serious-discussion

[warped carbon]

Guys.

Number theory and taylor series is way fucking past fractions.

[wild lantern]

Cool stuff.

But like

Paper is still pretty useful for more basic math

[leaden skiff]

it doesn't really change anything tbh

you learn how to do things in your head form just getting enough practice

like you do enough fraction problems on paper you'll learn how to do it without paper

[warped carbon]

If this was correct.

Then why is this?

[leaden skiff]

if you learn how to do it in your head, then that wont translate to doing them on paper

[toxic gale]

I don't mix up concepts, I mess up numbers. 😂

[wild lantern]

Lack of practice

[warped carbon]

That's backwards.

[leaden skiff]

what do you mean by an "easy problem"

cause we all have different defintions of easy

[toxic gale]

That is fair enough. I guess for me an easy problem would be something from the exercises section of a calculus or below book.

[wild lantern]

Yeah, I would def not avoid paper for calc lol

[warped carbon]

x^2 +8x +6.

No paper, draw.

Draw as in gunslinging.

Not.

Paper drawing.

[leaden skiff]

like i'd probably have trouble adding 2 fractions in my head, something like 1/13 + 1/11 would be kinda slow for me to do in my head
but like, give me a piece of paper and i can do it much faster
human beings don't have good RAM for math

and you very rarely need to do math in your head

[warped carbon]

Your RAM is as good as you've made it.

[wild lantern]

"Here's a random expression, give me the answer!" Lmao what.

[toxic gale]

I can do that, but like, I have to remember the equation in my head. I'd rather just write it down and not have to store information in my memory.

[leaden skiff]

what are you even asking

[warped carbon]

For roots.

[leaden skiff]

ok that's not obvious lol

[warped carbon]

I'm used to teaching Algebra.

[leaden skiff]

why would you solve for roots in your head????

[toxic gale]

I mentally completed the square.

[warped carbon]

Where it's usually implied that roots are the question.

[leaden skiff]

hmm i don't like implicit questions tbh

[wild lantern]

There's WAY more questions you could ask about polynomials than just that.

[leaden skiff]

it makes people think polynomials are a "question" rather than a mathematical object

[toxic gale]

But like, that's quite unnecessary to remember in my opinion. Why would I try to remember all the numbers when I can write it down? I'm not saying it's bad, I'm just saying I don't get why you'd do it when you could use paper.

[warped carbon]

You're both right.

[charred mortar]

I feel like this is heavily dependent on what you're doing

[warped carbon]

I'm used to teaching secondary school Algebra, my bad.

[leaden skiff]

like i get it, to an extent you need to learn to do some simple math in your head quickly

or else you're gonna spend forever doing arithmetic

[charred mortar]

like for a big proof if I'm not writing stuff down then I'll almost always be screwed over big time

[leaden skiff]

but stuff like the quadratic equation is fine to write down

[wild lantern]

It's a bad habit to ask questions that way even in that level of algebra.

[charred mortar]

maybe for very basic algebraic manipulation and algorithms I can see the idea behind not writing down too much

[toxic gale]

I mean, whatever works works. If that's effective for you, then by all means, feel free to do it.

[charred mortar]

but just saying "don't write things down" in general feels quite disingenuous

[toxic gale]

I never really cared about the approach so long as there isn't any grave conceptual mistake.

[charred mortar]

ultimately though yeah just do whatever works for you

[toxic gale]

I feel like it gets harder the higher you go not to write it down.

[wild lantern]

I guess there's no shame in trying to work on mental math skills in general though.

[warped carbon]

I was able to do some integrals and most derivatives without paper, that was a while ago though.

[wild lantern]

Somebody can always give you a derivative you can't do in your head I guess.

Lots of nested quotient/product/chain rule applications just get out of hand lol.

[warped carbon]

It just tilts me a little bit when people can't do like 15^3 even if their life depended on it.

Because the thing is.

[charred mortar]

I guess it can help for a test environment

Bruh

[leaden skiff]

i don't think i can do 15^3 in my head

[charred mortar]

I really hope you’re only talking about high school, where exams are the emphasis

[warped carbon]

I think it's because in order to do problems in your head, you have to get smart about it.

[leaden skiff]

i'd have to do 225*15 on paper

[warped carbon]

It's not hard, watch.

[warped carbon]

That's easy.

Look.

[wild lantern]

It's not hard on paper...

[charred mortar]

Because at uni nobody really cares if you can do fast multiplication in your head

[wild lantern]

I'd be impressed for a couple secs lol

[charred mortar]

Same deal for integrals and derivatives

[warped carbon]

225*15 = (225*10 +225*5) = 2250 + 1000 + 125 = 3375.

[leaden skiff]

it just doesn't seem worthwhile to learn a "trick" to do this when I can already do it pretty fast on paper ya know
like it's a cool trick but it doesn't seem very pracitcal

[leaden skiff]

that's what i would do but just on paper

[charred mortar]

It’s just a party trick really

[wild lantern]

You cheated by typing smh

[leaden skiff]

the hard part is keeping track of all the different parts of the calculation

[charred mortar]

Admittedly I do think mathematicians are better at arithmetic than they pretend otherwise

[warped carbon]

Here's one for 87^2.

[wild lantern]

I think it depends on what you're studying too.

[charred mortar]

Yeah I guess

[warped carbon]

c^2 = (a+b)^2 for some selected values of a and b.

Let a be the tens' place and b be the ones' place.

[leaden skiff]

but like my question is just why should i practice doing problems like this in my head, when i can do them on paper much faster with a much lower likelihood of errors?

[charred mortar]

I suppose there’s no harm strictly speaking in learning these algorithms

[leaden skiff]

like practicing getting rough estimates in your head makes sense

that's very useful

but if you need an exact answer use paper or a calculator

[charred mortar]

It can also teach you how to come up with algorithms on your own, and learn what makes an algorithm fast in the first place

[leaden skiff]

yeah but you can still apply those algs on paper

[warped carbon]

(a^2 +2ab +b^2), a=80, b=7, 6400 + 1120 + 49 = 7569.

[wild lantern]

You might be better off working out whatever algo on paper first.

[warped carbon]

The point isn't to know the algorithms.

[charred mortar]

But emphasizing the use of the algorithm in manual computation over developing or comparing it to other algorithms feels rather pointless

[warped carbon]

The point is to figure out the algorithm.

That's what's worth practicing.

[leaden skiff]

yeah but you can do that with paper anyway no?

[charred mortar]

Right, which is what I was saying

[leaden skiff]

what's so special about doing it on your head

[warped carbon]

You totally could, but you won't be motivated to.

[wild lantern]

How do you think a computer scientist works out a complicated algorithm?

[charred mortar]

And yeah you may as well just do it on paper

[wild lantern]

(It involves paper)

[charred mortar]

Or hell program it

Paper and computer

[leaden skiff]

i use all these techniques myself and i always used paper

[wild lantern]

I guess it depends on the person but it's usually not jusy "Imma do this in my head"

[charred mortar]

Yeah me too

[warped carbon]

I'm saying, doing it without paper will force you to discover (80+7)^2.

[charred mortar]

I suppose at the end of the day it depends a lot on what you’re working with

[leaden skiff]

i don't see how it will honestly

[charred mortar]

I mean you could also brute-force it with the standard multiplication method

[wild lantern]

You can "discover" that with paper...

[leaden skiff]

honestly to me it seems like you'd be less likely to

[warped carbon]

In your head?

[leaden skiff]

paper is a much easier sandbox for messing with math

[warped carbon]

Fucking hard.

[charred mortar]

sure

[leaden skiff]

it feels like to me doing shit on paper would make you better at doing it in your head better than exclusively trying to do everything without paper

[wild lantern]

Binomial theorem exists on paper there's no need to discover it in your head.

[charred mortar]

I could do normal multiplication in my head tbh

[leaden skiff]

yeah if you didn't already know what (a+b)^2 expands to doing it in your head is needlessly difficult

[charred mortar]

but in general nothing wrong with writing it out

[warped carbon]

I don't know anybody else in person who can do synthetic division without a piece of paper, measuring against people who have just done like twenty synthetic division problems.

[leaden skiff]

you learn the "trick" and formulas by messing with paper

and then apply them when you need to do shit in your head

[wild lantern]

Synthetic division is fast as fuck on paper lol.

[charred mortar]

it feels like you're more against rote learning in general tbh

[leaden skiff]

what's synthetic division?

[warped carbon]

Actually, one guy.

[leaden skiff]

do you mean long division

[warped carbon]

This.

[warped carbon]

It's this stupid fucking paper trick to do polynomial division.

[charred mortar]

but that's quite separate from doing it in your head versus writing things out on paper

[leaden skiff]

i don't see why you can't avoid rote learning with paper

[wild lantern]

A variation of polynomial division for special cases.

[warped carbon]

No one who learns it actually knows why it works.

[leaden skiff]

long division?

[charred mortar]

like trust me, I fill out like 50+ pages per week for my working out

[leaden skiff]

yeah i never understood it until i learned polynomial division

[leaden skiff]

but like in hindsight it's obvious as fuck

[wild lantern]

They literally teach polynomial division right before synthetic in almost every sane algebra course.

[charred mortar]

if I were to do all my math in my head it'd be a shitfest

[warped carbon]

This is really my complaint.

[wild lantern]

People don't know how it works because they're dumb and don't pay attention lol.

[leaden skiff]

what the fuck is the left hand thing?

[warped carbon]

America.

[leaden skiff]

that's not how we did long division

[charred mortar]

it's not really just america tbh, synthetic division is taught in quite a few places, and unfortunately as something that feels separate to polynomial division

[toxic gale]

I never got the point of synthetic division either. I get the idea, but like, it's not that much longer just to do polynomial long division.

[wild lantern]

It's just a convenient way to rearrange polynomial division when you wanna divide by polynomials of the form x-a.

[charred mortar]

it's good shorthand, kind of like how matrices are good shorthand for systems of linear equations

[warped carbon]

My sub-argument is that doing things without paper makes the situation so difficult that learning things by rote becomes untenable and so you have to get smart.

[wild lantern]

It's way faster for shit like factoring once you know the roots.

[charred mortar]

but ofc if you don't know why it's a good shorthand it's useless

[warped carbon]

Let me give you my anecdotal story.

[charred mortar]

I suppose I can sort of see your point now with this

[leaden skiff]

or you could be like me and be so useless at memorizing stuff that you have to learn tricks just to be fast on paper

[charred mortar]

it may be true to an extent, but eventually you will hit a brick wall if you do choose to continue further studies in math

[toxic gale]

I just try to understand the concept and the tricks come out naturally.

[warped carbon]

Get asked division problem. 
I don't remember what the numbers were, we'll say it was 60/3. 
Realize that 60 is 3*20 and accidentally rediscover factoring.```

Something like this actually happened to me when I was, like, in elementary school or something.

[toxic schooner]

[wild lantern]

s/discovered/discovered on paper/

[leaden skiff]

how did you realize 60 was 3*20 tho

[warped carbon]

#serious-discussion message

[leaden skiff]

were you doing it in your head

[toxic gale]

Yeah. Could I do $\int_0^{\pi/6} \cos^2 \frac{x}{3} : dx$ without paper? I know the idea, just use the double angle identity. Do I want to simplify the absolute mess of arithmetic without paper? Hell no.

[warped carbon]

I wasn't using a piece of paper.

[fathom swallow]

PhenomPlasma

[wild lantern]

I'm saying that sub argument is just silly and your example is also silly.

[charred mortar]

I just plug it into wolfram alpha

[leaden skiff]

anyway the important thing abt math isn't how to solve problems

it's understanding concepts

[wild lantern]

You can jusy as easily discover those kinds of things with paper.

[leaden skiff]

and understanding concepts without paper is needlessly difficult

[warped carbon]

But you're not forced to.

So who would.

[leaden skiff]

also yeah, i think it's much easier with paper

[sonic sentinel]

i had another technique, can anyone pls remind me what are the parts of a division equation so i can explain

[leaden skiff]

most people wouldn't bother learning tricks even if they couldn't use paper, they'd just try to memorize harder

[toxic gale]

Imagine trying to reduce a matrix without paper.

[warped carbon]

Apply more pressure until memorization is completely impossible.

[sonic sentinel]

ok i got it

[leaden skiff]

the reason kids don't bother puttting effort into deeply learning math isn't just because schools force rote learning on them, most kids just don't care to learn further than that

[woeful trout]

Who needs paper when you have electronic silicon?

[charred mortar]

Imagine doing anything without plugging it into a symbolic calculator

[wild lantern]

Me every day.

[leaden skiff]

then they won't bother putting any effort in

like shit i remember memorizing the shit out of all my social studies classes cause i didn't care enough to understand the material

[toxic gale]

Finding Fourier series without a calculator is the worst. Practically everything is integrating by parts multiple times.

[leaden skiff]

like sure maybe i could have tried harder to learn it, but i just could not give a shit at the time

[wild lantern]

I don't think I know any math major thay doesn't from time to time sit around doodling/writing/drawing to drum out some ideas/strategies to work out problems and junk.

[toxic schooner]

i on the other hand tried understanding the material

and that was fun

[leaden skiff]

in hindsight i should have tried harder

but like that's how kids are

they won't want to put effort into stuff they aren't interested in

[wild lantern]

Doing stuff in your head is good imo, just not to an exclusive extent.

[leaden skiff]

don't torture them by taking away their paper
just try to make it interesting for them

[toxic schooner]

this lol

i hated social studies in 8th

[wild lantern]

Well, not exactly doing things in your head. I mean more like pondering and calculating a bit and junk.

[toxic schooner]

and at the end of the year i read 4 books worht of material in 3 days for the exam

[wild lantern]

Hard to describe

[toxic schooner]

(it somehow worked)

[warped carbon]

I'm not saying to throw all the fucking paper out, I'm saying to try and avoid it as much as you can.

[charred mortar]

I also feel like doing things in your head becomes rather automatic too once you understand it well

[toxic schooner]

but next year i became interested and did better

why would u want to avoid paper?

[wild lantern]

That sounds like a terrible idea lol

[toxic schooner]

that does not sound like a good idea

[warped carbon]

I'll make one more comparison.

[charred mortar]

and to reiterate, that is an incredibly, incredibly bad idea for anyone doing uni math or higher

[warped carbon]

That's not most people.

But for what it's worth I managed to do single variable with basically no paper, I never tried to go past that so I don't know what happens.

Anyway.

One more comparison.

[charred mortar]

if you're dead set on using only your head for uni level math, or even first-year uni calc, good luck trying to do virtually anything

[toxic schooner]

single variable calc?

[toxic schooner]

this

[leaden skiff]

people who are interested in math will do worse without paper, they'll have a harder time learning and understanding
and people who aren't interested in math won't put any effort either way

[wild lantern]

Single var calc can be super fucking trivial or incredibly complicated.

[toxic schooner]

how can you do calc, something totally computational, without paper

[warped carbon]

If you were setting out to learn arithmetic, and you solved every problem with a calculator.

[wild lantern]

Depending on who's writing the problems.

[charred mortar]

maybe if you're some ultra supergenius like Euler or Gauss

[warped carbon]

You would learn no arithmetic.

[toxic gale]

I get what you're trying to do to make rote learning impossible, but at the same time, I do not feel like getting rid of paper is the solution. I agree the curriculum requires redesign, but like, not using paper is just handicapping yourself a lot of the time. So much of the time spent trying to figure out what went wrong can be avoided just by writing clearly.

[toxic schooner]

yeah u wont learn shit

whats ur point then?

[warped carbon]

If you were setting out to learn arithmetic, and you solved every problem with an abacus.

[leaden skiff]

find the intergral of 1/ ln(x)

[warped carbon]

You would learn.

More.

[toxic schooner]

[warped carbon]

But still not much.

[wild lantern]

I can teach you single var calc in a way where you can't just do it all in your head I promise lol.

[toxic schooner]

and if u did on paper u would learn more

[warped carbon]

The handicap of calculation instruments extends in a straight line all the way down to paper.

[charred mortar]

aka analysis

[warped carbon]

This is the last thing I have.

[wild lantern]

Not even jusy analysis, you can just make problems way too convoluted.

[sonic sentinel]

i would keep adding the divisor to itself until it got higher than the dividend: (so for 60/3 3, 6, 12, 24, 48, 96), assign each of the resulting numbers a value ({[1]3, [2]6, [4]12, [8]24, [16]48, [32]96}), then subtract the largest number i could from the dividend, subtract the largest number i could from that result, etc, then add all the values of the numbers i subtracted (60-48=12, 12-12=0 , 16+4=20), then that would give me the result (60/3=20)

[leaden skiff]

paper is a tool like anything else

if all you learn is symbol manipulation

then yeah, you haven't learned anything

but like, i think paper is the best enviornment to learn math

[wild lantern]

Don't rob yourself of the true pure joy of doodling cute animals for inspiration when you are stuck on hard problems.

[leaden skiff]

it doesn't let you cheat, you can't do anything that's not coming from your brain

[toxic gale]

This is just an algebra question. Would you do this without paper? Am referring to mostly the second part.

[leaden skiff]

literally all it does is increase your "ram"

[toxic gale]

I'm not saying you can't, but like how does doing this without paper help further your understanding. I don't get it.

[toxic schooner]

i can do it, but it will take a while
but with paper, it would be much faster

[wild lantern]

I'd just use paper.

[toxic schooner]

coz i can see my thoughts in a concrete form

[warped carbon]

This is cool.

[toxic gale]

My thoughts exactly. Why store everything in the brain when it can be written and ready for you when you need to refer to it?

[warped carbon]

It took me a second to figure out why this works.

[leaden skiff]

this is a tangent but i don't like that notation, just use f(x)g(x) or (fg)(x) smh

[warped carbon]

f(g(x)).

[wild lantern]

fg makes sense in certain contexts.

[charred mortar]

oh yeah that is honestly shit notation

[toxic gale]

This is from A levels. I actually think fg means composition here.

[toxic schooner]

i think they meant like not f(x)g(x), as thats multiplication, but yeah lol

[charred mortar]

at least if you ask me

[toxic gale]

I agree it's bad notation.

[leaden skiff]

this is kind of how long division works already,

[wild lantern]

Even for composition fg makes sense in certain situations.

[leaden skiff]

wait is it supposed to be f(g(x))?

[wild lantern]

Like groups of permutations and shit.

[charred mortar]

(fg)(x) makes it clearer

[leaden skiff]

ok then it's terrible notation

it looks like multiplication to me

[toxic gale]

I usually write $(f \circ g)(x)$.

[fathom swallow]

PhenomPlasma

[charred mortar]

since as it is it could be either f(g(x)) or (fg)(x)

[leaden skiff]

but is that f(g(x)) or g(f(x))

[wild lantern]

Well for ex cycle notation and multiplying cycles is literally function composition.

[leaden skiff]

does this mean f applied to g, or apply f first, then apply g

[toxic gale]

g first then f.

[charred mortar]

well sure but I'm pretty sure that in this case they want one of composition or standard polynomial multiplication

and those are different

[toxic gale]

That's the common interpretation. The thing closest to x is applied first.

[leaden skiff]

is function composition associative?

[wild lantern]

Yah in this context I agree that the notation is bad.

[wild lantern]

Yeh iirc

[charred mortar]

it is

very convenient fact

[toxic gale]

Pretty sure it's composition. A levels doesn't even teach adding and multiplying functions as far as I'm aware. And quite frankly I don't see the need for it to be taught either. It's just multiplying expressions.

[leaden skiff]

i should learn proper LA

[toxic schooner]

like i have been telling u to do for months

smh

[warped carbon]

Notation question.

[leaden skiff]

[charred mortar]

yeah polynomial multiplication is really just distributivity

[toxic schooner]

do it, and then teach me

[warped carbon]

If f(x) = 2x.

[charred mortar]

not much to teach specifically

[wild lantern]

Ez to verify (a o (b o c))(x) vs ((a o b) o c)(x).

[warped carbon]

Then f^-1(x) = x/2?

[leaden skiff]

with taylor series, all function multiplication is distributivity

[toxic gale]

Yes.

[toxic schooner]

yes

[warped carbon]

Thank you.

[toxic schooner]

i think

[charred mortar]

it is

[leaden skiff]

hey guys what's $\sin^{-2}(x)$

[fathom swallow]

Ninja

[warped carbon]

fg(x) = 4*(x^2+x+1), yeah?

[toxic schooner]

since (f(f^-1(x)) and f^-1(f(x)) are both the identity functions

[charred mortar]

1/(sin(x)^2)

[toxic gale]

I know! It's called bad notation!

[wild lantern]

[toxic schooner]

Not clear

u have to clarify

[leaden skiff]

i actually like $\sin^{-1} x$ as notation tbh

[fathom swallow]

Ninja

[charred mortar]

or sin(x)

[toxic gale]

I hate the $\sin^{- 1}$ notation. $\arcsin$ rules.

[toxic schooner]

same

[leaden skiff]

i think convention dictates it's $\frac{1}{\sin^2 x}$

[toxic schooner]

i really like it

[charred mortar]

ah yes the U+2010 notation

[toxic schooner]

thonk

[wild lantern]

sin^2(x)=sin(sin(x))

[fathom swallow]

PhenomPlasma

Ninja

[charred mortar]

there we go

[warped carbon]

Or is it 2x^3 + x^2 +6x +3?

[toxic schooner]

again, it could be someone saying (sin^-1(x))^2

[warped carbon]

I miss my alt codes.

[toxic gale]

Gives me nightmares.

Wait, wrong quote.

Was talking about the permutation groups one.

That stuff made me give up learning algebra for the first time.

[wild lantern]

I remember it being weird at first but feeling kinda nifty after.

[leaden skiff]

hey did any of you guys struggle to understand special functions at first

i remember trying to find the "formula" for sin when i learnt abt it

[toxic gale]

I struggled with hyperbolic functions for a while.

But I think I was too young when I learnt the trig functions that I just accepted whatever, so I didn't have that struggle.

[leaden skiff]

internally i think i thought sin x was just like a "name" for some "formula" of standard operations

i guess i ended up being kinda right since taylor series exist

but i don't think infinite polynomials would have satisfied me back then

[toxic gale]

There are certainly things I struggled to comprehend though.

[leaden skiff]

there are things im currently struggling to comprehend

[toxic gale]

Namely how rearranging a conditionally convergent infinite series can change its value.

[leaden skiff]

it's a very cool trick

the proof's very slick

[toxic gale]

I'm sure it is, but it just does not agree with my intuition at all.

[leaden skiff]

it's like if you seperate it into positive and negative parts

they both go to infinity, and the terms approach 0

so you have infinite precision to work with, and you can get it to be any number

[toxic gale]

Fairly sure someone here has told me this before and I'm more convinced now, but I was certainly very confused.

[leaden skiff]

lol was it in a vc?

[toxic gale]

Nah.

[leaden skiff]

i rmb talking abt this to someone in vc

[toxic gale]

I think it might've been Namington who told me.

[dense belfry]

I used to talk about this a lot

[waxen lily]

it might be possible with javascript, youd just need to search each day and save the number

probably against TOS

[bright hill]

that's why people make alt accounts 😉

[waxen lily]

i wanna do it with this account tho

[bright hill]

bold

[hearty portal]

One question please

Please tell

[charred mortar]

#❓how-to-get-help

[stone ferry]

$\frac{e^{ix} - e^{-ix}}{2i}$

[fathom swallow]

nHail

[leaden skiff]

yeah this woulda blown my mind back then

[stone ferry]

And also, I had the same questions. I never liked that there wasn't a good way to just compute the sine of a thing by hand

[leaden skiff]

i mean, my problem was that i didn't understand what a function was at the time

that like you didn't need a "formula"

it was just some map from one set to another

[stone ferry]

Yeah

Just the ones with formulas are usually easier

[charred mortar]

This is why I dislike how functions are often introduced as formulas tbh

It took me a bit to understand that functions are just any sort of mapping

[sick burrow]

https://modeltheory.fandom.com/wiki/Main_Page

why

does this exist

[deep mango]

Lmao

[neat lintel]

That's why people make IP bans ig

[bright hill]

that's why vpns exist

[neat lintel]

whats abstract algebra?

[alpine kindle]

the study of operations on sets

[neat lintel]

ok?

[alpine kindle]

like

addition, multiplication, function composition

it finds common properties across different operations and generalises

[alpine kindle]

for example
integers can be factorised, but many other structures (like polynomials) have similar properties to integers with addition and multiplication
so if you generalise things about integers to all structures with these properties you can learn more about them
because we already know a lot about integers but not as much about eg polynomials

[deep mango]

abstract algebra is about groups, rings, and fields. groups are sets with a multiplication operation. rings are sets with a multiplication and addition operation. fields are rings where every nonzero element has a multiplicative inverse (so you can divide by stuff in fields)

[alpine kindle]

i mean that's not everything

[errant furnace]

Those two spaces after the period bother me to no end

[deep mango]

an example of a group is the set of all configurations of a rubiks cube. examples of rings are the set of all nxn matrices, the set of integers, the set of integers mod n, or the set of all polynomials. examples of fields are the rational numbers, the complex numbers, the real numbers, the set of integers mod p for p prime, the set of all rational functions (fractions of polynomials)... etc

so there are lots of natural examples of these objects beyond the basic sets of numbers

[toxic schooner]

ryc thinks that it is standard to do that

[alpine kindle]

"set"
you forgot to mention the operations

[toxic schooner]

but just ends up annoying everyone

[cerulean ibex]

How can I Open a channel

[toxic schooner]

No need to be pedantic when introducing someone to AA lol

[deep mango]

abstract algebra is all about proving things about groups, rings, and fields (among other stuff: modules, vector spaces, categories, and so on) and seeing how they interact

[errant furnace]

Tell that to the books

[deep mango]

the operations are all implicit

[toxic schooner]

u can introduce without mentioning operations

[alpine kindle]

there's quite a need to be pedantic on this
because people always get it wrong

[toxic schooner]

[deep mango]

i would need to define the rubiks cube group operation i guess

[alpine kindle]

yeah

[toxic schooner]

wdym

[alpine kindle]

the books i have read mostly all say that new students often say a group is "a set such that there exists an operation which is..."

[deep mango]

that one is just "to multiply position x and position y, do the moves that take you from a solved cube to position x, except do them starting from position y"

[deep mango]

just go to a channel in Math Help Available and type your question in one. If you want to see the full instructions on this look at #❓how-to-get-help

[deep mango]

It is you bum

[toxic schooner]

what

u think its ok to put double spaces after periods

[deep mango]

It is standard

Yes!

[toxic schooner]

it is no standard

[deep mango]

I think it's required

[toxic schooner]

not in this universe

[alpine kindle]

which would imply every set with at least 1 element is a group

[toxic schooner]

its never required

[toxic schooner]

and thats wrong?

[alpine kindle]

yes

[toxic schooner]

how so?

[alpine kindle]

a group is defined as a set with an operation

[toxic schooner]

so?

[alpine kindle]

consider: the set of endomorphisms on a set

[toxic schooner]

whats an endomorphism

[alpine kindle]

function from something to itself

these don't form a group under composition

which is the only real operation you'll ever put with them

[errant furnace]

Technically a morphism from something to itself

[alpine kindle]

yes

[toxic schooner]

they can form a group under something else

doesnt have to be composition

[alpine kindle]

yes

but the set isn't a group

you have to define what operation you're using

[toxic schooner]

set itself isnt yes

but i would say there is nothing wrong with introducing people to AA like that

But u should mention operation asap

[alpine kindle]

i think there is something wrong with that
because the entire point of AA is operations

ways of combining things

[deep mango]

Automorphisms of a set

[toxic schooner]

yes but then again, when u introduce someone to analysis, its not wrong to say "calculus done rigorously", and not mention much about bounding anything

[alpine kindle]

but like

bounding isn't the entire point of analysis

operations are the entire point of algebra

[toxic schooner]

haha....

[deep mango]

yeah i kind of agree with alison in the end

[toxic schooner]

i mean i dont disagree lmao

but i dont find it particularly wrong to not instantly throw the word operation in someones face who isnt that familar with it

[deep mango]

but i think there's a difference in how you approach this if you are introducing someone to abstract algebra pedagogically versus if you are just answering someone's question "what is abstract algebra"

[alpine kindle]

i guess

[deep mango]

[toxic schooner]

[errant furnace]

[alpine kindle]

i think you should at least give an indication like "integers with addition" instead of just "integers"

[toxic schooner]

sure, thats better than just saying sets with operations

[alpine kindle]

yeah

[toxic schooner]

coz for people not well versed and mature with math

saying "sets with operations" is going into hardcore abstractness territory

[alpine kindle]

sorry

[toxic schooner]

no need to say sorry lol

[warped carbon]

I thought y’all were talking about Alcoholics Anonymous.

[toxic schooner]

wha

[alpine kindle]

i don't think msny religious addiction management organisations are particularly interested in algebra lol

[warped carbon]

“AA”.

[somber coyote]

Question

What is on your pfps hat

Remembertheroyals

[alpine kindle]

[somber coyote]

It doesn't look very good

[toxic schooner]

[alpine kindle]

oh no

[median zinc]

Wow

[toxic schooner]

for sometime i thought it was the discord brilliance logo

but up close

uh

[alpine kindle]

do we ping mods

[somber coyote]

Yeah no that's not the discord brilliance logo

[toxic schooner]

i see that now

[median zinc]

You can send it to modmail

[somber coyote]

Lmao

[median zinc]

I think it's instant ban

[toxic schooner]

send it to modmail yeah

[median zinc]

You can send it to trust and safety

To get the person banned from Discord

Might be more effective

[somber coyote]

@warped carbon you are probably gonna get banned anyway but you should probably change your PFP for other servers

oh nevermind

[alpine kindle]

<@&268886789983436800>

[warped carbon]

If I’m going to be executed, I might as well make it worth my while.

[alpine kindle]

there we go

i did it

[warped carbon]

Bravo.

[somber coyote]

But uh question

Why.

[steel mantle]

?

[toxic schooner]

u can still change ur pfp u know

[somber coyote]

Why have that on your pfp

[warped carbon]

Honestly don't remember.

[alpine kindle]

nazi hat

[warped carbon]

Bite me.

[toxic schooner]

see the pfp of RemembertheRoyals

[somber coyote]

I see.

[steel mantle]

Oh

Lmao

[pale orchid]

it's not appropriate, please change it

[steel mantle]

gotem

[pale orchid]

oh well

[toxic schooner]

dghost doesnt delete messages?

interesting

[median zinc]

I made a report on Discord

[steel mantle]

Depends on what was posted

[median zinc]

Should be perma'd from Discord

[toxic schooner]

[steel mantle]

If it's spam or the messages themselves are bad I do

[alpine kindle]

maybe delete this

thx

[toxic schooner]

what even is this

[median zinc]

Nazism being public

Just ban

[toxic schooner]

i meant the image

[median zinc]

or

oh

[somber coyote]

Nothing you want to know

[compact tartan]

Oh its the nazi pony whatwashername

[steel mantle]

yeah lmao

[somber coyote]

Is

[alpine kindle]

bdsm thing
doesn't belong on this server

[median zinc]

Oh are they famous

[somber coyote]

Is this person normally here?

[steel mantle]

so stupid

[compact tartan]

Arianne?

[somber coyote]

I assume on ALTs

[steel mantle]

swastika my little pony

swastika my little pony

[median zinc]

?? I do not comprehend

[steel mantle]

anyway

[compact tartan]

Anyway yea

[toxic schooner]

[somber coyote]

It's scary when the owner knows the person

[toxic schooner]

as i suspected

[somber coyote]

Lmao

[compact tartan]

Not the person

[toxic schooner]

?

[somber coyote]

As in they have a reputation

[compact tartan]

Its a chatacter that appears a lot on the internet

[somber coyote]

Oh I see

[toxic schooner]

ohh

[median zinc]

So the nazis take that as their public symbol?

[compact tartan]

A meme almost

Lol

[median zinc]

I really don't understand

If it's satire

[somber coyote]

Probably satire

[median zinc]

It might not be

[deep mango]

Pepper has active

[alpine kindle]

it's probably fake satire

[median zinc]

yas

[compact tartan]

No I think there is some intersection

Between the two clubs

[somber coyote]

I see

[median zinc]

In Wolfenstein you know the game has anti nazi tendencies

I don't know about this character

[compact tartan]

Yeah no

[median zinc]

sounds bad

[compact tartan]

It is

[somber coyote]

"tendencies" I think killing Nazis is bit more than tendencies

[compact tartan]

Anyway

[hushed turret]

morning chat

how is everyone today

[alpine kindle]

morning

wait twice it's almost midday

I'm doing good

[hushed turret]

so it is

im vibin

[compact tartan]

What a week huh

[median zinc]

every week sucks

[hushed turret]

one more week before easter break

[median zinc]

I think my weeks will suck all the way until September

[alpine kindle]

one more week before proper revision time

[compact tartan]

You guys get a break huh

[hushed turret]

gcses

[alpine kindle]

certificate of general secondary education?

[compact tartan]

How to get up from bed

[hushed turret]

https://tenor.com/view/viralhog-cat-fall-side-of-the-bed-instant-regret-gif-11703569

like so

[median zinc]

That's not what I mean when I say roll out

[alpine kindle]

what were you talking about here

I don't know much analysis at all

[deep mango]

Analysis is absolutely filled with inequalities

[alpine kindle]

oh

[dire mulch]

[neat lintel]

That's true

[toxic schooner]

this

[toxic schooner]

starting from epsilon delta proofs (or even before that depending on how/where u do it from) , analysis goes on to be inequality spam

its a bit of a joke, that analysis is inequality spam and algebra is symbol spam

lol

[toxic schooner]

yeah

[charred mortar]

isn't that epsilon-delta anyways, just for sequences

although even before that there's still a bunch of inequality stuff for like suprema and infima, or just some basic properties of R

[neat lintel]

no

[errant furnace]

Btw @devout nacelle if I can ask, what have you been doing to supplement the lack in uni course

[devout nacelle]

Trying to stay ahead of the classes and learn some things beyond the curriculum but my own lack of learning discipline gets in the way.

So not all that much

[errant furnace]

Lmao yeah fair enough

Do you apply for masters programmes this year?

[devout nacelle]

Next, or 2024 even

Depends on how prepared I feel to go ahead with it

[inner finch]

wtf

manan in masters program is surreal

[devout nacelle]

Hahahahaha

[ancient flame]

gmod in masters program

[errant furnace]

Unreal

[errant furnace]

Are you looking at places besides Germany?

[devout nacelle]

India/Germany at the moment, US if I can figure out the finances

[errant furnace]

Germany seems a bit more expensive too

Just living wise

[devout nacelle]

That's probably going to be an issue regardless of the place you choose

Kinda not helpful that INR is so cheap

[errant furnace]

Well its pegged to be that way

Do you / are you doing any undergrad research stuff

[devout nacelle]

Nothing so far, I bailed out on a couple of applications midway because I felt I needed more time to iron out an understanding of basic math

I might look into it next year

Or winters, if that's possible

[errant furnace]

Good luck!

Hope to see you next year lol

[devout nacelle]

Good luck to you too!

[neat lintel]

@devout nacelle ur 2nd year?

[devout nacelle]

Yes

[bright hill]

do you mind pings manan?

[devout nacelle]

No, as long as they're within reason

[bright hill]

oh cool

just wanted to ask for permission if ever there was need

[devout nacelle]

As long as they're not spam I don't mind pings

[neat lintel]

lol

silly things

if someone doesnt want pings they deactivate them

[bright hill]

not really

maybe it's not that you don't want pings, you just don't want to be flooded

besides, it's better to be polite anyhow

[frigid lark]

monday my exam. ;_;

Will be my first time I am gonna have to do a proof in front of eyes. Hope I will manage the proof somehow.

[modest rune]

Have you not done proofs on your homework?

[frigid lark]

I did, but like not with time pressure and infront of two people.

[fair mural]

sounds stressful

[frigid lark]

I think the examinators are very nice people regarding the protocols of earlier exams.

also hi quantum.

[fair mural]

hi

[neat lintel]

Guys. anyone can recommend a software for graph visualisation ?
like graph theory graphs (vertices, edges)

[static loom]

there's sagemath but idk if I would recommend it

but it's better than nothing

[neat lintel]

thanks

[prime oyster]

Oh my god guys I solved the bofa conjecture

[fervent pebble]

oh my god i solved the ligma postulate

[cold needle]

#chill

[sonic sentinel]

they solved a postulate and you're telling them to go to #chill?

[fervent pebble]

it's a joke

[wooden flax]

[fervent pebble]

uhhh i think the original guy was making a joke too but not sure

[wooden flax]

this is too funny

r/woooooosh

[fervent pebble]

or or alshfik was making a joke

and i got wooshed

anyways this is the wrong channel

[sonic sentinel]

bertrand's postulate is the only poorly named theorem i know

[fervent pebble]

it is, isn't it?

it's archaic though

kinda like how we call it the riemann hypothesis

when conjecture is the more accurate term

even though i think both are technically fine

there's also the continuum hypothesis

[limber thunder]

it's a hypothesis in the traditional sense

a supposition

[fervent pebble]

hm

i think conjecture is still more accurate

[limber thunder]

that kinda thing happens with older math

[fervent pebble]

since there's some reason to think that the riemann hypothesis is true

[limber thunder]

words and customs change with the years

[fervent pebble]

it doesn't really matter though

and yeah it's also just linguistic drift

[fervent pebble]

i think that's the term >.> could be wrong tho

[gray loom]

Any Excel/Google pros able to find a good video guide for this?

I wouldn't mind just a quick walkthrough either I guess

The tasks aren't hard really

I just can't read or understand them

I've been speaking and reading English for slightly less than 21 years but I really don't get it lol

Even did the little training module for this kinda stuff but when applied the format is different

[bronze pelican]

https://youtu.be/0VQjrCROkpA

why did he choose this thumbnail

[ancient flame]

LOL

[bronze pelican]

legit once the video starts there is no bunny girl

its just the thumbnail for some reason

[ancient flame]

lmfao

[ripe wasp]

mathematician's version of clickbait

[fading hull]

I want an anime girl to explain Stokes theorem to me so bad

Its unreal

[ripe wasp]

stokes theorem is so cool

[ancient flame]

trivial

[brave hollow]

how do you even find this? literally 46 views :/

[bronze pelican]

yt rec

[toxic schooner]

[neat lintel]

wadaf lol

[lyric axle]

lol what

more views

he knows the way

[jovial ember]

Me when I open the stacks project

Or nLab

nLab is tutorial hell even more than stacks project

[waxen lily]

you didn't like my awful joke? classic are slash woosh moment

[karmic zealot]

is there a set-theoretic term for a many-to-one function?

i don't think i've seen the classification "many-to-one" outside of highschool

[leaden torrent]

noninjective

[toxic gale]

Injectiven't. Please don't kill me.

[heady hemlock]

Arithmetic is Easy're

[karmic zealot]

now i feel stupid

[shadow glacier]

its not a function set-theoretically

[dire mulch]

One to many is not a function.

[shadow glacier]

yeah

since functions are defined as relations, where for every element in dom F, there is only one y such that xFy

[modest rune]

Many to one is just noninjective

[shadow glacier]

yea otherwise its just noninjective

wait yea nvm im being weird

[neat lintel]

maxwe

How is grad school going?

[modest rune]

Well!

[neat lintel]

Good to hear

Are you going for a PhD or a masters first?

[modest rune]

PhD

[maiden lily]

anyone familiar with arm assembly

[neat frost]

You want to assemble an arm?

[stray kite]

yes.

[leaden torrent]

just pop it into the socket

thats how it works for lego figures

[leaden skiff]

who dis

[neat lintel]

why?

[maiden lily]

I just wanted some feedback on multiplying two ieee754 numbers in arm, I am at the point where I need to multiply the mantissas and I don't know how to go about it

considering the values are 24 bits and the registers are 32 bit, I am having issues storing all of the numbers in the product

wondering if there was a way to store some in other registers idk

[torn willow]

Well,You are missing the point of IEEE 754

You just ditch parts of mantissa

@maiden lily

[maiden lily]

i know i was gonna do it after but if there is a way for me to do it without that thatll be good

like multiply the top bits of the multiplier/multiplicand

[torn willow]

Well why do you think 0.1+0.2=0.3000000004 memes exist

[maiden lily]

i guess i could right shift the values 16 times and then multiply accordingly

[torn willow]

Also are you designing an instruction or something?

[maiden lily]

that way itll hold in 32 bits

designing an instruction? no

i just have the values in two registers, i want to store the product in another register

[dense belfry]

I study partial multivalued functions sometimes

[hushed turret]

what does that mean emma

[torn willow]

I am guessing like Non Deterministic Finite Automata in Automats theory

[dense belfry]

For example, consider the problem "closed choice on [0,1]". This means that given a closed subset of [0,1] you want to pick a point from it (so you want a function f from the set of closed sets in [0,1] to [0,1] with f(C)\in C). We can phrase this as a realizer for a partial multivalued function from closed sets to [0,1], namely the partial multivalued function G which maps C to C. Then a realizer for that partial multivalued function means a partial function f with f(C)\in G(C)

So you can phrase a lot of problems in terms of these partial multivalued functions

[hushed turret]

i feel like i lack the prerequisite knowledge for this

[dense belfry]

Here's a nicer way of saying this

So let's say you have a theorem of the form "for any X, there exists Y with Z property". Then you can turn that into a partial multivalued function by saying "map X to the set of all possible Y with Z property"

And then a realizer for that theorem means an actual selection of some Y for each X

So this is a way of turning theorems into sets

[hushed turret]

oh i see
that makes sense

[bronze pelican]

https://youtu.be/kgN9L6W5Gv0

[vernal granite]

Wsg cuh

[late valley]

is this p_i, p_j, p_f, or p_1

[brave hollow]

p_i based on context

looks more like p_1 tho

[late valley]

kk yeah that's what i thought too just making sure

yeah

but p_1 wouldnt make sense imo

[brave hollow]

yup wouldn't make sense

[gusty orbit]

Poo

[junior jolt]

what is up

i came up with a cool question

until it gets brutally debunked by someone here

basically in statistics why is it valid to apply logarithm to the data

why stop at logarithm

so when you plot log(x1), ..., log(x_n) against log(y_1), ..., log(y_10)

you get a good correlation (lets say you do)

but what if given arbitrary data

i can find a function that allows you to correlate it 😹

and then any old data would have some "correlation" because i can transform the data however i like

[near fox]

that is the principle behind machine learning, or rather statistical learning

but finding that function (or rather, space of functions) is potentially arbitrarily challenging

[junior jolt]

#TurnsOutIHadAValidMathematicalThought

[near fox]

There is of course no single function that can be used to correlate all data. But you can still seek more general functions that can be used to fit data sets.

[junior jolt]

@near fox what's wrong with using f(x) = 1

then all the data is perfectly correlated

i think you'd have to say something about "information loss" (i.e. you want a bijection)

But isn't that still an arbitrary decision to not want information loss?

[dense belfry]

bijection is much too weak for this

log has a lot of properties

[junior jolt]

• cool
• feels like a "standard" curve
• bijection

[dense belfry]

lol

maybe you want transformation of random variables?

[junior jolt]

sorry wdym?

as in you'd want to use something that classifies as a transformation of random variables?

[near fox]

There is nothing wrong with it, but you don't get anything interesting. Indeed, the point of machine learning is to seek mappings that represent your data in some (ideally) low complexity way

[dense belfry]

tbh I don't know or care a lot about stats so I'm going to step out

[near fox]

But with f constant then eliminated all the informational complexity

[junior jolt]

how is "low complexity" defined, is it somewhat arbitrary

[dense belfry]

there's a formal definition

well of complexity

[junior jolt]

yeah there would be, but a lot of the time

[near fox]

There are various ways to measure it. There is kolmogorov complexity but it's nearly impossible to compute

[junior jolt]

even formal definitionns in statistics are completely arbitrary

half the time

lol

[dense belfry]

kolmogorov complexity isn't nearly impossible, it is impossible

[junior jolt]

Yeah i see

[dense belfry]

if you could compute kolmogorov complexity you could solve the halting problem

[junior jolt]

damn

so if you can approximate the kolmogorov complexity can you approximate the halting problem?

[dense belfry]

you can approximate the halting problem

lol

[junior jolt]

oh 😃

i dont study CS

[dense belfry]

but you can't computably approximate the halting problem (in the sense of computing the N for a given epsilon)

[near fox]

In general yes, but for a specific string it is still possible sometimes to calculate its Kolmogorov complexity

[junior jolt]

how enjoyable do you two personally find ML

[dense belfry]

That doesn't seem plausible to me except maybe in some incredibly trivial cases

[junior jolt]

i still havent gotten round to learning it

[dense belfry]

I do computability theory

Lol

I am a pure math PhD student

[junior jolt]

but idk ML kinda looks like a cool concept but quite boring to actually apply and use

so all of statistics

i was just wondering if you guys agree with that

[dense belfry]

It looks like a lot of fun I guess, a lot of my friends do ML but I don't really pay attention to what they do

[junior jolt]

ah

it seems fun to toy around with lol

[near fox]

I can only think of trivial cases too, but that goes to show that it is possible, even if no Turing machine can compute it for an arbitrary string

[junior jolt]

but all the hard work gets done by the AI itself

[dense belfry]

No I think that's a bad take. I think there are a very small finite number of strings possibly that can be computed, but that should be dependent on your definition of kolmogorov complexity, and different definitions of kolmogorov complexity give you different strings whose kolmogorov complexity can be computed

By definition of kolmogorov complexity I mean the universal Turing machine you are fixing to define kt

Lots of possible choices there

[near fox]

I'll take your word for it I suppose. It just seems to me it is possible to brute force compute it for, say, a 2 bit string

[dense belfry]

I think you have to consider the definition of kolmogorov complexity

Like I think you can design your universal Turing machine to make any finite number of strings have Computable kolmogorov complexity

But that's not that interesting imo

[near fox]

Sure. In the context of analyzing data, we might just be interested in a single numerical value.

[dense belfry]

And from my pov I care more about asymptomatics for kolmogorov complexity, so this sort of finite stuff comes out in the wash

[near fox]

There is no universal way to compute definite integrals either, but nonetheless a technique exists to compute one such integral

[dense belfry]

I actually really don't know how people use kolmogorov complexity in practice, I've only really used it for algorithmic randomness

[junior jolt]

Yo how good is ML at computing integrals 😂

[dense belfry]

There is a universal way to compute a definite integral lol

[junior jolt]

is that just wolfram alpha

[dense belfry]

idk what we're talking about now

So I'm going to go to sleep

[junior jolt]

yeah my awesome questions are always unanswerable, what can i say.

[near fox]

There are, vaguely, ways to "learn" to estimate integrals from data, but I would not call it machine learning

I think the issue here is merely semantic. By compute I do not mean anything related to Turing machines that can handle general input.

[dense belfry]

I think the notion of compute you're using isn't really well defined from my pov

But anyway I'm going to sleep

[near fox]

Let's not use the word compute since it does have semantic meaning. I just mean, can I find the value for certain strings

Either way, this tangent is only to qualify my statement "nearly impossible" 😛

In the context of ML, there are simpler forms of complexity. At its simplest, we might speak of just vector space dimension

One might find that your data can be projected into a linear subspace of lower dimension than when you started

[fair mural]

rudin is looking pretty appealing for single variable analysis currently, but i heard that chapters 9 and 10 weren’t very good. would it be ok for me to do chapters 1-8 and chapter 11, skipping 9 and 10?

or would there be some information in chapters 9 and 10 needed for 11

asking because i have absolutely no clue

although now that i think about it i would guess that it would be fine

[vivid halo]

yeah some of the later chapters aren't very good

imo skip everything after the chapter on special functions

so skip the chapters on differential forms and the chapter on basic measure theory

Rudin does quite a poor job with both of these topics

[fair mural]

is 11 very bad?

[vivid halo]

for differential forms and integration you might benefit from reading the first chapter of Bott-Tu, and for measure theory you might benefit from reading the first 100 pages or so of Stein-Shakarchi

[toxic schooner]

just use apostol quantum, smh

[fair mural]

ok one more question, after finishing LA and reading rudin or a book similar to it, i plan on reading munkres’ analysis on manifolds. is there anything else i should do before that, or is what i just said good enough?

i’m aware i might be planning a bit far ahead

[devout kernel]

Hello !

[limber thunder]

since that book is essentially MVC with proofs I think that's a reasonable plan

[fair mural]

ok thanks

[limber thunder]

well, proof-y mvc plus some intro differential geometry which still requires some analysis and linalg only

[fair mural]

because i’m curious, specifically what parts are intro differential geometry?

differential forms?

[limber thunder]

that I guess

[fair mural]

i guess manifolds too

[limber thunder]

yeah

it's in the title lol

I've only skimmed it but the book probably does all over R^n and then uses that to carry over to manifolds

[fair mural]

also, i’ll probably only read rudin up to chapter 8

that plan still sounds fine then right?

[vivid halo]

yeah

[fair mural]

ok thanks

[limber thunder]

these are like the only important chapters in rudin

covering your typical (honors?) analysis in R

[ancient flame]

what is the most complicated type of differential equation

I saw these quasilinear PDEs

does it get worse???

[near fox]

nonlinear system of PDE would have the least structure, at least if the nonlinearity is allowed to be arbitrary, meaning you'd have very little information to use to study it

[deep mango]

nonlinear stochastic PDEs

Nonlinear PDEs in noncommutative variables

[ancient flame]

pain

[fair mural]

just proved that trace is sum of eigenvalues 😎

[ancient flame]

nobody asked

[fair mural]

imagine being unnecessary rude

gmod doesn’t have to

[modern geyser]

What is trace

[fair mural]

sum of diagonal entries of a square matrix

[modern geyser]

I c

[ancient flame]

NOBODY ASKED!

jk

[surreal sapphire]

would've been super funny if you answered "sum of eigenvalues"

[ancient flame]

damn

that would've been funny

[deep mango]

The only proof that is coming to mind is using the characteristic polynomial

[ancient flame]

watch rice man is gonna do it now

[deep mango]

I don't like that proof

[ancient flame]

aw

[deep mango]

I'm trying to think

[ancient flame]

I thought he was going to

oh

thinking is for casuals

I often don't think before I act or speak

and thats how I lose friends all the time

[fair mural]

darn you

[fair mural]

i just used properties of trace and that the eigenvalues of a triangular matrix are the diagonals

[deep mango]

Hmm

Ok

So you turn your matrix into an upper triangular one

[fair mural]

i used trace(B+C) = trace(B)+trace(C)

[deep mango]

I see

[fair mural]

and decomposed a matrix A into a triangular matrix B and a matrix C with all diagonals 0

[deep mango]

Yes

[fair mural]

unexpectedly simple proof

[fair mural]

i have regrets

[near fox]

and how do you check that the sum of the eigenvalues of B are the same as the sum of the eigenvalues of A?

[terse flax]

equate them

$\sum \lambda_{iB}= \sum \lambda_{iA}$

[fathom swallow]

The Fractalogist

[fair mural]

maybe i didn’t prove it

idk

[fervent pebble]

lmfao

[worn garnet]

At the job fair at my uni today pretty tame to be honest

Also why do people associate Mathematics with Business they have nothign to do with each other

[frank orchid]

is a math tutor there to help you self study math

like...often i simply don't get math and need a problem explain to me

[cobalt star]

well if it's just specific problems then

ask on this server

if you like don't understand the material in general then get a math tutr

[fervent pebble]

holy shit i've been skipping on the original harder better faster stronger cuz i thought the beat was a bit annoying but omg the two minute mark

[ripe wasp]

quantum ur working through ladw right

[fair mural]

yes

[ripe wasp]

how do you like it?

i just started it

and its pretty nice so far

how long do u think it'll take to finish it

[fair mural]

it’s good so far

i don’t really know how long it would take to finish

maybe 3 months

if you’re rushing you can go faster

but i suggest going through each section in a way that at the end of the section, you understand almost everything

[ripe wasp]

yeah

[fair mural]

you won’t instantly understand everything

[ripe wasp]

im trying to do every exercise

[fair mural]

you probably shouldn’t

[ripe wasp]

i mean theres only like 5 at the end of each section

[fair mural]

some have like 10

or 12

[ripe wasp]

oh

ill do all the ones that seem useful then

[fervent pebble]

say, quantum, wdyt of Linear Algebra and its Applications

[fair mural]

i don’t know anything about any books other than book of proof any ladw

plus i haven’t heard of that book

[fervent pebble]

dang

[rustic vortex]

can anyone help with my hw please

[fervent pebble]

#❓how-to-get-help

[hearty portal]

Guys please tell if Time Dilation comes in Einstein law of relativity?

[wicked ore]

How long would it take to self-study a book like Basic Algebra I

[fervent pebble]

by who

if you're talking abt knapp's then after glancing at the pdf i can confidently say a long time

👍

[wicked ore]

Jacobson

[frozen venture]

What can I do with a math degree that involves helping others?

[torn willow]

I guess become a teacher or prof?

[frozen venture]

Besides teaching

I tend to get impatient lol

[wicked ore]

What qualifies as helping

Helping people understand math? Or helping a company analyze their stock portfolio? Lol