serious-discussion

[granite bridge]

anyways if you divide by n+1 you can have nonzero numbers multiply to zero

and if you don't then the product doesn't work

[gusty pelican]

I'm not saying that such an example doesn't exist but is there a way we can find that example?

[granite bridge]

yes

(1, -1, 1, -1, ...)*(1, 1, 1, 1, ...)

[gusty pelican]

as I said that's (1,0,1,0....)

[granite bridge]

no it's not

look at term number two

(1 * 1) + (1 * -1) + (1 * 1) = 1

[gusty pelican]

um

no

on the second term there you missed a -

[granite bridge]

where does the second - come from??

[gusty pelican]

a_0 * a_2 + a_1 * a_1 + a_2 * a_0 / 3= 1x1 + -1x-1 + 1x1 / 3 = 3/3 = 1

[granite bridge]

don't use a for both sequences

it's a_0 * b_2 + a_1 * b_1 + a_2 * b_0

[gusty pelican]

wait

wait

you're right

I was stupid

[granite bridge]

b_1 = 1, a_1 = -1

[gusty pelican]

uh

hmm you have a point then

sorry for that

[granite bridge]

lol no worries

[neat lintel]

why discussy 2 more active than discussy 1

[granite bridge]

we are discussying

[neat lintel]

quit it.

[alpine verge]

Maybe its time to abandon ship and treat {N-->Q}/{(a,b) | a-b is cauchy} in a vector space setting.

We will not be able to define the product without it being nilpotent, or having the unit be equal to 0.

[granite bridge]

however it's quite easy to prove that when we restrict out view to cauchy sequences it is the same as component-wise multiplication (under our equivalence relation where their difference is cauchy)

[gusty pelican]

we discussidi discussoileting

[neat lintel]

not very discussy of you

[granite bridge]

it could probably be an algebra

[alpine verge]

yeah.

That would allow us to exploit the order of N, otherwise it would go unused except for the cauchy sequences.

[granite bridge]

yeah

but in which case, the cauchy or component-wise product wouldn't make a difference

i get the feeling that there's not a nice choice of product which makes this into a field though

so we're probably gonna end up with nonzero elements multiplying to zero regardless

[alpine verge]

yeah.

[gusty pelican]

well rip multiplication I guess

[granite bridge]

i'll try to prove this

ill be back if/when i do

[gusty pelican]

btw there's no point of extending Q to R since I'm pretty sure you can construct an "equivalent" N -> Q sequence for every N -> R sequence

[alpine verge]

yeah.

[gusty pelican]

in fact technically we could probably go from N -> {a/2^b: a, b in N} but we don't have to go that far. I like Q more anyway

[alpine verge]

yeah

[gusty pelican]

would it be possible to define integrals?

it doesn't require multiplication, only like eqivalence class to natural number multiplication which we can define

I guess it would be like a path integral or something

though a straight one of course

I feel like I'm missing something with the integral thing

wait

it requires multiplication

oh shit

[alpine verge]

If we want to define integrals of functions on {N-->Q}/{(a,b)|a-b is cauchy null sequence},
we need to know if the space is measurable

I'd first treat {N-->Q}/{(a,b)|a-b is cauchy null sequence} as a vector space and see if we can find a basis.

(in the absence of a product.)

Interestingly (1,0,0,...),(0,1,0,...),(0,0,1,0,0,...) are not basis vectors, as they are equal to zero

[gusty pelican]

huh
well if we are going down that route I guess we should start with that

[alpine verge]

(1,1,1,1,1,1,1,...), (0,1,1,1,1,1,1,...), (0,0,1,1,1,1,1,1,...) ,...
would be a basis.

[gusty pelican]

they are all equivalent

[alpine verge]

shit you're right.

[granite bridge]

they are all equivalent to 0

not equal

anyways the real problem is that a basis requires a finite set of them sum to any sequence

[gusty pelican]

yep

[granite bridge]

you can't construct an explicit basis unfortunately

[alpine verge]

what about bounded infinite linear combinations.

[granite bridge]

as the existence of a basis depends upon the axiom of choice

and the basis is gonna be the size of R i think

or more

[plain owl]

not more

[alpine verge]

But if Q^omega has dimension omega, why do we need AC for a basis?

[plain owl]

there are only R sequence

[granite bridge]

lol you're right

[granite bridge]

it has R as a subset

and the existence of a basis for R over Q requires the axiom of choice

[alpine verge]

I'm confused. I mean for e.g. Q^omega we have this basis (1,0,0,0,...),(0,1,0,...), (0,0,1,0,0,...) without AC.

[granite bridge]

it's not a basis

how do you get (1, 1, 1, 1, ...)?

[gusty pelican]

(remember you have to do a finite sum to get there)

[alpine verge]

Then a basis is not what we are looking for.

This finite sum stuff is flawed.

[plain owl]

well if you have a topology you can define a schauder basis

[alpine verge]

I dont think we have a topology. Lets just try to define a basis* ad-hoc.

[granite bridge]

do we have an inner product?

for orthonormal to make sense?

[alpine verge]

nope.

thats why I want to look for a basis*

[granite bridge]

i dont think integrals are gonna work without a basis or inner product

[solid snow]

you utilize zorns lemma which is equivalent to AC

[alpine verge]

yeah.

Anyway, for our setting lets just define a (well-ordered) basis* as a mapping:
B: omega -> {omega-->Q}/{(a,b)|a-b is cauchy null sequence}
(the well-ordering is so we fix an order when we do the summation, in the square summable case this is order independent, but here its nots square summable.)

[granite bridge]

how do we even define infinite sums on this space

[alpine verge]

we do well-ordered sums and hopefully they converge. Otherwise idk.

[granite bridge]

because the rationals aren't complete so we can't just take their limit

[alpine verge]

whatever just take the metric completion IDC.

[gusty pelican]

could we find some hack for that with this?

basically gettting the N to R sequence and then just getting a N to Q sequence

[granite bridge]

you could but i don't think the concept of a basis that requires infinite vectors is very useful

or like infinite sums, rather

[alpine verge]

None of this is useful, but I think in this its the most elegant solution to arrive at some kind of "basis", for this setting.

[neat lintel]

is a pad thats 420.4 x 2 Inches good for space cuz i wanna make some math vids and write on it

[alpine verge]

We are explicitly dealing with unbounded infinite vecotrs.

[neat lintel]

is it small

[granite bridge]

pad?

[neat lintel]

electronic writing pad

[alpine verge]

So I think unbounded linear combinations are also "allowed" here.

[granite bridge]

420.4 inches x 2 inches?

i think that's like way too long

[neat lintel]

HUION H420X OSU Drawing Tablet Upgrade of Model 420,4 x 2 Inches OSU Tablet Graphics Digital Writing Pad with 8192 Levels Battery-Free Pen, Compatible with Chromebook, Mac, Windows, Android, Linux

this is the thing on amazon

[granite bridge]

it's 4 x 2 inches

[neat lintel]

if u google it, it will show up

[granite bridge]

not 420.4 x 2 inches

[neat lintel]

hahahahahha

[granite bridge]

if not i wanna see a pic of the like 30 foot long drawing tablet

[neat lintel]

ohhh i didnt see the "model"

[neat lintel]

is that big

[granite bridge]

idk use a ruler lol

[neat lintel]

like is there good enough space to write

[neat lintel]

i dont have one

[granite bridge]

well depends what you want to use it for

as obvious as it sounds, if it's not a basis, it's not gonna be completely interchangeable with a basis

[alpine verge]

In this I only want to consider (well-ordered, possibly unbounded) Schauder basis.
Maybe see if we can define an inner product or exterior algebra.

But first I wanna find a "basis"

Maybe (1,1,1,1,1,1,...), (0,1,0,1,0,1,0,1,0,1,0,...),(0,0,1,0,0,1,0,0,1,...),...

[pliant prairie]

i had a question, i cant type it its long, any idea where i can find possible answers?

[granite bridge]

nowhere if you can't type it

but #❓how-to-get-help

[pliant prairie]

thanks

[gusty pelican]

I'mma go to sleep
If you guys continue this conversation then I'll read the rest of it later
this was actually an a lot more interesting conversation than I thought it would be

[frank sage]

What are radical axes

I can not understand

[urban berry]

hi

[fierce scroll]

,calc sin 37

[fathom swallow]

The following error occured while calculating:
Error: Unexpected type of argument in function multiplyScalar (expected: number or Complex or BigNumber or Fraction or Unit or string or boolean, actual: function, index: 0)

[stone ferry]

It's not a quotient

and afaik it's not a tensor

Let me give you the example of R_3,0,0

it's a fairly simple one

you have the vector space R^3, right?

let e_1, e_2, e_3 be its basis

[vale plover]

https://old.reddit.com/r/math/comments/1b2ap8z/whats_a_field_that_was_really_prominent_and/

[stone ferry]

then the basis of $\mathbb R_{3,0,0}$ is:
$$1, e_1, e_2, e_3, e_1e_2, e_2e_3, e_3e_1, e_1e_2e_3$$

[fathom swallow]

MSC2020 47A15

[tender tulip]

I think all I needed was that x^2 = Q(x) for Q(x) a quadratic form

[stone ferry]

and you define a product (written with juxtaposition)

sure

[tender tulip]

So it’s $\frac{T(V)}{(v^2 - Q(v)}$

[fathom swallow]

Dyfunction Executive

[stone ferry]

orthogonal vectors anticommute

I'm not sure what T(V) is but I think I can guess. That probably works

yeah it's the tensor algebra

[stone ferry]

yeah this construction should work

and I was wrong about both counts of it not being a tensor or a quotient

[tender tulip]

Orthogonal in respect to Q(v + u) - Q(v) - Q(u)?

geometric algebra over char 2 seems fucky and unimportant

[stone ferry]

yes, but the inner product is usually taken to be half that

[tender tulip]

char 2 funkiness

[stone ferry]

I don't think this is ever done outside R

[tender tulip]

@jagged forge wallflower ass mf

Probably for good reason

Not much that it can be applied too

[jagged forge]

i was going to say something pedantic but i am not sure if was actually true

[stone ferry]

doing it over C is useless because you can reduce it to something over R

[tender tulip]

Do it

[stone ferry]

since C is a clifford algebra

specifically R_0,1,0

[jagged forge]

strictly speaking they're not tensors, but i think over dim =/= 2 you can represent them as tensors, idk

err

[tender tulip]

I mean

[jagged forge]

char(K) =/= 2

[tender tulip]

Tensor algebra

[jagged forge]

yeah but quotients of tensor algebra

not the same thing tho

[tender tulip]

Any element of an algebra can be thought of cosets of tensors in that regard

Fair enough

[tender tulip]

Like the “tensor structure” works with the algebra or they just happen to be a vec space isomorphism

Because I can say my finger is an appendage but that means fuck all shit in flipping you off

[jagged forge]

i think it was you could define the multiplication in terms of tensors

but i actually think maybe i was reading about something else like the symmetric algebra or something

idk

[tender tulip]

I don’t really get what you’re getting at but I don’t know tensors all too well aside from their construction and definition as a tensor product pretty much

So when I see contravariant and covariant I assume by default that’s just related to base changes on the regular vs dual

for finite dim spaces

And it’s a tensor product of the vector space and it’s dual so many times

I do not know the applications or how it’s used though in that sense

[jagged forge]

the tl;dr is quotients of the tensor algebra are not necessarily subalgebras of the tensor algebra, but in some cases i read sometimes they can be in characteristic not 2

for some specific quotients

[tender tulip]

Eh I guess

Probably some exotic examples of little use I assume

I know tensors are used in physics but idk how outside of the exterior algebra

[jagged forge]

ah it was the exterior algebra where i read that

in characteristic not 2 the exterior algebra can be identified with antisymmetric tensors

[tender tulip]

What do you mean

By antisymmetric tensors

I don’t get shit like “stress tensors” or any christoffel shit

Like I assume there is a MUCH simpler definition with tangent spaces and tensor powers of it

[jagged forge]

here's a simple example of an antisymmetric tensor

ab^T - ba^T

which is uhhhh

an element of V \otimes V

the idea is if you swap any two positions you get the negative

so if you swap the first factor with the second you get ba^T - ab^T

so...... basically that but with arbitrary tensor products

[tender tulip]

how so?

[jagged forge]

right, well i guess maybe i should write $a\otimes b - b\otimes a$

[fathom swallow]

suremark MSC2020 60G40

[jagged forge]

since the transpose is kinda vague here

but it's kind of the same idea, if you pretend x is a dual vector and that a^T x = x(a) (the dual pairing) and not the dot product

ab^T x = a * x(b) gives you a map from V* -> V

which is the same as V x V by duality, or the same as a map V* x V* -> K

i dont think im explaining this well

[tender tulip]

The transpose confused the actual fuck o ur big me

[tender tulip]

Okay that helps

[tender tulip]

Very confused yes

The fuck is a dual pairing

[jagged forge]

you know, the natural map between V x V* -> K

which exists and is basis independent

[tender tulip]

so the valuation?

[jagged forge]

uhhhh… yes

[tender tulip]

Ah okay

[jagged forge]

i’m gonna assume we’re talking about the same thing lol

[tender tulip]

so the dual of V (x) V*

[jagged forge]

hm. yeah i guess you could say that lol

an element of the dual

[tender tulip]

V* and V aren’t naturally isomorphic I think though

For finite dim

[jagged forge]

nope!

aren’t they just straight up not iso at all in infinite dim

[tender tulip]

One’s a direct sum over the field, the other a direct product

[jagged forge]

ohh….

[tender tulip]

So they correspond for finite bases lol, that’s my justification

[jagged forge]

direct product in infinite dim yikes

[fair mural]

looks like something i would see from wraith

[stone ferry]

It is literally the exact thing wraith posted about

[tender tulip]

That’s not hard to visualize

[jagged forge]

i just thought the direct product is like, badly behaved in a number of ways a lot of the time

[tender tulip]

not visualize I mean

Explain

[neat lintel]

wassup guys

[jagged forge]

yeah ik what it is. well actually i haven’t studied category theory so maybe i don’t

[tender tulip]

Essentially V is a direct sum indexed by the basis since every element is some sum of a finite subset of the basis. However to look at the dual, you consider maps to V. Which are infinite product instead, by looking at the image of each basis vector

[stone ferry]

what is natural

[jagged forge]

ah that makes sense actually

[tender tulip]

Need not only be finitely many. And the image of each basis vector is additive since you just add the outputs

[stone ferry]

I'm sorry I'm not category pilled enough

[tender tulip]

This isn’t really a category theory level concept

[stone ferry]

I wanted to do algebra and then I got sucked into functional analysis

[tender tulip]

If you know direct sums and products of abelian groups

It is literally that

[jagged forge]

well naturally isomorphic (which he was asking about) definitely is tho

[stone ferry]

yeah I know this lol

I meant natural isomorphism

[tender tulip]

I don’t really remember the definition of natural very well

[stone ferry]

V* and V are about as isomorphic as you can get in my mind

for finite dimensions

or any hilbert space

[tender tulip]

Yeah

[tender tulip]

not algebraic, pain

[tender tulip]

I just assume shit like how tensors are used in physics are tensors over tangent spaces and such

Or cotangent spaces

[azure frigate]

hi guys just a quick question. pi/4 * d^2 is an area of a circle right?

[tender tulip]

Idk how they are used and the symbols are scary

Yes

[stone ferry]

Physics notation is fucked up

[azure frigate]

oh i thought it was pi * r^2

[tender tulip]

I tried reading about some thing for physics and got jumpscared by something called Christoffel symbols and shit

Also the metric tensor being called a fucking tensor and not just a form

It’s just a bit confusing

[tender tulip]

Think. Think real hard

[stone ferry]

it is one of them

[azure frigate]

lol the professor fucked me up with one a nanometer question

[tender tulip]

It’s a bilinear form, of course it’s a tensor

[azure frigate]

fluid dynamics xD

[tender tulip]

But I’m not going to call the inner product or dot product the “dot tensor”

Gotta compute the cross tensor

[jagged forge]

the fuck is a dot tensor

[tender tulip]

IT ISN’T

[stone ferry]

ew cross products

(does not generalize)

[jagged forge]

well to be fair it doesn’t really exist in general

[tender tulip]

The dot product is technically (excessively nasally) a tensor

It’s an element of (V x V)*

[azure frigate]

OHHH now i get it

thanks haha

[rocky shuttle]

Well, call it the metric tensor then

[tender tulip]

metric form

[rocky shuttle]

first fundamental form

[stone ferry]

I did think of a fucked up new linear algebra course structure idea

topic 1: vector spaces

topic 2: tensors

topic 3: linear functionals

topic 4: matrices

[tender tulip]

No I'm pretty sure tensors and multilinear algebra are expected to magically appear in your head after one intro course of lin alg

[rocky shuttle]

top(olog)ic(a) 1: vector spaces

[rocky shuttle]

what space

[neat lintel]

@burnt knot hey

[burnt knot]

Hi

[neat lintel]

look, I won't tell you I am perfect or even an expert

but as I've spoken with you with logic

I will continue in logic

[burnt knot]

Are you in uni rn?

[neat lintel]

if you don't like what you've done, leave it and go to another on

[neat lintel]

yeah

[burnt knot]

For pure math?

[rocky shuttle]

space is flat

[neat lintel]

I learn Mathematics on my own online, I do business management degree and I do an internship in mathematics

[burnt knot]

Oh cool

[neat lintel]

But always have a plan

don't just destory everything and run to what you love with no plan

if you don't have a good life now but I think it might be stable to some extent

[rocky shuttle]

you're moving along a geodesic in spacetime

[burnt knot]

Yeah its not horrible rn

[neat lintel]

Set dreams, goals, plans, ...etc and start work on it.

bear with what you do until you could give up upon it if you hate it

once you can give up upon it, do it but be sure you won't affect bad on yourself

[neat lintel]

you mentioned deep learning, make your mind and once you make it if you need resources lemme know

[burnt knot]

Alright thank you!

[neat lintel]

my pleasure

[burnt knot]

Im just at a crossroad right now not knowing what to do

[neat lintel]

you give me some time of your time, right?

give yourself time and be alone and create who you want to be

and when I say create I mean it, because we don't find ourselves we create it

if you want to discuss anything, just hit me up my DMs are open and we could chat or even have VC about it

[burnt knot]

https://tenor.com/view/bow-bowing-michael-scott-steve-carell-the-office-gif-1242852755589233352

[rocky shuttle]

Spacetime can be curved, but the universe is flat, at least according to this: https://www.nobelprize.org/prizes/physics/2019/popular-information/

Measurements of cosmic background radiation, as well as theoretical considerations, provided a clear answer – the universe is flat.

[flint island]

Flat essentially just means "as Euclidean as you're gonna get" (on large scales)

really though it means Minkowski (not Euclidean)

[wet glacier]

since this server is alot more busier then chem server can sm1 help me understand this table ? its a** chem question**

[rocky shuttle]

The organic chemistry tutor can

[minor current]

Hi

[rocky shuttle]

Hewwo

[loud snow]

Post

Dont have to

I was just gonna send to friend who is analytical chemist

[wet glacier]

dm? cant post image here

[loud snow]

K

[neat lintel]

i think i’m over math 😭

biggest struggle

[fresh comet]

social sciences?

[orchid badger]

hey
the vector equation of line

like
r(t) = a + at
(t is parameter)
like what you really mean by this

a is a point on the line

right
then why we have to add the point

[unborn trellis]

it's really r(t) = a + bt, where a and b are points

a is the origin of the line, b is the direction

You can think of it as the points in direction b shifted to a

[neat lintel]

earth is flat confirmed

It's cool if you think its cool

[orchid badger]

weather the thing is cool or not
is just how we are looking at the thing

[orchid badger]

so wait
2 main qustion
how can I find the len of the line(at a parameter of t)
and second what really "a" represents here

like I know it's from where the vector begins but still

[neat lintel]

the same way you find any length?

[austere merlin]

erm guys there’s a problem…

[neat lintel]

a is like the transformation of the vector from the orgin

[austere merlin]

I forgot how to write a quadratic function in standard form

[neat lintel]

$f(x) = a(x-h)^2 + k$ something like that

oh wait lmao

different thing

[austere merlin]

huh

y = 4(x - 2)^2 + 4

wait how would I write that

[neat lintel]

expand

[austere merlin]

y=4(x-2)(x-2)+4

[neat lintel]

continue

[austere merlin]

wait I’m going crazy

LOL

I know how to do this

tyyy

[hardy grove]

is learning calculus at grade 8 normal

or am i a bit behind

[neat lintel]

Yeah its normal

[forest vale]

yea, like we can normalize it

[alpine kindle]

Gaussian, even

[rocky shuttle]

So, diagonalizable

[placid finch]

unitarily

[dark escarp]

hello

[hollow vessel]

can someone help me with this crossword:
How prawns save $
6 letter word, starting with S and has M in the 5th position

[vocal vessel]

Scrimp

[hollow vessel]

ty

Where subsistence-level farmers start to end up at their mouths
4 letter word with A as second letter and D as last letter

[vocal vessel]

That sentence doesn’t make sense to me.

At their months?

[hollow vessel]

wait

mb

mouts

mouths

[vocal vessel]

Not clearer

Only thing I can think of with farming is “land” but I don’t get how they start at land and end up at their mouths

[hollow vessel]

i wrote yard but idk

[hollow vessel]

land was apperently wrong

[vocal vessel]

Yard to mouth? Hmm. Makes zero sense

Hand?

[hollow vessel]

ohhh

that make much more sense

but still idk

[vocal vessel]

🤷‍♂️

Unrelated. Thanks for playing.

[hollow vessel]

👌

[vocal vessel]

The shortest war in history lasted only 38 minutes. It was between Britain and Zanzibar on August 27, 1896.

Bananas are berries while strawberries are not.

Some cats are allergic to humans

No

[formal pebble]

hi

so I'm just wondering..

have you guys had heard about magic triangle

the thing where each sum of the side of the triangle will be equal

just wondering if there any ways or tricks to solve it aside from trial and errors?

[high topaz]

i also have a question: is there any method of predicting if the set of numbers at hand could actually be used to create that magic triangle

or even more interesting how many magic triangles could we create with one set of numbers

[pearl moth]

what is a magic triangle nvm looked it up

there are number-theoretic approaches to finding solutions, but for low orders exhaustive search is often easiest

there aren't that many possibilities to consider

for example, for order-3 you know the sum has to be at least 9 and at most 12 since 6+2+1 is 9 and 1+5+6 is 12

for order-4 similarly you get at least 16 and at most 28

i just found a paper that offers bounds for the sum on order 4 of 17 to 23 using a different argument

and they provide a formual for the bounds that apparently works for any n

although the paper is lacking in rigor: it sets forth formulas but rarely proves them

[high topaz]

why thank you... and can i have a link and see these myself

[pearl moth]

https://publications.azimpremjiuniversity.edu.in/4892/1/14-Jayaditya_MagicTriangles_Final.pdf

written by a 9th grader lol

stiull not bad for high school work

[knotty sedge]

guys

i have taken as an undertaking

the task of obtaining

every utm

and gtm book

[fresh comet]

ask @ripe needle to aid you

[ripe needle]

I have most of them via pdf lol

My physical collection is lang and stillwell

[grizzled grove]

But why you're collecting so many pdfs?

[fervent pebble]

free dissemination of information fr

[high topaz]

thank you so much✨

[alpine comet]

what the fck is elliptic cohomology?

I feel like I'm a 9-year-old reading Rudin

[knotty sedge]

im obtaining them by purely legal means!!!! /j

[meager sonnet]

So you can take a formal group law from an elliptic curve

and using something called landweber exact functor theorem (LEFT) get a cohomology theory

[alpine comet]

I did not know about this

is there a one-to-one correspondence between homology and formal group law?

[meager sonnet]

no

only certain cohomology theories

Uhm

I should start over

[terse comet]

🧊

[meager sonnet]

MU_* is isomorphic to the graded Lazard ring which is effectively a classifying ring for FGLs over R

so a formal group law over R is equivalently a graded ring homo. L -> R

Using this iso this gives R the structure of a MU_* module

And so we can take the extension of scalars

$E(X) = MU_(X) \otimes_{MU_} R_*$

[fathom swallow]

cofibrant woman

[meager sonnet]

Now we want E to be a cohomology theory and it's pretty easy to prove that it satisfies everything but Mayer-Vietoris

[meager sonnet]

So for this to be an actual cohomology theory we need tensoring with R to preserve exact sequences, i.e. Meyer-Vietoris

Asking R to be flat over MU is really hard to do so LEFT gives sufficient conditions for this tensoring to preserve Meyer-Vietoris specifically

And elliptic cohomology defines a formal group law

I can't say much on that myself I'm not super familiar

There's also a theorem which says that this assignment of an elliptic curve to the multiplicative cohomology theory can lift through a map which first assigns an E_infty ring spectra to the curve

Then a map that takes the cohomology theory that spectra represents

This gives you an assignment of E_infty ring spectra to elliptic curves and you can take a homotopy limit of these over the moduli stack of elliptic curves

Combining the data of all the E_infty ring spectra for every elliptic curve into one E_infty ring spectra, which is called topological modular forms

[vivid halo]

Tfw sheaf of spectra

[meager sonnet]

Yeah

[vivid halo]

restrict to Tate curve
get KO[[q]]

[meager sonnet]

I saw this, actually wtf

[vivid halo]

Yeah I mean this is cute and natural

[meager sonnet]

S^1 equivariant K-theory of free loop spaces tensored with Laurent series

Admittedly IDK much about Tate curves or anything but this is weird to me

IK there's some statement of all height 1 FGLs obeying <property> give either ordinary cohomology, K-theory, or are elliptic curve FGLs and give elliptic cohomology

[vivid halo]

Tate curve is the formal neighborhood of the point at infinity in M_ell

So it’s the formal neighborhood of the nodal cubic

The stuff you get when degenerating to the nodal cubic is very much height 1 stuff

[orchid badger]

ig this is going to be a very dumb question but still I want to ask
if I have a vector called 𝐚 which has some value in the x , y and z direction
but I break that down and writes the value as x , y and z
and scale them up by some quantity
will that still be a vector

[vivid halo]

[meager sonnet]

ah

[vivid halo]

It is such a shame that you can’t really play this game with higher rank formal groups

[orchid badger]

and any tips on doing vectors
cause I am watching a lot of theory and also attending my lectures
(first semester uni student)
but still sometimes struggle to do some basic vector question

[plain owl]

do you know what a vector space is

it looks like not

so that would be a good place to start

[fresh comet]

by what name am i supposed to refer to this discord server as in a conversation?

give me some names to call it lol

[neat lintel]

lol

are you gonna tell someone irl about it?

[jagged forge]

mathcord

[fresh comet]

not quite

[neat lintel]

when i'm on the server i call it lowmath

[jagged forge]

how dare u

[neat lintel]

when i'm complaining to my bf about something on it i just say "the math server"

[fresh comet]

yeah i call it the "global math (discord) server" if i ever mention it to my friends rn lol

i omit "discord" when im lazy

yes, i call it "global"

idk why

the name stuck for me lmao

maybe mathcord is better tbh

[fresh comet]

my friends already know about it

some of them are here too

[neat lintel]

[fresh comet]

but they dont often type

none of them are very into math i'd say

[visual breach]

How do you guys get to such advanced concepts, dealing with moduli stacks and K-theories

[vivid halo]

you build up to it

[visual breach]

It would take lots of time, right

[vivid halo]

it often takes a couple of years yeah

[visual breach]

Perhaps too late for me

Would not going to reach there during my doctorage years

So excession reached there that fast? Woah.

[visual breach]

I wish there were a cure for my mathematical dumbness

[neat lintel]

It's called a textbook

[visual breach]

Textbooks cannot cure me of my slow learning speed

[neat lintel]

Yes they can

[visual breach]

Do you have experience in this?

[orchid badger]

those people who are studying mk and AI stuff
how important is vector for you

[neat lintel]

My knowledge says otherwise

Classes that you can pass by just attending the lectures are nice for an easy A, but you miss out on a lot that you could had learnt from the textbook

my discrete math class doesn't require a textbook and its so much easier than actually reading the book, but I'm 100% missing out on so much stuff because of it

[rocky shuttle]

Which math textbook?

[visual breach]

Pre-uni textbooks

I'd say, depends.

[tall minnow]

you are still in pre-uni so you have time to fix that

learning habits develop as you go higher and you figure out eventually you need to read stuff properly instead of just winging it like in high school

[pearl moth]

or you don't and you fail out and become a barista

[neat lintel]

hey does anybody here know like a list of all the math topics or lessons in the world and in order from easiest to hardest? i need the resource badly

[solid snow]

theres no such thing

[glass peak]

There is no such thing, and there never could be because there is no inherinantly hardest or easiest topic

[deep mango]

Instead of interpreting this question completely literally like the last 2 ding dongs

[glass peak]

Rude

[deep mango]

You should check out Khan Academy, it's free and should list all the math topics you'd learn from elementary school all the way up to the middle of college

(And has tons of lessons and problems on all of them)

[final rivet]

ye khan academy is really good

[pearl moth]

khan academy is a perfectly reasonable option for learning basic math

it's not perfect but it's free and readilyt accessible

and yes there is no canonical all-inclusive list of math topics, let alone one ordered by difficulty, in part because that's clearly at best a partial order and it's also extremely subjective

[fresh comet]

50 minute tests are too stressful

I feel like they shouldn’t be allowed lmao

[pearl moth]

yeah, should be either 49 or 51. even numbers of minutes are just wrong

[neat lintel]

anyone here that uses a WSL? I got bombarded with Zone.Identifier copies in all of my files for whatever the fuck and im trying to delete them

[neat lintel]

ok fixed

cd ~ && find . -name "*:Zone.Identifier" -type f -delete

does the job

[tawdry spindle]

What distro you using btw

[neat lintel]

ubuntu because im a basic bitch

[pearl moth]

how did you do this? i use wsl fairly frequently and never had this happen

[neat lintel]

probably because i imported files from windows directly and some security thing of windows did that

[pearl moth]

oh you used edge

[neat lintel]

i actually didn't which makes it more peculiar

[neat lintel]

this does the job tho so its fine

[pearl moth]

it's got to do with writing into the linux filespace from the windows side, apparently. i never do this so i don't run into it

[neat lintel]

was a bit worried tho because i had my hw due soon and i thought i had to manually delete each one

[neat lintel]

yeah i had to import some assignment to there and i am not linux savvy enough to know how to access that from the linux side independently

[pearl moth]

the connector for the filespace access does not properly understand the request to open an alternative data stream, which is a feature that NTFS supoprts but the filesystem used by the linux emulation does not

[pearl moth]

typically /mnt/x/... works

where x is the windows drive letter. by default wsl mounts all of your windows drives in /mnt by drive letter

this also avoids bloating the linux-space file images

[sacred furnace]

i feel like i'm the opposite

i can never learn from videos tbh

i go out of my way to buy textbooks even if they're expensive even

[neat lintel]

oh okay thanks

[sacred furnace]

idk learning by video just doesn't do it for me

[vivid halo]

imagine buying textbooks in the current year instead of [redacted]

[sacred furnace]

you have to understand

i am very easily distracted even from things i actually like

i will see a shiny thing and go "oo shiny thing"

i have to actually put a sizeable distance between me and a distraction machine for me to actually learn

[tall minnow]

you are going to need to fix that because more likely than not you need to write latex notes while you learn / draft stuff etc.

I have embraced the distractions as I write my paper while listening to streams in the background. if I need to hugely focus I put on instrumental music

[sacred furnace]

im already in grad school and i can do latex just fine

uh

maybe i overstated my distractability

i should have said

i like doing it the way i do

honestly quite a few people find my methods to be weird

but it got me this far so

[tall minnow]

well some people prefer paper books and fountain pens

[sacred furnace]

i am actually a fountain pen person lol its funny you mentioned that

[tall minnow]

what's your specialization btw

[sacred furnace]

nothing yet

my program is officially

applied math in life sciences

[tall minnow]

so analysis, optimization, statistics, numerical etc. ?

[sacred furnace]

i have to do a lot of numerical analysis

i have a numerical analysis exam in 4 days actually

[tall minnow]

I knew someone who entered PhD as an applied analyst and then switched to stochastic PDE research

well it depends on the department's flexibility as well

[sacred furnace]

by "nothing yet" i meant i haven't started research yet not that my program isn't specialized in something

[sacred furnace]

oh cool

[tall minnow]

I'm also slowly getting into stochastic myself. lots of things happening.

[cunning plaza]

I have been writing notes in my iPad while typing up homework in LaTex. You recommend doing it all in LaTex?!

I'm not yet at the phd level, so just curious on what you would recommend there

[tall minnow]

I wrote notes from grad school on tablet for years.
Now I recommend writing Latex notes in Lyx for anything long term, and writing is for drafts / doodling.
And in fact, most long calculations I now do in Lyx directly.

[cunning plaza]

Gotcha. Maybe I'll give LyX a try at some point. I've been typing up LaTex in vim

[tall minnow]

#discussion message

[vivid halo]

Lyx is goofy

[static stirrup]

What Is the best argument for beginners to start in mathematics ? ( i study ICT so I would like to have topics that fall into that area)

[old plover]

dont want to step on anyone's convos in here. i'll be posting a mini discussion in #optimization

[pearl moth]

there's no convo in here to step on

[foggy snow]

Name some good books for integral calculus or whole calculus,which contains solved problems most

[neat lintel]

#book-recommendations

[fervent pebble]

#book-recommendations message

[alpine comet]

I write on paper

[neat lintel]

Clp-2

https://batch.libretexts.org/print/Letter/Finished/math-89169/Full.pdf

[neat lintel]

It's been a year since I've written this program and it finally stopped working.

Time to spend a week rewriting

[digital galleon]

contributing to deforestation

[sonic sentinel]

wtf do you mean we don't know if pi+e is rational

all this math and shit and we don't even know if pi and e are in a conspiracy

[pearl moth]

math is hard, what can we say

at least we know that sqrt(2) + sqrt(3) isn't rational!

[alpine comet]

say that to AI researchers

[tall minnow]

they are irrational with probability 1

[plain owl]

that's not an easy problem

[plain owl]

what's the probability of e*pi being irrational then

well tbf, as an informal statement it's fine

just obviously it's either 1 or 0

[tall minnow]

rationality reduced by mod 1 to the torus equipped with the Haar measure

[old plover]

there's no convo in here to step on
well too late I guess. i dont want to copy and paste it. those with langrangian experience can check it out in #optimization . it feels like a long shot at this point

i have another engineer working on it (the general problem), i just wanted to try this approach myself to see where it got me (nowhere fast sofar)

bout to stop work for the day but i'll check back tomorrow or next week

[wraith forum]

here I am finding theorems on infinity craft

[solar hawk]

ayo?

[orchid path]

fk

[hallow maple]

Anyone doing a level maths?

[rapid yacht]

Could someone help with stats pls

[ocean harbor]

#❓how-to-get-help

[tired harbor]

hello can someone answer my question in #1021175428326633542 ?

[ocean harbor]

no

[vernal token]

What's that

[shrewd ledge]

Hello

[neat lintel]

A browser game by neal.fun where you start with four basic elements and you can craft your way into practically infinite items or just script them in

[stable sage]

what row operation can i do to make A1,2 A1,3 and A2,3 all 0

1 + 1 + 1
0 + 1 + 2
0 + 0 + 8

only the diagonal elements need to be non zero

iam doing some gauss elemination thing

[vernal token]

A_2 -> A_2 - 1/4A_3

A_1 -> A_1 - 1/8A_3

The next step you'll see

[scenic pond]

omg ty i love these

gonna find riemann hypothesis wish me good luck

[scarlet lark]

Does anyone know what happened to the STEM server?

[ocean harbor]

it got deleted

[scarlet lark]

frick!

I had about all my proofs in there.

Why did it get deleted?

[loud snow]

Shouldve saved them

[scarlet lark]

I did.

Just the convesation were fun to read.

[loud snow]

Huh

O

Rip history

The logs are probably still out there

Might be able to ask discord

[ionic glen]

hi

[neat lintel]

hi

[deft prism]

i like creamy penutbutter

[ionic glen]

...

[ionic glen]

w-what

[mental stratus]

crunchy is better

[jagged forge]

pika knows what’s up

[lethal tree]

bro guys

i thought my math was done in 2022 after my hsc

just realised

i have math in uni

fmd

[tender tulip]

Like crunchy peanut better is best if you just eat it straight

Creamy is better for adding it to shit or using it on a sandwich

In other words, crunchy peanut butter is gluttony

[neat lintel]

peanut butter is

[ripe needle]

Oh boy discussion-2

[fresh comet]

you cant be jailed for tax evasion if you never get caught

[ripe needle]

Just flee the country

[orchid badger]

worst way to study maths-
remember the formula and solve qus
i mean thats worst than not studying maths

what you all say

[ocean harbor]

what

imo if you just sleep during the lesson and then when you get a hw/test or whatever, you don't know anything

but "remember the formula and solving questions" isn't that bad tho

[strange garnet]

yes you need to learn the formula. but just because you know the formula doesnt mean you'll understand it. there's so much more to a math problem then the formula. for some people (me) no matter if i barely know the formula or know the formula 100%, i need to ACTUALLY understand the problem. which is why i work better 1on1, peoples minds work differently. its always hard being in a classroom with 11 other people, they all understand it by the formula but im completely lost.

[orchid badger]

damn
you are right
fir me the concept is more important the remembering the formulla

[atomic locust]

gotta take the proof out for a few dates first

[prime jasper]

yall are fucking nerds

[dire glen]

hey hello

when i solve a system of equations i am looking for points that are a solution for both all the equations..

so if i have 1 equation like x+y+z = 4 this means all the points that when you take the dot (1,1,1)*(x,y,z) = 4

[tacit magnet]

Yes(?

[dire glen]

and if i have 2 equations the points xyz are further restricted.

is this finding an intersection between the 2 equations?

[tacit magnet]

Yeah

[dire glen]

could this be written equation1 ∩ equation2 ?

[tacit magnet]

Sure

[dire glen]

if i were to write this in code, this would correspond to "and" ?

[river moon]

an intersection between solution sets, not equations

[dire glen]

intersection between equations doesnt means anything right?

[river moon]

intersection is an operation between sets

[dire glen]

ok all makes sense

[tacit magnet]

Yeah, all points that satisfy that eq

[dire glen]

ok cool, thanks! 🙂

[keen kiln]

what is 4x2

[neat lintel]

https://www.jdpower.com/cars/shopping-guides/what-is-a-4-x-2-truck

[keen kiln]

what is this

anyways

I need to learn pi

by today

cause

my teacher said im gonna get in trouble if I don

dont

so if theres any albert eisnstion

einstein

who knows the 10 digits of pi

first 10

[neat lintel]

albert einstein died long ago, i'm sorry to inform

[keen kiln]

well thtas a shame

no pi for me I guess

[neat lintel]

did he even know that many digits of pi?

[neat lintel]

just compute them

by hand

is this for a numerical analysis class?

[dire glen]

if det(A) = 0 Ax=b usually has no solutions, but has solutions for some b

i understand if determinant is zero, i can have zero solutions or infinite solutions. what does it means "solutions for some b" ?

[keen kiln]

whats this mean?

[river moon]

if b is in image of A, then there are solutions

[neat lintel]

for example if b=0 you have the solution A0 = 0

[dire glen]

but they assume b is not zero here

[neat lintel]

there might be other b's for which Ax=b is solvable

[dire glen]

would that be the infinite solution case?

[keen kiln]

Whats that mean

[river moon]

homogeneous system with singular matrix have infinite number of solutions, yes

[keen kiln]

say what

[neat lintel]

over an infinite field yeah

[keen kiln]

why are u guys talking like scientist

[neat lintel]

i never saw a scientist talking like this

[lone rover]

pi number?

just gg it and the gg will tell you

[deft willow]

can anyone help me factorise this
5x2+ 12x – 9

[keen kiln]

oh my bad man

[neat lintel]

what have you tried?

[keen kiln]

what about mathmatictitiaitaian

[deft willow]

wdym

[rocky shuttle]

mathematactician

[deft willow]

i couldnt understand it so i used chatgpt to give me an in depth step by step answer which my teacher said is wrong

[lone rover]

lollllllllll

just solve to have the solution

and take the solution back to fractorise

[lone rover]

you can even google it then

[deft willow]

chatgpt searches the web via google or any other web browser so the answers will be the same

[lone rover]

so what is that answer?

[river moon]

answers provided by manual search are often far more reliable than what chatgpt says

[lone rover]

at I can see in the google that is just : 5x^2 +12x-9 = 5x^2 +15x - 3x - 9

and you can fractorise it fo (5x - 3)(x+3)

[limpid bridge]

even me cant remember 10 first digit of pi, i just remember about 3.1415927

*rounded, because if i do so, the 2 last digit is my birthday

[keen kiln]

i dont know bro

[vernal token]

Are you being asked to write down the first 10 digits of pi in your math class or what

[keen kiln]

i dont know

just have to learn it

[vernal token]

Of course you should know pi is about 3.14

Maybe your teacher meant that?

[keen kiln]

maybe she did maybe she didn't

I have no diea tho

theres a song about it right?

[vernal token]

I'd really ask, it doesn't really make sense to memorize lots of digits of pi, it's just not useful to mathematics

[keen kiln]

song about pi

[keen kiln]

so we dont need pi in math?

ok

[vernal token]

We do, but not by memorizing 50 digits of it

[keen kiln]

oh

alright

got it

[vernal token]

Like you can find series expansions of it, like Ramanujan did, then you can compute billions of digits with a computer fairly quickly

[keen kiln]

whos ramanujan

[vernal token]

An indian mathematician, he was largely self-taught, barely had resources but discovered very influential things

He was also extremely poor and couldn't even afford paper

[keen kiln]

where is he now?

[vernal token]

He lived from 1887 - 1920

[keen kiln]

ohhhhhhhhh

got it

[vernal token]

He discovered this

For pi

With every single summand, 6 or 7 digits of pi are added

Also, it's not really known how he discovered it

[keen kiln]

do we got any photos or videos of him?

[vernal token]

No videos, but photos

https://www.google.com/search?client=tablet-android-lenovo-rvo3&sca_esv=ae0256cbc04b73df&q=Ramanujan&tbm=isch&source=lnms&prmd=ivnbz&sa=X&ved=2ahUKEwi8tf6qldiEAxVl9QIHHeR1BYcQ0pQJegQICxAB&biw=1280&bih=800&dpr=2

[keen kiln]

is this link safe

[vernal token]

It's just a google link, google it yourself if you don't wnat to click

[keen kiln]

ok ill click it

[vernal token]

I googled "Ramanujan", went to "images", and linked it

[keen kiln]

ok its safe

[vernal token]

Why'd someone who has been in this server for this long, using it daily, post an unsafe link and get banned

[fresh gull]

Hello!

[cyan parrot]

Well he used to worship the god "Namagiri" appearing in his dreams, who gave him all the ideas.

I don't know if that was supposed to be modest or actually true.

[neat lintel]

so that's where the people malding over cleo on mse got it from

[glass peak]

Holy shit Cleo is the reincarnation of Ramanujan

[dire glen]

there is at least one movie about him as well

[latent edge]

That would make sense

Cleo, the integral God

[cyan parrot]

Typical janitor at MIT

[fresh comet]

i wonder how cleo is doing nowadays

[latent edge]

same

[sly flint]

Some people speculate she had a rare medical condition which led to her untimely death

but again, those are just speculations

[latent edge]

why talented people are cursed

[sly flint]

Ikr

[stoic relic]

No its not

snot

[little quest]

she "accidentally" recreated the formula for a proton bomb which could blow the earth to bits, so she unfortunately died due to a rare medical condition. ||she was killed with 1000 bullets to her head||

[vernal token]

Yep, to his friends, he described that he dreamed of a bloodstream flowing down, then suddenly a hand started to draw elliptic integrals into it

[latent edge]

[neat lintel]

Guys pls

Help me

Does anyone here know how too make like a ying yang or like an apple polar graph on desmos

Oh this isn't main woops

[rocky shuttle]

H&M

[burnt ledge]

https://www2.hm.com/en_gb/index.html

[proud oriole]

?

[burnt ledge]

im not scamming

thats just what H&M is

they sell clothes

[burnt radish]

yoo

is there an actual formula for finding square roots

idk

haven't found one

I hope i don't get kicked for talking to myself

bro

you won't

so an formula for finding square roots,

why not try google

i tried

[wild lantern]

I've only ever done it by hand using newton's method or series stuff.

In the US apparently people used to be taught methods for calculating square roots by hand.

[burnt radish]

but now they don't?

damn calculators

[wild lantern]

Yeah afaik it is uncommon

[burnt radish]

wait

your about me

is it just random

or did you

i ain't gonna touch grass

[wild lantern]

Lmao

Apparently there is a wiki page discussing a bunch of different square root calculation methods

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

[burnt radish]

bro thank you

[wild lantern]

No problem

[neat lintel]

hi

[strange mesa]

https://youtu.be/A5w-dEgIU1M?si=PLy_Ho9xgblzqmT6

[neat lintel]

IS ANYONE um german and good at maths

[granite hound]

So I'm TAing a class and I'm usually pretty good at responding to questions by email

But there was an assignment due yesterday and tons of people wanted help on Saturday/Sunday

Which I was very much not going to do

But the assignment got extended to Tuesday, so now I need to answer all these emails I was ignoring 😭

(People had 3 weeks to ask me questions during work hours, so I feel justified in ignoring them on the weekend)

[neat lintel]

I need some help regarding PINN (Physics Informed Neural Network). Please DM if u can help. I need a serious help

[night notch]

I got no help in #discussion , I set my role to studying yet I still get Helper pings? All it did was revoke my access to general channels.

[vernal token]

What class is that

[granite hound]

3rd year Compsci class, programming language paradigms

[vernal token]

You have to TA that as a math major?

[vernal token]

You have the helper role

[night notch]

Yes someone told me its only for turning off general chat

I'm dumb anyways

there's literally a do not disturb feature on discord

[granite hound]

I'm actually a compsci major, but I'm moving to math for my masters

[night notch]

I'm usually on my laptop which has do not disturb connect to phone as well so I just set my phone to do not disturb and it blocks everything for me

but since I'm on my pc I was still getting notis lol

[granite hound]

And that was the class that really opened my mind to just how mathy compsci could really be

[vernal token]

Ah, alright

[vernal token]

Say ,iamnot helper or something like that in bot commands

Or just go to id:customize and remove it

[night notch]

its okay, like I said it was a total brainfart because do not disturb mode solves this issue for me and blocks all channels. I've just never had to use it before so it didn't occur to me

[surreal sapphire]

the helper role is for helper pings, if you dont want general channels, you want the studying role

#info

[night notch]

I know that now. I thought studying was to remove all pings, but I understand that would not only be pointless due to discord's built in silence feature and since you might want pings for helper channels on if you're studying and maybe getting help with a problem haha

Was just not thinking 🙂

[strange mesa]

It's been like 6 hours.

[ocean harbor]

I know

I check this often now

[strange mesa]

Well thank you for checking up on me.

[ocean harbor]

np

[strange mesa]

I appreciate it.

[ocean harbor]

[ocean harbor]

try the physics server in #old-network if you still looking for help

[scenic thunder]

Hi, guys, how do people know that certain university has a strong faculty in certain directions

[river moon]

asking people involved in it's work or it's students

[scenic thunder]

Thanks!

[neat lintel]

I need some help regarding (PINN-Physics Informed Neural Network) to make an AI that solves a non linear differential equation. Someone with enough knowledge about this please DM.

[neat lintel]

I did. No one has responded so far from there

[mental stratus]

hmm

[ocean harbor]

why do you even turn the ping off smh

but I guess be more patient?

[cloud vector]

dead aah

[worldly root]

cat :)

[ocean harbor]

that's me

https://cdn.discordapp.com/emojis/1048660781123780749.gif?v=1&size=48&quality=lossless

[brazen mulch]

literally cat

[brazen mulch]

please describe foto

[bright hill]

cat desperately tries to stop light from using the death note

[burnt ledge]

A person writes a numbered list in very small Japanese script on centimetre grid paper with a pink ballpoint pen with black ink. A very small kitten is sitting on the hand, maybe looking at the writing. In the background there is a messy arrangement of stationery

[brazen mulch]

partial headline

[bright hill]

cat teaches hooman how to write japanese (it's getting frustrated with how slow hooman is)

[brazen mulch]

alternative text

[brazen mulch]

clickbait video title

[burnt ledge]

If I had to guess, that's centimetre grid paper

Looks slightly bigger than my regular 8mm ruled paper, in relation to the pen

[brazen mulch]

is 8 mm or 10 mm grid better to you

[burnt ledge]

ive never seen 8mm grid

[brazen mulch]

I have

mostly in primary school notebooks

[burnt ledge]

thats 5mm grid

[brazen mulch]

nah, it’s 8

[burnt ledge]

8mm is ruled

[brazen mulch]

(I measured fr)

[burnt ledge]

when theres only horizontal lines its 8mm, when theres a grid itd 5mm

[brazen mulch]

I don’t buy 8 mm grid anymore, but I swear they existed

and 5 mm is the one that never appeared here

[burnt ledge]

here = ?

[brazen mulch]

where I live

[burnt ledge]

U said orimary school so i assume UK

But i also mean UK

[brazen mulch]

💀
we operated under a bad assumption of the other’s place of residence

“primary school” isn’t exclusive tho
at least when it’s translated

[burnt ledge]

Ah okay

id still be surprised about 8mm grid ngl

[icy ember]

https://cdn.discordapp.com/attachments/1190624626976505857/1212695016556986398/win_102926.png?ex=65f2c53e&is=65e0503e&hm=e3fa3a172ee5feaa8015144fdd3b43ade7a80754ddd17a708cc8ce6fb03188c6&

[ocean harbor]

https://tenor.com/view/no-gif-20395215

[hazy ice]

Yw all

[naive galleon]

Anyone wanna hear my cool proof i have to present infron my entire class tmr?

[vapid furnace]

What subject ?

[naive galleon]

Differential equations

[vapid furnace]

I don’t know enough about it, sorry

[ocean harbor]

@tame egret you are alive 😮

where have you been?

https://cdn.discordapp.com/emojis/1048660781123780749.gif?v=1&size=48&quality=lossless

[magic meteor]

why don't more people study math on their own terms, by themselves

[midnight briar]

its not meaningful for most

like how can you make money?

[magic meteor]

most people, even if their interested, wait until they can get a degree out of it

why this clinginess to life

[fresh comet]

wait wtf

why did i get Helpful role

i havent helped people consistently in weeks

wtf

[visual breach]

Did you use to help people a lot?

[fresh comet]

yes

that was like 2 months ago

[visual breach]

Yeah, that's likely why

[fresh comet]

my consistency in help channels hasnt been there for weeks now

[visual breach]

Hmmm

[fresh comet]

who assigns the Helpful role

bot?

or is it like the mods or something

[fresh comet]

@neat lintel update on uoft's restrictions on UG math students: apparently no 3rd year UGs or below can take grad courses starting next semester

really annoying actually

[jovial ember]

Not surprised

[vale plover]

why

too many people taking them?

i can understand if ugs are crowding out grad students

[midnight briar]

i just turned in my homweork and realized every questions had divergence as an answer now im paranoid

[bronze pelican]

Thats insane

Literally what is the reasoning

[fresh comet]

I don’t know the reasoning

I heard it from a senior

if I had to guess, it’s probably for some stupid reason as usual lmao

[fresh comet]

I guess I should add the caveat that I don’t know if this is referring to non-cross listed grad courses, or all of them (the senior wasn’t clear about this)

Either way, it’s a very stupid policy imo

[solid snow]

Theyre losing out on money too lel

[neat lintel]

uoft can gargle on my hairy nutsack

shit like this is why i accepted my other offer

[vernal token]

ODEs?

[fresh comet]

you’ve accepted Waterloo’s offer?

[neat lintel]

yeah

toronto just keeps getting worse and worse

but the worst mistake they could ever make was failing to immediately accept me

[fresh comet]

[mental stratus]

[full tusk]

hello guiz do you know how to laplace tranform?

[neat lintel]

no

[neat lintel]

which place?

[full tusk]

HAHHAAH

that's not a place hahaha

[sharp cave]

lap

[mint patio]

@fresh comet

so basically

given a physical system (described by a linear ODE) with an input and an output, we take the Laplace transform of the system and take the ratio of the output to the input

so if the output is y(t) and the input is r(t), the ratio is Y(s)/R(s)

we call this the transfer function

now uh basically the idea is

[vernal token]

Isn't it just defined by that integral

[mint patio]

we design a "controller" (a brain) that changes the input based on some parameters we select right

one important part of the controller is what's called the gain

dw about what it means technically, just know that higher gain means a faster controller (your brain responds faster) but it also leads to greater instability (your brain might overshoot the proper answer or start going into a spiral)

and so the gain is something the engineer chooses based on some design criteria

now, given a system whose transfer functionis defined as G(s)