serious-discussion

[misty smelt]

I mean it's a very natural way to describe things, and there are not too many rules to define what a set is and the basic operations on it

[neat lintel]

can someone quiz me on an sat math question

[tender tulip]

literally ANY algebra problem .

[neat lintel]

yes

anything

[neat lintel]

are you looking for one

@tender tulip

[tender tulip]

No I just said practice any algebra one

[neat lintel]

.. ok lol

i don't want to choose any though, cus i wanted to get a random one

to see if im ready for anything

[long matrix]

what is 'sat math q'

[tender tulip]

There’s khan academy

[neat lintel]

some algebra

[long matrix]

List the number of subgroups of S4

[neat lintel]

30

[long matrix]

really?

[neat lintel]

yea

[long matrix]

how did u instantly know that

[neat lintel]

lol

its easy

just count

[long matrix]

go on, let's hear

.....

man imagine.

24 - 1
12 -
8 -
6 -
4 -
3 - 4
2 - 9
1 - 1

[neat lintel]

s = 15 and 4 means times 2 so 15 * 2 = 30

[long matrix]

I'm stuck here already

[neat lintel]

I guess non troll response is to spam lagrange theorem

It isnt 30

what is the real answer

[long matrix]

i dont know either

[neat lintel]

wait

[long matrix]

() - 1
(1 2) - 2
(1 2 3) - 3
(1 2 3 4) - 4
(1 2)(3 4) - 2
ok, is this all the possible element structures

[neat lintel]

it very well may be 30

[long matrix]

conjugation classes?

So for the order 2 subgroups..... I pick anything that is (1 2) or (1 2)(3 4)...

4c2 + 4c2 . 2c2/2

i think.

This is probably a stupid way to count

[neat lintel]

I remember having an exercise like this in Algebra 0 by aluffi

[long matrix]

sounds like brute force.

[surreal sapphire]

it most certainly is

groupprops should list a strategy

[long matrix]

yh oki cba =....=

[surreal sapphire]

https://groupprops.subwiki.org/wiki/Subgroup_structure_of_symmetric_group:S4

[long matrix]

my point kinda was, maybe be more specific in the types of Qs you wanted smh

[surreal sapphire]

tables for quick information should tell you what to use

[neat lintel]

give me some pre university algebra

How many subgroups of order 4,6,8,12

[surreal sapphire]

does google not work?

[neat lintel]

nope

[long matrix]

Solve the inequality
$$6\sin^2x + \cos x \geq 5$$

[long matrix]

Oops I accidentally chose a cursed number there lel

Well give answer in exact form

[neat lintel]

lol

who remembers values of trig functions

[neat lintel]

yeah cant really

[empty temple]

What do you think could be the value of tan 20 degrees, not in decimals.

[tender musk]

0

[neat lintel]

no clue

[empty temple]

I got an approximate value of √(658/4967)

[neat lintel]

damn

my only guess

would be computing 3rd order taylor polynomial of arctan at 20

but thats not smart way im assuming

[long matrix]

tan 20deg = tan 20deg

answer is fine as is.

[empty temple]

I thought of solving the cubic equation x³-9x²-9x+9=0

[neat lintel]

that works als

[empty temple]

Anyone who can solve it no decimals.

[neat lintel]

well yeah

just write out the expansion at 20

[empty temple]

I'm not really good on abbreviations, what does als mean?

[neat lintel]

ALSO

$\sum_0^\infty (-1)^n \frac{x^{2n+1}}{2n+1}$

[fathom swallow]

Toysem Teans

[neat lintel]

at x= 20

[empty temple]

And the answer will be....

[neat lintel]

You choose the percision

[empty temple]

Way too complex

[neat lintel]

instead of going to infinity you can go to whatever index you think is good enough

[neat lintel]

nah not rly

lots of computer libraries do things this way

[empty temple]

How exactly does this relate to tan... Is it a function of tangents?

[neat lintel]

did you take a calculus class yet?

[empty temple]

No

[neat lintel]

ok

so you know how tan is sin/cos

[empty temple]

But I'm learning on my own.

[empty temple]

Yes

[neat lintel]

there happens to be formulas for sin and cos

[empty temple]

I know that.

[neat lintel]

these formulas are infinite series

an infinite series is a summation that goes on forever

[empty temple]

WHAT!?

[empty temple]

Also know that

[neat lintel]

there are also infinite series for the inverse functions

[empty temple]

Thanks for telling me. I was hoping to find the function MYSELF!

[neat lintel]

Well do you know euler formula with e^i theta?

[empty temple]

e^iπ=-1

[neat lintel]

thats the identity

the formula is e^i x= cos x +i sin x

if you know about this, its evidence telling you about formulas of cosine and sine

since the formula for e is an infinite series

[empty temple]

So that's the formula for tangent.

[long matrix]

I think they use even more efficient methods

[neat lintel]

?

like wut

[long matrix]

idk

[neat lintel]

lol

[long matrix]

but they almost certainly dont just use taylor for everything

[neat lintel]

its used a lot

[long matrix]

There are more efficient algorithms to compute stuff

[neat lintel]

in roblox its used for that

[long matrix]

because cs ppl smart

[neat lintel]

and minecraft

[long matrix]

and think of these things

[neat lintel]

yes there are depending on contexts

the whole idea is balancing speed and precision

[long matrix]

🤔

speed and precision, wut

not sure what the balance is

[neat lintel]

typically the more precise a result is the slower it is

and the faster the less precise

[long matrix]

i guess

but there are algorithms

[neat lintel]

its true in general

[long matrix]

which outperform taylor on both fronts

For specific stuff

you can look more into it

but they really dont use taylor for a lot of stuff

cus more efficient algs exist

[neat lintel]

I dont know who they is

[long matrix]

calculators

and programs

That doesnt stop taylor being obsolete ofc - the main point of the series isn't just to compute stuff

[neat lintel]

my point still stands in general

[neat lintel]

after reading cordic is inefficient

[long matrix]

idk 🤷‍♂️

well they wouldnt implement it if was not better than taylor for reasons

[little vine]

It's called "tangent" because it is the length of the line segment tangent to the unit circle in this diagram.

[neat lintel]

not true

[long matrix]

???

[neat lintel]

sometimes people dont have knowledge base

[long matrix]

What

[neat lintel]

my example being roblox api

[long matrix]

I'm sure calculator companies

wouldn't implement cordic over taylor just because they didnt know taylor

[neat lintel]

there is a reason for everything

im not saying taylor series is most efficient but its most definitely not obsolete

people need polynomial approximations often

[long matrix]

Never said it was obsolete

I only am saying your calculator/program probably doesn't use taylor for many things

For whatever reason

I was assuming because there are more efficient algs for some functions.

https://stackoverflow.com/questions/2284860/how-does-c-compute-sin-and-other-math-functions

interesting

[pearl moth]

taylor series often converge very slowly whjen they converge at all

and they're often expensive to compute

furthermore, the standard expression of a taylor series is often not conducive to numerical stability, so you'd have to rewrite it significantly to get a numerically stable approach

[long matrix]

Well even if the writers don't use Taylor, something worth mentioning is they might start with Taylor as a baseline to figure out something better

So 'useless' is false regardless. 'not used as is' is more like it

[pearl moth]

the intel x87 triggy functions are implemented by first reducing the argument to the range [0,2*pi) (using a 66-bit approximation of pi)

[modest rune]

i guess ive been lying to my calc students

whoops

i always motivate taylor series with computation lmao

[pearl moth]

the spec doesn't state the algorithm used, but guarantees it's accurate to 1.5 ulps

but only within the [0, 2pi) domain

[long matrix]

There certainly is the computation aspect of Taylor regardless 😂

[pearl moth]

there's nothing wrong with taylor series, they're just not all that good for numerical computation

[long matrix]

On the other hand, when it comes to graphical integration/differentiation, I suspect Taylor/Laurent would probably be most handy?

eg. when desmos or wolfram integrates/differentiates your function

Or maybe even there we have more efficient methods

[pearl moth]

using a taylor or laurent series is a strategy when you don't have a better one

i worked on a graphic visualization project in the early 90s that involved a mix of symbolic and numeric differentiation, and we used a lot of taylor expansions, as i recall

radius of convergence is an issue

[neat lintel]

Is there a good way to learn math if you never really learned it properly in the first place? Like shaky foundations in algebra sort of not learned it properly.

[long matrix]

What kind of algebra

high school or uni

In any case, try some refesher video tutorials?

and exercises

If there is something you don't get, look it up 🤔

[neat lintel]

Like I honestly probably fell off the wagon in elementary school after we got past long division/multiplication. I had a learning disability and just stopped getting math at that point.

[vivid halo]

I would start with something basic like khan academy then and do lots of exercises

[neat lintel]

Yeah that’s a good idea, thanks.

[sullen charm]

who's the server owner?

[leaden torrent]

mniip, why do you ask?

[sullen charm]

just curious

[leaden torrent]

if you want to contact the moderation team, it's probably best to DM @polar panther

[sullen charm]

ok

[bronze pelican]

niom

[neat frost]

Nyooooooom

[bright hill]

next time, tell them about the guy that computed $\sqrt[3]{3}$ to 8 decimal digits to get out of prison

[fathom swallow]

DarQ (Shuri for honorable)

[bright hill]

I'm sure that story is cap but it was the story I was told
and 14 y/o me was INTRIGUED

[fair mural]

i could do it

it would be very annoying but i could do it probably

[untold sapphire]

what technique would you use

[reef onyx]

Why does Nullstellensatz sound so cool?

[surreal sapphire]

its german

[reef onyx]

Like why was it named that? I know it has something to do with zeros

[surreal sapphire]

its named after zeros, yes

'theorem of the zeros'

[frigid lark]

😂That guy in prison was probably Galois.

[worn garnet]

How much does Undergraduate maths is covered in the US realized there are some gaps in my background. In my linear algebra class we never did linear algebra over the complex-plane. Was doing a project in Representation Theory and didn't know what a Jordan Canoical Form was

[velvet dagger]

US is pretty non-uniform

Depending on how high you're aiming for grad school (or if you're not)

Let's say if you're trying to fill in gaps I'll give a more aggressive suggestion, so it's a lot but if you can fill it in you're in A+ shape

[sick burrow]

I mean isn't a lot of this stuff fairly easy to pick up as it becomes relevant

you'd know better than me Dami, but that's the impression I get

[vivid halo]

yeah

[sick burrow]

could easily be wrong though

[velvet dagger]

From linear algebra:
Fields, vector spaces, subspaces, dimension, linear maps <-> matrices and associated notions (kernel, rank, row reduction, change of basis, etc), products/quotients, dual/Hom spaces, multilinear algebra and determinants, k[x] is a PID, characteristic and minimal polynomial, eigenbusiness, diagonalization/triangularization, Jordan and rational form, bilinear/quadratic forms, Euclidean/Hermitian inner products, self-adjoint/orthogonal/unitary matrices, spectral theorem, ideally some symplectic linear algebra and matrix decompositions if you got time

Sorry for the delay I got some food

This is on the ambitious side but I'd say useful

[worn garnet]

Please for the arggressive suggestion 🙂 the foregin grad student was laughing at me and as much as we was being mean he had a point I need to grind up on things that weren't covered in class. For Real-Analysis, and Abstract-Algebra whats your recommendations as well

[velvet dagger]

Also toss in any additional suggestions @vivid halo

I'm basically making this list with a mindset of like, obviously there will be things you'll just run into in the wild, but these are things that come up enough that I'm like, better to do it systematically earlyish

[vivid halo]

this looks pretty good yeah

honestly if you're comfortable with all these things I don't think you can reasonably say you still have holes in your linear algebra background haha

[worn garnet]

Can't believe this 😦 in my real-analysis class I got scammed the course advertisement said we were going through the full course but we only got up to uniform continuity

Abstract Algebra I don't think we ever went over the definition of a group action

[vivid halo]

ouch

[velvet dagger]

Yeah. I guess when you hit abstract algebra you'll transplant a bunch of these ideas to other settings. Free modules, Smith normal form, etc.

And depending on what you Perron-Frobenius is good to know

Anyway for the other lists since they seem to be more important for you atm

[worn garnet]

The school I go to is a good school I had to size down to a BA from BS1 due to the amount of money math classes cost over the summer

Can't believe this came this far struggled through some brutal problems and there still bosses left to clear (at undergrad level) what a shame 😦

[velvet dagger]

Real analysis - one variable:

• R as a ordered field with suprema (construction is cute but expendable)
• Topology (open/closed sets, continuity, convergence, connectedness, compactness)
• Series
• Differentiation/integration/FTC
• Uniform convergence
  Somewhere you should go into detail on stuff like exp, log, trig, trigh

Real analysis - multiple variables (this is super aggressive and some of this can be deferred to grad school but might as well say):

• Metric/normed spaces, Hilbert spaces
• Differentiation on normed spaces
• Measure theory and multivariable integration
• Function spaces (C(K), Arzela-Ascoli, Stone-Weierstrass, differential equations, maybe L^p spaces)
• Ideally a bit of Fourier analysis
• Submanifolds of R^n, differential forms

[worn garnet]

Thanks @velvet dagger for the suggestions 🙂 I should be able to retake the classes and get to the missing parts of my knowledge saw an advanced grad certificate place thats doing remote courses

@velvet dagger what do you recommend for Abstract Algebra as well ? I'll need to take a topology course as well

[velvet dagger]

Group theory:

• Basic notions (groups, subgroups, homomorphisms, kernels, quotients, normal subgroups, iso theorems)
• Cyclic groups
• Symmetric and alternating groups, group actions
• Free groups, group presentations
• Products, semidirect products
• Counting problems related to finite groups, Sylow theory
• Solvable and nilpotent groups
• Matrix groups, maybe basic representation theory
  *Probably good to see the defs in the context of monoids too, pretty similar

Ring/module theory (some of this is more specialized/graduate material):

• Basic notions (rings, subrings, homomorphisms, kernels, ideals, quotients, iso theorems, units, polynomial rings, nilpotents, operations on stuff,...)
• Prime/maximal ideals, factorization, ED => PID => UFD, Gauss lemma
• Basic module notions (module, submodule, homomorphism, kernel, algebras, operations on stuff,...)
• Free modules, linear algebra
• Finitely generated/presented modules, Noetherian rings/modules, maybe Artinian too
• Exactness
• Smith normal form/STFGMPID, application to abelian groups and Jordan/rational form
• Tensor products, ideally symmetric/exterior products too
• Ring of fractions, if not localization more generally (depending on how far you go, a bit on valuations/local rings)

This list is a bit tricky. If you're gonna be mostly analysis then some stuff on this list isn't really as important. If you're gonna do more algebraic stuff eventually you'll want other stuff too

But in a lot of places grad algebra will cover a lot of this

[halcyon mist]

Is it normal to be stumped about the process when first introduced to related rates? If so, how long does it take for it to come together?

in general

[worn garnet]

I'm aiming for Theoretical Computer Science/Physics think things like Quantum Information Theory, Complexity Theory, Computational Physics, Vulnerability Research, Programming Languages, Physics of Computation, Number-Theory, Cryptography, etc

So Algebra, Analysis, Geometry is a must !

[umbral oxide]

if thats the case can you rate my syllabus?

this is what've covered so far

[neat lintel]

Lol, that looks like a fun syllabus

[worn garnet]

I'll need to grab Linear Algebra Done Right

No wonder the foregin students scare the crap out of everyone

[umbral oxide]

in addition to homework problems, we'll delve into vector spaces, linear transformations, orthogonality and change of basis

[neat lintel]

That sounds really cool

I wish my class got such a great syllabus

linear transformations are cool

(i hope your teacher is good)

and so is changing basis, although it might be a tiny bit annoying

[umbral oxide]

he is a soviet expat

literally the hardest prof because the problems he assigns are difficult

[velvet dagger]

Eh doesn't do a lot but it's good stuff to know

[neat lintel]

Can you show me one?

[velvet dagger]

Plus there are books

And you can read them

[neat lintel]

LOL

[umbral oxide]

reading books is so hard though

[neat lintel]

you sound so Boreded by it

[neat lintel]

ikr

[umbral oxide]

if we had a book along with lectures

this would have been a perfect combination

[neat lintel]

I take it you hate LA

[worn garnet]

50% of mathematics is linaer algebra

[neat lintel]

how long are the lectures?

[umbral oxide]

1:30 hours

2 days a week

[neat lintel]

Wtfish are you talking about?

[neat lintel]

ok thats reasonable

just to tell you, LA is very lovable

[umbral oxide]

mathematics is such a vast field; I sincerely doubt that math of in itself is only linear algebra

[neat lintel]

if and only if it is taught right

[neat lintel]

ikr

which is why I asked my question to that other guy

[worn garnet]

Other areas of math employ a lot of linear algebra tho like Representation Theory, Mutivaible Calculus, Differential Equations, etc

[neat lintel]

ik you see matrices in other math subjects, But not 50% as much

like wthell

[velvet dagger]

When people say math is linear algebra, first off really throw in combo and calculus

[neat lintel]

you mean like in MV calculus?

ik

but not everything in mathematics is MV calculus

[velvet dagger]

And basically the idea is

[umbral oxide]

calculus, differential equations, and linear are all fundementals to understanding higher level math

[neat lintel]

ik

[velvet dagger]

There's a ton of math out there but it's hard to actually "do" stuff if that makes sense

For example you have topology

[neat lintel]

but it is not like you turn your head every second equation and see a matrix

[neat lintel]

No, I dont

where are you getting topology from?

[velvet dagger]

How do you show that the sphere isn't "equivalent" to the torus?

[neat lintel]

where do you learn it from?

[neat lintel]

ik that is topology

but where are the numbers?

[velvet dagger]

You either think of it as a manifold

[neat lintel]

or the calculation?

[umbral oxide]

maybe if the volumes are the same?

[velvet dagger]

In which case you're doing calculus and linear algebra

[neat lintel]

idts, topology counts the holes in objects I believe

[umbral oxide]

im not sure

[neat lintel]

I hope so, it sounds exciting

but how the fish do you know that?

[velvet dagger]

Or you're putting combinatorial structures and studying them algebraically

Which is combo/LA

[neat lintel]

are you like a late-class uni student or something?

[velvet dagger]

Representation theory as well, you're using LA to do group theory and geometry and all

So it comes up everywhere

[neat lintel]

I guess

[worn garnet]

@velvet dagger I think a better way of putting is that matrices are like cameras they capture the properties and paterns of the object your interested in studying in linear algebra this is done with system of linear equations which allows us to gain insight to properties and characteristics of more general vector spaces. Matrices (under addition I mind you) also from an abliean group which carry extremely nice properties and is easy to manipulate. By reducing problems to linear algebra your probability of solving that problem becomes much much higher

[surreal sapphire]

every category you study has a useful functor into the category of vector spaces

[worn garnet]

I think in Undergrad over here you don't do Linear Algebra in other spaces like C^{n} you spend a lot of time in R^{n} which is quite a shame

[neat lintel]

You are clearly good at abstract algebra

[neat lintel]

I agree, I wonder why so many people hate complex numbers

My idiotic teacher is literally in denial about there not being a solution to x^2=-1

[worn garnet]

For context I was doing representation theory with a graduate student and didn't know how to do linear algebra stuff in the complex plane (I was able to inutiion some stuff) and he kicked me out because of it now i'm really motivated to cover the holes in background !

[neat lintel]

I bet you it is pretty much the same

except with imaginary numbers aswell

[surreal sapphire]

linear algebra over C is easier than over R, so this is really weird

like, i can get focusing on R and C in undergrad

but not just doing the theory over C is just wrong

[neat lintel]

no, it is a crime against mathematics

[worn garnet]

We used this book https://www.google.com/books/edition/Linear_Algebra_and_Its_Applications/L8SUoAEACAAJ?hl=en

[surreal sapphire]

this does complex eigenvalues in chapter 5?

[worn garnet]

ye

[surreal sapphire]

this should at least hint at the theory being easier in C

[worn garnet]

They should have talked more about things being done in C in Rep Theory it's important to be able to do lienar algebra over C. I had be swtiched with someone else and we are doing some tasty functional analysis

[surreal sapphire]

well yes but i dont think rep theory is the kind of application they have in mind

in the title that is

[worn garnet]

fair

[surreal sapphire]

but yeah for math majors covering vector spaces over C and R is important

the move to other fields and their algebraic closure is then not that bad

my class focused a lot on why C is "better" than R

and some attempts to "fix" this

[worn garnet]

In my class we had a mix of math majors and non math majors so that could explain why some stuff just got skipped

Oof I can see now why people get slapped in graduate school

No wonder the foreign students are ruling when it comes to graduate school had a look at their curriculum 👀

[neat lintel]

do they, or is this a joke?

if it isnt I am in the ceiling

[worn garnet]

I was at the DRP meetup and someone explained to me a lot of graduate students from the state school (in the US) struggle when they come to their grad program because of gaps in their background

[neat lintel]

Oh I can believe that

[worn garnet]

The foreign students are insane the sheer amount of math they do in undergrad they scare the shit out of everyone

[neat lintel]

I hope not

But I bet it has partly got to do with prior passion in math

where do these "foreign students" come from?

[worn garnet]

Europe, China, Austrila, etc had to deal with a particularly arrogant one

[neat lintel]

Oh I am so sorry

mathematically arrogant?

or in general arrogant

[worn garnet]

generally arrogant while I was at the drp he talked a lot of stuff while I was in front him to another graduate student

[neat lintel]

lol

bcz I can be boastful and roasty if I want to 😉

but ofc playfully

[worn garnet]

nahh it was pretty bad they also crapped on other students who was strugling

I decided to just ignore and take this as a lession for grad school and its given me more motivation to learn more. Its given me insight into why researchers get so egoistical

[neat lintel]

oh, now that is straight rude

I'd like a vc with that guy

and give him a load of neurons

[worn garnet]

shit on me as well for not being able to write the basis of GL(V) to be fair there are holes in my game which need to be addressed

But the fact that he just gave up on me and is now craping on me is just oof

[neat lintel]

disgusting

btw, what does GL stand for?

[worn garnet]

General Linear Group

[neat lintel]

he requires a diss track

[neat lintel]

ok, i have no idea what that is, I'll google though. But I am 100% sure I wanna challenge him to a math contest at some point

[limber thunder]

ironically all the crazy knowledgeable people I've met are really chill people and not egoistic at all

like if you're boastful about it you're probably coping lmao

[neat lintel]

yes

that is true

[worn garnet]

For context the guy is at the top of the program in terms of gpa and went to cambridge he claims to be working towards Algebraic Geometry

[limber thunder]

but yeah there's always that one guy at most grad schools

[neat lintel]

the times that I have thought i knew everything in my class, was the times when I did the worst mistakes (I mean I did know the stuff, but I was being dismissive and impatient)

[limber thunder]

something something dunning-kruger

[worn garnet]

wait what do you mean by that "one guy"

[neat lintel]

Geometric algebra >>> Algebraic geometry

[worn garnet]

He has serious knowledge and experience

[limber thunder]

boastful rude people

[worn garnet]

ahh kk

[limber thunder]

yeah won't deny that

[worn garnet]

I'm glad I ignored him something tells me his egotism will come to haunt him at some point. Heard of cases of top-tier grad students breaking down due to lack of life experience and social development

[neat lintel]

😉 Id have semi experience

btw, how good is he at mental maths?

[worn garnet]

a funny thing happended doing one of sessions he calimed that the idenity matrix was not of full-rank while I was going through an example (it is I checked)

another near mistake he made was nearly claiming that you shouldn't be able to write the S_n as the product of transpositions but that a result you see in any abstract algebra course

Those should have been red-flags in regards to his ego but I overlooked them at the time

[neat lintel]

i would too

[worn garnet]

btw what happended ? Did just have a rough semester

[neat lintel]

No

No

Nothing of the sort

The thing is

One time my teacher was introducing the idea of trigonometry I believe

I studied trig 4yrs ealier

and was very dismissive of what she was teaching (which was the bear basics like sin=opp/hyp, which I obv knew)

I was a bit of having the approach of "ik it all"

so when she went through an example

I fished myself over

because my ignorance impaired my algebra

lol

[worn garnet]

I've heard that at a high-level math guys will not even bother with someone unless they have had undergrad done.

[neat lintel]

lol

[worn garnet]

Now grad schools are doing personality tests before admitting candiates in

[neat lintel]

wthell

thats rediculous

isaac newton wouldve faild such tests

[worn garnet]

Nahh it makes sense at a certain point you have to be able to work with others

[neat lintel]

tell that to him

[little vine]

How does the personality test go

[neat lintel]

badly

[sick burrow]

that seems cringe

like I understand wanting people who know how to work with others, but can you not get that from rec letters and research experience?

or literally any other part of the application

like haven't personality tests been shown to be kinda bullshit

[neat lintel]

no it isnt kinda

it is bs

a really stupid one

[worn garnet]

At MSU one of the women in Physics say they do this as well as other grad schools they wanna see who can persevre when things get hard

In CS we have the same thing as well at some top-tier places

From what the lady said there seems to be more then just personality test theres also the interview as well + (personal statement)

[umbral oxide]

wait

what

[long matrix]

There certainly isn't within the reals.

[neat lintel]

ik

[umbral oxide]

sure but complex numbers are literally the biggest set

[neat lintel]

ik, hence the second word

[umbral oxide]

how did he not know about this

[neat lintel]

ikr, she is in denial and fishing the class

[umbral oxide]

what class is that

[neat lintel]

he does, but he is trying to hide them

[neat lintel]

math class, 10th grade

[neat lintel]

doesnt matter who gives a sish

[long matrix]

no?

[umbral oxide]

let me double check

[long matrix]

There's no reason you can't construct a field containing C

[umbral oxide]

its the biggest set

[long matrix]

🤦

[umbral oxide]

the rest are subsets of complex numbers

[long matrix]

You are relying on some random diagram from the internet to back your statement up

[flat harbor]

b bbb b b u bb b h b b bbut q w w qua q aq r q q aur q aiqtnt quatenrn a anq

[long matrix]

And that diagram does not even necessarily contradict what I just said.

[umbral oxide]

not really this diagram also happens to be in my set theory book

thats how we were introduced to proofs constuctions

[neat lintel]

it is not a random diagram, it is the truth

[long matrix]

And does the same book tell you there is no field containing C?

[neat lintel]

how=

[long matrix]

If it does, I suggest you burn it.

[neat lintel]

?

[neat lintel]

probably not

but what kinds of fields are beyond C?

Do you mean like

quarternions?

[umbral oxide]

there is nothing beyond C

[long matrix]

Prove it.

In the first place, your original statement was vague

'nothing bigger than C'

What does bigger even mean?

The only thing that could make sense is the idea of a set inclusion

subset.

[umbral oxide]

C cant be a subset of any other number

[long matrix]

but 'nothing'?

....

I introduce you to C union {banana}

Which contains C

as well as banana

[flat harbor]

but yea there is no algebraic extension of C

[umbral oxide]

C cant be a subset of anything

[long matrix]

this is just plain wrong

[umbral oxide]

then whats this argument about

[long matrix]

This is correct. There is no non-trivial algebraic extension of C.

Precision in what you say is very important.

[flat harbor]

nonalgebraic extensions

[long matrix]

There are certainly sets and even fields containing C

[neat oriole]

C is a subset of C and the set of quaternions

[flat harbor]

you can still make a well defined "number system" that properly contains C

they just get less and less "numberlike" as u go up

[umbral oxide]

alright did not experience it for myself, but maybe in future studies

[flat harbor]

u can adjoin a variable to C that doesnt satisfy any algebraic relation

and still get a field

[umbral oxide]

i understand you can costruct sigma algebras that contain imaginary numbers'

[flat harbor]

u can generalise C to clifford algebras and still get an associative algebra

[umbral oxide]

because there is no limit on what you can put inside of the set

[long matrix]

C(x) is a field that contains C as a proper subset

Easy example

[umbral oxide]

was not aware of this, thanks

[empty stratus]

This presumes that your definition of natural numbers excludes 0.

[empty stratus]

It should also specify "real" irrational numbers vs. complex irrationals. It also fails to mention purely imaginary numbers. xD

[sick burrow]

most intelligent #serious-discussion conversation

[sick burrow]

personal statement + interview is good

personality test is stupid

like genuinely idiotic

[umbral oxide]

i'll study up on it further, thanks for correcting me

[empty stratus]

No problem! 😄

[young lagoon]

i find it hard to believe they would use a personality test as an actual criterion.

[charred mortar]

yeah it seems pretty dumb, but if they're just using it as one small part when choosing candidates I can see it happening

I still think that those tests are at best useless and at worst just give the wrong impression of someone, but so long as they're not a big criterion it's hopefully not too bad

it's probably because it's really easy to conduct, so it seems like a cheap way to get extra data, even if the data itself is extremely dubious

[tropic mist]

help

[sly vale]

#❓how-to-get-help

again

[charred mortar]

this seems like an oddly violent version of this type of question

[sly vale]

I mean the original statement of the Josephus problem was violent

[inner finch]

josesus

[umbral oxide]

damn that book is hardcore

where was that problem derived from

[empty stratus]

There was a Numberphile video on youtube about this.

[empty stratus]

Yep.

[tropic mist]

guys

how to close the help 19

im already done with it

[long matrix]

.close

[tropic mist]

ok

i close it

[gloomy flower]

Quick "soft question" : How do you deal with morale / motivation?

Currently revising two years worth of material and it's not going well.

I'm often face to face with the fact that I forgot many of the stuff that I already studied. Whenever I make a mistake/take longer than I should be doing something it feels wrong and uncomfortable and I end up trying to get away from studying. (My body keeps making stuff up to make me get away from it)

It feels as if I just lack "a certain type of motivation"

How do I get motivated?

(I can no longer motivate myself with the material because I'm just redoing everything we've done. And If I try to motivate myself with success in the competitive exams [end goal], It doesn't work.)

[flat harbor]

damb i wish i knew too fam

[empty stratus]

Write up an explanation of your understanding of the material in your own words for your future self to revisit if and when you ever find yourself needing to revisit it.

It helps if you do so in an enjoyable / fun manner.

[gloomy flower]

That's what I've been trying to do as of late, and yeah.. it helps : )

[empty stratus]

Good notes written for yourself are as smooth as silk and as sweet as caramel.

[charred mortar]

also if you're reviewing old material you could try to relate it to what you're currently studying too

[gloomy flower]

but in my case I have severe time constraints (1 month left..)

[empty stratus]

For future situations, make the notes whenever you reach the end of a course.

[gloomy flower]

I'm at my last year (last month even) and not studying anything new

[empty stratus]

Or the end of your independent study.

[charred mortar]

you could also try and find connections between areas that you are studying too

[gloomy flower]

True :"3 (kinda regret not doing so..)

[empty stratus]

This can help.

[charred mortar]

I also second the writing up and focusing on exercises that complex and yohan said

[empty stratus]

In particular, if you can, try using the approach of subject B to examine subject A.

My favorite example of this is measure theory.

The best way (IMO) to study measure theory is to do functional analysis at the same time.

[gloomy flower]

Yep

[empty stratus]

Or a topological review of complex analysis.

[gloomy flower]

I'll try doing more of that

[empty stratus]

Those kinds of connections are very precious.

[gloomy flower]

I just don't want to invest too much time into it

[empty stratus]

Are these qualifying exams you are studying for, perchance?

[gloomy flower]

(I have a bad habit of losing my self in stuff)

[gloomy flower]

Exams for engineering schools

[empty stratus]

I see.

[gloomy flower]

(in France, two years after highschool, after a preparatory school..)

[empty stratus]

Well, the most important aspect of time management is learning to recognize when you need to interrupt yourself.

Not letting yourself get bogged down in a particular problem.

[gloomy flower]

Oh I do, but I just don't interrupt myself.. and even if I do

[empty stratus]

Learning when to stop and move on.

I know it is difficult.

[gloomy flower]

I just feel extremely exhausted

[empty stratus]

This is what preparing for exams does to a person.

It dries you up.

Makes you into a prune.

[gloomy flower]

:"

[flat harbor]

try some new stuff out

have u tried pomos?

[gloomy flower]

well yes

but since I have to work through past exams that are 4 hours long it feels like a bad strat

pomodoro I assume

[worn garnet]

They probably have a better criterion for sniffing out potential candidates.

[leaden torrent]

most personality tests are pseudoscience so that practice concerns me

yeah, im sure it's POSSIBLE they've found an actually descriptive one, but this seems ripe for abuse

as in like

i could very easily see it leading to discriminatory hiring practices based on other metrics, like race, if the personality test is set up (intentionally or not) to have indicators for that

i'm not sure on the legality of this stuff but at the very least it seems very morally questionable to me

and it seems like it'd be impossible to determine whether the personality test really "works" in an objective sense as (1) defining the objective standards for "working" is very hard and (2) existing data is biased by human factors [such as the aforementioned racial discrimination]

both of which are the same issues ML stuff falls into, but at least ML hiring practices have the excuse of being algorithms working off data rather than humans throwing together some semi-arbitrary metrics that confirm their priors about what personality a "good worker" should have

that bias in ML stuff could, theoretically, be eliminated if you find good sample data and if the algorithm is balanced impartially (both of which are gonna be hard, but hey)

i would never be confident in a personality test designed by a corporate entity, even if they hired an academic psychologist or whatever to do it

[tender musk]

https://youtu.be/Q5pggDCnt5M

[tender musk]

https://youtu.be/lN7Fmt1i5TI

[neat lintel]

idts

[obtuse zealot]

hello

[neat lintel]

personality tests are fake

cuz my harry potter test said i was ginny

[pearl moth]

myers-briggs was developed by two housewives

https://jobtalk.indiana.edu/HRMWebsite/hrm/articles/develop/mbti.pdf

[worn garnet]

I ended up contacting and asking that person about it and looks like its a lot more then just a personality test they do an interview where they ask you some deep questions like for example "What was your greatest struggle in Undergrad-Masters", "What do you do when you don't understand things on the first ry ?", and other questions

I've heard at places like ____ they conduct a simular style of interview but they have a couple of psychologists look at your entire life up untill that point

[pearl moth]

my wife interviewed for a job at this one company that had her do a very detailed and weirdly invasive psychological profile

we've since learned that that company is run by a rather weird dude with fairly strange beliefs (including believing in QAnon)

[inner finch]

just lie bro smh

[pearl moth]

just tell them that at times strange smells come to you

[inner finch]

lmfao

[pearl moth]

that question has long been used on the MMPI as an indicator for honesty

none of the people in the original testing pool answered positively to that question, and so they concluded from that that anyone who says that strange smells come to them is lying on the test

[neat lintel]

???????

That is weird

[pearl moth]

it is worth noting that most of the original pool from which the MMPI is derived were male prisoners in the minnesota penal system

personality tests are weird

[neat lintel]

True

[pearl moth]

the MMPI is basically a "what type of criminal are you" test

[neat lintel]

Arnt all these tests kind of flawed?

[pearl moth]

nah, some of them are totally flawed

complete rubbish, in fact

[neat lintel]

🤔

must be funny

[neat lintel]

True

[neat lintel]

?????

the test

Ya unless it decides your fate

[inner finch]

me when the month i was born in decides where i go in life

[pearl moth]

000000000000000000000000000000000000

[neat lintel]

what

[bronze seal]

Hello guys I have a small question, will I encounter difficulties if I study Real Analysis with doing calc 3? I know calculus 1, not done with calc 2 but everything I did was with proofs.

[coarse grotto]

real analysis using what text? You may find some trouble looking at metric spaces or any proofs of higher dimension results (from multivar), but if you’re comfortable with proofs, you should be okay

[bronze seal]

I'll probably use Apostol's, I heard that it's a good introductory book.

[coarse grotto]

Yeah, that’s a good place to start

[bronze seal]

Ok, thanks for the help.

[toxic schooner]

based

[sterile hare]

why waste your time with apostol when u can read jee books

[jade crane]

JEE I LOVE JEE

[sterile hare]

yes based you are

[odd narwhal]

why waste your time on jee

like, ever

[prisma swallow]

Velleman how to prove it is good I think

[sterile hare]

jee will give u wings

[prisma swallow]

Are every math book this good?

[odd narwhal]

so you can jump off a cliff?

[fossil rune]

Whats JEE

[odd narwhal]

don't worry about it

it's just some entrance exam for a certain indian university that people get really riled up about

[worn garnet]

Bruh guess what ____ is lol

[chilly egret]

I want to become even better at mathematics.

How do I start?

[cobalt star]

what level are you at right now be specific

what do you want to learn

what are your goals

[meager sonnet]

no that's red bull

[alpine kindle]

do you know calculus

[gray loom]

Chegg bad

Is there anyway to actually remove it from my search results without "-Chegg"

[inner finch]

unicode character

[ripe wasp]

wait are C^1 functions ones that are differentiable at least once or exactly once

as in are C^n functions differentiable n times or more or is it only exactly n times

[neat lintel]

least

[ripe wasp]

oh so all C^infinity functions are C^1

[neat lintel]

yeah

C^k means 1,2,…,k’th derivatives exists and are cts

[gray loom]

Any well educated opinions

[neat lintel]

Nice algebra

[gray loom]

I’ve been trying for 2 hours to understand how people understand it

I follow the guides right

But they skip over something

[sterile hare]

so you want to become better at mathematics aye? i can help you. what's your current level? and have you ever heard of jee?

[devout nacelle]

The ironic JEE-simping has to stop here

[sterile hare]

whats your problem with jee?

jee is good

in fact, we should have a jee channel

[devout nacelle]

And irrelevant to most people

No

I'm insisting that you shouldn't respond to any general query with some remark about JEE

It's pointless at best and misleading at worst

[sterile hare]

ok sir, have u done jee?

[devout nacelle]

Yes

[sterile hare]

oh i see jee ptsd

[devout nacelle]

There is no PTSD

It's annoying

[chilly egret]

Yes, I do!

[chilly egret]

JEE seems to be an Indian entrance exam, I would be willing to work on it.

India has a good mathematical level.

So does China.

The Gaokao is also an interesting exam.

I would also love to learn the Singaporian method in mathematics, going as far as learning about it from 1st grade.

There are also honoroble mentions : South Korea, Finland, France, Canada & the USA.

[toxic schooner]

i want to disagree

like

really hardcore

[stray kite]

if one knows differential geometry
how hard would it be to wrap ones head around general relativity

[neat lintel]

idk

i kinda want to take physics classes

[stray kite]

good point

[neat lintel]

to learn how diff top applies

i just know that symplectic forms have some relationship to phase space in hamiltonian mechanics

idk what hamiltonian mechanics is

but have an idea of what phase space is

its like a space of all possible states I think

[alpine kindle]

then if you're looking to learn maths outside of school, i would start with abstract algebra (the book "algebra" by michael artin is very good

[chilly egret]

I am downloading it, right now.

[toxic schooner]

[toxic schooner]

have you done any proof based maths?

[chilly egret]

I mean

All my life I have done that, in some way or another

[stray kite]

Can you do analysis on any arbitrary field with a metric
Does there exist an arbitrary field analysis?

[chilly egret]

Was that meant to me?

[waxen lily]

same ty

ty @ alison

[median zinc]

Is this satire

[devout nacelle]

You can do analysis on metric spaces, I'm not sure what you mean by arbitrary field though

[median zinc]

Not R or C I suppose

[devout nacelle]

Ye, then metric spaces should be it for starters

There might be more exotic places to do analysis though

[alpine kindle]

hope you enjoy it

[toxic schooner]

[waxen lily]

thats above lethal dosage, but it will save his life

[surreal sapphire]

i think if you have a complete metric space you can do some form of analysis, in the char 0 case this will probably just turn into either real/complex analysis or p-adic analysis due to ostrowski's theorem

in char p i have no idea

[chilly egret]

Thank you!

[neat lintel]

Did strad and ed leave the server?

[toxic schooner]

nope

they are still here

why did u think they have left

[mystic lintel]

Does anyone know what is meant by a ‘trend’ in an experiment, just a question that popped up in my head?

[neat lintel]

because they used to be more active

[toxic schooner]

true true

still

they are here

[long matrix]

show me some mathematical crankery

$\prod^{i\pi}_{k=1}e = -1$

[long matrix]

I shall start

[neat lintel]

LLLLLLLLLLLLLLLLLOL

[neat frost]

$f(x)=\sin^x(1)$, what is $f(-1)$ (sorry for repost D:)

[viscid lynx]

a+b

9+1-

[long matrix]

,calc csc(1)

[fathom swallow]

Result:

1.1883951057781

[neat frost]

,calc arcsin(1)

[fathom swallow]

The following error occured while calculating:
Error: Undefined function arcsin

[neat frost]

,calc asin(1)

[fathom swallow]

Result:

1.5707963267949

[long matrix]

Ignore this:

• Yes
• No

[long matrix]

@sleek wing mathematical crankery: go

[neat lintel]

Why is the answer of 16 - 5 x 9 + 8 ÷ 4 is -27

Why is subtraction used first?

[sleek wing]

9+10 = 19

[long matrix]

false

[long matrix]

a-b = a+(-b)

Does this help?

- can be seen as 'multiplying by -1`

[waxen lily]

multiplication/division were actually done first. though it doesn't matter here, subtraction was done first because operations of same precedence are done from left to right.

[sick burrow]

You're telling me a well ordered this set?

I mean there's no fucking way

[stone ferry]

Why would Cantor's diagonal proof not apply to the set of rational numbers? I know Q is countable and R is uncountable, but it seems to me that you could do the same diagonalization with the decimal expansions of both

[frozen merlin]

do you mean "why doesn't it apply to the set of real numbers"?

[stone ferry]

No I mean like if you make a list of every rational number, can't you then construct a new one along the diagonal like you can with the real numbers?

[vivid halo]

the main issue is that in Cantor's argument you are working with the set of infinite sequences of binary digits (so that a binary sequence {a_n}_n corresponds to the real number ∑_n a_n 2^n) but such infinite sequences don't always correspond to rational numbers

[stone ferry]

When do they not?

[vivid halo]

I mean they almost always do not

a decimal representation of a rational number, in a given base, is either finite or periodic

so any infinite sequence which is not periodic will do

[empty stratus]

Only if the base is rational.

[ancient flame]

happy pi day

I'm sure none of you knew

[long matrix]

pi approximation day

god, people keep getting on my nerves

its almost as bad as pi = rt g = 3 = e memes

[proven hornet]

thats actually true (im an engineer)

[alpine kindle]

what is everyone talking abt

[long matrix]

ok, someone come up with a geometry for me where pi = 3

[alpine kindle]

pi is obviously the homomorphism from a group to its quotient by a normal subgroup

[long matrix]

and I will be satisfied to call it 3 henceforth

[alpine kindle]

[neat frost]

There’s so much to make fun of engineers for, but this is the only meme we use? Kinda

[vivid halo]

right yeah

[neat lintel]

😉

[wooden flax]

u mean inv or power

like $\arcsin{1}$ or $\frac{1}{\sin(1)}$

[fathom swallow]

Invictus

[wooden flax]

rip my latex

[umbral oxide]

alright, hear me out on this.... i think the grading system should not exist

im ready for backlash

[vivid halo]

So true!!

[pearl moth]

i'm on board in principle, but at the same time i recognize that if student performance were entirely subjective many students would automatically pass or fail for reasons lacking merit and that having a grading system that has objective aspects to it at least mitigates this human tendency

[leaden torrent]

⛸️

[umbral oxide]

a grading system can't be objective because the questions you give to your students could easily be modified so that an entire class fails

its not a good metric on how well you know a subject

I haven't even mentioned how outdated the grading system is with the internet and what not

[pearl moth]

i'm less bothered by the entire class failing than i am with only the white male students passing

and if your entire class fails on an objective grading system, then you have failed at teaching

also i don't see what the internet has to do with grading

[umbral oxide]

its an efficient way of handing out exams, so that a student would be able to retake them infinitely many amount of times without paying for them to take them in person

[pearl moth]

this is not an argument against having grades, it's an argument against one particular method of evaluating students

[umbral oxide]

the entire premise lies on an objective grading system, because some people tend to build them so that a good portion of your students can flunk your class

while instructors in other schools tend to be more lenient and more transparent about the material that they are teaching

[pearl moth]

objection, counselor: facts not in evidence

[umbral oxide]

havent you heard of gaokao or iit jee?

[pearl moth]

no, i live west of greenwich

[umbral oxide]

compare the rates of suicides in those nations as compared to countries that dont put emphasis on testing

[pearl moth]

and don't pay much attention to indian or chinese educational systems

although i will admit that what i have seen of indian education is not favorable

[umbral oxide]

you can also observe how depressed the students are on campus, especially in ivy league schools

[pearl moth]

i still don't think you've made a coherent argument against grades

[umbral oxide]

the ones with lower grades tend to be linked with higher rates of suicides

https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5781286/

im not getting these arguments out of my butt

[pearl moth]

so we should not evaluate students in order to reduce suicide rates?

i mean, i can see a social utility to that, but at the same time how do you learn who really knows what they're doing?

how do you ascertain which students have learned and which have not? how do you tell if your educational methodology works at all?

[umbral oxide]

you have 2 options, you can either change how your grading system works, or abolish it all together

[pearl moth]

or could this be mitigated instead in some other way, like removing social factors that place pressure on students to achieve high grades

that's a false dialectic

there are other options besides those two

[charred mortar]

I feel like most evaluative systems can be gamified eventually

And part of what makes the grading system so attractive is probably dur to how easy it is to establish compared to most other evaluative methods

[velvet dagger]

ab you've given me a giga hot take

[umbral oxide]

From my experience the point of grading is to keep people out

[velvet dagger]

Most evaluative systems can be gamified eventually... except those which are entirely non-transparent

So get people whose evaluation ability you fully trust, and give them complete power and obscurity

@crystal stone let's get to it

[charred mortar]

Doesn’t this lead to the question of how you’re going to evaluate the evaluators?

[crystal stone]

huh what is this

[velvet dagger]

True but that's a one time problem so you only need a one time answer 🙂

[umbral oxide]

You can't evaluate evaluators because profs don't exist for the sole reason of teaching

They probably care more about research than students

[crystal stone]

Uh yeah sure

[velvet dagger]

Lmfao

[crystal stone]

Is it another one of the "Let's talk about grading"

[umbral oxide]

Was

[velvet dagger]

Well it's a mostly ironic take lmfao

[crystal stone]

Where people that talk about it have little to no experience grading

Alrighty, everyone else is wrong, I'm right. If people followed my grading scheme ideas, then the world will be a magical place and students will actually learn

[charred mortar]

Wrt the abolishing all grading, what alternative will you propose @umbral oxide

[crystal stone]

It's very simple. You throw the exams. The ones that land face up get an A

The ones that land face down get an F

[velvet dagger]

Moonbears you don't get it my idea is revolutionary because it encompasses all of them

See

You can use any system of evaluating that you want

Not just grading

Admissions, grading, etc

You just don't tell anyone

And then they don't game it

[crystal stone]

That's what Reed college does

[crystal stone]

The more experience I get

The more I like not being transparent in what a "grade" means

Although I can see this being incredibly frustrating as a student

(And it was)

[umbral oxide]

Khan academy has the right approach trial and error until you get a hold of a concept

[crystal stone]

Ultimately I don't think any of these superficial things amount to any real change

[umbral oxide]

And not pay 1.7k dollars to retake the class again

[crystal stone]

Takes too long and there are some ideas you won't understand within a year

[crystal stone]

You don't have to be in college or private school. It's completely optional

So you don't have to pay again to take a class you failed: you can just not go to school or leave

[umbral oxide]

Now you have another problem on your hands, most employers won't hire you if you don't have a degree

That's especially true in the field of finances and economics

[charred mortar]

I mean employers are going to want some form of measuring ability

College may be overpriced but that’s a separate issue from completely abolishing grades

[velvet dagger]

At some level there's one problem that education as an institution probably won't be able to overcome

Namely it serves two roles, one is in educating

The other is differentiating between students in a way that will have a serious affect on their future

And I don't yet know of any compromise that does a particularly great job at accomplishing those goals

[crystal stone]

A lot of low-income people within the US have low cost to free options for a College education

It's usually middle-upper-middle class that go to expensive schools & rack up debt on degrees

[charred mortar]

Fair enough

[crystal stone]

My sympathy level for upper middle class people looking down on state & cc schools & choosing to go to an expensive ~ 50k/year school

And then crying about student loan debt is pretty low

[leaden torrent]

ehh, i have some in that i think many genuinely arent aware that there are better options such that the difference is essentially negligible

(unless you're either an absolute top student, as in like near-full rides, or planning on a shaky career like academia)

universities spend a LOT of money marketing to high schoolers

and part of that marketing is trying to make them think "more $ = better education/future"

even if, in practice, your school choice doesnt matter at all past your first job for 99% of careers

[neat lintel]

ew imagine going into industry and not going into academia

/s

[fringe onyx]

I have a friend who does applied mathematics and claims set theory/type theory/topos theory have been "useless" to real life endeavor

Could you give me the major examples of useful applied mathematical concepts that were discovered thanks to set theory/type theory/topos theory?

[vivid halo]

No, because there aren’t really any examples of this happening

At best you can point to type theory’s influence on theoretical computer science and functional programming language specifications

But broadly speaking these topics are just not that useful for anything having to do with the real world

[velvet dagger]

I'll say this is a bit California-colored

Like idk imagine a star student who gets into NYU from a state like Alabama

[pearl moth]

as the middle-class parent of teenaged children, i have no idea how we're going to pay for our kids to go to college of any sort

[simple raven]

I'm no expert but Laurent Lafforgue (now working at Huawei) claims that topos theory can be applied to machine learning

[untold sapphire]

i'm looking at some of these huawei papers and this is insane

Every known artificial deep neural network (DNN) corresponds to an object in a canonical Grothendieck's topos; its learning dynamic corresponds to a flow of morphisms in this topos. Invariance structures in the layers (like CNNs or LSTMs) correspond to Giraud's stacks. This invariance is supposed to be responsible of the generalization property, that is extrapolation from learning data under constraints. The fibers represent pre-semantic categories (Culioli, Thom), over which artificial languages are defined, with internal logics, intuitionist, classical or linear (Girard). Semantic functioning of a network is its ability to express theories in such a language for answering questions in output about input data. Quantities and spaces of semantic information are defined by analogy with the homological interpretation of Shannon's entropy (P.Baudot and D.B. 2015). They generalize the measures found by Carnap and Bar-Hillel (1952). Amazingly, the above semantical structures are classified by geometric fibrant objects in a closed model category of Quillen, then they give rise to homotopical invariants of DNNs and of their semantic functioning. Intentional type theories (Martin-Loef) organize these objects and fibrations between them. Information contents and exchanges are analyzed by Grothendieck's derivators.

https://arxiv.org/abs/2106.14587

[inner finch]

lol

[fringe onyx]

Insane in a good way, or...? 😅

[untold sapphire]

this honestly just looks like throwing a bunch of jargon at a problem to me, like drowning it in a sea of hot / fancy math buzzwords, idk what the real content of the paper is in layman's terms

[pearl moth]

i know just enough math to realize that that abstract is not simply word salad

someone who has no math vocabulary wouldn't be able to differentiate that from TrekSpeak

"recalibrate the heisenberg compensators!"

[odd narwhal]

For some reason "Grothendieck's topos" instead of "Grothendieck topos" annoys me

Maybe because it somewhat implies that there is a specific topos which is grothendieck's, and not that it's a type of topos

[pearl moth]

partly this is because "topos" is a singular noun

it looks like a plural, but it's not. the plural is topoi

"Grothendieckian" might a better form, but ugh

[odd narwhal]

Or toposes

It's more the possesive that I have a problek with

[fair mural]

topoi

[pearl moth]

yeah, you want an adjectival form of the name, rather than a possessive

like "riemannian"

it's a Riemannian manifold, not Riemann's manifold

the latter implies that there is a singular manifold that "belongs" to Riemann

instead of there being a class of manifolds that have some specific property that Riemann characterized and is thus eponymized for him

[fair mural]

why would you say something other than riemannian

[toxic schooner]

just to piss you off

[pearl moth]

also, that paper intrigues me in a number of ways that i wish i had the knowledge to explore

[ancient flame]

riemannian sums

[neat lintel]

because it sounds made up

So just say what it is

not a name of a random mathematician

[pearl moth]

but the name of a random mathematician is what it is

mathematicians name things after mathematicians (at least if they're white men)

[fair mural]

[pearl moth]

see also chinese remainder theorem (not named after the non-white-man who documented it)

[fair mural]

https://en.m.wikipedia.org/wiki/Noetherian_ring

[neat lintel]

exactly

[neat lintel]

True but annoying

they should name it after what it is

not after the mompara who discovered it

[neat lintel]

ic

[pearl moth]

it's often not the dude who discovered it, either

[neat frost]

I think it’s nice that things are named after mathematicians

[charred mortar]

Half the things in math just have people’s names slapped on it

[pearl moth]

stigler's law of eponomy

[fair mural]

not like anyone has a better way to do it

[neat frost]

Because it’s a way to be remembered for almost ever

[charred mortar]

Ideally you’d have a good name that gives intuition, but that’s hard

[neat lintel]

Sure

[charred mortar]

I know I’m shit at naming

[neat lintel]

but it also sounds made up by the person

like a dream

[neat lintel]

yes

[fair mural]

probably because most of the time it was discovered by that person

so why shouldn’t they get to name it

[surreal sapphire]

mathematicians dont name stuff after themselves

[neat frost]

If I ever have to name something mathematically, I’m naming it after someone

[pearl moth]

it's other people who name things after other mathematicians

[surreal sapphire]

usually its another person working on it having it discovered in works of X, so they name it after X

[pearl moth]

zorn's lemma wasn't named that by zorn

[neat lintel]

they should, but they should know that these names should also be good names

[surreal sapphire]

this is one of the reasons why it often gets not named after the discoverer (at least in the past)

[pearl moth]

it's just "that lemma zorn came up with" turns into "zorn's lemma" over time

[neat lintel]

William Kingdon Clifford would have first hand experience in this regard

[surreal sapphire]

in modern times you see people actively fight this (scholze)

[neat lintel]

😦

[pearl moth]

matt parker has a thing named after him and he's totally embarrassed by it

[neat lintel]

😦

[neat lintel]

Good to know that he isnt clout chasing

[errant ibex]

hey ive heard there are people on this server who are looking to help others with their maths questions?

[neat lintel]

good to know

[neat lintel]

I hope so

[pearl moth]

zorn also has a streetlight named after him

[neat lintel]

aye

[neat lintel]

lol, well that I can live with

[pearl moth]

too bad he can't

[neat lintel]

😦

[surreal sapphire]

yes, you probably want to read #❓how-to-get-help

[neat lintel]

When did he die?

[pearl moth]

it's the max zorn memorial stoplight for a reason

1992 i think

that road had been killing students for years, but the university and the city did nothing about it

[errant ibex]

im in a tricky situation where ive been set a few Qs for thursday morning but i have work until the rest of today and a long hospital appointment tomorrow. does anyone know if i could vc with someone tmr evening to work through my hw with?

[neat lintel]

LOL

[pearl moth]

then max got hit by a car and died, and they decided "hm, maybe we should put a stoplight here"

[neat lintel]

what does this tell us about the guy?

[pearl moth]

so that stoplight is unofficially known as the "max zorn memorial stoplight"

[neat lintel]

hmm this is an unforfitting death for a "mathematician"

[surreal sapphire]

i dont think anyone will agree to making an appointment beforehand, better just ask when you are working on your homework

[neat lintel]

Hang on

wasnt it illegal to ask these kinds of questions?

actually no

I think cheating on these questions is illegal

[errant ibex]

is it plausible that someone will just be available?? i would feel bad asking for someone's help right there and then?

[charred mortar]

“Illegal” sounds way too harsh

[surreal sapphire]

hm?

[pearl moth]

depends on the institution's policy

[charred mortar]

True

[surreal sapphire]

this is hw, getting help seems fine to me?

[pearl moth]

getting help with homework from a tutor or guide is usually not prohibited

[charred mortar]

Yeah for like a tutorial set it’s even encouraged to an extent

[pearl moth]

as long as the student actually does the work themselves, with or without guidance

[neat lintel]

i guess it does

[pearl moth]

also, cheating isn't "illegal", at least in most countries

[errant ibex]

noo i will work at them myself i just need a little help!

[charred mortar]

For assignments it’s more different

[neat lintel]

But it is on this server

[pearl moth]

it's dishonest and a breach of terms, but not something you can get arrested for

[surreal sapphire]

i dont know, i dont ask for help much
it depends on how hard it is, best just read #❓how-to-get-help and ask again (in a help channel or relevant topic channel) at the time

[errant ibex]

trust me im normally hardworking just dealing with chronic illness

[neat lintel]

just ask the guy namington banned

[charred mortar]

Asking for help is fine here anyways

[pearl moth]

i reserve "illegal" for "something you can get arrested or fined by civil authorities"

[neat lintel]

lol

[errant ibex]

it's as level maths?

[surreal sapphire]

funny thing

[pearl moth]

you can't go to jail for breaching a discord's terms of service

[surreal sapphire]

cheating is literally illegal in bavaria, germany

[charred mortar]

Damn

[surreal sapphire]

so is not paying attention in class

[charred mortar]

Well

[pearl moth]

isn't everything illegal in bavaria?

[neat lintel]

das kann nicht sein

[surreal sapphire]

or at least actively preventing others from doing so

[charred mortar]

That’s one way to motivate students I guess

[surreal sapphire]

i dont think this law was ever used

but it exists

[neat lintel]

thank god

[pearl moth]

well, adultery is "illegal" where i live, but people still do it