serious-discussion

[pearl horizon]

Hey guys, how can I improve my math skills? I'm doing IB math, but I'm kind of struggling at this point. Any tips would be helpful

[woven axle]

@wary walrus hello

[neat lintel]

by doing math. Work on your foundations if you struggle with that.

[stray kite]

any tex editor suggestions which have a UI similar to vscode or smth
im using texworks but i hate the UI ngl
i was hoping thered be something like autocompleting commands etc possible with some editors/IDEs

[neat lintel]

There is atom I used it a couple times in the past.

Sublime

Vscode should have a couple extension if you need help with autocompletion.

[wary walrus]

AYO FIFI 😳

my man everywhere

[woven axle]

Yessir

[timid spindle]

Atom>vscode
FOSS
UwU

[neat lintel]

The reason I still use vscode is I am way to used to it. I have done most of my development on it so using a different editor like atom make me uncomfortably

[pale orchid]

vim ftw

[neat lintel]

Lol we don’t welcome that here

[timid spindle]

I think you're better off with vscode + texworks plugin.

There is a latex autocomplete addon in atom and texworks as well

[stray kite]

texworks plugin?

[timid spindle]

Yeah

[pale orchid]

in all seriousness, i use texmaker

well

texmaker and whatever text editor i have at hand. sublime, vim, and gedit all do color-code tex keywords

that's about all i need from them

[timid spindle]

it's more like a script. I installed it from 3rd answerr on stack https://tex.stackexchange.com/questions/13136/ide-with-autocompletion

[timid spindle]

Yeah pretty much. Syntax highlighting is handy

[leaden torrent]

oh wow

this makes me want to github copilot for math

see whether it actually produces mostly-correct arguments

or legitimate-sounding arguments that amount to absolutely nothing

[ancient flame]

quick

i need an example of an extraordinary differential equation

[leaden torrent]

x' = x

[ancient flame]

that is so extraordinary

thank you very much kind sir

my life is now complete

[wild jay]

'x=x

[pure raptor]

June 28th is Tau day

[deep mango]

omg i love tau! terrence taU!

[crystal stone]

I like celebrating february 71st in honor of euler

[dapper pivot]

has anyone token the ACT

[deep mango]

i took it quite a while ago

[dapper pivot]

how did you study for the science section?

[atomic cypress]

i didnt

just fail exams bro

[untold sapphire]

so true

[deep mango]

for that i just did a lot of practice exams

the science you can't really like

know a bunch of facts

most of it you get from the passages / tables they give you

practice is the most helpful thing there

[dapper pivot]

the questions at the very end are really hard though how do you deal with those i fail like 9/10 with them at the end

[untold sapphire]

didn't you just ask them that the other day and they said no

[neat lintel]

Mosh said no
AK

How do you guys know that? Are you stalking me

no
AK

And maybe you ate right

Ate right haha stupid auto correction

blocked
AK

[neat lintel]

What's ak?

Auradon Kids?

[summer elm]

Is there a similar group for Physics

[outer lion]

#old-network

[orchid helm]

https://discord.sg/physics

[neat lintel]

please refer to #old-network
AK

[orchid helm]

ur blocked

[neat lintel]

I'm in my senior year and we are required to do an advanced project consisting of atleast 15 pages. Any tips on possible maths projects?

[wild jay]

just choose an advanced or special math subject and make a mini paper about it

I had to do it at HS I made 45 pages

[simple raven]

p-adic numbers !

[vast surge]

I would speak with your advisor or with some professors you get along with; I'm sure someone in your school's department would be willing to help you work on some advanced topics.

[neat lintel]

Do you choose the topic for Phd or advisor?

What would be the minimum qualification of an advisor. Phd?
How do we make sure that what advisor picks would be good?

[slim meadow]

You usually want at least an assistant professor to be your advisor, and some even say that you should only have full professors be your advisor

[leaden torrent]

ideally you want an advisor who's well-known in your field of interest and whose students have a good conversion rate into academia (check math genealogy)

if your prospective advisor has had 30 students and none have went into academia, thats probably not a good sign

this info never tells the full story though

things like "how nice are they to work with?" are pretty hard to get through this method

[slim meadow]

Your professor wants to pick a good topic for you because if you do well then it looks good for them

[leaden torrent]

so you kind of need to rely on things youve heard

[neat lintel]

Can someone fail in Phd?

[leaden torrent]

yes, plenty of people drop their programs, but it generally looks pretty bad on the advisor if that happens

its not quite "failing out"

[slim meadow]

I mean, many people just decide to drop out with a masters if they think a PhD is not for them

[leaden torrent]

its like "both the student and advisor realize theres no path to the student completing a phd"

[neat lintel]

How do they cope with the loss of years?

[slim meadow]

Although, most PhDs in the US do have quals that you have multiple attempts at, but can end up failing out

[leaden torrent]

i have never heard of someone being straight up kicked out of a program for failing quals

im sure it happens

but its really rare

[slim meadow]

What does this even mean? Doing a masters still takes time so there's no real loss of time

[leaden torrent]

usually youre given a stern talking-to and told to retake

[neat lintel]

What, Phd comes after Masters, right?

[leaden torrent]

and that happens a couple times before they kick you out

[slim meadow]

Yes? So they spent a few years pursuing a PhD program, but decided they didn't want to finish the PhD and dropped out with a masters instead

[leaden torrent]

in america, you do a masters as "part of" your phd

in mathematics at least

some fields are different

but typically you apply for phds right after your bachelor's

this is different in other countries

even canada, for example, typically has students get masters degrees first

[neat lintel]

So, is it possible for a professor to make me his student for Phd without going through any competitive test if I am good in math and he thinks too.

[slim meadow]

Depends on the school

Some schools don't have what are called quals, like the school I'm at now

[leaden torrent]

thatll be more up to the department than the professor usually

youre gonna need a bachelors of some sort no matter what

[slim meadow]

All schools will have some requirements though, whether they be written tests, or oral tests, or required classes

[neat lintel]

We have UG,MS then Phd

[leaden torrent]

right

and phds in canada are shorter as a result

since youre not doing the masters first

[dry pier]

hi?

[leaden torrent]

hi.

[neat lintel]

Phd in India is 3-5 years. 3 is min and 5 is max for which you get paid stipend.

[dry pier]

i am new for this server

[leaden torrent]

okay, then sure, similar idea there

[neat lintel]

HS, College?

[leaden torrent]

you can drop a phd but it looks really bad

and youll probably know whether you can handle a phd after your masters

[dry pier]

no i am school

[leaden torrent]

more common than dropping a phd is going "over time"

and having to take an extra year or two

(thats actually what im doing right now, although im still paid for it)

[neat lintel]

You know trignometry?

[dry pier]

yah

[leaden torrent]

this isnt really looked down on necessarily

sometimes research takes more time

but its still better to complete it "on time" if possible of course

[dry pier]

i know polynomails

i mean polynomial

[neat lintel]

Then you are in HS.

[dry pier]

oh

any questions can you give me

that i can do?

[leaden torrent]

i have no debt?

what do you mean

phds are paid

[dry pier]

ok

[leaden torrent]

as are most masters

[neat lintel]

solve sin^2(x) - cos^2(x) = 1?

[leaden torrent]

exceptions exist in both cases but you really really shouldnt do an unpaid phd

if youre getting offered a phd without any sort of pay, theyre basically telling you "we dont want you"

unpaid masters you'd rather avoid but arent the end of the world if you can handle it financially

but unpaid phds are like, not good lmao

theyre saying youre not qualified for academia but might still be able to get a phd for industry

yeah masters depend more on the country

[neat lintel]

We pay for masters here.

[leaden torrent]

in some places its the norm for them to be unpaid

but as i said earlier, im most used to canada

[neat lintel]

For Phd we get paid.

[leaden torrent]

so im talking about that system

[neat lintel]

And it's pretty good as per Indian standards.

[leaden skiff]

damn everyone here is indian

[neat lintel]

Lol, When I saw the cost I left the plan in 2011

Still I can't

[neat lintel]

We are 120 core. So 1/6th everyone person you meet.
Or 1/6th of you.

[neat lintel]

solve lim of x to zero of arctan(e^x/x)

[neat lintel]

Why do we say it's arctan instead of tan inverse?

[leaden skiff]

try to solve collatz

[leaden skiff]

arctan is better cause tan^-1 looks like 1/tan

[outer lion]

3x+1 , ez

[leaden torrent]

[neat lintel]

because yes

[neat lintel]

Can I mail a professor with my theorems If I don't have formal math background?
Will I get a response?

[leaden skiff]

yes you should spam their emails with proofs about collatz, riemann hypothesis, and P=NP. especially if they're specialty is in a completely unrelated field.
mathematicians love ambition and new ideas

[vivid halo]

also remember if a professor doesn't respond it just means that the professor can't refute your argument

if 100 professors don't respond to your proof of the Riemann Hypothesis then it's probably correct

[neat lintel]

If all repsond then I think I need to ignore and mail again.

[delicate knoll]

Is mathematics a science??

[neat lintel]

No, science is mathematics, but mathematics contains many more things than science.

[delicate knoll]

What?

[neat lintel]

Science is a sub set of mathematics.
Mathematics is a super set of Science.

[surreal sapphire]

define science

[delicate knoll]

Here we go again...

[delicate knoll]

We couls say science is systematic enteprise thag builds and organize knowledge in the form of testable explanations and predications about the universe...or about some system

[delicate knoll]

Is that correct?

[vivid halo]

I don't think so

[delicate knoll]

The question of 1 millium dola

[surreal sapphire]

then math is science

[vivid halo]

I do think mathematics is a science not least because it shares many of the same empirical and sociological issues surrounding the scientific method

[leaden skiff]

math $\cap$ reality = science

[fathom swallow]

Ninja

[surreal sapphire]

math to me is just some culture thing we do

[leaden skiff]

tbh like what is the connection between like number theory and geometry

why are they both math?

[delicate knoll]

They have numbers

Lol

[leaden skiff]

what numbers are in geometry

tell me

[delicate knoll]

Abstractions

[leaden skiff]

???

[delicate knoll]

Good

[leaden skiff]

what

[delicate knoll]

Ok, well my answer is I DO NOT KNOW.

[deep mango]

Sub set.

[neat lintel]

Dom set.

[neat lintel]

see "arithmetic geometry"

[surreal sapphire]

math is things mathematicians care about

[leaden skiff]

are cats maths?

[surreal sapphire]

probably.

but well, number theory and geometry are very much linked

and they have been from the start

the greeks didnt really think of numbers like we do today

[leaden skiff]

math is something that transfroms like a math

[surreal sapphire]

they only thought about geometry

also when euler was asked to solve the königsberg bridge problem he did so with that is now essentially a theorem of graph theory

and he remarked that it was odd that he was asked since the problem (and the solution in his opinion) has nothing to do with mathematics

it was merely a "result of logical thought" and anyone could have easily arrived at the same conclusion (or something like that)

[leaden skiff]

i wonder what fields of math are waiting to be discovered

[surreal sapphire]

i'm just waiting for the release of math 2.0

[bronze pelican]

Math 2.0 finna be lit

[surreal sapphire]

everything will just be algebraic geometry

fueled by condensed mathematics

[honest phoenix]

i proved raiman hepotheses

[leaden torrent]

cool

[blazing pawn]

Fascinating

[pale orchid]

https://tenor.com/view/rayman-yay-peace-gif-22031437

rayman hypothesis

[deep mango]

How?! I was trying for a few months already!

[honest phoenix]

the zeros of the function with some log sums on the critical line have a match

• i have 14 years old

ryc ?

you still here ?

@deep mango ?

[deep mango]

log sums....

oh!

[honest phoenix]

ye

[deep mango]

like natural logs

i get it

[honest phoenix]

yeaaaaa

the infinit seiruis of log

products

my english bad sorry

[deep mango]

that's ok

i see what you mean

[honest phoenix]

so whene you do p(x)

the logarithmic function we got will match prime(x)

so for any value of x we can get the number of primes or in a way that i still earch we can get the primes it self as a sum with this

that will be the domain of f(x) mean we can do it from like p(x) domain will be in 2 lines if we count zero so from 0 to x

its a good idea if you apply it on paper

[deep mango]

thx

[honest phoenix]

np

we wont use the negative valuse bc basicly we will get zeros

[wispy dune]

can you explain why the zeta function is zero at -2

[honest phoenix]

i still not prove it yet but i have nice proprety zeta (-2n)=0 as n is z+

mean positive interger

[wispy dune]

cool

[honest phoenix]

i have all that and i am still 14 yo

i discover this server like hours ago

but i need help

[deep mango]

#❓how-to-get-help

[honest phoenix]

no not here in real life

i wanna show my works on phone

[deep mango]

[honest phoenix]

can i ?

[fast ivy]

[leaden skiff]

sure

no ones gonna stop you

[leaden skiff]

fair wairing. you probably haven't

[delicate knoll]

Lol

I really wan to prove P=NP

[bronze pelican]

My diff geo pronounced energy as UHnergy

[deep mango]

#❓how-to-get-help

[dapper pivot]

wrong chat oops

[unique kite]

whos good with yr 10 maths
i need help lol

[leaden torrent]

#❓how-to-get-help

[neat lintel]

Yes. Others are lying.

[bold fable]

Anybody can help .........I want to learn number theory from basic ......please give me link or book and pdf .....

[steep ore]

I am. I'm doing A level maths and I'm brilliant at it

Oh wait she left

[honest phoenix]

no one actuly prove till now

[timid spindle]

wtf

wtf

Jordan Peterson

is doing line integrals somehow

😮

[leaden skiff]

what

[icy forge]

Is this evolution

Literally evolution at the scale of the modern world

[timid spindle]

yeah, apparently in his new paper his using line integrals to predict psychological stress like quantity

[leaden skiff]

...

how?

what's the line integral with respect to?

what's the units of the function

hell what is the function for that matter

[icy forge]

Did someone just shift #serious-discussion and #math-discussion

WHO WAS IT

[leaden torrent]

is there something special about this

[leaden skiff]

wdym?

[icy forge]

no but I must have answers is a meme

[leaden torrent]

is quantitative modelling something unknown to the field of psychology before lobsterman (pbuh) enlightened them

[icy forge]

oh you meant integrals

But

[leaden skiff]

how the hell do you model anything in psychology with integrals?

[icy forge]

Using infinitesimal feelings

[leaden torrent]

stats is part of psych

er

not part of but

used in

[leaden skiff]

oh I guess. like in relation to chemicals then?

or like groups of people?

not like an individuals emotional state

[icy forge]

The only psych I know with reasonable integrals is choice modelling

[leaden skiff]

is that psych + the axiom of choice

[icy forge]

After that is 'econometric curves' (e.g. supply, demand) which IMO have massive error levels anyway

[icy forge]

no, discrete choice modelling, modelling utility from randomly choosing choices such as teddy bears, plushies of Applejack, or straight up just donating to a food bank

[neat lintel]

asking arithmetic question = blocked and banned as well
AK

[timid spindle]

I dunno. I didn't read the paper. I listened to his podcast with Krauss.

[honest phoenix]

hm ?

[wild jay]

jm

[neat lintel]

??
AK

[honest phoenix]

?

any new problem for discussion ?

[neat lintel]

no
AK

[timid spindle]

Wtf

[wild jay]

AK

[delicate knoll]

Give us a print of this paper

[candid oak]

hello guys

is it trivial to say: card(H) = card(aH) where a is real

[leaden torrent]

whats H

[candid oak]

(H, x) a group

[leaden skiff]

what's a

[candid oak]

real number as mentioned

[surreal sapphire]

what's aH then

[leaden skiff]

wait but like, how do you compose a real number with an arbitrary group?

[surreal sapphire]

you don't

[candid oak]

wait a sec

is that equality always true?

[leaden skiff]

if a is an element of H then aH is just H

what is aH?

[candid oak]

i mean, isn't it always true?

[candid oak]

no it's not an element of H

[surreal sapphire]

your equation has no meaning

what is aH?

[candid oak]

i see

here's a rigorous one

[leaden skiff]

what you've said is, "hey is 2+t = t where t is a right angled triangle" basically

[candid oak]

let (G,x) a group, H a sub group of G, and a an element of G, then card(H)= card(aH)

what about this one?

[leaden skiff]

ahh yeah that makes more sense

[candid oak]

okay

is it true?

i mean always

[leaden skiff]

well the set of aH is just a subset of G no?

[candid oak]

yea iy is

[surreal sapphire]

it's true, yes

[leaden skiff]

so if it's not infinite it's not true

[surreal sapphire]

all cosets have the same order

[candid oak]

if it's infinite then cardinality has no meaning no?

[surreal sapphire]

it does

[candid oak]

really?

[surreal sapphire]

yes

[candid oak]

tell me more please

[surreal sapphire]

you define it via injective or surjective maps

[candid oak]

ah yes

[surreal sapphire]

generally you say that A has cardinality less than or equal to B if there exists an injection A -> B

(then prove a whole bunch of stuff to see that this behaves like it should)

[candid oak]

if it has a bijetiion with N then it's countable

[surreal sapphire]

generally the coset thing is

two sets have the same cardinality iff there is a bijection between them

[candid oak]

what is coset?

[surreal sapphire]

if H is a subgroup of G and a \in G, we call the sets aH cosets

[candid oak]

oh that's related to my previous question

cosets have the save cardinality then

[surreal sapphire]

yeah, and here you can easily find a bijection between any two cosets

[candid oak]

damn that was the most rigorous explanation I got so far

thanks man

I appreciate that

[surreal sapphire]

sure, yw

[honest phoenix]

what

p=np

[last oxide]

n=1 or p=0

[wild jay]

or p=1 and n=1

,w p=np

[fathom swallow]

Results provided by WolframAlpha

Click here to refine your query online
Upgrade to WolframAlpha Pro!

Requested by Emma762#4230

[last oxide]

thats included in n=1

[wild jay]

AK

[neat lintel]

Does this break crypto?

[leaden skiff]

if P = NP then cryptography does get kinda fucked yes

[delicate knoll]

I kinda wanna prove that false or true, someday....

[leaden skiff]

you won't

no offense

[surreal sapphire]

there is a viable approach being developed

well, possibly

(it's super hard)

[deep mango]

Is that happening

[leaden skiff]

really? wow who woulda thought

[deep mango]

That feels like it's happening with several millenium problems

[leaden skiff]

imagine if it's undecideable. what would that mean

[surreal sapphire]

well

the main researcher believes if it works, it will take another ~100 years

[deep mango]

I know people are feeling more and more optimistic about disproving navier stokes these days

[leaden skiff]

disproving?

[deep mango]

Yeah

[leaden skiff]

why disproving?

[deep mango]

Finding a solution with blowup

That's what tao's trying to do

[leaden skiff]

wait what was navier stokes again?

[delicate knoll]

Why not?alright!, I am not offended easily for a long time,anymore

[delicate knoll]

Intresting!

[leaden skiff]

it might not happen within either of our lifetimes first of all. it will take a lot of work and you'll have to dedicate a huge amount of your life to it if you wanna be the one. also there wont be any single person to do it. science and math are group efforts

[deep mango]

Navier stokes problem asks whether the solutions to the navier stokes equations (for the motion of an incompressible fluid with viscosity) are regular (well behaved) or if they can blow up (get infinitely fast in finite time)

[leaden skiff]

what would proving it mean?

[deep mango]

Proving that all solutions are regular and don't blow up like that

If you found a counterexample

That would be disproving it

[leaden skiff]

huh weird. what does it mean like physically if it blows up

[deep mango]

Disproving "global well-posedness"

[leaden skiff]

well posedness?

[last oxide]

excuse me
I only use compressible viscoelastic NS

[deep mango]

It would mean that the navier stokes equations predict that a fluid can get infinitely fast in a finite amount of time

Which is obviously idiotic

So

[leaden skiff]

time travel 👀

[deep mango]

It would basically say that the navier stokes equations aren't a perfect model for fluids

But

They already arent

[leaden skiff]

oh so it proves that they're a close to useless model for fluids then?

[last oxide]

you already assume a bunch of shit

[deep mango]

And it's so hard to disprove this that obviously they work 99.9999% of the time

So

[leaden skiff]

wait what

[deep mango]

Planes would not fall out of the sky

[leaden skiff]

it's weird that it would work but also lead to idiotic results

[last oxide]

but Id assume most of the shortcomings of NS come from the main model itself
thats is, assuming fluids are newtonian in the first place

[deep mango]

Anything that has assumed the navier stokes model (which is everything) would still work

[deep mango]

Well the whole point of the problem being so hard is that as far as we know they dont ever have idiotic results

[leaden skiff]

what if fluid really can go infinitely fast and we just never realized

[last oxide]

its funny how a bunch of fundamental equations on physics are literally linear approximations

[deep mango]

But we cant prove they never do

[leaden skiff]

like what?

other than navier stokes

[deep mango]

Anyway the point is that Tao and his affiliates are trying to find a counterexample solution to navier stokes with a promising and very novel method

[last oxide]

the stress tensor on navier stokes is linear in terms of the velocity gradient

wave equation is a linear PDE
heat equation is a linear PDE

a bunch of shit is just linear

[deep mango]

Which is basically to show that navier stokes fluids are turing complete

[last oxide]

oh

thats sounds weird

[deep mango]

It's very weird

[delicate knoll]

Very interesting

[deep mango]

And if you show this then you can construct a solution with blowup

[last oxide]

what does that even entail for a fluid tho

like

[deep mango]

Well

Ok

[final anvil]

random question. what does a capital D on top of an equal sign mean?

[last oxide]

what does it mean for it to be turing complete

[deep mango]

Tao gave a great talk about this

[last oxide]

oh

[final anvil]

context

[last oxide]

gonna look for it

[deep mango]

I can find the link

I cant explain it myself

[last oxide]

maybe equal as distributions?

did they define any distribution equality?

[deep mango]

https://www.msri.org/workshops/950/schedules/29629

"We discuss some possible (and still speculative) routes to establishing finite time blowup in fluid equations (and other PDE), focusing in particular on methods based on establishing universality properties for such equations."

[final anvil]

dont think so, but that sounds fitting

[deep mango]

Universality in the sense of computable universality

[last oxide]

[deep mango]

I know, I had no idea what universality meant when I joined the talk either and when he unveiled he meant turing universality it was pretty shocking

[last oxide]

feel like I need to even understand basic computability first

[deep mango]

I dont know

[last oxide]

[deep mango]

The talk kind of just sets up a visual model for what a computation would look like in a fluid

Oh also

This has actually been done

But it's for fluids on some riemannian manifold in 10^30 dimensions

Isnt that wacky

[last oxide]

10^30

[deep mango]

Something like that

He mentions it at the end of the talk

Unfortunately their technique doesnt scale well locally

So it's hard to drop dimensions with it

But still, it shows that there's a lot of promise in this idea

And honestly indicates that navier stokes should morally be false

If it's possible to literally get UNIVERSAL behavior in a fluid

(computability-wise)

Oh so I can say the basic idea

[last oxide]

[deep mango]

It revolves around energy transfer between different fluid parcels

And tracking that

As a proxy for a computation

[last oxide]

funny how my phd is probably gonna heavily involve it

[deep mango]

[last oxide]

so Im gonna be morally wrong the whole time

[deep mango]

I mean plenty of things that are morally right are factually incorrect

It could be just too low dimensional or something

To situate an arbitrary computation like this

[last oxide]

who knows

[delicate knoll]

.

[mint patio]

I think in another life I was more interested in physics instead of mathematics

I love physics conceptually but have not explored much of it, and I hate actually doing physics (applying physical concepts to solve problems)

But I love math even more and usually I enjoy solving problems, even when I’m stuck with them

[trail lantern]

k

maths better xd

[bronze pelican]

yes this is wwhat algebraic geometry is known for

studying elliptic and hyperelliptic curves

[fast ivy]

oh, where is this statement from?

[bronze pelican]

a blog

https://asz.ink/2020/03/08/jacobians-of-hyperelliptic-curves/

[clever knot]

what about jacobians?

i still don't get them

the same jacobians for doing substition?

[fast ivy]

No

[clever knot]

oh :/

[fast ivy]

This is the jacobian variety of an algebraic curve

[clever knot]

and you lost me

isn't that what jacobians are for?

turn the curvy things into straight lines

so you can integrate

[fast ivy]

No like

In this sense you have an algebraic curve

And you associate to it a certain space

And this space gives you nice information about the curve

[clever knot]

wdym when you say space

like

[bronze pelican]

The jacobian is an abelianized version of your space

[clever knot]

R^1 , R^2, R^3

Idk what abelianized or space means 😭

[fast ivy]

Space as in abelian variety

[clever knot]

:/

too dense for me at the moment it seems

[bronze pelican]

Do you know about Riemann surfaces?

[fast ivy]

So an algebraic curve that is also endowed with an algebraic group structure

[neat lintel]

what book are you learning from

[clever knot]

nope

[neat lintel]

i can provide another book if you need

[bronze pelican]

I'm learning from various papers and blogs

What book?

[neat lintel]

i mean brandon

[bronze pelican]

Then it probably wont make sense to explain Jacobians then

[clever knot]

I am not on no book

i was just asking because i seen the word jacobian

[bronze pelican]

different meaning

[clever knot]

so this is a different meaning

i see

[neat lintel]

brandon have you read stewart's book

[clever knot]

I don't know math people names for books

so that is my level of math

:sad_StitchCry:

[neat lintel]

james stewart early trancendentals

[clever knot]

:sad_AVerySadPanda:

oh no

[clever knot]

my nitro

[fast ivy]

Jacobian variety in this sense lmao

[clever knot]

it died today

[fast ivy]

this is from a Serre lecture

[fast ivy]

WHAT

OK

For one sec I thought you were talking about Serre

lmao

[clever knot]

Im still in the very intro stuff like linear algebra and multivariable calc :/

so idk anything about alll this stuff

[neat lintel]

jacobian on page 1067

[clever knot]

still need to find a good way to learn proofs and all that on my own

[fast ivy]

what

Does Stewart cover the Jacobian variety of a non-singular algebraic curve on a book about multivariable calculus?

[clever knot]

That is the jacobian i was taling about

talking about*

the partial derivatives and change of variables one

and you do the determiant

but i think you all said it was a different jacobian

[neat lintel]

what grade are you in

[fast ivy]

yeah so, that's the jacobian of a smooth map at a point

[neat lintel]

just finished this book last week

because ninth grade is boring

[fast ivy]

in this case jacobian refers to a concept in algebraic geometry/elliptic curves

[clever knot]

first year uni 😭

I have been going through this https://ocw.mit.edu/courses/mathematics/18-02sc-multivariable-calculus-fall-2010/index.htm

on unit 4 and i guess it is all the stuff i already learned but applied in 3 dimensions

[neat lintel]

use the book i sent you

OCW skips through alot of stuff

[clever knot]

such as?

[neat lintel]

change of variables in triple coords

[clever knot]

idk just kinda got to triple coordinates so can't speak on that really

just started the whole spherical coordinates portion

i assume it is the same concept?

do you not still use the jacobian?

[neat lintel]

did you do double integrals or surface area

[clever knot]

I mean i know double integrals show up but i don't recall much about surface area

unless that is more in the triple integral stuff

[rose dock]

the thing that MIT really skips out on is parameterized surfaces, and surface/line integrals that aren't work or flux

[neat lintel]

@clever knotso you didn't learn anything on surface area

that

is not good

[clever knot]

idk havent finished

also with line integrals

is it like area under a curve but directed path?

like area under a directed path

[clever knot]

are they that hard to learn?

[dusk edge]

Hello guys, I'm new at this discord server. Can somebody help me about converting this (15.6%) into simplest form of fraction?

[fast ivy]

hi, you can get help by going into of the the questions channel

take a look at #❓how-to-get-help

[dusk edge]

Oh sorry. I didn't check it. Thank you.

[fast ivy]

np

[frank abyss]

Guys

did you know that

[weary river]

I have definitive proof of 9 + 10 = 21 if you're interested.

[fast ivy]

#chill

[frank abyss]

guys did you know that

Lim x -> infinity 1/x = 0

!!!!

like as X tends towards infinity.
we can just say that 1/X = 0

if that like truth?

[leaden torrent]

that's true.

as x gets large, 1/x gets arbitrarily small

[frank abyss]

What can we do with that

i feel like theres some calculus shit that we can do with that

[leaden torrent]

i mean... limits are the fundamental operation of calculus

[frank abyss]

yea but wat can be done with the statement 1/x as x approaches infinity is 0

[fast ivy]

It depends. For instance, this statement is particularly useful because it means that the real numbers are an archimedian field. And this is a very useful property to have.

But what kind of applications do you want?

[frank abyss]

how does that show that real numbers are an archimedan field?

[frank abyss]

idk maybe like physics or something. Or just something that comes up

[fast ivy]

Do you know what an archimedian field is?

Because the answer comes right away

[frank abyss]

yes

archimedan i believe is that

if X is any all real number

and Y is any real number

and X > 0

then there is a positive number such that nx > y

[fast ivy]

Yeah, this is equivalent to the statement that the natural numbers are an unbounded above set

meaning that for any real number x

there exists a natural number n

such that n > x

in particular

This is equivalent to saying that $\forall \varepsilon > 0, \exists n \in \mathbb{N}$ such that $\dfrac{1}{n} < \varepsilon$

[fathom swallow]

MisterSystem

[fast ivy]

But this sentence is equivalent to saying that the sequence $\dfrac{1}{n}$ converges to $0$

[fathom swallow]

MisterSystem

[leaden torrent]

thats a necessary but not sufficient condition for 1/x -> 0 fyi

[frank abyss]

how is it equivalent to this?

[leaden torrent]

replace "x" with "1/epsilon" and take reciprocals

[fast ivy]

yes, but we want to prove that if 1/x -> 0 as x -> infty, then the sequence 1/n -> 0

[leaden torrent]

oh sure

[fast ivy]

but this is clear

[frank abyss]

?

[leaden torrent]

!

[frank abyss]

oh

[fast ivy]

since if $\lim\limits_{x \to +\infty} \dfrac{1}{x} =0$, this means that for any sequence $(x_{n}){n \in \mathbb{N}}$ of real numbers with $x{n} \to + \infty$, then $\lim\limits_{n \in \mathbb{N}} \dfrac{1}{x_{n}} = 0$
\
\
In particular, this means that since the sequence $x_{n} = n$ is such that $\lim\limits_{n \in \mathbb{N}} x_{n} = + \infty$. Then $ \lim\limits_{n \in \mathbb{N}} \dfrac{1}{n} = 0$
\
\
So $\lim\limits_{x \to + \infty} \dfrac{1}{x} = 0$ shows that $\mathbb{R}$ is archimedean.
\
\

[fathom swallow]

MisterSystem

[frank abyss]

i still dont get it

lol

[fast ivy]

So yeah, that's how that limit shows that the reals are an archimedean field

in fact, it seems way stronger

[frank abyss]

idk what

means

[fast ivy]

This is a notation for sequence

so like

for example

x_{n} = 1/n

x_{n} = n^2

x_{n} = (1+(1/n))^n

x_{n} = n

and etc

[fast ivy]

since for any real number x there exists a natural number n such that n > x, we may take x = 1/epsilon where epsilon > 0, then n > 1/epsilon iff 1/n < epsilon

[frank abyss]

fuck

but whats epsilon lol

[tall badge]

any positive real

[gleaming yoke]

um... Hi
Do you know some good videos about category theory?
like indrocution and other

I only know how to construkt a cathegory, arrows are colled *morphism" and each object in category must have indentity arrows

Thx for answers

(sorry if I posted it on wrong channel)

I think category theory is very itresting field of mathematics
and just to know a little bit more about this field

[narrow rock]

idk if there are good videos on this, but the book "category theory in context" is good

[gleaming yoke]

yes

[gleaming yoke]

I don't know why some people react with under my message, and at this point I am to afraid to ask

[last oxide]

I think riehl has a video series about it

[neat lintel]

Why do engineers and physicists work with the cross product if the outer product is much better?

Especially talking about physicists

[fast ivy]

Because these are two different things, abstractly the cross product is a skew-symmetric bilinear map f : V × V -> V.

While the outer product would be the tensor product

But you made a choice of coordinate system

Also

Physicists do use the tensor product, in particular the outer product too.

[neat lintel]

Oh I get it

But you can relate the two

I guess it's notationally less elegant?

[deep mango]

Physicists need curls and such things a lot

Cross products are the nicest way of writing them

[neat lintel]

Thanks 🙂

I saw this amazing application of the outer product

$\nabla{F}=J$

[fathom swallow]

識繒 (Shi Zeng)

[vagrant kestrel]

qm has lots of outer products

[neat lintel]

To describe Maxwell's equation

And it contains all of the information in one neat expression

[leaden skiff]

was this sudgy lacmoes geometric algebra video?

[neat lintel]

Yeah it's great

The construction is really simple

[leaden skiff]

ya know there's a geometric algebra discord

[neat lintel]

Ooooh invite?

Do you have any other servers for specific mathematics?

[leaden skiff]

nop

only joined that one cause of his new series

[fast ivy]

[neat lintel]

These are more recreational but I was in a googology server and a polyotopy (naming shapes, don't think this is how to spell it) server before

[leaden skiff]

you want a link?

[fast ivy]

Shi

I would recommend you to take a look at the first chapters of Tu on smooth manifolds

It talks briefly about exterior algebra, tensor algebra and symmetric algebra

But only briefly

He doesn't mention anything related to their universal properties

Doesn't talk much about quadratic forms and stuff like signature and Sylvester's inertia law

But idk, at least that's where I first learned some basics of multilinear algebra

[leaden skiff]

quadratic forms 👀

jesus christ how deep does this shit go

[fast ivy]

Just about it lol

There's no deep theorems nor anything

[leaden skiff]

do exponential forms exist 👀

[fast ivy]

I think Sylvester's law of inertia may be the only real theorem in "geometric algebra"

[leaden skiff]

law of inertia?

[fast ivy]

Yeah

I have no idea why is it called this way

I think this is named this way

Because this theorem gives you an invariant of your quadratic form

Under change of coordinate basis

[fast ivy]

No, I don't believe so.

But you can define an exponential function for matrix spaces.

So they do appear in linear algebra

[leaden skiff]

forms are functions?

[fast ivy]

Form is a pretty generic name, but in most contexts of linear algebra it means a k-multilinear skew-symmetric function f : V × ... × V -> R

So for example, covectors are 1-forms

The determinant is an n-form

It is the unique n-form on R^n such that det(e_1,...,e_n) = 1 in fact

Where e_i = (0,...,1,...,0) is the standard basis of R^n

A quadratic form is a different thing

[leaden skiff]

ok you know what

i don't think im smart enough for this

[fast ivy]

They are functions Q : V -> R such that there exists a symmetric bilinear form g : V × V -> R for which Q(v) = g(v,v).

[fast ivy]

No

But it's ok, just take your time

[leaden skiff]

let me tell you each of the words that I got confused by
k-multilinear
skew-symmetric function
covectors
det(e_1,...,e_n) = 1
symmetric bilinear form

[grim pumice]

skew-symmetric is the same as alternating, or is it something different?

[fast ivy]

Same thing

[fast ivy]

Covector is an element of the dual of a vector space

[leaden skiff]

what is the dual of a vector space

[stable oar]

the space of all linear maps from that space to its ground field

[fast ivy]

Covectors are functions f : V -> R that is linear

The space of all such functions

Is the dual of a vector space

[leaden skiff]

do you have any like specific examples?

[fast ivy]

Sure

If we have R^n

We can take the projection maps

π_i : R^n -> R

Where π_i(v_1,...,v_i,...,v_n) = v_i

So it takes the i-th component

[leaden skiff]

oh it's all functions of the form av_1+bv_2+...

for R^n

[fast ivy]

Yeah

In particular

Codimension 1 subspaces of R^n are related to covectors

So like

If you have R^3

A subspace of codimension 1 is a plane

And for each plane

[leaden skiff]

wait what's Codimension 1 subspaces

[fast ivy]

If you have a subspace W of a vector space V

And then the codimension of V is dim V - dim W

Ofc

This works for vector spaces of finite dimensional

[leaden skiff]

like how many dimensions it's missing?

[fast ivy]

Yeah, you can think of it this way

So the codimension of a plane in R^3 is 1

And codimension 1 subspaces of R^n would be "hyperplanes"

But anyways

If you take a covector $\varphi : V \rightarrow \mathbb{R}$ that has full rank, then $\varphi^{-1}(0)$ is a codimension 1 subspace of $V$.

[fathom swallow]

MisterSystem

[fast ivy]

And reciprocally

If you take a codimension 1 subspace

There is a full rank covector

Such that this subspace is given by the preimage of 0

So like

You can study lines in R^2, planes in R^3 and more generally hyperplanes in R^(n+1)

By studying covectors

That's another example

So for example, to a plane like 3x+5y+z = 0

You associate the covector

[leaden skiff]

wait, what's full rank mean again?

[fast ivy]

The dimension of the image of φ is equal to the dimension of the codomain

Since the codomain is R

We ask for the dimension of the image to be 1

[leaden skiff]

ok look this is nice of you but i just don't have enough prereq knowledge in lin alg to understand

maybe one day

but this is close to pointless i think

like i need to learn the basics first

i have passing knowledge of some things

but i don't think it's enough

[fast ivy]

Damn, I don't even have a lin algebra Book to recommend

I used one in portuguese

[leaden skiff]

i have gilbert strang's in my house

will do it after real anal

[fast ivy]

Nice

Btw

I think prolly the coolest thing about quadratic forms

Is that they are related to quadric surfaces and conics

[leaden skiff]

what's a quadric surface?

[fast ivy]

Like an ellipsoid, a sphere, a hyperboloid, a paraboloid

[leaden skiff]

oh like 3d conics?

[fast ivy]

Yeah

You can study these things

Via quadratic forms

And stuff like studying the eigenvalues of the matrix of your quadratic forms

Gives you information about the conic/quadric surface

In fact, you can actually just think of quadrics and conics abstractly like this

[blissful delta]

Question regarding physics

[neat lintel]

[honest phoenix]

that confusing

$confusing$

[fathom swallow]

mustapha56

[somber parcel]

Found a cool article on the origins of life's most basic processes:
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6117946/
Maybe I'll just share it here. It's from 3 years ago.

[calm steppe]

,w cows per inhabitant in Alabama

[fathom swallow]

Wolfram Alpha doesn't understand your query!
Perhaps try rephrasing your question?
Click here to refine your query online

Requested by CoronaVirus#3275

[calm steppe]

,w number of sundays on average

[fathom swallow]

Wolfram Alpha doesn't understand your query!
Perhaps try rephrasing your question?
Click here to refine your query online

Requested by CoronaVirus#3275

[copper hinge]

$maths$

[fathom swallow]

Bee

[calm steppe]

$bees$

[fathom swallow]

CoronaVirus

[stoic ice]

$CoronaViruses$

[fathom swallow]

ZozzDude

[stoic ice]

I just had a random question

Are Physics questions allowed in this server?

If they contain some math

What about mechanics at least

Just some wondering coz I will kill this server when uni starts

(Not in a bad way)

Why does uni start in October at my side?? 😡😡😡 I am very bored 😡😡😡😡😡 I guess uni already started at wherever you all guys are

Kk guys bye a-gon slep

[placid coral]

Chess any1

[leaden torrent]

you can ask them but you probably wont have much luck.

see the physics server in #old-network

also @placid coral please dont spam messages in a ton of channels

[placid coral]

k

$OK I am sorry sir$

[fathom swallow]

TJ89899889

[placid coral]

$How is everyone's day$

[fathom swallow]

TJ89899889

[leaden torrent]

please dont spam bot commands.

[placid coral]

ok

but look I did something cool

$\frac{\frac{\frac{\frac{\frac{\frac{How}{Is}}{Everyone}}{Doing}}{On}}{Discord}}{Today}$

[fathom swallow]

TJ89899889

[placid coral]

Cool right

[bronze pelican]

$\frac{\frac{\frac{\frac{\frac{\frac{I'm}{Doing}}{Pretty}}{Good}}{Today.}}{Thank}}{You}$

[fathom swallow]

PTLanglands

[placid coral]

Did you do it by han

hand*

or?

[bronze pelican]

i copied

[placid coral]

oh ok

I never write it by hand

if you want to use Latex you dont need to write it by hand these days

$Epic Triangle$
$\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{ }{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }$

[fathom swallow]

TJ89899889

[cold needle]

#latex-testing

[placid coral]

k

[stoic ice]

I like this

Lol

[honest phoenix]

,tex \def\tmpa#1{{#1_#1^#1}} $\nest 6 \tmpa \cdot$

[fathom swallow]

mustapha56
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[leaden skiff]

is this a julia set?

https://cdn.discordapp.com/attachments/650617579525636110/886450572738306079/image0.webp

[last oxide]

no
this is more like hentai

[azure kettle]

[stoic ice]

?

What’s fancy

What are tags

,tex CoronaVirus

[fathom swallow]

ZozzDude

[stoic ice]

Or you can do

$CoronaVirus$ and some other text

[fathom swallow]

ZozzDude

[stoic ice]

$CoronaVirus \text{ and some other text}$

[fathom swallow]

ZozzDude

[stoic ice]

,tex CoronaVirus \text{ and some other text}

[fathom swallow]

ZozzDude

[stoic ice]

$this \ is \ a \ big \ text$

[fathom swallow]

ZozzDude

[stoic ice]

I guess that’s all to it

You can review them

Doing ,tex is like doing $surrounding the whole thing$

[surreal sapphire]

its not

[stoic ice]

It is

As far as I have experienced

Are there cases where it is not?

[surreal sapphire]

,tex Consider a finite extension $L$ of $\bQ_p$

[fathom swallow]

Lochverstärker

[stoic ice]

Ohhhh

But hey

[surreal sapphire]

$ denotes inline math mode

[stoic ice]

Consider a finite extension $L$ of $\bQ_p$

[fathom swallow]

ZozzDude

[surreal sapphire]

, tex just tells the bot to render the message in tex

[stoic ice]

The ,tex was useless here

[surreal sapphire]

yes

it automatically renders when it finds mathmode delimiters

[stoic ice]

We can omit it in this case

[stoic ice]

I can see that

[surreal sapphire]

or actually

[neat lintel]

,tex nobody eats until these problems are factored you hectopascals!

[fathom swallow]

Darth_Guappi

[neat lintel]

Heh

[stoic ice]

Hmm idk what’s that

You deleted it?

[neat lintel]

So question y'all.

[stoic ice]

That’s the first time I encountered it

[surreal sapphire]

yes, i was just checking something

[neat lintel]

Is there a flash cards app in the app store that you actually like?

[surreal sapphire]

\( \) is inline math mode delimiter

[stoic ice]

I hate visual learning

[neat lintel]

You my friend need Satan.

[stoic ice]

I don’t use flashcards nor mindmaps nor things that confuse me

I don’t know how you guys use them

[neat lintel]

But ... You LITERALLY have a piece in your brain dedicated towards visual memories!

[stoic ice]

Hey, it is a matter of preference after all

[surreal sapphire]

anyways, never put actual text inside $ ... $
as the name suggets, it is for mathematics

[stoic ice]

Yeah

I use \text{}

Sometimes

[fast ivy]

I remember using Anki for japanese

It worked I guess

[neat lintel]

Anki is good for words, awful for math in the way I study it

[surreal sapphire]

i used oldschool actual physical flash cards to study for some math exams

[neat lintel]

Yeah, I'm making this flashcards app. We can do so much better than Anki.

[stoic ice]

You guys write formulas on flashcards?

[fast ivy]

Yeah, I have other methods to study math

[neat lintel]

@fast ivy care to share?

I prefer retrieval after reading a chapter personally.

[fast ivy]

I mean, I just do problem solving lmao

[surreal sapphire]

i had them for like definitions and big theorems

[fast ivy]

And read books/watch lectures

[stoic ice]

I memorize math from lists, tables, etc

[neat lintel]

Yes that's what one does after retrieval.

[fast ivy]

I think that's the best way to get used to definitions and so on

Is by actually using them

[surreal sapphire]

when i was studying for linalg/analysis oral exams

[neat lintel]

Ye

[surreal sapphire]

had like big theorem and proof sketch on back

the most useful thing was writing those

since i had little room for proof sketches

[fast ivy]

Good lord, good thing I never had to do an oral exam.

How is it like?

[surreal sapphire]

and so had to think quite a bit about that

oral exams are great

(if you know your stuff)

if you dont, its hell

[blazing pawn]

they sound like theyd be terrible for ppl with social anxiety

(me )

[surreal sapphire]

well

its not a regular social situation

its a very technical talk about mathematics

so there is that

[limber perch]

in my linear algebra class

[surreal sapphire]

im not great in "regular" social situations but oral exams, teaching etc are much easier for me

[limber perch]

the textbook we’re using doesn’t name any of the theorems besides 2.3.1 or something

[surreal sapphire]

ymmv

[limber perch]

so my teacher has called them important theorem #1, important theorem #2, etc.

really good system

[fast ivy]

So like, is it more about discussing some results and definitions? Do they usually propose some problems in an oral exam?

[surreal sapphire]

best is to write ([name] [year]) after important theorems

[surreal sapphire]

sometimes its problems

i had to do some classification in my algebra exam

if you struggle, they abandon and ask easier stuff

[limber perch]

each theorem is like

[surreal sapphire]

but if you dont struggle, they will ask harder and harder stuff

[limber perch]

here are 5 logically equivalent statements

[surreal sapphire]

but you just talk about how to approach the problem

[limber perch]

so it’s more a combining of multiple results

[surreal sapphire]

solving it is (often) secondary

in my number theory exam i couldnt answer some question but i told him what i expect and that i would have to check

i did check and my expectation was (mostly) correct

he really liked that

[fast ivy]

Oh, that's what I had somewhat in mind what an oral exam would be like.

Still

Looks like utter pain

[surreal sapphire]

this gives some appreciation for the mathematicians and also puts it into historical context

as soon as your theorems were proved like after 1930, you are doing big boy math

🤷

to me oral exams are like talking with a colleague

[fast ivy]

I have some anxiety problems

Also

Quarantine just made it worse

[fast ivy]

[surreal sapphire]

i had some online oral exams via zoom

that was horrible

[fast ivy]

I think the newest theorem I know so far of is like Cartan-Serre