neat lintel
#

chinese to take over this world haha

velvet dagger
#

Wait how the fuck did I miss this

velvet dagger
#

While child labor in China at least at one point was, and likely still is, a problem, in context you give off the vibe as caring about that as a means to an end of going after China which isn't the way to play it

hasty leaf
#

Agree with the sloth

hasty leaf
#

(Probably made in China)

velvet dagger
#

Techno you seem to have a habit of trying to dictate to me when you decide something's banworthy

#

But frankly I have my eyes

#

I will use my own judgment to decide this sorta thing

brittle socket
#

YouTube comments be like

fast ivy
#

2-adics be like

alpine kindle
#

1/2-adics when

neat frost
#

piadics

neat notch
#

i am a 2 addict

brittle socket
#

Dyadic sotrue

tranquil cairn
# brittle socket

youtube comments are the greatest. i read comments on almost all videos, 100%fun from video, and another 100% from comments, = 200% fun

hasty leaf
neat lintel
#

I HATE DISCRETE MATH, ITS JUST NORMAL MATH BUT WITH RNG

torn willow
#

Ironically, discrete rng is easier to understand

neat lintel
#

im just mad chatgpt cant do my homework anymore

torn willow
#

It being able to do your homework was a mistake

#

Because well chatGPT's goal is to sound authentic, not being correct

alpine kindle
eager crescent
#

Is there anyone at U of Chicago here?

teal lion
deep mango
#

I don't think we have any current UoC students

teal lion
#

ah

deep mango
#

Maybe he'll still have access though

long matrix
#

university of ryc when

chilly hull
#

university of math discord

muted oxide
eager crescent
# muted oxide I am an undergrad there

Oh finally someone! Would you be willing to take some pictures/scans of a document in the library that can't be found anywhere else? It's a math article in an old discontinued journal and it seems that this libraey is one of the few places in the world that has it. I'd be very grateful if you were catlove

muted oxide
eager crescent
#

I am in fact not in the US (I'm french) and I have already graduated from my uni anyway, I only have minimal access to its resources now

#

If you can't that's ok, I think I can try to ask directly the library thanks to an online form. Though the form isn't really meant for that as far as I gathered so I don't know how they might respond or how long it would take for them to answer.

muted oxide
deep mango
long matrix
#

Ok, I bag the profits, u do the admin

deep mango
cinder zephyr
#

I volunteer to teach at the university of ryc

#

No admin work tho

neat lintel
#

Wtf am i looking at

eager reef
#

Laplace expansion

neat lintel
#

why

#

there has to be a better way right?

solid snow
#

there is, using row operations

neat lintel
river marten
zealous garden
velvet dagger
#

Even Laplace expansion isn't the worst if you immediately start with the last row

neat lintel
#

How am i supposed to remember any of this

velvet dagger
#

More you do it the more used to it you get

ripe wasp
#

you could convert it to an upper/lower triangular matrix and just keep track of the row operations iirc

#

@neat lintel

#

though that's probably what josemom meant

neat lintel
neat lintel
#

Gm

neat lintel
neat lintel
neat lintel
#

Is it possible to solve for x here?

neat lintel
neat lintel
river moon
#

factoring

neat lintel
#

Swap the side of equation might make it more familiar to you

void tundra
#

!help

quasi jettyBOT
soft bramble
#

im looking at perturbations to an equilibrium solution of a 50 dimensional ODE

#

some components of the 50 dimensional solution oscillate

#

what would one expect the jacobian's eigenvalues/evectors to look like?

#

if there's oscillation

river moon
#

There are complex eigenvalues

soft bramble
#

i get some really tiny complex parts for the eigenvalues

#

when i compute them

#

on the order of 10^{-19}

#
  • there's a few evals that are negative, order 10^{-2}
  • mostly positive real evals, order 10^{-17}
  • a few complex evals, with both real and complex part order between 10^{-17} and 10^{-19}
#

what does that mean?

#

and also when i plot the graphs, most components converge except a few that oscillate

#

so im just confused

grizzled grove
#

So the adelic Poisson summation etc and the adelic language do make thing interesting and easify understanding of Hecke original contribution to analytic continuation of Hecke L function. But what's with the K theory angle of talking about special values of L function. Does K theory angle really helps much in number theory stuff?

river moon
#

Is it really a non-zero eigenvalue when we're talking order ^-17

#

Even if you ask e. g. python to compute sqroot(-1) it'll produce a non-zero real part on the order of ^-17

molten pagoda
#

he l p

#

how can i use log to solve

river moon
#

Looks like a polynomial to me

river moon
wooden flax
#

then when you have y, you can solve for x as x=log(y)

molten pagoda
#

I got it

#

thanks!

#

Question 11

#

Why I cannot using this way to solve A?

#

The answer say A=3.67

river moon
#

You're trying to take a log of a value which is already measured on the log scale

molten pagoda
#

I got it already

neat lintel
#

https://www.youtube.com/watch?v=41HIXtBElH4&ab_channel=MichaelParloff who else thinks allegro molto is overrated? Allegretto is far better

00:00 Largo
05:07 Allegro molto
08:12 Allegretto
12:36 Largo
17:43 Largo

1st violin: Eugene Drucker
2nd violin: Philip Setzer
Viola: Lawrence Dutton
Cello: Paul Watson

This performance of Dmitri Shostakovich’s 8th String Quartet in C minor, Op. 110, by the Emerson String Quartet took place on December 16, 2018 on Parlance Chamber Concerts at ...

▶ Play video
#

i love shostakovich's quartets

patent folio
#

can someone help me on help-22 please?

storm sage
patent robin
#

if anyone can help me dm rq its geometry 10th grade math TY if you can

soft bramble
grave grail
#

If 100 cats exist, and 75 of them have orange shoes on. 3 of the cats run into the street and get hit by a bus. What are the chances that 2/3 cats have orange shoes on

fading pulsar
#

Now I want to see 75 kitties with orange shoes on

#

Are some of them just sitting in a giant boot

molten pagoda
void tundra
brittle socket
#

Learning math is such a slow process for me angerysad that I run outta copium sometimes sad

#

How do you guys deal with your own progress seeming slow to yourself tinktonk

south kelp
#

i personally don't

#

i just cry myself to sleep over my slowness

brittle socket
#

No but seriously though, how do you guys deal with it

#

I mean I get rationally that learning math is not a easy or quick process, and I shouldn't dwell too much on that. But it still is demotivating, from time to time, how little I skills and knowledge I have after putting in a certain amount of effort.

#

Again though, if I think about it rationally, I think I have improved a lot in both skills and knowledge over the past year

neat lintel
#

I hate that math is a competition

void tundra
#

It is not

neat lintel
# void tundra It is not

I hate that public schooling and standardized testing and limited seats in college and limited jobs has made the act of learning math culturally associated with competition

void tundra
#

Ah okay then yes

eager reef
#

i mean fair

#

but that's not specific to math

tiny saddle
#

XD

neat lintel
eager reef
#

yeah i can agree with that i guess

tiny saddle
#

what else is there?

eager reef
#

i'm very glad that the system is different in my country

#

well limited jobs are still a thing of course but well that's inevitable

neat lintel
tiny saddle
neat lintel
tiny saddle
#

yeah I get that

long matrix
#

I hate life being a competition sully

tiny saddle
#

but

such is life

long matrix
neat lintel
long matrix
silver aspen
#

competition is only good when you win

long matrix
#

the aspects you described - sure, i totally agree

#

exams are silly

long matrix
#

my issue about exams/tests is less the competition, but more that they fail to assess what they're designed to assess more often than not

#

And due to this, encourage certain unnecessary/useless/sometimes downright bad skills

hasty leaf
long matrix
#

unnecessary speed

#

for one thing

untold sage
#

Fair

long matrix
#

Is it better to be able to half-ass a question in 30 mins, or need a day to fully answer?

untold sage
#

Speed is still important tho

long matrix
#

That depends on context

hasty leaf
#

Time is money

long matrix
#

When it comes to research mathematics... idk about that.

untold sage
#

Like if you're doing research, that translates to more research output

long matrix
#

It would be wrong to say speed is totally irrelevant

#

but I don't think it should be prioritised over quality

untold sage
#

But sometimes they prioritise it too much

hasty leaf
#

I agree

long matrix
#

which exams kinda encourage you to do

untold sage
#

Like doing tons of easy questions in a short period

tiny saddle
#

and the repetition is just

#

._.

hasty leaf
#

So what are alternatives to exams....projects maybe

long matrix
#

projects monke

untold sage
#

I'd say stick with exams

tiny saddle
#

like I have no idea how many times I had to factorize a simple quadratic in class

untold sage
#

Well that's actually useful for stamina

long matrix
#

im not proposing something better over exams, no, its just how it is

#

What could be better is a personal evaluation

#

But that's logistically impossible, and inherently biased/flawed

untold sage
#

You can obviously change the exam format to make it better

tiny saddle
long matrix
#

i mean personally by someone else who is qualified to do so monke

hasty leaf
neat lintel
#

meritocracy is false. The number one marketable skill is inherited wealth. We should honestly do away with exams and grades

tiny saddle
hasty leaf
neat lintel
untold sage
#

Inherited wealth is not a skill

neat lintel
tiny saddle
neat lintel
tiny saddle
untold sage
tiny saddle
#

skullissue

long matrix
#

democracy is shit along with all other systems that ppl have come up with so far monke

tiny saddle
#

I mean tbh by what I'm considering "shit"

#

yr right

#

XD

neat lintel
tiny saddle
#

society is kinda bad in quite a few ways but welp just live with it till it gets better 1 day

tiny saddle
#

1000 years in the future we will determine it all by brain scanners trust ™️

long matrix
#

since you cannot change it (probably), it is better to try change yourself so its less so

tiny saddle
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mhm

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sadly

hasty leaf
long matrix
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you dont have to mold yourself to the system

neat lintel
long matrix
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u can simply accept certain parts of it and avoid actively warring with it (internally)

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like if u cant change it, theres not much good that will come out of complaining about it

hasty leaf
long matrix
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unconstructive criticism is just a waste of your own time

neat lintel
tiny saddle
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In the mathematical field of differential topology, the Hopf fibration (also known as the Hopf bundle or Hopf map) describes a 3-sphere (a hypersphere in four-dimensional space) in terms of circles and an ordinary sphere. Discovered by Heinz Hopf in 1931, it is an influential early example of a fiber bundle. Technically, Hopf found a many-to-one...

neat lintel
untold sage
neat lintel