serious-discussion

[neat frost]

uwu :3 ❤️💙💚💖

[deep mango]

I dont wanna go out into the cold

[neat frost]

HA

[deep mango]

I need to go to a covid test

[neat frost]

Imagine living somewhere where it’s cold

Oh, why?

[deep mango]

It's 11 C now

Not that cold

[deep mango]

NYU selected me for a randomized test

[neat frost]

FUCKIN 11?

[deep mango]

Yeah

[neat frost]

It was like 30+ the other day here

[deep mango]

Idk why its so chilly this week

[neat frost]

Awh shucks

[deep mango]

It was like 20 before

[neat frost]

Damn

Sucks to be an American

[deep mango]

A storm came through and brought in a cold front

[neat frost]

Oof

Storms

[deep mango]

I like storms

Actually this one was really bad

My mom almost got into a really really bad car accident

Like

So bad that I cant even really process it or be nervous about it because I will freak out

Sigh

[neat frost]

Ohno

She’s okay though?

[bright hill]

nothing lol

[neat frost]

You’re walking a fine line young man

[bright hill]

that might be the case

but I'm nimble af and luck is with me

[neat frost]

Nope

[bright hill]

I therefore give no heed to empty threats

[neat frost]

Wow

EMPTY

Wow

Watch yosef

[bright hill]

on that matter

I know where you live slurp ( ͡° ͜ʖ ͡°)

[deep mango]

Yeah everything is totally ok

Just like

2 super close calls within 5 minutes of each other due to the weather

[neat frost]

Wow

That’s scary

I’m glad everything’s okay though

[neat frost]

Pray tell little man

Tf autocorrecting man to mama

[bright hill]

I don't need to

besides, I have no means to get there anyhow (atm)

so you needn't worry

[modest rune]

Glad to hear shes all right

[sleek wing]

cope more heatcel

[modest rune]

imagine living somewhere cold or hot

San Diego perfect weather gang

[bright hill]

weak

[deep mango]

Yeah. she totally spun out on black ice on a (thankfully empty) highway

And then like

[modest rune]

holy shit

[deep mango]

Right when she regained control and got off to the side of the road a semi barreled through in the right lane

fucking moron

[modest rune]

insane

[deep mango]

no visibility, horrible conditions, 11pm, this guy is an idiot

[neat frost]

Oh my god, that’s insane! I’m glad that she’s fine though, that sounds really scary

[modest rune]

no visibility is so scary to drive in

like even if i trust myself

everyone else acts fucking crazy

the second it starts raining all drivers get a death wish somehow

[deep mango]

usually my modus operandi with these things is to get very angry about all the ways that this could have been prevented but obviously that's not helpful so i'm just trying not to engage with it

[modest rune]

this is one of those moments where I am worried i will forget whether I am supposed to turn into or out of the spin

[deep mango]

Yeah

I don't remember how to handle that

I mean

I haven't thought about driving since driver's ed

[modest rune]

Yeah and like, most importantly, your mom did everything right so its just like

a freak accident

[deep mango]

Yeah

[bright hill]

I'm glad it turned out ok

[deep mango]

Thank you, I am too

but in a kind of fucked up way

lol

[toxic schooner]

holy shit

slurp is very active

baseddd

[bright hill]

yeah, he got it the other day

[toxic schooner]

:(

[bright hill]

at the same time I got active, actually

[toxic schooner]

slurp wasnt very active yesterday

[neat frost]

Yesh I was

[neat frost]

[deep mango]

Shashwat are you ok

[neat frost]

Why would he not be

[toxic schooner]

i dont remember u being active yesterday

well then again

my yesterday ended what

,ti

[fathom swallow]

The current time for Samsyet is 09:25 PM (IST) on Wed, 20/04/2022.

[toxic schooner]

21 hours ago

[toxic schooner]

yeah i am

lol

[neat frost]

I became very active 2 days ago

[deep mango]

fuck

i was asking if shyshu was ok cause i was gonna claim that slurp has been very active for 2 weeks

i wasn't fast enough

[neat frost]

ooof

I’m sorry

I messed that up

[deep mango]

it's ok

[neat frost]

I regret that

[deep mango]

i shouldn't be gaslighting our users

[neat frost]

A good trolling is always fun

[neat frost]

Wtf no ryc, that’s exactly what you should do

[sick burrow]

smh ryc gaslight isn't even a real word

[sleek wing]

past tense of gaslight is gaslighted

it cannot be a real word

[waxen lily]

no way

gaslit

,w gaslit

[fathom swallow]

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

Requested by DETOX#0236

[waxen lily]

,w gaslighted

[fathom swallow]

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

Requested by DETOX#0236

[waxen lily]

ok neither are a real word

[sick burrow]

🤓

[waxen lily]

thts dum

[clear parcel]

actually that’s a very interesting caveat of the English language

[static loom]

this is all a huge conspiracy to gaslight you into thinking the past tense isn't gaslit, wake up sheeple

[clear parcel]

there are other words that do the same thing

[pale orchid]

everyone knows the proper conjugation is gassedlight

[clear parcel]

apparently physics majors have higher average iq than math majors by 2 points

[bright hill]

iq again

[neat lintel]

That wouldn't surprise me

[sleek wing]

gaslit is the past tense of the adjective "gaslight", gaslighted is the past tense of the verb

[clear parcel]

I think it’s prob because math is taught in elementary and middle school while physics isn’t

[pale orchid]

if you lower the temperature or increase the pressure enough, you can alternatively use liquidlight

[clear parcel]

so there are ppl majoring in math but really it’s just like to teach addition etc

[bright hill]

poor wew

didn't get to gaslight anyone

[sleek wing]

sure I didn't

[bright hill]

[neat lintel]

I think it's easier to escape into math than into physics

[brave hollow]

escapism

[sleek wing]

why do you need escapes when you can just disassociate continuously

[brave hollow]

wew "midlands" tbh

[bright hill]

is it possible to learn this power?

[torn willow]

Ah yes,My 2 DID personalities: One who likes doing math and one who does physics

[sleek wing]

you don't want it

it's like the hit film "Morbius (2022)"... the power comes at a great cost...

[clear parcel]

LOL

[sick burrow]

Morbius's power is he's a non orientable surface when he takes his clothes off

A Morbius strip

[sleek wing]

Homorbiusism

[lunar spear]

Any electrical engineers or engineers in general here?

I wanna know what it's like

[surreal sapphire]

i think there is an electrical engineering discord linked in #old-network

there is indeed @lunar spear

[lunar spear]

Ight ty

[clever sapphire]

verifie that a²|b² => a|b (a,b) in N*²

[fresh oriole]

it might be overkill but the fundamental theorem of arithmetic should make that clear

[primal seal]

My proof for this is posted elsewhere but I have a general question regarding the problem type

I often don’t know where to “begin” imposing the conditions. That is, should I consider conditions on V? W? The S’s?

Is this just a matter of grappling with the problem?

[modest rune]

yeah

[sleek wing]

V and W I'd imagine

[modest rune]

the only trick to it is intuition

[neat frost]

Start just making observations

Like you can scale S and it’ll still span W

Things like that

[primal seal]

Yeah okay, that’s what I did

So I’m just slow because I’m New

[neat frost]

And you can add vectors to S, etc

[modest rune]

yes

you will always be slow at math that is new to you

thats just how it is

[primal seal]

🙏 thanks guys

[clever sapphire]

to verifie that a|b => a²|b² is normal but from the other side idk how

[primal seal]

Eh still quiet over there

Well just to confirm, I came up with this:

[sleek wing]

4 phones....

[neat frost]

Is this related to your previous q?

[primal seal]

🤣

[primal seal]

It’s the attempted proof

[neat frost]

Proof of what? They’re asking a question, not asking for a proof?

[sleek wing]

hi

[primal seal]

The proof states the conditions and proves the result using them

[neat frost]

So by W = S1 + … + Sn
You mean W is the sum of n subspaces of W?

[primal seal]

No just the sum of the subsets

[neat frost]

How are you defining the sum of subsets?

[primal seal]

They way they always are

[neat frost]

[primal seal]

At least the way he did previously

[neat frost]

I’m not sure it’s really defined…

[neat frost]

And in any case, assuming that it is, the claim you made is false

[neat frost]

Those are sub spaces

[neat frost]

Take two subspaces W1 and W2 != W such that W1 + W2 = W. But the span of W1 and the span of W2 are W1 and W2 respectively, and they don’t equal W

[sleek wing]

I do have to point out it is defined for general subsets slurp

[neat frost]

Ah

Yes

I misread

[bright hill]

how do I stop feeling I'm going too slow?

[neat frost]

I was looking at the problem not the definition, my bad

[bright hill]

it's quite annoying how disappointingly slow I am sometimes

[neat frost]

But nevertheless, this is still a valid counter example to your claim

[neat frost]

Learn with someone dumb, like yours truly

[neat frost]

But like unironically

[primal seal]

Processing this

[bright hill]

and never forget to tell them how faster you are compared to them

[neat frost]

No

[bright hill]

just to make yourself feel good

[neat frost]

You gotta make them feel welcomed as well so they don’t leave you

You make fun of them after the fact

Rookie mistake

[bright hill]

that's great thinking

[neat frost]

I know I have experience

[bright hill]

bruh, lmao

are you learning anything in particular atm, slurp?

[neat frost]

Atm atm or like during this period of time?

[primal seal]

I’ve imposed the condition that the spans are pairwise equal though

[bright hill]

this period of time

[neat frost]

Wdym?

[neat frost]

Well yeah… I have my uni courses

[primal seal]

It’s in the proof

Your counter example doesn’t account for that

[bright hill]

I thought you were in HS

[primal seal]

Span(W1) would have to equal span(W2) in your case

[neat frost]

Yes

Okay

So fine

But uh how does this help you answer your original q?

[neat frost]

I am..?

[bright hill]

anyhow, what courses are you taking

[neat frost]

Calc 2, prob and stats

[bright hill]

hmm, that's good

I've been setting aside prob and stats for a while now

[primal seal]

I’m just looking for confirmation that the conditions I express satisfy what the problem is asking for

[bright hill]

maybe after calc3

[neat frost]

But what are your conditions, that W can be written as the sum of n subsets which have the same span?

[neat frost]

All calc boring

[primal seal]

That’s one; the other is that the spans of the $S_i$ are pairwise equal

[fathom swallow]

LosAngeles

[primal seal]

But that’s only needed for one direction

[neat frost]

Right

But I think

You may be overthinking this

There’s a much simpler condition

[primal seal]

There may be, but if it involves bases and linear independence and such it’s just that it hasn’t been covered yet

[sleek wing]

it does not

[primal seal]

Oh ok, please then

[neat frost]

You want the answer? Or you want a hint?

[sleek wing]

actually yeah

which one

[primal seal]

Well I have an answer so I’ll take a hint

[sleek wing]

consider what happens when V is infinite (cardinality wise)

[primal seal]

Eh

[sleek wing]

oh and of dim > 1

[primal seal]

Could it really be looking for something like that in section 1.4?

[sleek wing]

I didn't say infinite dimensional

this is kinda just set theory

slurp give your hint boss

[neat frost]

Uh

I was gonna say that I’m shit at giving hints

[primal seal]

🤣

[neat frost]

And that I always just end up giving away the answer

But okay, maybe a bit more revealing of a hint, idk:
||Think about adding stuff to a spanning set||

[primal seal]

Am I wrongly having a hard time swallowing that something like friedberg would resort to cardinals for a proof this early on

[neat frost]

It’s not really cardinals

[sleek wing]

what?

bro what??

ghujysroygh

[neat frost]

Bro to me

Or bro to them

[sleek wing]

them

oh right cause I said "infinite" so you naturally assume I'm talking about some set theory nonsense, I'm not

[primal seal]

I am certainly a bro

[sleek wing]

it's just incredibly trivial when V or W is finite (there's only a finite number of distinct subsets in general let alone generating sets)

[neat frost]

Good, I was scared you were broing my hint and I was scawwwed

[primal seal]

Yeah I assume he’s not limiting it to finite cases or he would’ve mentioned

Is my means really that off-putting?

It’s just saying a vector in W can be made by a combination in any of the S_i’s

[neat frost]

Well yeah if he was, the answer would be trivial

[sleek wing]

anyway slurp what's ur hint

[neat frost]

This was my hint

It’s not very good

[neat frost]

But like what if you just take S1=W, how does that prove anything?
Sorry I’m still confused what exactly you’re trying to show with that proof

[primal seal]

Don’t forget you can have only finitely many S

You definitely could

[neat frost]

Exactly the point is to think when you can make infinitely many

[primal seal]

Then you’d just take the cosets of the W quotient space?

[sleek wing]

ok as I'm writing my proof out I realise it's probably overly complicated

oh well

actually I've accidentally proven a stronger result

slurp post your solution lmfao

[neat frost]

Uh

[primal seal]

Is the question asking what conditions RESULT in finitely many subsets S?

If so I may have misinterpreted it

Guess everyone’s trippin

[sleek wing]

ok here's my probably wrong and overly complicated solution
||dim W = 0, trivially true as W is finite. Let dim W = n > 0 and W infinite (as finite W is again trivial), then there exists a basis set of vectors {x_1, x_2, ..., x_n} which generate W, however we can swap out any x_i with any other vector in its span and you get another basis set (this is just a change of basis in W), but at least one of these spans has to be infinite (as W is infinite) so we have infinite choices for one of the x_is, and thus infinite basis sets, and thus infinite generating sets - so W is finite implies there are finitely many generating sets||

[primal seal]

Dawg dimension isn’t defined yet

[sleek wing]

I've got fucking no clue then

[primal seal]

Lol

[sleek wing]

that's like the main property of vector spaces

should be a page 1 thing ngl

[primal seal]

I know, I know about it that’s why this one stumped me a bit

[sleek wing]

I did say it was a stronger result

[primal seal]

That’s a Herculean result

I’ve got subsets and sums to work with lol

And spans

[neat frost]

Okay, so W has a finite number of spanning subsets if and only if it itself is finite.
It is obvious that if W is finite, it has finite subsets, thus finite spanning subsets.
If W is infinite, then there must be some spanning subset S such that W\S is infinite (because spanning sets are defined as finite I’d assume right now for you), so then you can take any vector from W\S and add it to S and that’s still a spanning subset. There are infinite choices for this, so there are infinite spanning subsets.

[primal seal]

My result holds if W is infinite though

[sleek wing]

"If W is infinite, then there must be some spanning subset S such that W\S is infinite"
is this true?

I'm thinking like

[neat frost]

I’m assuming finite dimensions

[sleek wing]

uncountable dimension and countable S

ok but the question doesn't

[primal seal]

Look, imagine W is 2 space

[neat frost]

But this is like introductory LA

[primal seal]

So infinite

[neat frost]

Everything is finite dimensions

[primal seal]

I can divide it into quadrants

[sleek wing]

if they wanted finite dimensions they should've specified

[primal seal]

The span of those quadrants is W

And equal each other

That’s what my proof shows

[neat frost]

You assumed finite dimensions as well though?

[primal seal]

Guys that shit isn’t even defined yet

[sleek wing]

there's nothing saying the basis set had to be finite

I just couldn't be bothered to write it

you can just replace {x_1, ..., x_n} with {x_i}_{i \in I} for your favourite indexing set I

[neat frost]

Ah okay

[sleek wing]

and assume choice, of course :trollshiro:

[neat frost]

But

[zenith tinsel]

just assume everything

problem mathematic?

[neat frost]

Hmm

[zenith tinsel]

https://tenor.com/view/troll-troll-face-ragememe-rageface-trolling-gif-4929853

[sleek wing]

look in the back of the book and post the answer

I have no idea what you mean by a "2 space"

[primal seal]

Good call

Haven’t looked yet

Annnd of course it’s not

[neat frost]

This is probably a fine answer

No dimensions

[primal seal]

2 space is Euclidean 2 space

[sleek wing]

and how are each of the "quadrants" W, you can't just partition V arbitrarily and get a subspace

[sleek wing]

ok so R^2

[primal seal]

They’re not subspaces

They’re subsets

[sleek wing]

W is a subspace

[primal seal]

W is

S are not

[sleek wing]

oh ok you're partionining W into quadrants

[primal seal]

Yes

Or any way you like

But they must sum to W

And be finitely many partitions

If you assume the partitions’ spans are pairwise equal

We should be good

I feel like I’m crazy

[sleek wing]

I'm wacky!

[neat frost]

Oh also wew, it’s obvious that there must be some spanning S such that W\S is infinite if W is infinite.
Take a basis, and choose a vector v in it. Then you take the set v + S, and that must be distinct from S. And it’s a subset of W, and it has the same cardinality as S, so if S is infinite then W must be as well (since v+S has the same cardinality), and if S is finite, W\S must be finite

[sleek wing]

yeah didn't follow a word of that

I'm so tired man

[neat frost]

(By obvious I mean obviously not me because it took me like 10 min to come up with that)

[primal seal]

Lol

[neat frost]

I just found an injective function from S to W\S

[sleek wing]

oh ok

this convo man jesus

octupled my impostor syndrome in the past hour

[primal seal]

This got intense

Took me longer than I’m willing to admit

[sleek wing]

it really shouldn't've been though - your proof was perfect from the start

[primal seal]

Kinda makes me feel better

[primal seal]

Me or him?

[sleek wing]

you

[neat frost]

Oh?

[primal seal]

Oh ok

[neat frost]

Wait now I need to reread his proof

[primal seal]

🙄

Maaaan

[sleek wing]

of course just take W infinite and cut it in half and you can just keep cutting it in half over and over again and then union back up into a 2 set partition

infinite possible ways of doing this

and the finite case is trivial

[primal seal]

Right

[sleek wing]

elegant

[primal seal]

Welp

There’s my last 24 hours

[neat frost]

wew could you explain their proof then? Because I don’t understand how
A) this answers the original question
B) this is related to what they wrote before

[sleek wing]

they need to find infinite generating sets right slurp

[neat frost]

Yesh

[sleek wing]

hold on

does the set of "half" the vectors (assuming choice) always generate the space

[neat frost]

I’m not sure? Probably

[sleek wing]

yeah probably

it definitely does for finite dimension

[neat frost]

Uh well

No

[sleek wing]

fuckin infinite dimension cases

[neat frost]

It doesn’t

Yeah

[primal seal]

We are in finite dimension

[sleek wing]

this is why I work with finite groups, slurp
I hate infinity SO much

[neat frost]

Because the span of a single vector can have the same cardinality

As the vector space

Wait so not even infinite dimension?

[sleek wing]

wait

how the hell do we formalise this idea

without just using a fucking basis like any sane person

because we're basically proving this for a general module

[neat frost]

[sleek wing]

ok maybe declaring that S+W/S = W works

no again only finite cases

I literally do this for a living I'm so pissed at myself why can't I do this

[neat frost]

It’s like past midnight for you no?

It’s fiiinee

[primal seal]

Lol

Honestly I think it actually hurts this problem viewing it from an advanced perspective

[sleek wing]

hold on you have direct sum defined

[primal seal]

Yes

Could be replaced but isn’t needed, right?

[sleek wing]

again I'm wanting to use a way more powerful theorem to do this

[primal seal]

Yeah that’s what I’m saying

Problem makes you want to jump the gun

Why it took so long for me

Do undergrads really get assigned this?

[sleek wing]

this is first year

[neat frost]

This is a perfectly simple solution though
Also LosAngeles, is there a solution in the book?

[primal seal]

There is not

[sleek wing]

my solution is perfectly simple

[neat frost]

But

Does it work?

[cyan goblet]

the proof is trivial

you can utilize theorem 4,

[neat frost]

I will utilize your mom

[cyan goblet]

anything ana"ψ(x) = Ce^-βx + De^+βx"mono says is trivially true is trivially true

and i say that this is trivially true

therefore it is trivially true

QED

[sleek wing]

any surjective projective map f : V -> W will decompose V into ker f direct sum W and then we can just map a generating set of V through this map into W and thus reduce the problem to just thinking about V

which is far easier for me to visualise

[neat frost]

I think wew…

[sleek wing]

but no can't do that

can't actually use things to solve this problem can I

[neat frost]

I think you may be trying to kill an ant with a nuke

[primal seal]

Lol

[cyan goblet]

sometimes you gotta do that

[neat frost]

Ants do be scary, I give you that

[sleek wing]

you wanna see me kill an ant with a nuke, shuri

[cyan goblet]

wew i tihnk you should know

ive been laughing at this for the last 10 minutes

[neat frost]

Shuri?!

[sleek wing]

I will use character theory some how to solve this problem

you've all got the SAME FUCKING NAMEEEEEEEEEEE

[sleek wing]

thanks

[cyan goblet]

of course

[neat frost]

YEAH BECAUSE SHURI MADE ME

[cyan goblet]

you should do math standup

[neat frost]

I’m so hurt

[primal seal]

I’m gonna bounce y’all

Thanks for the chat

[sleek wing]

oh no you don't

[primal seal]

Appreciate it

[cyan goblet]

please dont bounce me

[neat frost]

My solution is perfectly perfect and I’ve gotten 0 validation

[primal seal]

No

[neat frost]

What is even the point

[primal seal]

I mean I’m bouncing

[cyan goblet]

oh

at what bar?

[primal seal]

Lol

[brave hollow]

what problem are you guys solving?

[neat frost]

ITS SOLVED

[sleek wing]

got it

[brave hollow]

what problem did you guys solve?

[sleek wing]

wait fuck is span defined

[neat frost]

Wew is just trying to nuke the remains

[neat frost]

Yes

[primal seal]

Yes it is

[sleek wing]

good

[primal seal]

Let’s see it

Since mine isn’t good enough lol

[neat frost]

@brave hollow

[sleek wing]

let S be the span of a single vector in W, which we're assuming to be finite, then W = S + W\S

[cyan goblet]

just couldnt resist the urge to use direct sum huh

[neat frost]

Blunder

[sleek wing]

there are infinite choices of S, thus infinite choices of W\S

[neat frost]

I saw that blunder wew

[sleek wing]

I forgor 0 isn't in W\S ok

[neat frost]

Okay

Go on wew

[sleek wing]

what you mean go on

[neat frost]

How does that solve anything

[sleek wing]

it solves it all, shuri

[neat frost]

Fuck you im not Shuri

[sleek wing]

now take your original vector v that generates S

[neat frost]

And shove it up my ass?

[sleek wing]

{v} U W\S generates the whole space

[neat frost]

Yes

[sleek wing]

tada

[neat frost]

Oh

I see

[primal seal]

Yup

[neat frost]

But

You are

A wee bit

[sleek wing]

there are no buts this time buster

[neat frost]

No

[cyan goblet]

damn i need to go back to learning lin alg

[neat frost]

Z2

[cyan goblet]

i forgot what generating means again

[sleek wing]

it's the whole thang

[neat frost]

Z2

[sleek wing]

the whole gosh dang thang

[neat frost]

Or any finite field

[sleek wing]

what ABOUT Z^2

[neat frost]

Span(S) can still be finite

[sleek wing]

no problem my friend

all we need is infinite choices of v

[neat frost]

WAIT A SEC

ITS ALMOST LIKE

THIS IS MY FUCKING SOLUTION

Just worse

Or better

[sleek wing]

my solution only uses the pieces provided

[primal seal]

So what exactly are your conditions?

[sleek wing]

which was the actual issue

W is infinite that's it

only condition

[neat frost]

No

W is finite

[sleek wing]

oh yeah

[neat frost]

Then you have finite

[sleek wing]

contrapositive

flip flop the switch swotch

[neat frost]

This is literally what I fucking said an hour ago

But nooooo wew has to do fucking character theory or some shit

[sleek wing]

yes shuri the problem was NOT that we didn't have a solution you knucklehead

[neat frost]

No

The problem was that

[sleek wing]

it's that our solution was too advanced by some weird metric

[neat frost]

NO IT WASNT

[primal seal]

Actually

Yeah kinda

[neat frost]

It was perfectly perfect

Don’t fucking disrespect my solutions

[sleek wing]

as was my first one

[modest rune]

what is going on here

[cyan goblet]

complicated solutions stay losing!

[sleek wing]

we're trying to prove a basic lin alg result using nothing but set sums and spans

[primal seal]

Just changing a lightbulb

[neat frost]

Oh wait wew

[sleek wing]

wot

[neat frost]

Oh nvm

[sleek wing]

finite dim over finite field?

[neat frost]

No

I thought there may have been a flaw

But no it’s fine

[sleek wing]

cool

[neat frost]

Still

My proof is better

[modest rune]

The solution to 15 is like one line unless Im losing my mind why is there so much convo about it

[neat frost]

It is!

Wew is just fucking insane

[sleek wing]

we can literally only use spans and set sums max

and the cardinality of W I guess

I proved it ages ago using basis sets and dimensions

[primal seal]

That’s not needed either I’d argue

[sleek wing]

but they weren't covered in the book at that point

yeah

turns out, they weren't

[neat frost]

I proved it ages ago without that shit

My proof was perfectly within whatever conditions required

And still. 0 validation.

[cyan goblet]

am i losing my mind or does basis define dimension

[sleek wing]

it do

[neat frost]

Why do I even come on this server if I don’t even get validation

[primal seal]

Basis is undefined also

[neat frost]

Answer that wew

[cyan goblet]

y we using dim without basis then

so weird

[sleek wing]

we're not

[neat frost]

We’re not

[cyan goblet]

weird lin alg book

ye but like

the book

[modest rune]

Let S be any spanning set and let k be any element of the underlying field. Then kS is a spanning set distinct from S unless S is just 0. So we either need S=0 or finitely many choices for k. If there are finitely many choices for k the vector space has finite cardinality and we are done.

[cyan goblet]

teaches dim without basis

or i guess basis comes later

[primal seal]

It’s friedberg lol

[modest rune]

(all vector spaces assumed f.d., you can drop that assumption with one more sentence of proof)

[neat frost]

This isn’t a strict enough condition

Actually

[modest rune]

What on earth do you mean lol

[sleek wing]

the question didn't specify finite dimensions so I didn't assume it

[modest rune]

Vector space usually means f.d. in intro texts

Again not hard to fix

[primal seal]

It does here

[modest rune]

cool

[neat frost]

Wait am I being fucking stupid

Don’t answer that

[brave hollow]

what is the problem with that condition slurp

[modest rune]

My condition is sufficient and necessary. Cleary its true if W is the 0 vector space and clearly its true if we are f.d. over a finite field

[cyan goblet]

"sufficient and necessary" is such a funny phrase

[neat frost]

You can have finite choices for k and still have infinite spanning sets, no?

[modest rune]

No

[neat frost]

No?

[modest rune]

If you have finitely many coefficients you are over a finite field

[primal seal]

@modest rune can you look over mine please? Less elegant but hoping also plausible

[neat frost]

And the vector space can still be infinite?

[modest rune]

any f.d. vector space over a finite field is a finite set

[neat frost]

No?

[modest rune]

I said finite dimension like 6 times

Yes

[sleek wing]

so glad someone who actually knows what they're talking about is here lol

[neat frost]

But we’re not assuming finite dimensions?

[primal seal]

You guys don’t??

[neat frost]

Because we haven’t assumed finite dimensions

[modest rune]

one, the textbook LosAngeles is using does make that assumption

as any reasonable LA text does

[neat frost]

Oh that’s what f.d means

[zenith tinsel]

what is written in (=>)

wtf

T\piZVZAL

[cyan goblet]

focal distance vector space

[modest rune]

I'm not sure what the notation means LosAng

What does W=S1+...+Sn mean

[primal seal]

Subset sum

[modest rune]

This should not be true

W={0}+W

but {0} doesn't span

[primal seal]

Subset

Not space

[neat frost]

They’re requiring it to span I think

[modest rune]

Spanning is the conclusion...

{0} and W are both subsets

I am not sure if I am misunderstanding you

{0}+W is the set of elements w+0

where w is in W

[primal seal]

Right

[modest rune]

i.e. all of W

but Span({0}) is not W

[primal seal]

But I impose the condition in the second direction

On the subsets’ spans

[modest rune]

I'm very confused now

[sleek wing]

I believe he means the union of the all the Si?

[modest rune]

The assumption is just that W is a subset of V

for one direction we then assume that W has finitely many spanning sets

But they don't have to interact

[primal seal]

Right

The sets don’t

The spans do

[modest rune]

The spans don't either

We are claiming two things, in effect

[primal seal]

I enforce that as a condition

[modest rune]

1. There are sets S_1,....,S_n such that Span(S_i)=W

2. If Span(X)=W then X=S_1 or S_2 or ... or S_n

I don't see how this is related to what you write

[primal seal]

I’m saying we divide W into a finite number of (distinct) subsets

[modest rune]

Okay

[primal seal]

Such that the subsets’ spans are each pairwise equal

[modest rune]

Okay Im with you

[primal seal]

Then it follows that each S_i generates W

[modest rune]

Sure, by assumption

[primal seal]

Yes, the question was about establishing those conditions

Which I have now confirmed(?)

[modest rune]

I am not sure how these assumptions will interact with the problem

[primal seal]

The assumptions ARE the problem

It’s asking what assumptions you need

[modest rune]

Ah, your claim is that the only possible way for this to be true is to be able to divide W in such a way

[primal seal]

I’m claiming it’s one such way

[modest rune]

Oh, then again I don't see how it relates to the problem because the problem asks you to classify all of them

[primal seal]

And suppose I were saying it’s the only?

[modest rune]

I would have to think about whether its correct

[primal seal]

Ah

This is what motivated my question hours ago

Wasn’t sure how to look at this problem

[modest rune]

Are you assuming S_i is finite

[primal seal]

No

The number of S_i, yes

Cardinality, no

[modest rune]

Oh then its certainly not correct. Let R be the real numbers. and let V=W=R. Then choose S_1=W. Let's check our assumptions. One, S_1 contains all of W, clearly. Two, the span of S_1 is W, also true. But W doesn't have finitely many spanning sets

[primal seal]

I could make two though

[frozen merlin]

is V a real vector space? or is this over an arbitrary field

[modest rune]

Okay let me just clarify something to make sure we understand eachother because one of us is confusing the other lol

[primal seal]

Yes please

You didn’t need your last line, you showed it had one- span(S_1)

[bright hill]

this is still going?

[modest rune]

Let us say that a subspace $W\subset V$ satisfies property $P$ if $W$ has finitely many spanning subsets. Let us say a subset decomposition of $W$ is a sum $W=S_1+...+S_n$ where each $S_i$ spans $W$. My understanding is that your claim is that $W$ satisfies property $P$ if and only if it has a subset decomposition.

Is that correct?

[fathom swallow]

i_hate_printers

[modest rune]

Having one isn't enough

you need infinitely many

[modest rune]

sometimes problems take awhile

this is not awhile

[primal seal]

Yeah I agree with that

[modest rune]

Okay

Then my example above gives you a counterexample.

R has a subset decomposition but does not satisfy property P

[primal seal]

Ah I see, I was looking at the problem the wrong way

I want a condition (on something) that forces the S_i to come out

In finite number

[modest rune]

I think you might be approaching it incorrectly

These spanning sets shouldnt interact with eachother necessarily

they could be disjoint

they could intersect

[primal seal]

Right right, they just need to span W

[modest rune]

yeah

[primal seal]

So I need to figure out how to break W down

[modest rune]

I think the idea here is to show concretely that its basically impossible

[primal seal]

Ah

I’ll try the reductio

[modest rune]

Are all your vector spaces over R

or are you allowing finite fields

[primal seal]

Not necessarily

[modest rune]

okay any field?

[primal seal]

It usually indicates any restriction

Yeah

[modest rune]

okay

Here's a hint

assume that the field F is not finite first

and show that it is only possible if W is the 0 vector space

You can do this by starting with a very nice spanning set, and using F

also, we should move to #linear-algebra

[primal seal]

Ok

[fervent pebble]

ayyy lagrange error shit makes sense now 👍

and all it took was one yt video to explain in ten minutes what my teacher couldn't in days

[viscid sun]

Whats more worth it, going to a top 50 uni or a top 10 uni but 1 year older

[empty stratus]

Top 10.

[viscid sun]

ok I believe you. But why is that? I really cant grasp the rankings, they seem so arbitrary, I cant quantify them so I cant make decisions based on that

[empty stratus]

It's more about what you want to do for yourself.

[primal seal]

Is this for undergrad or grad?

[viscid sun]

this is for applying to university, so undergrad yes

[viscid sun]

Well, I am considering the perspective of academics, finance and opportunities

[charred mortar]

Also depends on whether there’s some stuff you’d want to do in that year

[primal seal]

My opinion tends to be an unpopular one, but undergrad rankings never seemed to be as meaningful as they’re made out to be

Grad, definitely; undergrad, to me, not so much

[velvet dagger]

Undergrad rankings matter a fair bit but in a complicated way imo

[primal seal]

Yes. I can agree to that

[velvet dagger]

Overall, better ranked university is correlated with higher quality peers, better opportunities

This is not something you can apply too specifically. X university is ranked 5 slots higher than Y university so of course X is better

[primal seal]

True, but a great student on paper will usually outweigh a good one on paper from a higher ranked school. Two great students they may consider where you attended (among other things)

[viscid sun]

yes but I want to account for time. Is choosing the better uni still a better idea even if I lose a year. Of course we are talking top 10 to top 50 which is somewhat of a diffeence

[velvet dagger]

Well I'm considering the student to be held constant LosAngeles, since I'm taking it from the point of view of deciding which to go to

[primal seal]

That said, then yes

[velvet dagger]

Scandinavian it's hard to talk about things much in the abstract because there are a lot of confounding variables

[near fox]

if anything, I'd even say that being slightly older is better for university. I think when I was slightly older, I was simply better at focusing on work, being patient, and retaining information

[velvet dagger]

For example, money might also be a factor. Top 10 schools generically have better financial aid than top 50 schools, unless you get merit scholarships or are at an in-state public university

Maybe flexibility of the department or the specific structure of their course layout is a factor. UChicago was better for me than, e.g. Berkeley would've been, from the pov of accelerating as a math major

[primal seal]

You should definitely also make sure you can evidence what you used that year away for, if you do; because an undocumented year can also look bad on your app

[velvet dagger]

Because they have the honors calculus and honors analysis sequences, that are designed to take people with no background and get you very fast through proofs

So I didn't have to sit through Calc 1-2-3

You wanna make sure you're doing stuff in that time. You wanna consider the finances, and you wanna consider the details of the places you're thinking of

Also when you say top 10 in a year, do you mean you're gonna apply again for top 10 and fingers crossed? Or are you effectively guaranteed it?

(Also top 10... in Scandinavia? US?)

[primal seal]

This I believe too

[viscid sun]

I probably should have elaborated more. I am in 10th grade( I skipped 9th to 10th this year) in Germany. I can finish my Abitur(German qualification) in 2 years and then all I need is 70% average in Math, English and Physics to get to ETH in Switzerland. What I could also do is try and do my A Levels until 2023 and apply in a top 50 German university like LMU or TUM and get in because there is just a C restriction for math and the hard part is really not failing the classes

[primal seal]

I’m surprised you’re using phrases like “all I need is 70%..” when you’re considering top 10 schools at all

[viscid sun]

It says it on their website

Here

[velvet dagger]

There's the bare minimum for consideration, and then there's being competitive. In the US there's def a gap there, not sure about Europe

[primal seal]

Yeah, I know.. I guess what I’m trying to say is… the problem seems to be with your ambition

Not trying to sound like a dick, but you need to know you’ll be going up against the best

You can’t have a “settle for 70%” mentality

There has to be a cutoff somewhere, yes

[velvet dagger]

Fwiw I didn't interpret that as "I intend to coast to 70%" so much as

[viscid sun]

I am not, I am very very interested in mathematics and I always get 100% in math and physics, thats why I skipped the grade and I still get 100%

[velvet dagger]

"That's the bar I'll have to clear"

Or idk if I'm saying it well but

[primal seal]

Oh then I very much misinterpreted!

Sorry about that, maybe read it too quickly

[velvet dagger]

Like high schoolers to some degree have uni admissions as an endgame. So oh as long as I can pull this off I have at least cleared the entry requirement for X place, and thankfully that's not too difficult

Though my warning still holds, it might be that less than that requirement makes you ineligible for any form of consideration... but they still choose a subset of the acceptable applicants, so there's a much higher "effective bar"

Worth researching, esp since my impression is that ETH Zurich is an S tier school

(In my mind the best European places are basically that, Bonn, Oxbridge, and ENS)

Maybe throw in Poly as well? Idk Europe too well tho so I might be very off

[near fox]

I would strongly recommend the first option. Studying for longer before entering university is a good idea, and ETH is of course a great school. Also, since you are on the younger side, I think it is worth developing your mathematical skills at home for longer before you go to university.

[viscid sun]

Here in Germany and Switzerland you just need to make the requirements and you are in. They just try to make the courses harder so usually people with the bare minimum fail

[velvet dagger]

The UToronto approach I see

[primal seal]

Oh wow

That’s pretty interesting

That’s why I was confused

[velvet dagger]

Yeah so this changes the game a lot

If you can ensure yourself a slot at ETH Zurich I'd hard go for that, especially because you already skipped a year

[primal seal]

I would think there is definitely some considerable ‘weed pulling’ those first years, then

[velvet dagger]

Yea

[velvet dagger]

I think overall there's a rat race that's a bit hard to avoid, the sentiment is oh the sooner I can get my degree the better. But really for the most part, there's not a massive difference. Timers start after school is over more than before

And if you already skipped a year then going to college young can be somewhat disadvantageous. I'm not familiar with Europe unfortunately, but in the US being 17 years old in college feels like it can be mildly annoying since you're not legally an adult

And ideally you'd use the extra time to level up

[cyan goblet]

you also mingle around with people who are older than you

so if you're looking to spend time with people your age, it may be an issue

[primal seal]

What @near fox said above too; you’re human and more wisdom and maturity in general come with age

[viscid sun]

These are good points but Im really much more interested in academic benefit in broadening my mathematics

I think though I have alredy done calculus, analytical geometry and linear algebra and trying to learn some real analysis. So that is the reason why I am trying to rush going to university

But I find other subjects painful and annoying

[velvet dagger]

I mean the point I was making was, oh losing a year isn't as bad of a cost as it sounds, given the benefit of ending up at ETH Zurich

Do you know if they're flexible with courses?

e.g. will they let you skip intro stuff if you know the material already?

[viscid sun]

I havent found anything on their website

[velvet dagger]

I'm not sure if anyone here goes to Zurich or not tbh

Anyway this info can be acquired and I'd recommend doing so somehow

[brave hollow]

little narwhal goes to zurich I think

[near fox]

I can give some advice from my own experiences. It is not worth skipping too much material. In terms of standard classes, the goal here should be to master the fundamentals, not to take as many math subjects as possible. To master the material it is always worth going over the material again a second time, maybe even a third time. I was a very advanced math student when I was in high school and I still found it very valuable to review everything again, when I went to university.

[velvet dagger]

Perhaps, I guess my bringing up this point has a bit to do with the fact that I feel like I'm sorta behind now in my PhD

End of third year and don't really have any research going yet. My advisor had a problem in mind that he gave a couple months back but I wasn't vibing with it so over the summer we'll try a different direction. But yeah I felt like this should've been happening over a year ago. Part of it was stuff like burnout and covid for sure

But I guess I sorta felt like I had a bit of a late start, especially given that I ended up doing number theory

[near fox]

Ah I see. That does suck, but usually even in graduate school you'll take a bunch of foundational classes again, right?

[velvet dagger]

I came into college pretty much having had, let's say something homotopic to AP Calculus AB background. Thankfully Chicago had the honors calc/analysis sequences

Which really helped me speedrun a lot relative to if I had to sit through the non-proofsy calc 1-2-3/linear algebra/ODEs before really getting into proofs

But then I still only took e.g. algebra in my third year

It was fine by something that you could call the standard timeline, e.g. I was able to knock out the algebra qual here immediately. But I feel like given how competitive number theory seems to be at this point, you wanna be way ahead of that

[near fox]

I guess I see your point, but even taking algebra in the 3rd year does not seem so bad tbh. Most graduate students I know mostly came in to their programs with just the basics (e.g. perhaps a year of algebra, analysis, and topology each)

[velvet dagger]

Yeah that's I think the standard, I guess I just felt like for my area in particular you wanted to be a fair bit ahead of that. I guess time will tell lol

[near fox]

I agree that number theory, algebraic geometry, arithmetic geometry, together those subjects do require a fair bit of foundational preparation.

[velvet dagger]

Yup

So it goes lol

[sonic timber]

sqrt(cos(x))cos(300x)+sqrt(abs(x))-0.7)(4-x*x)^0.01,sqrt(6-x^2),-sqrt(6-x^2)from -4.5 to 4.5

[devout nacelle]

[untold sparrow]

i am somewhat worried about this
i think i might want to go into AG
but feel like i don't know anything about AG compared to everyone else

i also have to study for quals first before i take another crack at hartshorne

[near fox]

cute

[sonic timber]

^^

[cyan goblet]

i one up you

[primal seal]

@velvet dagger is there financial incentive for you to finish sooner, or do you feel behind just relative to what you see/hear is the norm?

[cyan goblet]

,w ContourPlot3D[(x^2 + 9/4 y^2 + z^2 - 1)^3 - x^2 z^3 - 9/(200) y^2 z^3 == 0, {x, -2, 2}, {y, -2, 2}, {z, -2, 2}]

[fathom swallow]

Results provided by WolframAlpha

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

Requested by anamono#1010

[velvet dagger]

No I mean in the sense of, on a standard timeline of 5 years, usually you wanna start getting research to be competitive for postdocs earlier than I am

[primal seal]

So you feel it may look disadvantageous when it comes time to apply for post doc positions

[velvet dagger]

Yea

[primal seal]

I see

[untold sparrow]

do many people in NT/AG actually manage to get a lot of research done as PhD students? i thought spending a while getting up to speed was common in these fields

[velvet dagger]

Not getting good jobs is also common 😛

[near fox]

I feel this is premature optimization in some sense. The original poster was in high school and should not be thinking about what will optimize a math postdoc. He may not even decide to do a math postdoc.

[untold sparrow]

fair point

[velvet dagger]

Tbh I'm prob not gonna end up doing academia at this rate. My mindset has always been that I'm gonna go for it iff I feel like I'm gonna do well. If I'm just hanging by a hair then at that point I'll just go for industry

[deep mango]

i feel the same way

i don't even really know if i see the appeal anymore

[primal seal]

I’ve never understood academia for career unless you’re passionate about teaching

[velvet dagger]

It's more about research than teaching

[primal seal]

Industry funding is way higher and more flexible anyway

[deep mango]

i think teaching is fun

[primal seal]

Although, I speak from different discipline

[velvet dagger]

Basically the way I see it

[deep mango]

but i don't know if it's fun enough to overcome this

you can do research in industry

[velvet dagger]

If you like teaching that's good because unless you're cracked you'll be doing some amount of teaching

[primal seal]

Industry stress is brutal, yes

[primal seal]

Yes

[velvet dagger]

The main pull of research in academia compared to industry jobs is that you're working on stuff you wanna work on

[deep mango]

well, that depends on what you wanna work on

but yeah i would say that for you for sure

[worn garnet]

@velvet dagger had some experience industry can give some insight

[velvet dagger]

Well ryc what I mean is, if you're interested in the types of problems that you'd be working on in industry research

Then I don't see a huge appeal to academia anyway

[deep mango]

yeah

i guess that's where i'm at

[velvet dagger]

Unless you like the teaching element or the idea of tenure

[deep mango]

yes

[velvet dagger]

So better way to phrase it is

[worn garnet]

I'm heading to industry back to grad school then industry again

[velvet dagger]

"The main benefit academia has over industry, if applicable, is that academia gives you freedom to work on your own problems"

[worn garnet]

Hey with industry theres always time for side projects 🙂

[untold sparrow]

it's unfortunate that im terrible at everything that's used outside of academia

[velvet dagger]

Plus possibly the teaching or the tenure (though I doubt the latter counters the pay unless the relevant industry has really bad job security)

[untold sparrow]

maybe i should've actually learned more than the bare minimum analysis and probability I needed to get by

oops

[velvet dagger]

For me, as I see it, my research area is automorphic forms and now I'm hoping to pursue connections to Ramanujan graphs and the like

[worn garnet]

@velvet dagger look into places like this https://topos.site/files/topos_RSE_call.pdf

[untold sparrow]

but i like teaching enough ig

[worn garnet]

Topos Instutie is a prime example of an industry lab

[velvet dagger]

Part of me hopes that, well okay tech people kinda care about Ramanujan graphs I think? So maybe if I can't continue in academia I could try tech research. Obviously that'll prob be hard to get, and I'd approach it from a more CS angle than an automorphic forms angle, but it's still cool either way

[worn garnet]

Yes CS people do care about Ramanujan graphs 🙂

[velvet dagger]

So that would be a nice pivot possibility. Otherwise I'm gunning for quant finance, data science, or software development

[untold sparrow]

high school me was interested in cryptography
kinda wish i stuck with that instead of falling down the algebra rabbit hole

[velvet dagger]

Let's say more or less in that order. I'm not very well-prepped for those options yet, but I'm doing a data science boot camp in May

[worn garnet]

Your in good hands 🙂

@velvet dagger what places have you looked into ?

[velvet dagger]

Quant I can hopefully grind for, plus the data science camp

[worn garnet]

👍 Quants actually do get to do nontrival maths from what i've seen but mostly Analysis

[velvet dagger]

And then software dev... I'm not likely much of a candidate at places like MANGA unless I'm lucky, but I know at least one company in Madison that hires a bunch of software devs out of UW and they're doing well

Zophike1: I'm prob just gonna grind hard and then spam lol

[worn garnet]

I've been getting some offers but holding off till I finish

[velvet dagger]

SIG is one of the sponsors of that data science camp I'm looking at, corollary they probably like to recruit from it. Though it seems they pay less than e.g. Jane Street or DE Shaw

(then again I like the culture there and surely their pay isn't bad so...)

[worn garnet]

I thought about applying for the Topos Institute but I'm scared too I did apply for Chain-link labs but did not get a response 😢

[velvet dagger]

Main places that come to mind are like

[worn garnet]

which ones and also do they take fresh undergrads ?

[velvet dagger]

JS, SIG, De Shaw, Two Sigma, Radix, IMC, 5 rings, Hudson River

Idk about them taking undergrads straight or not tho

[worn garnet]

I know Finace cares for gpas and stuff like that

[worn garnet]

Has anyone seen this thread: https://academia.stackexchange.com/questions/55882/do-graduate-schools-care-more-about-my-grades-in-math-courses-or-my-general-gpa

[cinder zephyr]

they do for trade and SWE

Quant research roles out of undergrad wouldn't be unheard of but it is harder to get into

there is a decently good quant server if you want me to shoot you an invite

I want to get my PHD but quant research is probably my backup if I don't go into teaching

[worn garnet]

dosen't the finance side of things care about gpa and all that I heard there more stingy then the tech industry

[cinder zephyr]

they do

well idk about quant

I had a quant interview where my interviewer only had a GED

but was just mad smart (and of course knew some people but he was clearly extremely intelligent)

[worn garnet]

Places like DE Shaw I heard care about gpa

[cinder zephyr]

quant, for better or worse, seems to be one of the most meritocratic places in terms of hiring

yea DE Shaw and Citadel are pretty hardcore with that kind of stuff from what I've heard

[worn garnet]

I seriously wonder why A&H is soo emphasized up until your first gig in the US

[cinder zephyr]

I'm not an expect in what place has what culture tho (talking to people who work at those places would be the best bet, i.e. recruiters)

what is A&H

[worn garnet]

Arts and Humanities

[cinder zephyr]

oh

like gen eds?

yea idk I hate it lol

I get the argument but also ugh it's tedious

[worn garnet]

It seems like at least in the US it makes up the bulk of early education all the way to university

[cinder zephyr]

yea

[worn garnet]

I saw in the thread that I posted that Peter L Clark something he said stood out

Most academics take all academics seriously: generically speaking we are "overachiever types" across the board.

[worn garnet]

I remeber a guy named Erickson not taking is undergrad seriously but eventually succeeded in graduate school

[near fox]

In case it is relevant to some of you guys for the above discussion, I work as a professional mathematician in industry. The opportunities for this are not super high, but they exist. But of course, the nature of the research will generally be applied.

[rancid meadow]

whats the pay like

or is it all government stuff where ur hard capped

[near fox]

I work in the semiconductor industry currently, but my general research area is PDE, optimization, inverse problems. In my current work, I work on the mathematical analysis and general algorithm design for the rigorous PDE-based modeling needed for building computer chips, which is of course coupled with machine learning based modeling (not my main focus however). This is ultra high impact work --- slightly incorrect results from our PDE solutions can lead to huge problems in the semiconductor supply chain. And conversely, some of the advances of my team (but not me) are the backbone of some of the major advances in chip fabrication over the past 10-15 years.

If one considers theoretical CS people as some flavor of mathematician, then there is some need for those people too, though fairly limited, primarily in large companies like Microsoft.

For those who have more of a statistics/probability background, it is possible to transition to doing machine learning research at some of the many big software companies that do that. And I don't mean being a data scientist, but actually genuinely doing research in ML. However, to land such positions, you will likely need to make this transition while you're in grad school, and to find collaborations with people within those companies before you graduate.

In terms of more algebra/number theory sorts of research, the only areas I know for this are cryptography-related at government institutions. However, this is no longer nearly as active now as it once was, so I do not know if the opportunities exist anymore. During the cold war these things were far more popular. However, government institutions are always looking for mathematics people, but I don't expect that the type of research you'd be asked to do will be very theoretical.

[rancid meadow]

Thats so cool wtf

So do you do logistics stuff?

[wicked ore]

isogeny-based cryptography uses supersingular isogeny graphs which are ramanujan I believe, it's super lit stuff

[near fox]

No, I work on the PDE used to model the physics of semiconductor fabrication.

[rancid meadow]

You have a phd then?

[near fox]

I did my PhD in mathematics, and then also did a postdoc where I worked on inverse problems in earth sciences. I was somewhat interested in continuing along the earth science route, but this opportunity to work in semiconductors arose, and the work they do is mathematically very similar to my previous work.

I would go as far as to say that essentially it is impossible to work as mathematician without having a PhD, whether in academia or industry. Such jobs are already not very common, so given the competition there is rarely a need where an employer would go for somebody who has not had PhD-level training.

As for how to land such jobs...ultimately I think it comes down to connections, just like in all areas of life. You might know somebody previously in your school, or who worked with your adviser, who went into industry, and then they can refer you. This is mostly how it goes for our group. The people in our group have connections to academia, and when we hear that some new PhD graduate or current postdoc is on the job market, we look them up.

For government positions this is probably less the case, though my familiarity is only with one particular national lab, and there connections are definitely still very important.

[rancid meadow]

this seems like really cool work

I know the big chip manufacturers are super into formal verification stuff, that's probably closer to what I would want to go to grad school for

[near fox]

If you want to work on the more CS-y stuff, industry connections are really important to build during grad school itself. A lot of Google Research team members were basically already collaborating with Google while in grad school.

For Google, those grad students are basically like interns, and then they can hire them full time after they graduate, if their work is satisfactory.

More on the PDE and optimization side, I already mentioned the semiconductor industry, but other major areas of engineering also have some need for applied mathematicians, e.g. energy industry, aerospace

For those who are more on the topology and geometry side, there are some growing opportunities for applying that stuff, but only in national labs.

In terms of pay, the government/national lab jobs do follow some fixed pay grade, at least in the US and EU. In the EU the pay is not good at all I believe, but in the US I think the salary is OK. For reference, a position I applied for at a national lab in California, USA had a salary of 140k USD, and probably tops off at like 180k or something.

For private industry, your pay will depend on the industry. For engineering industries like my own, you will be treated like an engineer in terms of pay grade. This would still be significantly more than the salary of a government job in the US, maybe. For big software companies like Google or Facebook, the salary can be very high depending on if your area of research is highly relevant to their interests. Because if it is, they'll be willing to pay top dollar to retain you, or at the very least, to prevent you from joining the competition. One person in my field joined a research position at one of the major software companies and I believe his compensation was about 400k, and this was back in 2015 or so.

I know a fair number of people who also went into finance, but I do not think any of them do genuine mathematics in their work, more like data analysis and applied machine learning. But that can also be very high pay. I've heard however that if you want to make money in finance, you want to be a trader.

[primal seal]

The best part of the National labs is their resources, in my opinion. I’ve spent time in one (outside mathematics) and essentially anything you need that’s pertinent to your work they will provide for you at the blink of an eye, not hesitating the least regarding cost, availability, restrictions, anything

Your work sounds very impressive though

[near fox]

I was a little apprehensive about working at a national lab because the funding structure can be even more rigid. I would have to write research proposals more often than if I were at a university. And thank you, though I don't think I've actually mentioned anything about my actual work. I'm happy that I've been able to continue working on PDE though.

[velvet dagger]

Possibly, for now I'm just learning the arithmetic construction of Ramanujan graphs (Lubotzky-Phillips-Sarnak)

And my advisor said he'd talk to people he knows in the area to see what's up and to find a problem

[shut falcon]

Anyone able to help with proving Identitys??

[velvet dagger]

#❓how-to-get-help

[wanton marten]

would studying philosophy help getting deeper intuition in math?

i mean analytic philosophy not this postmodern bullshit

[neat lintel]

may be an odd question but aren't 92% of semiconductors in the world produced in Taiwan, or at least that's where the components are made? I think South Korea then produces 6% but I may be thinking of something else

[neat lintel]

I think the more you learn mathematics and physics, the more philosophical you become. They're both very analytical and logical subjects so it makes sense. So I'd say so yes

[shut falcon]

Yeah I tried that

[rapid folio]

I studied ethics and epistemology at university alongside the mathematics I was doing. I'd definitely say I'm more attentive to my own knowledge and my confidence in what I know. Which has the affect of me saying I know these things really well and then saying I know these other things not as well, but I'm getting better.

I know that overall that might not sound like a good thing because there's doubt in some spots of my knowledge, but my own confidence in what I know and what I can know to an even greater degree is really optimistic.

The philosophical methods of reasoning has 100% been useless in developing my problem solving and mathematical reasoning. There's even the whole philosophical study of mathematics that you can get into.

[wanton marten]

epistemology is a subject which i am interested in. I noticed that studying physics or chemistry made me connect some dots in maths. Altough I feel that math connect the dots on those subjects too.

[near fox]

The actual factories that produce the semiconductors, yes. However since I'm only working on the mathematical problems we can work anywhere

[median zinc]

For high tech yes, if you include more lower-end technologies it drops slightly

[rapid folio]

I'm in the camp of maths being the foundation of chemistry and physics. I've done some chemistry courses, but I'm only now doing physics in my own time and the mathematical background is priceless in understanding it.

But even all of that has come from knowing how I learn and how I can self-check that I do know something/I'm confident in my knowledge of something. That's been the effect of philosophy for me, getting me to really thinking about what I know, what I believe and what are the foundations of those things.

[median zinc]

Regarding epistemology I think there's a lot of valuable low hanging fruit if you go a bit into it, but it gets harder and I don't think you really need to go deep to get the most valuable ideas for yourself

[rapid folio]

Definitely agree with this 👌 my course went pretty far in, but what's stuck with me were some of the simplest ideas

[worn garnet]

Theres actually a lot of stuff in industry if you know where to look

[charred mortar]

Even without a PhD?

[worn garnet]

yeah 🙂

[charred mortar]

Huh

What sort of research jobs are available with just a bachelors/masters

[worn garnet]

https://www.indeed.com/viewjob?jk=4032322aa8493ce8&tk=1g161ejkhj46c800&from=serp&vjs=3

[worn garnet]

Have a look at anything cs basically

Theres also goverment work

[charred mortar]

This doesnt look like math bachelors tho

Moreso CS/engineer degree

[worn garnet]

@charred mortar https://jobs.lever.co/chainlink/53bbb447-181c-472f-b900-6d3550d95b70

[median zinc]

Fail job

It's always written LaTeX and not LATEX

[charred mortar]

Hm interesting

I guess there’s always some decent stuff if you search deep enough

[worn garnet]

Still theirs actually tons of math-cs jobs in industry 😉 that do deep and meaningful stuff

[charred mortar]

Yeah it’s quite a bit more than I thought

[median zinc]

This chat is turning

[worn garnet]

wdym ?

[arctic pollen]

Can a continuous polynomial function also be a piece wise function

Or are they two completely different functions?

[fair mural]

take two non equal polynomials with a zero at the same point

you can probably get it from there