#serious-discussion

1 messages · Page 519 of 1

worn garnet
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he could just define a piecewise function with polynomials over each of his respective intervals

leaden torrent
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man this is why you shouldnt multipost

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i already answered this question

worn garnet
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whoops my bad

neat lintel
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Yeah, the factories is what I meant. Was thinking about this the other day, if China invaded Taiwan, they would have control of only not only a monopoly in semiconductor factories, but also pharmaceuticals, solar panels, and the digital infrastructure - they could just invade and then shut those exports to the West off to deter them from any sanctions and reaction

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maths is the language of the universe essentially so it'll help connect everything. it's a very philosophical subject and especially for applied maths you need a good imagination

worn garnet
neat lintel
velvet dagger
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Etienne Le Masson does quantum chaos on graphs if you're familiar with him

near fox
bright hill
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guess what guys

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you know the math olympiade I was supposed to participate in, in a month?

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turns out, it's not in one month, it's in 2 days.

neat lintel
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I'm not updated on your life so no

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Worst that can happen is you'll write it bad

bright hill
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how dare you say something reasonable

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no

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unacceptable

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so

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how do I git gud in 2 days?

rare pond
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Do some math problems I reckon

bright hill
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genius

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what else?

neat lintel
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You don't

bright hill
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how dare you say something reasonable

neat lintel
zenith tinsel
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how dare you not say something agreeing with the status quo

hushed turret
toxic schooner
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oh shit

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u cant get good in 2 days

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sorry

rapid folio
neat lintel
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I'm learning about mechanics in uni

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Mostly classical but there's Hamiltionian and Lagrangian as well

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The thing is, the practice questions are mixed and there seems to be stuff from all over physics there, not just mechanics

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Are they expecting me to be able to differentiate between them

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I'm no physicist god damn starebleak

mellow moon
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Bro your job seems so cool

surreal sapphire
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lets hope that NIST agrees nozoomi

bright hill
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yeah

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it's just the regionals tho, so I'm sure the test's gonna be easy

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I need to worry about if I make it through to the nationals or beyond

toxic schooner
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all the best

bright hill
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thanks

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How tf did JohnDS go through rudin in a single week? starebleak

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how is that even possible?

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I'm just realizing how ridiculous that is

static loom
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lol

ripe wasp
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how tf

bright hill
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he did it in HS too monkey

ripe wasp
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i can't even read a normal book in 1 week...

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did he like

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study 18 hours each day

vale bridge
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Can anyone give me an article which shows full working of solving a associated legendre's diff eq?

neat lintel
calm frost
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but not more than that

dire mulch
light needle
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It was

fair mural
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john crazy

charred mortar
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Damn

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World record first go analysis rudin speedrun

ripe wasp
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are you just crazy efficient and knew all the answers to every problem at first sight or did you stay up for a week straight or smth

toxic schooner
bright hill
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Like

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Do you just never get stuck at all?

charred mortar
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I suppose I can see it if he did like 15 hours a day straight of rudin

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But like if I did that I’d have only a very broad surface-level understanding

light needle
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I came in with comp math experience and much higher math maturity then the avg Rubin reader, so the problems didn’t take too long

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And idk I felt after I got ch 2 which really for me was the hardest thing, everything started falling in place

fair mural
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the entire thing?

light needle
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Up to ch7

bright hill
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Comp math is so OP uhhhh

light needle
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And about half the problem per each ch?

fair mural
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i thought you said you did every problem in 2 weeks

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i am less impressed considering all this new information i have opencry

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you were already very mathematically mature and didn’t do all the problems

light needle
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I mean you shouldn’t do all the problems of a text unless it’s something like Ativan Macdonald smh

fair mural
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that’s why i was so impressed

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john i am disappointed

light needle
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Lol

toxic schooner
bright hill
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I'm pretty sure I would've been a far better mathematician if only my country had as much care for comp math as the US or EU

toxic schooner
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wait how many exercises does rudin have

dim swift
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Anyone?

light needle
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30 per ch I think

toxic schooner
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per chapter

toxic schooner
light needle
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Or a bit less

toxic schooner
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apostol has like, a lot of exercises

bright hill
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Close to 20 I think

toxic schooner
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the topology chapter had 50+

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and the chapter about limits had more than 70

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and most of them are not simple at all

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i will do them all one day

fair mural
toxic schooner
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per chapter?

fair mural
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no for the topology chapter

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and even that was wrong

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it’s like 167

modest rune
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You should do exercises until they become straightforward

fair mural
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i shall not

modest rune
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Once you know how to do them just by reading them

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You should stop doing them

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Even if like the details are fuzzy

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If it’s not actually intellectually challenging it’s kind of a waste at that point

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Unless you’re genuinely curious about the result

toxic schooner
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i agree with this

bright hill
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I wonder if I should focus more on Comp math to get god level advantage like John

toxic schooner
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god i really want to start with apostol right away

bright hill
toxic schooner
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picking it up makes me want to do it so bad 😭

modest rune
bright hill
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Bruh

modest rune
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Spending that same amount of time on actual math is more efficient

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There’s a difference between “if I had done comp math for the past two years I’d be better at math” which is true

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And “I should do comp math for two years before pure math” which is nonsense really

ripe wasp
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im terrible at comp math

modest rune
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Oh me too

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Well

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I just don’t find it interesting

toxic schooner
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i dont think u would have much problem with like an algebra problem max

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but geometry might be bad

modest rune
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Probably not but I don’t know any of the tricks of techniques

ripe wasp
light needle
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It depends on the person, I think categorically disqualifying comp math isn’t like, smart. But yeah like, you have alternatives

bright hill
toxic schooner
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yeah and geometry is just about that

modest rune
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I mean

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Marginal advantage of spending time on comp math instead of pure math

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If the goal is to learn pure math

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Is I think clearly worse

light needle
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Idk I don’t think I would be nearly as fast at solving problems if I just did pure math out of the gate, and this has helped me out a lot over the years

toxic schooner
modest rune
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I am not really sure I believe you

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It seems kind of nonsensical

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But obviously I can’t like

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Disagree lol

light needle
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Idk comp math is more than anything training you to solve problem’s quickly ig. Idk maybe I would have gained this skill if I just did pure math too but it’s hard for me to imagine being as good without comp math

toxic schooner
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i believe that if u did pure math, the start might have been harder, but in the end u would turn out as good, if not better than someone who did comp math at the start and then started with pure math

modest rune
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I think you just get fast at something if you do it a lot

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There’s also some like

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Details under the rug

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You’d have to spend like the same amount of time

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But maybe kids find comp math more engaging

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So they might end up putting in more hours overall

light needle
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Yeah I think in particular the existence of competitions around it make it compelling

modest rune
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I’m like

light needle
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I do think there should be more options for pure math tho

modest rune
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The least competitive person I know

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So I can’t relate lol

light needle
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I see lol

modest rune
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I’ve never cared about winning things

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Seems boring

light needle
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Lol

modest rune
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Idk what’s the saying

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If you’re winning the race you’re in the wrong heat

toxic schooner
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i heard that "if you are the smartest person in the room, then change the room"

torn willow
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Well some races you have to win

modest rune
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So

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I guess I gotta move out

toxic schooner
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so true....

toxic schooner
light needle
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Lol perpetually changing rooms bc of this

toxic schooner
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moving into the room with 50 people

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but they are all premeds

ripe wasp
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the primary reason why i dont like comp math is because i feel insecure and like not good enough whenever i can't solve a problem fast or even solve it at all when my friends can solve it pretty easily, but thats prob a bad mindset lol

toxic schooner
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john premeds are the smartest

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didnt u know?

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smh

bright hill
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Maybe I'll just give "the art and craft of problem solving" another dig

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Especially if I pass the regionals

modest rune
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Some of the smartest people I know were premeds

light needle
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I don’t think giving comp math a try is necessary at this stage

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I refuse to believe it Max smh

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(Jk I knew some smart ones too)

modest rune
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Some of the dumbest people I knew were math majors so…

light needle
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Now you should be nice to yourself

toxic schooner
modest rune
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I’m always nice to myself

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No uchi math majors were all around smart

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I didn’t really know dumb ones

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Econ majors on the other hand

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Truly unhinged

light needle
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Lol

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I haven’t met an Econ major irl thank god

modest rune
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Uchi doesn’t have a business major

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So ofc every like

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Obnoxious business bro

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Goes to econ

toxic schooner
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oof

light needle
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Business majors I have met, universally annoying ppl

toxic schooner
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max u are at uchi? catThin4K

modest rune
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I graduated

toxic schooner
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oh, so u were a ug there?

modest rune
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Yeah

toxic schooner
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Noice catThin4K

modest rune
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Nothing convinced me grad apps were a sham

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More than attending UChicago

toxic schooner
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how so?

bright hill
light needle
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Oh ur like, senior or smth right

toxic schooner
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darq is a senior in hs like me ig

bright hill
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ye

light needle
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Yeah like, by the time it takes for you to get used to comp math ur yr will be over ykwim lol

toxic schooner
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lol

bright hill
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lmao

toxic schooner
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darq, do u graduate in 2 months?

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or so

bright hill
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I will

toxic schooner
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Noice

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so will i

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well

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my exams will be over on june 13

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school exams

bright hill
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I'll start my exams on june 12

toxic schooner
bright hill
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lol

toxic schooner
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from 12th june to?

bright hill
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17 ig

neat lintel
bright hill
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but I'll finish HS in a month or so

toxic schooner
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so ur result will come long before mine i suppose

bright hill
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eh

toxic schooner
bright hill
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oh dope

toxic schooner
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my exams begin on 7th may

bright hill
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I have my mock exams on may 15

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lmao

bright hill
toxic schooner
bright hill
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I'll get them somewhere in july

toxic schooner
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my results wont come until like

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july

bright hill
toxic schooner
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or even maybe early august

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lol

bright hill
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I don't know why I often forget words while typing lel

toxic schooner
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happens lol

feral folio
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I hate exams

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🥲

zenith tinsel
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me too buddy

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me too

neat lintel
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Anyone have tips on how to get faster solving problems? (And I mean the true superset of, "problems" that "math problems" are a subset of). I've kind of struggled with being slow at problem solving my whole life and it's starting to really impact my career. My previous logic was, "as long as I got enough repetitions in, the speed would come," but this is turning out to be untrue.

mild nebula
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insert "understand, don't memorize" here

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Finding easy ways to understand and justify the "rules" to yourself makes you much stronger when curveball questions come up. Repetition will never ready you for these. Perhaps these are your problem?

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That being said, repetition is important.

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@neat lintel

neat lintel
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I wonder if doing some remedial work might be beneficial then. Like taking a 09X math course just to solidify my foundations. However, what's concerning is this slowness intersects nearly all parts of my life. I'm slow at interviewing for jobs, I'm slow at chess with time controls, and I'm slow at math problems/tests. I'm worried its something more systemic.

neat lintel
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hunger?

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seems like the reoccurring themes are "logic" + "time pressure"

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So fear makes sense. I'm curious what you mean about hunger though!

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literally don't eat until you improve

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chronic rage

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I don't think my doctor would approve haha

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i mean it's differential steps

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and you don't do it all the time

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but if you have homework that's running late into the night or something

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maybe you had to skip dinner

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maybe if it keeps causing you to skip dinner, you'll get to the point where it delays dinner

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maybe if it delays dinner you'll get better to the point where it doesn't

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poof

static loom
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I guess what I'm asking is, how do you know you're slow and not just facing the same problems everyone else faces

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I think this is a common problem people face, they live in their own internal world and can't really observe what it's like from the inside of another person's brain, they can just see the exterior and that leads to things like imposter syndrome in a lot of smart people

neat lintel
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another bit is that maybe you're just not using the right tools -- it's tempting to think you can compete with other just using pen and paper, like you were taught for the most part

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maybe you're not using pen and paper as well as you should organizational tools like quad-boxes

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pros and cons, hierarchical outlines

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they only go so far

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I think the biggest metric is that I was a Software Engineer for 8 years but haven't been able to find a new job since the industry switched to using LeetCode problems. "Par" would be to solve two problems in a 50 minute interview, but it takes me about 60m to solve one. I've been on the job hunt for exactly one year now and no luck.

Another data point is that I frequently lose to time in chess (11% of the time) while I've never won on time against an opponent, which seems like a statistical outlier. Just means I'm consistently using more time per turn than the average opponent of my skill level by a significant margin.

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are you fat?

neat lintel
neat lintel
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do you have good sleeping habits?

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I play contact sports though, so I'm quasi-fit.

neat lintel
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When I'm nervous about an interview/test I find it especially hard to be hungry.

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well if you know how to train your body, i'm sure it's the same thing with you mind

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pick your training parameter and reinforce

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it sounds like you might just want to memorize a list of things

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whip out your DS&A, your favorite OOP manual (idk if ltcode uses python or waht?) and start memorizing the shit

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If I fit everything into a problem-space where I can use spaced repetition, I think I'm in a relatively good spot. There's always the odd chance they might ask me a problem that I don't know, but maybe I can model it after a problem I have already memorized?

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try project euler

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for coding challenges

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those get pretty spicy

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and they're not some shitty silicon valley scam bullshit surveillance program asshole anus shit

neat lintel
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for shitheads

bright hill
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better UI + active community + you can use any language you want and the problems are classified from easy to hard

bright hill
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this just means that your playing style errs on accuracy over speed (I'm guilty of this too lol, falgging still feels like cheating to me tbh)

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anyhow, I would claim chess abilities and problem solving prowess are almost disjoint

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being good at chess has far more to do with how much experience you have/how much time you spend actively trying to improve

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just as an anecdote (and take this with a grain of salt) iq score seems to remain constant even with prep whereas chess elo can obviously improve with practice

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At the end of the day, I think it's all just relative

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and it has far more to do with your self-perception than anything else

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just like how the most attractive people can be the most insecure

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and I personally think the time you spend lamenting over how slow you are compared to arbitrary standards you set for yourself can be far more productively spent elsewhere

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@neat lintel

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PS if you think there might be a more pathological cause to your concerns, feel free to consult a neurologist. But honestly, I seriously doubt it.

charred mortar
bright hill
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since I was under the impression that iq was designed to be roughly constant

charred mortar
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There’s most likely more

bright hill
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"may"

charred mortar
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And keep in mind that IQ is a test, nothing more nothing less

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Pretty much any test can be prepared for, and with practice there’s a decent chance you’ll get better at it

bright hill
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I did say I was being anecdotal and he should take it with a grain of salt

charred mortar
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I know that, I’m not saying you’re being bad or anything, just a small note of mine

bright hill
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anyways, I doubt practice would improve your score by much

charred mortar
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In any case I myself put very little stock in IQ tests specifically

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Then again this is only like one or two sources; I’m not a clinical psychologist who’s spent years combing through studies of IQ tests either

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Maybe there’s some good review paper of this topic that answers the question a lot better one way or the other

bright hill
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honestly, I don't have the energy to investigate this further myself lol

charred mortar
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Completely fair lol

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There’s a huge body of research on IQ

ripe wasp
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something that does that at like a uniform pace

swift sinew
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Depends on your definition of uniform pace but you could plot the point (a,f(a)) [after defining f(x) of course] and let desmos do the cycle thing with that new variable a you added

ripe wasp
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ohh right perfect just what i needed

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thank you

ancient flame
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where did edd go

umbral forge
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Asking here just to be sure but this is false right

IMG_1696.png
fervent pebble
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the fuck lmao

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yeah that's bs

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5 * \inf = \inf

fair mural
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yes, if i remember correctly (0.1,0.2) and (1,2) both have the cardinality of the reals

umbral forge
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I mean this is tiktok so not surprising it’s false info lol

fervent pebble
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they do

fair mural
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but there are different sizes of infinity

fervent pebble
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yes

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but 5 * inf = inf

umbral forge
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Infinity sizes are determined based on how you can attribute one number from one infinity to another infinity right

fervent pebble
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no

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welllllllllllllllll

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i guess you could phrase it like that?

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the size of an infinity is defined by starting with the cardinality of the integers as a base

umbral forge
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Maybe it’s a weird phrasing

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But tbh I just remember the proof of the irrationals being larger than the naturals by making a new number with the decimals of the irrationals

fervent pebble
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yeah that's called cantor's diagonalization argument

umbral forge
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Btw last question but is there an infinity smaller than the naturals or is there no in between from a finite set to the set of the naturals

cobalt star
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nope

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idt there is a smaller infinity

fervent pebble
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i don't think so

fresh oriole
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I'm bracing myself before somebody swoops in with some bizarro alternate foundations where there are an infinity of infinite cardinalities smaller than aleph_0

fervent pebble
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i mean

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there is probably

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but like

cobalt star
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according to stack exchange there may be a smaller one if not using axiom of choice??

fervent pebble
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who really cares abt it

cobalt star
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true

fresh oriole
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well, if there are cardinalities between the naturals and the reals is undecidable in ZFC

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aleph_0 is certainly the smallest infinite cardinality in ZFC

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if |S| < aleph_0, |S| is finite

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but I have no idea what other fringe approaches to this could be out there

cobalt star
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i think the person probably wanted a proof

fervent zephyr
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That's above the naturals, though. Below, there really isn't classically

cobalt star
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from the other definition of an infinite set as one that is in 1-1 correspondence with a proper subset

fervent zephyr
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Hm, although I'm not sure there's an injection from N into every infinite set without some choice axiom

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Without choice the cardinals aren't linearly ordered

swift sinew
fervent zephyr
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In general, it can help too think about cardinality as taking about structure, not size.

fervent zephyr
swift sinew
fervent zephyr
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"set that has a non-injective surjection into itself" (or non-surjective injection)

cobalt star
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oh yeah jesyspa urs is equivalent to mine

fervent zephyr
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"set with no bijection to a natural number" (this is a common definition of "non-finite")

swift sinew
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I suppose, I guess I had grouped all these into the same definition in my mind

fervent zephyr
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"set X with an injection n -> X for every n"

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They're all equivalent classically with choice, but in other foundations you can find differences

cobalt star
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cool

swift sinew
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Is choice necessary for equivalence of definitions

fervent zephyr
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It's hard to show that it is, but I suspect for some it will be

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Actually perhaps not so hard: I suspect for some of these, the equivalence with your definition implies countable choice

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But that's just gut feeling

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(when I say "you need choice" I mean "you can't do it with plain ZF", not that you need all of choice, by the way)

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Oh, another one is "admits a linear order without endpoints"

swift sinew
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“is big”

fervent zephyr
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"admits a non-discrete Hausdorff topology"? I think

vale bridge
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Can anyone tell me, how can I analytically prove that a function is increasing/decreasing?

fervent zephyr
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Assume x < y and show f(x) <= f(y)? It depends on f how that goes exactly.

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@vale bridge Can you be more specific?

neat lintel
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Multipost

fervent zephyr
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Oh, how rude.

stark charm
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bijection to a subset of natural numbers?

fervent zephyr
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A common definition in this setting is "a set is finite if it is in bijective correspondence with a natural number (i.e. a finite cardinal)"

fringe needle
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My grandma told me my little cousin likes math

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I’ll finally have someone to talk to in the family lmao

toxic schooner
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thats actually nice

bright hill
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I have no one to talk with about math irl sadcat

stark charm
toxic schooner
primal seal
fickle yew
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am i allowed'

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to ask a math question

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?

fair mural
bright hill
brave thistle
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Do we have a channel in this server where we have 'top problems' of week/month?

old fox
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no

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but I think that'd be nice

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just put the Millennium Prize Problems and don't tell people they haven't been solved

grizzled grove
bright hill
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currently? a mix of LA, analysis and CS

grizzled grove
bright hill
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thank you

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I appreciate the offer

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but that won't be necessary since this whole server was made to make a place for people to discuss math (at least, that's what I feel)

sick burrow
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This server was made to shitpost

umbral lava
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@median girder I have some ideas for your question, but the thread timed out before I could type, is that question still something you'd need some help with?

neat lintel
rich hamlet
fervent pebble
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drug update day 4

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bruh i literally feel depressed lmao

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not cool, drugs

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no increase in focus

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yet

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gods this sucks

vivid halo
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lol what drugs

primal seal
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I’ll guess amphetamine salts

fervent pebble
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vyvanse

vivid halo
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what dose

fervent pebble
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30

vivid halo
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huh

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how the hell are you depressed on amphetamines lol

fervent pebble
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idk

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im not even getting any extra energy

primal seal
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How did I know

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Are you diagnosed with ADHD?

fervent pebble
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yeah

primal seal
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You do realize they won’t affect you the same way as you hear it does all these students abusing it, right?

fervent pebble
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yeah

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i was expecting to feel more focused tho

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like at least a little

primal seal
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No, not really

vivid halo
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yeah so two things here is that amphetamines and stimulants affect those with ADHD very differently from neurotypicals, and also it might take a bit longer than just a few days to notice much of a difference

primal seal
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That’s true too

vivid halo
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you don't necessarily get a huge amount of sharp focus, but you might notice it makes things work better in the long run in subtle ways

primal seal
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Especially if it’s been a day

vivid halo
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that, or you could try a higher dose

fervent pebble
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hm

primal seal
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No, stop

fervent pebble
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i might stick it out for like another two or three weeks then

vivid halo
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yeah definitely

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it could just be other factors muddying it

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that might average out over a longer period of time

primal seal
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Stick it out bro; it’ll make you more even-keeled once the plasma levels stabilize- but don’t expect the hyper focus you hear it gives some of these kids abusing it report; you don’t want that anyway. You’ll be able to focus much better, but not in that regard 👍

fervent pebble
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gods know i already have enough issues with hyperfocus lmao

vivid halo
#

also just be aware that the medication alone won't solve everything; behavioral therapy and building good habits around work and focus is just as important

#

a common pitfall that happens to people that take stimulants for ADHD is they will end up hyperfocusing, but on the wrong things

#

this usually happens when there is no other behavioral intervention that goes along with the medication

fervent pebble
#

hm

neat lintel
#

Hmm

#

I was mentioned here?

ionic belfry
#

thoughts on this article

fossil geode
#

dont think anyone can stop it though

frail sail
#

Atleast it should take over all the menial labrous jobs that people do

charred mortar
#

Well it does potentially open up new jobs too involving AI (as the article does note)

shut grail
#

What is the logic of the inside out product . can u explain

neat lintel
zenith tinsel
#

outer product?

#

instead of inner?

#

that's a thing right

#

outer product

deep mango
#

The outer product is a thing

#

It's when you make a matrix out of two vectors (v_i) and (w_j) by setting A_ij = (v_i * w_j).

#

this can be written as A = vw^t

#

somehow it corresponds to the tensor product of v and w (up to an identification)

neat frost
#

Why is everything about tensor products bleak

deep mango
#

I finished another problem sharkpog

cyan goblet
sleek wing
#

ryc guilt tripping me to do past papers sharkpog

toxic schooner
#

me as well sharkpog

bright hill
neat frost
#

Good morning DarQ

bright hill
#

,ti

fathom swallowBOT
#

The current time for DarQ is 02:59 PM (BST) on Sun, 24/04/2022.

neat frost
#

Ah and once again, you are burdening us with your bad takes

bright hill
#

Good morning

neat frost
#

Math and shitposting may not be mutually exclusive

bright hill
neat frost
#

But this server is for shit posting

#

Not for math

#

Don’t what me DarQ

#

Unacceptable

bright hill
#

My takes aren't bad

neat frost
bright hill
#

I bad

neat frost
bright hill
#

No

neat frost
bright hill
#

Unga bunga?

neat frost
#

Ooga booga.

bright hill
neat frost
toxic schooner
neat frost
#

Good morning shyshy

toxic schooner
#

its nearly nighttime slurp

#

but good morning

#

,ti

fathom swallowBOT
#

The current time for Samsyet is 07:34 PM (IST) on Sun, 24/04/2022.

neat frost
#

Good morning shyshy.

toxic schooner
#

Good morning slurpy.

neat frost
toxic schooner
bright hill
#

Slurpy sounds weird

neat frost
#

Excuse me?

#

I do not sound weird

bright hill
#

No, I meant "slurpy"

neat frost
#

Excuse ME?

#

I do not. Sound. Weird.

#

,ti 345954969628704779

fathom swallowBOT
#

The current time for DarQ is 03:06 PM (BST) on Sun, 24/04/2022.
Slurp is 2 hours ahead, at 05:06 PM (IDT) on Sun, 24/04/2022.

neat frost
#

Good morning DarQ

bright hill
#

Ooga booga

#

Mornin'

neat frost
#

Oonga bonga

rocky shuttle
neat frost
#

Delete that

rocky shuttle
#

Why

neat frost
#

I am the one and only

bright hill
#

Yeah, but that's not pronounced slurpy, it's pronounced slurpy

neat frost
#

Ahh okay

bright hill
#

There's a difference

neat frost
#

Yesh

#

DarQ you know set theory?

bright hill
#

Who on earth knows set theory?

neat frost
#

I don’t mean in depth

#

Just the basics

zenith tinsel
#

what are the basics

neat frost
#

Nah but like just simple operations on sets

#

Specifically symmetric difference

zenith tinsel
#

I know how to go about $\bigcup \bigcap \mathcal{A}$

fathom swallowBOT
#

texaspb

135198261232271360.png
neat frost
#

I wanna know what your notation for it is

zenith tinsel
#

basic

#

I use

bright hill
zenith tinsel
#

$A \Delta B$

fathom swallowBOT
#

texaspb

135198261232271360.png
zenith tinsel
#

for symmetric diff i guess

#

but ive seen

bright hill
#

Vellemen used Delta

zenith tinsel
#

$A \oplus B$

fathom swallowBOT
#

texaspb

135198261232271360.png
zenith tinsel
#

Ive seen both

neat frost
#

Dis-fucking-gusting

bright hill
neat frost
#

You are all irredeemable

neat frost
rocky shuttle
fathom swallowBOT
#

Zanarcane

299974051127099396.png
zenith tinsel
#

$A \oplus B = (A \cup B) \setminus (A \cap B)$ is this the def btw?

fathom swallowBOT
#

texaspb

135198261232271360.png
bright hill
neat frost
#

$A\mathbin{\vcenter{\hbox{\scalebox{0.7}{$\triangle$}}}}B$

fathom swallowBOT
neat frost
#

All other notation is wrong

#

I am sick of seeing ugly sym diff notation

#

$A\mathbin\Delta B$ is ugly

fathom swallowBOT
bright hill
#

The latex tho monkey

bright hill
neat frost
#

$A\mathbin\triangle B$ is ugly

fathom swallowBOT
neat frost
#

$A\oplus B$ I’ve never seen. Tbh it’s understandable. I accept

fathom swallowBOT
umbral lava
#

@worthy yoke Sorry to bother, to give one final clarification which I should have included earlier, the reason why I could just call a term dependent on z a constant is specifically because the question tells us we should take constant z amplitide and the term I called k was just a power of this constant amplitude, so would not influence the angles of the solution and would not give rise to solutions that have the same angle but different amplitudes. In general, absorbing terms of the equation which contain the variable into constants needs to be done carefully and with justification, my justification at the time is now I feel insufficient, so this is the real reason. But in all honesty, the method you used first is probably the easiest since after obtaining the 4 possible angles, each subsequent equation of the form z^L = re^ix where x is one of the four angles will have L solutions since it is a polynomial equation of degree n. The r is the amplitude we can take as fixed. We know that for this particular type of equation there will not be any repeated roots so there are 4L solutions all of which definitely have angles between -pi and pi as this is the full range of angles in an argand diagram, so no need for any of the algebra. Sorry for the long message, just felt I should address this.

near fox
#

It should be a Delta not a triangle, to signify "difference"

neat frost
#

But I object to the delta’s ugliness

bright hill
#

Based slurp

neat frost
#

Thank you deary

rocky shuttle
#

Delta doesn't look symmetric

neat frost
#

True true

#

Based take

neat lintel
neat lintel
neat lintel
neat frost
neat lintel
neat frost
neat lintel
#

axiomatic is based

neat frost
#

Linear algebra is fuckin ZASED

neat lintel
#

O

neat frost
neat lintel
#

Do you know what's more based?

#

Affine geometry

neat frost
#

Ye that’s above my pay grade

neat lintel
#

oh

#

Even though my math level is still below the "acceptable" level, I know how to work with the Chin Cheng Hanji theorem

#

Or as u call it, the chinese remainder theorem

neat frost
#

Isn’t that elementary number theory?

neat lintel
#

btw

#

It's my 1st year

neat frost
#

Affine geo is first year material?

neat lintel
#

But I'm studying it rn

#

And at the same time I'm learning linear algebra

neat frost
neat lintel
#

Let's call it a "challenge"

neat frost
#

You do calc/anal yet?

neat lintel
#

I've done it

#

In one and several variables

bright hill
#

How did it feel?

neat lintel
#

Anal... idk

bright hill
#

Haven't you done anal yet?

deep mango
neat lintel
#

I used to like integration a lot

#

Before studying linear algebra

ancient flame
rocky shuttle
neat lintel
#

They told me that the day I start studying abstract algebra or contemporary algebra or whatever you call it here that starts with group theory, I'll like that a lot

neat lintel
#

btw, I prefer complex anal

ancient flame
#

if u take a linear algebra course, are you expected to be able to make these massive computations?

#

bc my memory is shit

neat lintel
bright hill
#

Anal didn't feel good for me starebleak

ancient flame
#

I won't remember the determinants and cross products and matrix multiplications and all that

bright hill
#

It was so rough and dry

neat lintel
#

The harder, the more I like it

ancient flame
#

this whole conversation is a sully

neat lintel
#

🤨

ancient flame
#

smh

neat lintel
#

At least in my degree

ancient flame
neat lintel
#

We have a first course where they teach you until linear maps

neat lintel
ancient flame
#

lol

ancient flame
neat lintel
bright hill
#

Other things? 🤨

neat lintel
neat lintel
bright hill
neat lintel
rocky shuttle
#

Anal has always been analysis, what are you talking about?

bright hill
#

,w anal

neat lintel
fathom swallowBOT
bright hill
#

Anal is a language? monkey

ancient flame
neat lintel
neat frost
neat frost
neat lintel
#

Diagonalization with 16x16 matrices sully

rocky shuttle
#

What's the best way to diagonalize a matrix numerically?

ancient flame
#

lol alright

rocky shuttle
#

I have learned about QR algorithm

#

But what's actually used in practice?

neat frost
#

GV method is my personal favorite

neat lintel
rocky shuttle
#

Because QR, even with reduction to Hessenberg matrix, feels really slow

rocky shuttle
neat frost
#

Guess + verify

rocky shuttle
#

Lol

neat lintel
#

Well

#

I've find an old friend

#

SVD

#

Singular Value Decomposition

rocky shuttle
#

Yeah

neat lintel
#

Idk if this is useful for what you are asking

rocky shuttle
#

I thought about that too

neat lintel
#

But it's in the same chapter

#

So it must be useful for that

rocky shuttle
#

My course never discussed the numerical aspects of SVD though

neat lintel
#

https://en.wikipedia.org/wiki/Jacobi_eigenvalue_algorithm#:~:text=In numerical linear algebra%2C the,a process known as diagonalization).

Jacobi eigenvalue algorithm

In numerical linear algebra, the Jacobi eigenvalue algorithm is an iterative method for the calculation of the eigenvalues and eigenvectors of a real symmetric matrix (a process known as diagonalization). It is named after Carl Gustav Jacob Jacobi, who first proposed the method in 1846, but only became widely used in the 1950s with the advent of...

#

Also found this

rocky shuttle
#

Yeah, I know about that too

#

But I'm rather interested in whether those algorithms are actually used in practice

neat lintel
#

I found this book

rocky shuttle
#

Or maybe my own implementations are all considerably more inefficient than the usual libraries

neat lintel
#

It's about eigenvalues of large matrices

ionic belfry
ionic belfry
neat lintel
#

I don't like philosophy

rocky shuttle
ionic belfry
neat lintel
#

I'd like to learn logic

#

But I don't have much time

#

I know the open logic text

#

But it looks as something very very fast that won't teach u much... well, that means I'm searching something slower

frail sail
ionic belfry
#

yeah

#

ikr

#

so idk

#

im confused

toxic schooner
#

for a second i thought i had found someone else with the name samsyet

#

lol

neat lintel
#

anyone help me with an easy maths question?

surreal kindle
neat lintel
#

yea

#

sorted it

surreal sapphire
languid atlas
#

what's the difference between this channel and #discussion

surreal sapphire
#

this one has a 2

sleek wing
#

this channel is for discussion of the number 2

languid atlas
neat lintel
#

doubt

#

So you can discuss here as well, it's simple

languid atlas
#

guys

i think i found the plant cell equation

Screenshot_from_2022-04-24_19-54-07.png
#

jk

inner finch
#

based

languid atlas
#

what is this

inner finch
#

looks good

zenith tinsel
surreal kindle
#

alien ship vibe

thumbnail_image3_1.jpg
neat lintel
#

The white spots are probably desmos not being able to graph it because of too much oscillations

languid atlas
#

nah i think the white spots are supposed to be there

#

looking at bottom left

neat lintel
#

Did you try zooming in on them

languid atlas
#

yep

neat lintel
#

I see

neat lintel
#

Because that's f obvious

surreal kindle
neat lintel
#

btw, if we change the objects there and we are studying logic

neat lintel
languid atlas
neat lintel
#

Mathematician juggles with trivial things

neat lintel
#

But then you find a lot of beauty in trivial things

#

I used to think a lot about the word "useful"

neat lintel
#

Some people say that maths are either "useful" or not "useful". After thinking a lot about this question, I concluded that it is a stupid question

#

Because it doesn't matter if math is useful or not. It is used worldwide everyday, so it's impossible to say that it isn't useful

#

And about those branches that may seem useless

#

Like topology

#

They have computational applications always

#

btw, I don't want to make you think I'm saying math is useful (while I'm saying that exact thing), because my point is far from the question

#

My point is that it's useless to ask if math is either useful or not, because we shouldn't care about usefulness

#

Sure thing

#

Not my way of judgement anyway

#

If we care too much about "useful", then we will have some difficulties trying to learn abstract math

#

If you don't care about if what you are studying is useful or not, you avoid those silly questions that make you waste a lot of time, and you go straight to the point of understanding concepts

#

For example, the dual space

#

If you want applications of the dual space as a premise in order to understand what is the "dual space" then you will walk a very long way

#

But if you don't care a little bit about applications

#

You just see that we define the vector space of linear applications that go from any vector space to a field

#

And in your mind, this is what you see

#

$f: E \to \mathbb{K}$

fathom swallowBOT
#

math simp

967778748550250607.png
neat lintel
#

And then you are able to understand easily the dual basis, dual applications, bidual, and other things

neat lintel
# fathom swallow **math simp**

But, if for understanding this you immediately need examples, that will be very very difficult to understand, and the point of pure maths is not to understand things, it isn't enough, you have to interiorize them

#

btw, I think that even inside the world of mathematicians, this POV isn't supported, so

#

I said everything, bye

languid atlas
#

when in doubt

#

type cos(x)^y = cos(y)

zenith tinsel
#

could this pattern be useful?

#

it looks like something that could be applicable to somewhere

languid atlas
#

i would love to see (x²+y²-1)³ = 2.7x²y³ being used

#

guess what that draws

languid atlas
zenith tinsel
languid atlas
#

giving you another one

#

waitt

#

testing latex rn

neat lintel
zenith tinsel
#

ok

languid atlas
fathom swallowBOT
zenith tinsel
#

so do I just plug that in desmos

#

awwwwwww

#

that's so sweet

#

😍

languid atlas
#

$x^\frac{2}{3}+0.9\sin{50x\pi}\sqrt{3.3-x^2}$

fathom swallowBOT
zenith tinsel
#

thanks fwend

languid atlas
#

those are the two i know

#

oh

#

and

#

$r=a(1-\sin{\theta})$

fathom swallowBOT
languid atlas
#

in polar coordinates

#

$0.6x^2+(y-(0.6x^2)^\frac{1}{3})^2=1$

fathom swallowBOT
languid atlas
#

this is also a good one

languid atlas
zenith tinsel
#

hmm this one actually looks neater

languid atlas
#

you can actually adjust the functions by adding parameters

#

like replace every "x" with "ax"

#

then vary a

ionic belfry
#

thoughts on this article

#

im conflicted

#

idk if it should or should not be regulated

limber thunder
#

the problem isn't AI but the lack of social security for most workers

#

the idea of automating all tedious tasks sounds great and should be a goal of humanity, but not if a huge portion of society is left impoverished in the process

#

regulating AI rather than tackling the actual social issue at hand would just stagnate innovation

#

(no need to post on multiple channels btw)

charred mortar
#

Ideally those out of jobs could be shifted into new ones involving say development or maintenance of the automated system

#

Ofc that’s not really feasible right now

torn willow
#

Ah yes,Capitalism ruining innovation

gray loom
#

Any stats experts present?

#

It should be 214, but apparently not

sonic timber
#

How to solve the recursion relation a_n−1= 2_an + 4^n ; a_1 = 3, n⩾ 0. with generating function?

mild fiber
#

Idk

fair mural
fervent pebble
#

drug update day five (i think?)

#

didn't take em today

#

bc i took them after like twelve yesterday

#

and didnt go to sleep until four today bleak

#

i feel literally no difference

#

which is either good or bad

#

not sure

neat frost
fossil geode
#

damn

#

and what does me claiming AI being a huge step of human technology

#

has anything to do with governments trying to regulate it lmao?

surreal sapphire
#

funnily enough i just read an article about current challenges of AI

fossil geode
surreal sapphire
#

hm?

fossil geode
#

whats funny about it

surreal sapphire
#

nothing, its just odd that AI came up here (again) while i was just reading this thing

fossil geode
#

coincidence

neat lintel
torn willow
#

You know, It's weird how economists use graphs for literally everything

#

I don't think I would use an isocost line over the corresponding isocost function

#

Graphs are hard and confusing to read for me compared to a lookup table

leaden torrent
#

bad take

torn willow
#

Why,does it get bad with a large number of inputs?

#

Ok,fair if you don't have a readymade function,you need to use graphs

old fox
#

you don't put spaces after your commas?

fair mural
bright hill
#

yeah, what up with?

fair mural
#

that’s cringe

#

half the time i don’t even put commas for some reason though

old fox
#

better than not putting a space after a comma

bright hill
#

I would love to see your code, blue bye

#

I bet you use

func()
{

}

instead of

func() {

}
#

smh

#

smh

neat lintel
#

the best indentation is
func()
{

}

bright hill
neat lintel
#

i bet you don't use tabs either

bright hill
#

why tf would I click 4 times as many click to do the same thing?

#

tabs are just superior

neat lintel
#

that's why i meant

neat frost
#

You didn’t have to go so hard DarQ

neat lintel
dim needle
#

I missed the Collatz talk

#

What is a hydra map?

#

I remember the last time I tried to dive into p-adic theory... I learned it was similar to ergodic theory, I found an online textbook somehow, and then I struggled to understand anything in that textbook. I'm honestly intimidated by a lot of the higher level math concepts because Calculus 3 prepares you for absolutely nothing if you want to get into the good stuff.

#

Here's what I mean:

unknown.png
#

Is this typically taught in an intro to liner algebra class?

primal seal
#

@violet spade i want to thank you for the Rec last night to Roman

#

In finding Artin very good too; it just seems very natural to me to present AA and LA intertwined

dim needle
#

Huh, interesting. I don't recall learning about spectral theorem or inner product in my intro to Linear Algebra class. Maybe I got the Com Sci lite version or something.

#

Oh, I know what dot product is

#

Oh, okay.

#

Diagonalizable rings a bell, but I don't remember what that means.

#

I'm curious how this relates to the Collatz map. What is the advantage to having a diagonal matrix or knowing any given matrix can be diagonalized?

#

Is the goal to create a formula or algorithm that can predict the future of the Collatz trajectory more or less? If say 7 has a diagonal matrix, the hope is a scaled version of 7 also has this behavior?

#

I'm sorry, what does i represent? Is that the position of the matrix like an index or does it represent something else?

unknown.png
#

Oh, okay

#

I just realized matrices have two indices per spot in the matrix and I'm confused again

I'm looking at working out the M2 matrix. In the first spot (1,1), The first spot is a one so that's given. When I move onto (1,2), I have two parts: the first part and the second part. I'm not sure if I'm supposed to look at both parts or just one of them

#

oooohhhh It's just the first part

#

I'll probably come back to noob post more about this paper another time, I may need a break for now.

In the n/2 method, that's going to hide a lot of the growth behavior until you actually get to that number. Also, calculating the determinant for some of these matrices sounds like hell. Also, I'm not sure how this says anything about the two-one cycle being the only one, but I think I have a lot more reading and understanding I need to do. Once I understand what's going on I'm going to throw 3x+5 at it and see if it actually holds up

vast surge
light needle
#

lolz

vast surge
#

Nice picture. Of course you also watch Young Justice

light needle
#

indeed

#

very exciting that they basically made GLAS canon adjacent

vast surge
#

Yeah

#

And gave some amount of closure to Razer's character arc

light needle
#

yeah

#

also they made him like

#

really cute lmao

vast surge
#

The GLAS animation style was not very flattering to him

light needle
#

yeah lol

deep mango
#

And apparently it's "very based"

light needle
#

ultrazuki

deep mango
#

It's basically him spending an entire huge paper condescendingly teaching basic logic to scholze

vast surge
light needle
#

true

static loom
deep mango
#

Hmmm

#

Curious proposal

toxic schooner
#

that would be good

deep mango
#

It could be an emote, we do have quillen infty1category ursmooth wizard no

light needle
#

add it

vast surge
#

integration and differentiation on - i.e., so to speak, the "differential geometry" of - the real line

toxic schooner
#

it should exist as something people of the server can use

toxic schooner
deep mango
#

I think namington is the one who wastes his time cropping and adding mathematician faces

toxic schooner
#

idg it

vast surge
static loom
#

true he made the last few stickers that were being discussed haha

toxic schooner
#

lol

deep mango
#

The rest of us feel shame at adding silly stickers and emotes

#

He has no shame

vast surge
#

Oh god, this is terrible. "Section 1: Summary of non-mathematical aspects for non-specialists. Why the fuck would you include that in a math paper?

deep mango
#

Lmao

#

The paper exists as a scholze-stix roast

limber thunder
#

new mochi diss track dropped

vast surge
toxic schooner
#

i see

toxic schooner
zenith tinsel
#

why do you guys roast this mochi guy

vast surge
#

Because he's hilarious

zenith tinsel
#

is he a meme

#

around here?

limber thunder
#

he's himself a meme

vast surge
#

He's a distinguished math professor from Japan who made numerous contributions to anabelian geometry. Then he turned to crankery and invented IUT

zenith tinsel
#

Inter-universal Teichmüller theory

#

?

vast surge
#

The one and only

zenith tinsel
#

interesting

zenith tinsel
#

it's an actual thing

vast surge
zenith tinsel
vast surge
#

Various multiple copies of certain mathematical objects in inter-universal Teichmuller theory are redundant and hence may be identified with one another. On the other hand, once one makes such identifications, one obtains an immediate contradiction.

zenith tinsel
#

this paper is so weird

#

everything is weird

#

but I get it maybe I just don't understand the concepts

brave hollow
#

so RCS = Scholze and Stix right?

vast surge
#

I think so, but also "One fundamental reason for the use of this term "RCS" in the present paper, as opposed to the names of mathematicians, is to emphasize the importance of concentrating on mathematical content, as opposed to non-mathematical - i.e., such as social, political, or psychological - aspects or interpretations of the situation."

brave hollow
#

so in terms of diss tracks this is a subliminal diss track

#

on the date thing

unknown.png
#

the link leads to the same link you posted tho