help-26

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[vernal vale]

I'm trying to tell if im on the right track for this question:

[vernal vale]

here is my attempt so far

[thorny flame]

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

[vernal vale]

I feel like im not really going in the right direction

am i starting in the right way?

[sweet shard]

Do you know relationship about the singular vectors u_i and v_j

[vernal vale]

is there a relationship?

i know theres a relationship between columns of U and V

i mean, within each individual matrix

but i wasnt aware of anything linking the two

[sweet shard]

What is it

[vernal vale]

well theyre orthogonal matrices

so $\cdot u_i \cdot u_j = \delta _{ij}$

[thorny flame]

jan Niku

[vernal vale]

likewise v

sorry extra dot

and I guess the equation that generates the u

so ...

$Av_j = \sigma_j u_j$

[thorny flame]

jan Niku

[sweet shard]

Yea plug that u_j into the product at your last equation

[sweet shard]

And use this

[vernal vale]

lemme see

we start with $u_iv_j^Tu_jv_j^T (tr \Sigma)^2$

[thorny flame]

jan Niku

[vernal vale]

uhh

$\frac{Av_j}{\sigma_j}v_j^T\frac{Av_j}{\sigma_j}v_j^T (tr \Sigma)^2$

[thorny flame]

jan Niku

[vernal vale]

but i think this is a problem

because weve turned a number into a matrix

[vernal vale]

wait doesnt this imply that $A=\sigma_j u_j v_j^T$

[thorny flame]

jan Niku

[vernal vale]

but that cant be true

am i working with the right equation?

no wait im being dumb sorry

[sweet shard]

This is true after you put a sum over j

[vernal vale]

yea but the manipulation is invalid

its backwards

$v_iv_i^T \neq 1$

[thorny flame]

jan Niku

[vernal vale]

clearly

[vernal vale]

i tried working with this too but its even worse

lemme see

yea im not certain whats the move here

[vernal vale]

it doesnt seem like theres a way to use this without creating an invalid equation

actually, i guess im starting with an invalid question

it began as a matrix

but ive tracked this through to this point twice now

[sweet shard]

Just twice?

[vernal vale]

no, more times

twice on paper

[sweet shard]

This would take me hours

[vernal vale]

yea, im at about hour 4

ive done it several times on a white board too

[opal vault]

I would have suggested a different approach maybe to prove this

[vernal vale]

im just trying stuff blindly

i actually dont know what the answer is

i have a feeling its like trace sigma

[opal vault]

it's not that far off

[vernal vale]

my intuition is that somehow orthogonality is gonna kill the u's and v's

but i cant get it to plop out

so im all ears

if you have another place to start

[opal vault]

but you could use this hint : rewrite $|A|^2_{frob}$ as the trace of a certain matrix

[thorny flame]

rafilou2003

[vernal vale]

you may have to be more explicit than that

im really horrible at linear algebra

[opal vault]

ok

Check out AA^T (or A^T A)

[vernal vale]

? what do you mean

[opal vault]

well, compute the coefficients of AA^T on the diagonal

[vernal vale]

👀 why would that help

[opal vault]

this feeling can hint towards why it would help

[vernal vale]

i should restate im not really great at linear algebra

i dont have any intuition of svd besides that U and V are orthogonal

im hesitant to spend a bunch more time just blindly stabbing into the dark

given that i cant chase my intuition much

[sweet shard]

This expression is pretty close to A A^t

[vernal vale]

I mean the expression is invalid

unfortunately

maybe i can find the mistake

[sweet shard]

You should be plugging in for u_i here

[vernal vale]

it was invalid before i plugged in

i think

its supposed to be the entry of a matrix

but its not a number

its a matrix

so its invalid

im gonna start over

[opal vault]

what went wrong I think is transforming ui . vj into uivj^T instead of vj^Tui

uivj^T gives you a matrix

vj^Tui gives you a number

[vernal vale]

actually getting to $A_{ij} = \sum _p \sigma p (UV^T){ij}$ is not that bad

[thorny flame]

jan Niku

[vernal vale]

so i guess

$A_{ij} = (UV^T)_{ij} tr(\Sigma)$

[thorny flame]

jan Niku

[vernal vale]

i will check on this

im sorry

i dont see it

what is supposed to happen

$A_{ij}^2 = \frac{1}{\sigma_i^2} v_i^TA^Tv_jv_i^TA^T(tr \Sigma)^2$

[thorny flame]

jan Niku

[vernal vale]

oh no i lost something somewhere

bleh

lemme start over

[opal vault]

really I feel like this is a very tiresome approach

[vernal vale]

im sorry but i had no idea what you were talking about with the other approach

[opal vault]

try to compute tr(AA^T), this could set you up the right way

[vernal vale]

idk what link would be between the trace here and the svd

[opal vault]

not the svd

the norm

[sweet shard]

Just calculate and see what you get

[vernal vale]

in terms of the svd?

[opal vault]

no, in terms of A's coefficients

[sweet shard]

.

[sweet shard]

Although unmotivated right now, this approach is much shorter

[sweet shard]

But it makes sense to look at A A^t if you're told the definition of frobenius norm

[opal vault]

yes, and AFTER you've computed tr(AA^T), THEN look at what AA^T is with A's svd

[vernal vale]

why is it the norm

[sweet shard]

?????

[vernal vale]

the trace of AA^T is the frobenius norm

err

its the square of it

so then you can use the SVD

and it falls out $tr(USV^TVSU^T)$

[thorny flame]

jan Niku

[sweet shard]

Did you prove this

[vernal vale]

so ... $tr(US^2U^T)$

[thorny flame]

jan Niku

[vernal vale]

yea its only 3 lines

[sweet shard]

So what are you asking?

[vernal vale]

why are they the same

[opal vault]

goes further than that using tr(AB) = tr(BA)

[opal vault]

well because

:)

[sweet shard]

What answer are you looking for

You said you proved it

[vernal vale]

i dont mean how i mean why

[opal vault]

In a sense, Ig it echoes to the 2-norm you use for R^n vectors

[sweet shard]

The answer to why is the same as how

[vernal vale]

no it isnt

[sweet shard]

"why does this work" is just the proof

[sweet shard]

.

[vernal vale]

im gonna assume that i'm just asking my question poorly

its not a big deal

[sweet shard]

What's an example of a simpler math result that you can explain "why"

[vernal vale]

i guess i was hoping itd be a source of intuition

[sweet shard]

E.g. fundamental theorem of calculus

[vernal vale]

but this obscure hint shortcutting the problem and the answer just falls out is fine too

[sweet shard]

"intuition" is also poorly defined

[opal vault]

As intuition, Ig if the 2-norm for R^n vectors is u^T * u (which is tr(u^T u)), then the frob norm is a generalization

[vernal vale]

riemann youre always so nice im gonna assume youre being pedantic to teach me a lesson about the thing im doing wrong here

[sweet shard]

It's not obscure once you look at the definition of the frobenius norm

[vernal vale]

or correct something about my thinking that is bad

[vernal vale]

i guess

[sweet shard]

This is really all I'm trying to get at

[vernal vale]

id have to think about it more

[opal vault]

In a way, "why" the frob norm square is tr(AA^T) is the same "WHY" the 2-norm on R^n is u^T u

[vernal vale]

its just some norm

[opal vault]

"why" in VERY BIG quotations

It's because there's a proof

[vernal vale]

i guess i felt kinda smart for figuring out roughly what the norm would be

i still dont have the answer but ill get there

i guess it doesnt have to enforce intuition

or make sense

it can just be the answer

i had my expectations set too high

[sweet shard]

You can build more intuition once you do more linear algebra

You don't get it from any single problem with a 3 line solution

[vernal vale]

@sweet shard @opal vault thank you both I'm happy to put this one behind me. Couldn't have done it without you 🙇

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[neon iron]

hi guys

[neon iron]

I'm lost

I watched a video ab ODE

about integrating factr

or

but this question throws me off a lot

because p(0) = A

and

dP
dt = − r
V
P + F,

that equation

idk what to do with it

tbh

[sweet shard]

You don't use the initial condition until after solving the ODE

[sweet shard]

Yes this is correct easy to find the general solution

[sweet shard]

Read equations 1-7
https://tutorial.math.lamar.edu/classes/de/linear.aspx

[neon iron]

is it like the first equation but rearranged?

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@neon iron Has your question been resolved?

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[heavy cove]

Okay so

[heavy cove]

How do I find the orthogonal complement?

I know that the orthogonal BASIS of A onto B is found by making the projection a unit vector

but how do I find the orthogonal component of A to B?

[topaz sinew]

@heavy cove Has your question been resolved?

[worthy storm]

"vector component of a orthogonal to b"
isn't this just
a - proj_b(a)

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[heavy cove]

ohh yeah

[heavy cove]

cuz orthogonal is perpendicular

so its the line thingy

[heavy cove]

BRO BUNGO

[worthy storm]

yo penguin

[heavy cove]

so basically they assigned this complicated Gram Schmit and Orthogonal Projections

And I did that HW

and then they assigned Vector / Scalar projectioin

WHICH MAKES NO SENSE

cuz the gram schmit stuff BUILDS OFF the vector/scalar projection

[worthy storm]

yea that's right

[heavy cove]

so its like they made me build a skyscraper AND ONLY THEN taught me how to build a wooden hut

[worthy storm]

oh, haha

[heavy cove]

AHHHHHH

[worthy storm]

yea you need to be fairly comfortable with orthogonal projections to understand G-S

[heavy cove]

bungo I promise you imma learn linear algebra properly after this lin alg class

gonna grind axlers and the other book after

[worthy storm]

nice

[heavy cove]

IM GONNA BE A GOD AT LINEAR ALGEBRA

one day

[worthy storm]

i think most people learn LA by multiple passes

one more computational then one more theoretical

you understand it better after the second pass

[heavy cove]

yeah after I get computation down i'll read axler's

[worthy storm]

nice

[heavy cove]

my goal is to master linear alg, diff eq, and intro to proofs before senior year

[worthy storm]

fairly good book although it has some strange parts

[heavy cove]

and then during summer

i'll learn math analysis

[heavy cove]

wdym?

[worthy storm]

yea, analysis is the fun stuff

[heavy cove]

i can't waiiiit

I was going to do rudin but apparently that is way t ohard

[worthy storm]

strange treatment of the characteristic polynomial and a few other things

[heavy cove]

so I am going to do Tao 1 & 2

[worthy storm]

are you self studying? if so then avoid rudin

abbott's "understanding analysis" is good for self study

[heavy cove]

hmm would you reccomend better books then? I heard this book called "linear algebra done WRONG" but that sounds weird asf

[worthy storm]

i don't know the tao books but i think they are well regarded too

[heavy cove]

I'm choosing that because it starts at the basics

and goes slowly

which is usually bad

[wispy hedge]

ive heard good reviews on linear algebra done wrong

[heavy cove]

but good for me

[worthy storm]

that's actually a pretty good book, the guy is just having fun calling it "wrong" because axler called his "right"

[heavy cove]

ahhh lmfaoo

math humor at its peak

[worthy storm]

they're both legally free, no reason not to get both and see which you like

[wispy hedge]

a few of my friends found linear algebra done wrong a good book to start off with

[heavy cove]

is the "linear algebra done wrong" like axler's without the "wierd stuff" you mentioned earlier?

is it good to learn the "wierd stuff"?

[heavy cove]

got it

so maybe I choose that over axler?

[worthy storm]

i'd say that's somewhat true yea

[wispy hedge]

yeah well

its your choice in the end

[heavy cove]

okie dokie

[wispy hedge]

but you could look up some book reviews

to see what the books go over

[worthy storm]

axler's is a nice clean treatment that is a good preparation for functional analysis (his proofs are in that style), but it can be confusing in some places as a result

he used to have a horrible treatment of determinants too, but he mostly fixed that in the new version

[heavy cove]

I want a solid understanding of theoretical + computational linear algebra (akin to the classes that are taught in university). I assume the books cover what is taught in university right?

because imma gonna beg the professors to let me test out of the courses

[wispy hedge]

well

yea pretty much

[heavy cove]

ain't no way am I gonna do lin alg a 3rd time in college as well

[wispy hedge]

you said you wanted to master linear algebra before senior year right?

id start from a simpler book that starts with the basics and then go for the more complex stuff

[heavy cove]

yeah so I have 5 months left

[worthy storm]

the honors undergrad LA course here usually uses either axler or friedberg/insel/spence, another good book (more conventional than spivak)

[heavy cove]

5 months to GRIND

bwahahhaha

[wispy hedge]

5 months to start linear alg from scratch

and master it?

[heavy cove]

I mean I am doing linear algebra with my community college class

but they don't teach at all

so I learn from asking Mathematics discord for help on problems

[wispy hedge]

5 months to master something like linear alg from scratch

[heavy cove]

so I have a "kinda" understanding of linear algebra

[wispy hedge]

is pretty challenging

i have a similar goal to learn linear alg before senior year

[heavy cove]

by master I mean have the level of knowledge akin to a student who has taken a university class in linear algebra

[heavy cove]

YOOOO

[wispy hedge]

oh

well if you wanna learn exactly what they learn in university

[heavy cove]

wait what does master linear algebra mean

💀

[wispy hedge]

you can search up course lectures and stuff

and use a few books

[worthy storm]

yea this ^

[heavy cove]

I'm probably gonna use a book and no lectures - is that fine?

or should I use lectures

[worthy storm]

follow some univerity's syllabus

[wispy hedge]

yeah you can still learn well

but

books dont necessarily follow university syllabus

[worthy storm]

supposedly the gilbert strang lectures (MIT open courseware) are good, i've never watched them though

[heavy cove]

also there is no point in learning the "theroetical" diff-eq right? Like I know learning the proof based lin alg is good, but I assume computation based diff eq is good enough?

[wispy hedge]

if you want to learn exactly what they learn in uni

[heavy cove]

gotchya

[wispy hedge]

id use lectures too

[heavy cove]

yessah

[worthy storm]

really depends on what you want it for ig
most likely at least start with an intro "computational" one

[heavy cove]

I am majoring in computer science

and want a strong basis for machine learning

I also want a good grasp of the mathematics field

[wispy hedge]

valid

[heavy cove]

hence modern abstract algebra + analysis + topology

[worthy storm]

i think a computational version would be fine then ,from what i see of ML it doesn't require a theoretical treatment of differential equations

[heavy cove]

which iirc are like the main math fields

[heavy cove]

bet

[worthy storm]

make sure you study probability though, that's really important

[heavy cove]

but because linear algebra proof based is important I want that

[heavy cove]

yeah but i'm lokey fire at probability

[wispy hedge]

yea well

[heavy cove]

so like that is later

[wispy hedge]

after like linear and abstart algebra

and some analysis

the math field opens up

to a bunch of different topics

so its like your choice which way you wanna go

[heavy cove]

yeah, I don't wanna major in math, but I want the background to be able to have a good grasp of it

do you know what I mean?

its like

I don't wanna be an olympic diver

but i want to be a god damn good diver

like good enough to flex on my friends?

[wispy hedge]

yeah thats pretty much what im tryna do in my long run

[heavy cove]

YAYYY

and ur in high school too

twinsies

🤩

[wispy hedge]

yeah im only a freshman though

ive got a long way to go

[heavy cove]

what the fuck 💀

wait what math do you know?

[wispy hedge]

ive self studied up to calc bc

i mean

im almost done with calc bc

[heavy cove]

dude that is amazing

[heavy cove]

so going for the 5 on the ap test calc bc?

[wispy hedge]

yeah

[heavy cove]

just curious, are you gonna dual enroll or self study?

[wispy hedge]

im tryna self study physics 1 and c after im done with calc bc

and then do advanced math

like linear alg and analysis

[wispy hedge]

probably both

[heavy cove]

I recall someone who got into a top college for math emailed a bunch of profs and just went to the lectures

[wispy hedge]

im def gonna self study a lot but ill dual enroll too

[heavy cove]

not officialy for credit or anything

[wispy hedge]

yea

[heavy cove]

dude I wish I started earlier

I only got into math senior year

I WASTED MY POTENTIAL

😭

[wispy hedge]

nah you still have a while

4 years of uni

[worthy storm]

haha listen to you, you're still in HS, you have not wasted your potential

[wispy hedge]

and as many years as you want post graduation

[heavy cove]

💀

math doesn't pay

😭

oh wait you mean self study while having a job?

[wispy hedge]

yeah but if you learn math aside of your job

youre only a senior in hs you have atleast 4 years of uni

[heavy cove]

Bungo I pinky promise you that imma do real analysis before college

[wispy hedge]

to fully focus on math if you want

[wispy hedge]

oh nah

i have a feeling the worst is yet to come

[heavy cove]

💀

[wispy hedge]

im almost at infinite series

[worthy storm]

aim for something more like honors calc imo
jumping straight into real analysis is gonna be a leap if you're not already comfortable with epsilon-delta proofs and such

[heavy cove]

bro lagrange error bound messed me the fuck up in calc BC

I just decided to take the L and not learn it lol

[wispy hedge]

nah but calc bc isnt even that bad

there are way worse courses

and thats what im scared of

[heavy cove]

I am going to read one of those "how to prove it" books - that would be enough right?

[worthy storm]

see spivak or apostol calculus for what i mean by honors calculus

[worthy storm]

maybe! i've never read one, just learned proofs by studying the subjects

[wispy hedge]

do as many practice questions as you can

[heavy cove]

yeah I told someone I was going to do spivak --> real analysis, but they reccomended a proof book instead

[heavy cove]

hm got it

[heavy cove]

wait so bungo

[heavy cove]

Spivak
Linear Alg done wrong
Diff-eq Computational based

once I get those three out of the way

that is enough mathematically maturity to start real analysis right?

[worthy storm]

sure

you don't even need diff eq for that

spivak, and basic linear alg if you're gonna do multivariable

[heavy cove]

i feel like everyone takes diff eq before higher level math classes haha

[wispy hedge]

after calc bc

[heavy cove]

oh I already did calc 3 last quarter

[wispy hedge]

what topic/course should i go for

[heavy cove]

CALC 3

[wispy hedge]

do i do multivariable

[heavy cove]

its fun

mhm

very visual

[worthy storm]

it's true, but it's not required for real analysis (not conceptually, although the university may have it as a prereq)

[wispy hedge]

so like

calc bc -> multivariable calc

and then

[heavy cove]

linear algebra

differential equations

[worthy storm]

good, this is also important for ML

[heavy cove]

I'm probably going to do a proper book and learn it again though

[wispy hedge]

calc bc -> multivariable calc -> linear algebra -> diffeq

and then analysis or something

[heavy cove]

I want to make sure I have really really reallyyyyyyyyyyyyyyyyy strong fundamentals

like SUPER DUPER STRONG

right now my calc 3 is very weak lol

[heavy cove]

you can do lin alg at the same time as diff eq

that is what I am doing

[wispy hedge]

makes sense

[heavy cove]

lin alg has two components, proof based and computation based

[umbral herald]

You’re literally in a senior like me 😭 and you’ve done way more than I have

[heavy cove]

(right Bungo?)

[wispy hedge]

im probably gonna take maybe a year or year and a half of break from focusing solely on math

because im tryna self study physics 1 and c

which is kinda math but still

[heavy cove]

its okay lapras satvik is in calc BC as a freshman

he makes both of us cry inside

[worthy storm]

more or less yea, some books might try to do both but i don't really recommend it

[umbral herald]

I- 🗿

How to feel useless 101

[heavy cove]

honestly I wasted my time in high school

getting A's

I shoulda got C's and shit

and just studied math and functional programming

SMH

[umbral herald]

Frfr should’ve done more with my life 😭

[heavy cove]

ALSO BUNGO

I got into a cs + math program

[worthy storm]

nah don't worry about it, you have plenty of time to fly through the math curriculum at university

[heavy cove]

for ocllege

is it going to be super duper fun

[umbral herald]

Omg nice!!!

[heavy cove]

YAYYYY

[worthy storm]

nice, killer combo

[heavy cove]

BRO RIGHT

my two favorite subjects

[umbral herald]

That was what I was originally gonna do but I’m going into pre-med so biochem and neuroscience

But I still love math

[heavy cove]

yooo

lapras

[umbral herald]

[heavy cove]

I know someone who did MIT CS major

and then harvard med school

[umbral herald]

💀

[heavy cove]

lokey be pre-med and major in math

[umbral herald]

wtf

[heavy cove]

💀

[umbral herald]

💀

[heavy cove]

wait r u a senior too?

[umbral herald]

Yeaaaaa

[heavy cove]

YOOO where did you apply?

[wispy hedge]

damn

[umbral herald]

I just eded 😭 and that’s it

[wispy hedge]

bigpenguin

how do you self study

[umbral herald]

Where did you get into?

Or are planning to go

[heavy cove]

honestly I have a lot of regrets - I signed up for diff eq and linear algebra at online community college

and because they didn't have lectures

I didn't learn anything

[heavy cove]

I would reccomend reading the book, and then once you finish dual enroll

[heavy cove]

uiuc

[umbral herald]

You at least did that I’m just

[heavy cove]

its okay high school senior year is supposed to be fun!!!

[umbral herald]

Omg GLLL!!!

[worthy storm]

nice, great cs school

[umbral herald]

I got into Penn

[heavy cove]

you can't get drunk if you are doing diff eq HW can you 😵‍💫

[heavy cove]

YOOO

UPenn???

[umbral herald]

Yeah 😭 it always gets confused with Penn state

[heavy cove]

And the great thing is that I really want to go into systems so UIUC is perfect for systems

[heavy cove]

THAT'S CRAZY

UPENN AS IN THE IVY

man just casually says

"I got into Penn"

mother fcker

[umbral herald]

Now because I feel so outclassed 😭

You got into UIUC and you’re saying this 😭

[heavy cove]

upenn has the sexy factor tho

plus

[umbral herald]

💀 and UIUC doesn’t?

[heavy cove]

you can prolly find someone rich to marry there

think about it

[umbral herald]

👀 you’re soooo right

[wispy hedge]

yo upenn is crazy

[heavy cove]

flirt with some frat boy

and you are set for LIFE

[wispy hedge]

oh

[worthy storm]

no way would you regret going to penn (except maybe for the cost haha)

[wispy hedge]

i usually just read the book and do problems off it

[umbral herald]

FRFR Yknow what

Life plan ++

[wispy hedge]

and search whatever i dont get on youtube

[heavy cove]

(unless the college teaches off a book, in that case do book alongside dual enrollement)

[heavy cove]

3B1B 😍

[wispy hedge]

yeah

he comes in clutch

and the organic chemistry teacher

[umbral herald]

OMGGG HE DOES HE SAVEA ME

[wispy hedge]

yeah he saved me for so many calc topics

[umbral herald]

I’m taking orgo this year and literally kill me now

[heavy cove]

honestly i wish my high school teachers were just replaced with youtube videos

if I am being real

[umbral herald]

Cannot relate 💀

[worthy storm]

facts

[heavy cove]

AP Chem was my worst AP Score

💀

[umbral herald]

Omg that was my only 4 😭

[heavy cove]

BRO SAMe

NAHH

[umbral herald]

Let’s not talk about it

[heavy cove]

wait

nvm

I had a 4 in ap us history but I didn't even take Ap us history

[umbral herald]

Going into premed with a 4 in ap chem like

I’m so stupid 💀

[heavy cove]

so that doesn't even count

[heavy cove]

AT UPENN

[umbral herald]

😂

[heavy cove]

wait so does the credit not transfer then?

I heard ivy's be strict like that

they only take 5's?

[umbral herald]

A 5 doesn’t even matter 😭

You need to take a test

[heavy cove]

LMFAO

[heavy cove]

wait just do fire on the test

[umbral herald]

To skip gen chem

[worthy storm]

tbh if you have to take the class again at penn it'll probably 100x better than the high school AP version anyway

[heavy cove]

waint bungo r u in college

[umbral herald]

[heavy cove]

yepp

[umbral herald]

👍

[worthy storm]

oh hell nah, that was a million years ago for me

[heavy cove]

a million 💀

[heavy cove]

wait what did you major in?

Math?

how did you know uiuc is a good school for CS 💀

like tbh not many people know that

its mainly known for being in the middle of a corn field LOL

[worthy storm]

math and electrical engineering for undergrad, also a year in phd program for math but i bailed and got a job as a sw dev instead

[heavy cove]

NAHHH you sold your soul

[heavy cove]

what kind of math?

ooh also what kind of area are you doing sw in?

[worthy storm]

also i grew up in the chicago area, and i spent years interviewing applicants for dev jobs, i know UIUC's reputaiton

[worthy storm]

analysis

[heavy cove]

I think the dream job for me is to do a cs job that is very mathy-centric

or at least

anything but frontend

💀

[heavy cove]

wait bungo you interview people!!!

big boss

[worthy storm]

most of my dev work was system-layer on smartphones and stuff related to GPS and other location technologies

[heavy cove]

yooo that sounds fun

[umbral herald]

That was gonna be me since my brother does comp sci and he’s living pretty comfortably but getting that initial job I feel like could be a struggle

[worthy storm]

i did! then i retired early and i don't have to interview anyone now

[heavy cove]

I do competitive coding so lokey interviews are gonna be fire

its getting an interview that is gonna be hard

💀

[wispy hedge]

yeah i found youtube videos more helpful than hs teachers

[umbral herald]

[wispy hedge]

self studying and yt videos have always been easier to grasp from

compared to hs teachers talking

[heavy cove]

what do you do in your retirement? On the Math Arc rn?

[worthy storm]

the sheer numbers almost guarantee that a really good hs teacher is gonna be a rare thing
whereas a good youtube series can reach everyone

[heavy cove]

pov you have like 50 absenses from classes because you just end up teaching the content on your own via youtube

[heavy cove]

plus, a youtube video gets like 5 hours of work put into a simple 30 minute video

like 3B1B puts sooo much effort into it

wheras teachers yolo it

[worthy storm]

self studying whatever interest me mostly!

[heavy cove]

that sounds like the dream

[umbral herald]

Self studying I feel like I learn better but it’s more time consuming for some reason

[heavy cove]

bungo I also wanna learn functional programming one day

omg there are sooooo many things I want to learn

but not enough time!!!

[heavy cove]

imo its better for your logical abilities to self study

[worthy storm]

story of my life haha

[heavy cove]

you get a better intuitiion

[umbral herald]

While I just laze around

[heavy cove]

and its less "memorize formula" and more "book makes you derive it"

[umbral herald]

I actually have a coding assignment I need to do for comp sci rn 💀 my procrastination levels are off the charts frfr

[heavy cove]

I HAVE TWO FINALS TMMW

lol

mutually agree to get off discord

[umbral herald]

Omg I have this crazy calc teacher that gives a pop quiz every other day and I feel just so demotivated to do any of her work

She’s a great teacher tho

[umbral herald]

😭

[umbral herald]

Mb but I’m too attached

Also how the hell are you supposed to synthesize aspirin from benzene

Like Istg it makes 0 sense

So off topic 💀

But I’m just looking over my hw rn

[wispy hedge]

bigpenguin

have you done any math contests

like amc

[umbral herald]

It’s like I don’t even wanna look at anything anymore. Senoritis is hitting hard

[umbral herald]

Omg I tried AMC this year and I didn’t even realize it was AMC 🤡

Until like the competition

I thought it was just like a fun little like math club thing 🤡

[heavy cove]

haha

@ me in two days

that is when my finals will be done

💀

[umbral herald]

What finals do you have?

[heavy cove]

AIN'T NO WAY

Y OU CALL It

"FUN LITTLE MATH CLUB THING"

[umbral herald]

NOOO VECAUSE I WAS CLOWNINGG AND TRIPPING

I WAS DELULU

[heavy cove]

diff eq

and lin alg

midterms

[umbral herald]

LITERALLY I DIDNT KNOW

[heavy cove]

SMH

[umbral herald]

SO I CAME IN UNPREPARED

[heavy cove]

WERE YOU ABLE TO SOLVE AT LEAST LIKE THE FIRST 10

[umbral herald]

Yeah I’d hope so 😭

[heavy cove]

WAIT I CAN'T BE DISTRACTEd

BYE

[umbral herald]

But like I was like hello

Why is this timed

🤡

I was like can I take this home 💀

IDK WHAT I WAS ON THAT DAY

[tulip monolith]

Do you have linear diff eq of higher order

[umbral herald]

😭

[wispy hedge]

are we allowed to take up a help channel to just talk about math

[topaz sinew]

@heavy cove Has your question been resolved?

[topaz sinew]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[topaz sinew]

Available help channel!

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Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
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[muted inlet]

what is x-2 * x+2

[muted inlet]

pls help

[neon iron]

huh simplified? what is the original question

[muted inlet]

Examine three consecutive even numbers. For example, the numbers 2, 4 and 6. Multiply the middle number by itself and multiply the largest number by the smallest number. Calculate the difference of the products. Do the same with three new numbers.a) What can you say about the difference in the two surveys?b) Show that the difference is always the same. Feel free to use a general solution.

[lusty marsh]

there is an identity which says $ (a+b)(a-b) = a^2-b^2$

[low nymph]

problem being there were no ()

[muted inlet]

how do i do this question

pls or im failing

[low nymph]

if only you had (), you would have done it perfectly

[restive inlet]

use the factorisation identity for the difference of two squares
or expand fully / simplify

[lusty marsh]

how is it related to the prev question you asked?

[muted inlet]

they told me to use a general sulution and i used one. I uses even numbers like they told me that are like 2 4 6 on a row like that

[low nymph]

indeed, you can just follow what they said:
three consecutive even numbers x - 2, x & x + 2
middle number multiplied by itself x * x
largest multiplied by smallest (x + 2)(x - 2)

[rigid ivy]

-x+2

[low nymph]

that's oddly correct, but wrong context, so the equation is useless

[muted inlet]

the diffrance between the numbers is always 4 so i need to take x * x = x2 and i need to take x2 - -x+2

that seem impossible to me

[low nymph]

because your notation is messed up

[restive inlet]

i need to take x2 - -x+2
what?

[muted inlet]

idk im so bad at english

om so sorry

[restive inlet]

its not the english

[low nymph]

you did not write the numbers correctly

[restive inlet]

you're not representing proper math

[muted inlet]

yeah but i need to translate the whole question

that is from my school test

[low nymph]

the question was translated acceptably
the problem was the mathematics

[restive inlet]

largest multiplied by smallest (x + 2)(x - 2)
you missed the () when you attempted to type that out

use the factorisation identity for the difference of two squares
can be used to expand that

alternatively distributive property (god forsaken foil) to expand then simplify

[muted inlet]

That is -x+2?

[restive inlet]

no

-x + 2 is what you typed out without () would simplify to
is in acuality irrelvant to your question

[muted inlet]

What’s the product of it then

[restive inlet]

use the factorisation identity for the difference of two squares
can be used to expand that
alternatively distributive property (god forsaken foil) to expand then simplify

[muted inlet]

Sorry my English is bad I don’t understand

I wanna know what it becomes

[low nymph]

expand (x + 2)(x - 2), not x + 2x - 2

hint:
(a + b)(c) = a(c) + b(c)

[restive inlet]

look up difference of two squares

[low nymph]

or that, yes

[muted inlet]

Look at the first question I needed to take 4 * 4 = 16 and then 2*6 = 12 16 - 12 = 4 the difference is always 4. Then I need to do the same with a general sulution. So i took these three numbers x-2 X X+2

And I had to do the same with them

[restive inlet]

we are aware

[muted inlet]

Yeah and x*x = x2

[restive inlet]

look up difference of two squares
that'll tell you how to efficiently expand (x-2)(x+2)

[muted inlet]

Ok

👍

[topaz sinew]

@muted inlet Has your question been resolved?

[muted inlet]

I just sant the answer to the question

The one on the school test

[low nymph]

?

[muted inlet]

Forget it

You can close the question

[outer portal]

you have to be the one to close it

so that way someone else doesnt go "you sound done enough"

you type .close or .solved

[muted inlet]

.close

[topaz sinew]

Channel closed

Closed by @muted inlet

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Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[waxen herald]

.show

[fading crescent]

continuation of #help-39 message

[fading crescent]

@outer portal so I'm not talking about equal temperament, I know how it works, I'm talking about just intonation

one of my friends noticed that the number sequence I posted are {1,5,17,19} times a power of 3

https://oeis.org/search?q=1%2C5%2C17%2C19&language=english&go=Search

[outer portal]

that was just in case you didnt know but my point was something else

the point was that most likely the first couple of tones line up nicely with a seemingly equal 12-tone scale so they chose other tones that were as equally spaced

so if you want to aim for something similar youd also have to choose similar fractions

maybe it's just a thing of "they are closest to the P_n = P_a2^{(n-a)/X} way of diving the range 1-2 into X parts"
I really dont know a better way than just this

[fading crescent]

ok I think I posed that hypothesis in my initial question as well

yeah exactly

maybe

[outer portal]

maybe youd be able to find something when searching up rational approximations

because first, theres not a way to change or otherwise tweak the sequence to get something else out of it that we can easily do

and second, part of those numbers are like thousands of years old, we cant really determine the one purpose of it anymore

[outer portal]

as for why they work, I think theres something you could find here but I wouldnt know

maybe a better question would be "why do these particular overtone ratios fit nicely with the 12th roots of 2"

and another question would be "how can I generate more for Nth roots of 2"

[outer portal]

I do have a potential idea for the powers of 3 part

you remember the circle I showed?

I marked the 3/2 ratio on there and it was really close to one of the roots

[fading crescent]

yeah

[outer portal]

I forgot to say its a rhetorical question, sorry

[outer portal]

now the /2 part would only move it down an octave

if you just had 3,

it would make a full loop around the circle and then a perfect 5(ish to equal temperament's)

its close enough that if you kept doing it, you should see the rest of them

[fading crescent]

yes it's the perfect fifth in just intonation

[outer portal]

7/12 in particular,

7 is coprime to 12

so you should be able to get all 12 tones from just the perfect 5ths

[fading crescent]

yeah you can do this with 1 5 7 and 11

[outer portal]

maybe thats how or why they found the others?

[fading crescent]

since they're all coprime

I call this method the "just intonated step method/algorithm" and implemented it

but you know

[outer portal]

its got better and more accepted names I reckon but I wouldnt know them

this idea is way too common and can appear in any sort of way

[fading crescent]

https://cdn.discordapp.com/attachments/942552701143769189/1202369934324142150/v6XLFSS.png?ex=65cd3543&is=65bac043&hm=03130b85f85431ec2923583eee6fd0831831a247c029a760278aa8ecc9310a42&

[outer portal]

personally I dont prefer giving long names to prevalent ideas

[fading crescent]

you get 2.027 as the octave

[outer portal]

cant be too bad

[fading crescent]

on the left you see just intonation

on the right the step method

[outer portal]

Im assuming you took M and manually matched the columns rows for J

unless you figured out how to get that automated too due to 7/12

[fading crescent]

https://cdn.discordapp.com/attachments/942552701143769189/1202377412780888104/3zjJ5uE.png?ex=65cd3c3a&is=65bac73a&hm=365c9b2f3be455bdeb18d6e2ff77abfd61e7f5ee2f62856c74643dea98353c41&

i tested my theory first

and then automated it

[outer portal]

I mean the matching rows part not the 3/2 part

[fading crescent]

I don't understand

[outer portal]

did you manually copy-paste the values in column M to get column J, or did you figure out a way to derive which entry belonged to which position?

[fading crescent]

I manually sorted them

but you can easily automate it

it's just modulo 12

here's my implementation

https://github.com/float3/float3.github.io/blob/master/ts/playground.ts#L199-L214

[outer portal]

then again if you stack enough of them its too far off so a different prime like 5 would be used

theres also no reason getting the fractions from composite numbers wouldnt work, like borrowing them from a "6-tone" scale

[topaz sinew]

@fading crescent Has your question been resolved?

[fading crescent]

maybe I can construct a 6 tone scale and see what the method to extrapolate to twelve tone is and then copy that pattern!

[outer portal]

@fading crescent Ive got a dumb idea

what if you keep generating intonations until one of them is within 0.1% of the kth power of the Nth root of 2

I dont think the results youd get would be very useful nor pretty

[fading crescent]

that's if they're really arbitrary

[topaz sinew]

@fading crescent Has your question been resolved?

Channel closed

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[proud sand]

what would be the complement of this

[somber eagle]

for all x,y : x<y or x²>y²

[zinc cove]

< or ≤

[proud sand]

why do we have or here?

Oh its the negation

Thanks

.close

[topaz sinew]

Channel closed

Closed by @proud sand

Use .reopen if this was a mistake.

[topaz sinew]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
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Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[finite steppe]

someone explanation plss for context
it require concepts of Vector/matrix/and system of linear eq

[opal vault]

you know that $Ax_1 = b$ and $Ax_2 = b$

[thorny flame]

rafilou2003

[opal vault]

so the question is really about what is $Ax$ when $x = x_1 + x_2$ and $x = x_1 - x_2$

[finite steppe]

ohh

[thorny flame]

rafilou2003

[finite steppe]

so what approach I follow for this question

[opal vault]

well

what is $A(x_1 + x_2)$

[thorny flame]

rafilou2003

[finite steppe]

Ax

I think

[opal vault]

uhm well yes if x = x1 + x2

but

[finite steppe]

oki

[opal vault]

you know this

[opal vault]

so maybe use it to compute this

[finite steppe]

how to compute that this is first time learnt about Ax = B

i mean from the vid lec earlier

[opal vault]

imagine a,x and b are just numbers for now

if ax1 = b

[finite steppe]

oki

[opal vault]

and ax2 = b

how do you find a(x1+x2)?

(with numbers)

[finite steppe]

umm
we do cross mulipication
and so we will reach some thing like
a( (b/a)+(b/a))

[opal vault]

really unneeded

[finite steppe]

😅

[opal vault]

imagine if a = 0 we couldn't do that

[finite steppe]

yup

[opal vault]

no what's a more efficient method

[finite steppe]

😅

[opal vault]

can you not express a(x1+x2) in terms of ax1 and other?

[finite steppe]

yup

[opal vault]

how?

[finite steppe]

like ax1 +ax2

like that?

[opal vault]

yes exactly like that

[finite steppe]

ohh cool

[opal vault]

you used what's called the distributive property

[finite steppe]

im sorry but let me cheak meaning of that

[opal vault]

is this chatgpt

[finite steppe]

ohh gottt itt 🥳

[fast mist]

im a serious math student so thats how i type 😭

[opal vault]

really? and "A=2" makes sense when A is a matrix?

cut the bullcrap

<@&268886789983436800>

anyways

[finite steppe]

can we continue pls? 🥺

[opal vault]

yes no worries

[finite steppe]

thank youu

oki so, we did opened brackets and did multiplication ..

so how it relates?

[opal vault]

well, your class is named "linear algebra" right?

do you remember stuff about linear maps?

[finite steppe]

I think so, I understand those it's just that I missed on some fundamental lesson but I am now focused to master maths
well unfortunatly i am degree and I know it feels crazy to ask these quess

[finite steppe]

in this ques can we just answer it with intuition bcz
Ax = b in 2 of all statements makes sense only
so first and 3rd option is correct?

[opal vault]

intuition would be wrong then

Really, recall that we can "distribute" the product when a, x, b are numbers

wouldn't it be great if it also works when A is a matrix and x,b are vectors?

[finite steppe]

yup, i would be really great

[opal vault]

guess what then

[finite steppe]

they do have same property?

[opal vault]

yes

this is linear algebra, and so :

remember that for $f$ a linear map, $f(au+bv) = af(u) + bf(v)$ (a and b scalars, u and v vectors)

[thorny flame]

rafilou2003

[opal vault]

well f in this case is our trusty matrix A

[finite steppe]

yes yes

[opal vault]

so applying this to $f=A$, this gives $A(x_1+x_2) = ?$

[finite steppe]

and au is x1 and bv is x2?

[thorny flame]

rafilou2003

[finite steppe]

right?

[opal vault]

goddamn right

[finite steppe]

🥳

[opal vault]

(a =b = 1 for simplification here)

[finite steppe]

oki dokii

after reading ques again I understood
x1 and x2 are solution of lin eq Ax=b
which also means it will have infinite solutions
but how do we relate it with
x1 +/- x2 is solution of Ax = b or Ax = 0 or else?

[opal vault]

well if x1 is solution of Ax = b

that just means that Ax1 = b

same goes for x2

[finite steppe]

yes

yes yes

[opal vault]

then you just compute A(x1+x2) using what we said earlier

[finite steppe]

which means ax1 +ax2 = b +b
which leads to a (x1+x2)=2b?

correct?

[opal vault]

correct

[finite steppe]

🥳

thank you sirrr

[opal vault]

try it with x1-x2

[finite steppe]

yes yes, just a min (trying)_

it will lead to 0

bcz as we know ax1 = b and ax2 =b
and then ax1-ax2 = b-b
which is a(x1-x2)= 0

correct?

[opal vault]

yes

[finite steppe]

I can't believe so simple of a concept are been used here. 😱

Thank you @opal vault sir

.close

[topaz sinew]

Channel closed

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• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
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Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[main pollen]

hi

[main pollen]

hi

i got 10 question s due in 10 mins Can you guys please help me solve them

hello

Anyone

<@&286206848099549185> please help

they are geo and easy

[restive inlet]

!15m

[topaz sinew]

Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.

[restive inlet]

don't ghost ping

we're not here to give answers away

[main pollen]

I only have 10 mins left

i’m in a big problem

[restive inlet]

should've started earlier, its not practical to go through multiple questions in this time

[main pollen]

they are so easy

like this look

[restive inlet]

and people might not bother trying since you abused pings

[main pollen]

please help

anyone

.close

[topaz sinew]

Channel closed

Closed by @main pollen

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[topaz sinew]

Available help channel!

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Remember:
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• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
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• Be polite and have a nice day!

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[jade vortex]

Children born in Japan today can expect to live five years longer than their American counterparts. Life expectancy has been rising in all countries, but the slowest rate of increase has been in the USA. What could account for this, given that the percentage of people who smoke is roughly the same in all rich countries? Of course, the USA is the birth- place of fast food restaurants that sell unhealthy food. Moreover, a recent survey of Amer- ican lifestyles has found that overeating and failure to exercise are widespread amongst the population. So we must assume that obesity and lack of exercise have caused the USA to lag behind in the increase in life expectancy.

Which one of the following, if true, most weakens the above argument?

Most rich countries have the same standard of medical expertise.

Japanese children had a healthier diet in the 1960s than they do today.

*American fast food restaurants are now found in most rich countries.

In the 1960s and 1970s the USA had the highest percentage of smokers.

The USA spends more money on fast food than any other nation.

[jade vortex]

Plz READ I need your help :B

[torpid matrix]

okay what are your thoughts

I'm not sure how to walk one through a problem like this but we can talk about the answer you have and why it's right/wrong

[jade vortex]

I think the answer is American fast food .... Most rich countries

Because the passage is talking about the life expectancy in us and why it has a gradual increase compared to other countries

[unique fog]

However it is asking what weakens that argument

[jade vortex]

In case of others they still have the fast food restaurant but they have a increasing life expectancy

[unique fog]

If we say usa spends more money on fast food it supports the fact that obesity and such is rising in the usa causing a dip in live expectancy

Oh wait sorry

I thought you meant the 4th option

[jade vortex]

Yeah there was a typo I fixed it

[unique fog]

Your answer then Seems correct to me

[jade vortex]

But answer is 60s 70s option

I don't get it but I think there is a mistake

On question

.close

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[unique fog]

Actually no that sounds better

Because the passage says that all of the people have equal smokers however saying that us used to have more smokers gives a bit of argument against that

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[jade vortex]

Why

[jade vortex]

. reopen

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[jade vortex]

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[modern drift]

what is the formula for this?

[craggy haven]

do it in two steps, first find the amount of time it takes for the car to stop

[atomic wadi]

nvm

[pseudo sonnet]

we don’t need to though

[atomic wadi]

v^2 =u^2 + 2as

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[cloud scaffold]

it's an exercise in calculating elasticity
Prices and quantities demanded at dates t = 0, 1 are as follows:
P0 = 8, P1 = 10 and Q0 = 30, Q1 = 20.
What is the arc elasticity of demand?
and I obtain -1.33

[cloud scaffold]

but I have the impression that the result is not very correct.

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@cloud scaffold Has your question been resolved?

[cloud scaffold]

<@&286206848099549185>

[sturdy ingot]

can you define elasticity?

Elasticity is calculated as percent change in quantity divided by percent change in price. is this a correct definition?

[cloud scaffold]

is the sensitivity of demand to price variations

in part yes

[sturdy ingot]

wait a sec

it is correct

sorry it took too long i was struggling with the TeX bot lol

[cloud scaffold]

thanks

and for this question I found 0.8
Consider the following supply function: D(P)=5+2P
For a price P=10, what is the elasticity of supply?

[cloud scaffold]

mdr

[sturdy ingot]

2

slope of the function

[cloud scaffold]

20?

[sturdy ingot]

no

2

elasticity is the rate of change of demand with respect to the prices. the following function (D(P)=5+2P) is a line with a slope of 2

[cloud scaffold]

there is no 2 proposed in my manual i don't understand i had fallen on 2 at the beginning but it doesn't seem coherent to me a.
1,25

b.
0,8

c.
20

d.
1,33333

[sturdy ingot]

so in any place where Price and Demand is defined, the elasticity is equal to 2

[cloud scaffold]

but c elasticity of demand the

[sturdy ingot]

maybe it is a typo

are you sure its not 5+20P?

[cloud scaffold]

no

It's okay, I'll try it again and see.

[sturdy ingot]

im pretty sure it should be 2

funny thing I'm studying derivatives and rate of change right now lol

[cloud scaffold]

the question is Consider the following supply function: D(P)=5+2P
For a price P=10, what is the elasticity of supply?

you're studying math