Mathematics - 2017-05-24 (page 2 of 6)

Dair

03:00

still need to remove terms to make it finite.

Secret

yeah, which is why I have no idea how will $\pi$ under such representation will behave like. My guess is that since $\pi$ is irrational, there might be no pattern in the distribution of 1s in that expansion

First 4 terms of $\pi$ under base-$\omega$: The terms decreases very rapidly: $$\pi=3+\frac{1}{8}+\frac{1}{61}+\frac{1}{5020}+\cdots$$

But no pattern so far

Dair

oeis.org/…

Semiclassical

@Dair The Kempner series is weirder.

Dair

03:15

@Semiclassical Basically everything in math dealing with infinity is weird lol.

Semiclassical

point

Dair

trying to explain people that the rationals have the same cardinality as the integers causes issues...

Semiclassical

Eh, that's not nearly as weird as the real numbers having a higher cardinality than either of those.

Saying that the integers are as infinite as the rationals? Weird, but hey---infinity is weird.

Dair

it isn't that weird but try explaining it to a non-math friend lol.

I feel like I've seen Kempner series while preping for Putnam.

Semiclassical

Saying that the real numbers are 'more infinite' than the integers? Weeeeird.

Dair

03:20

there is a classic question about omitting 9s from harmonic and getting a good series... which I believe is a Kempner series?

wait yeah, that is exactly the Kempner Series... lol. silly math.

Semiclassical

I think I first saw it here: smbc-comics.com/index.php?id=3777

Though in retrospect I think that said comic is a little silly. The math translation is: "Almost all really big numbers have a nine in them."

Dair

so there is no closed form for the sum?

what happens if $5$ is removed instead?

Semiclassical

pretty sure it's convergent then as well.

plus there are some methods for estimating such series.

Dair

i'm rather suprised that Wikipedia doesn't have an "Open Problem" box.

Semiclassical

There is something like that for "Physics" topics here

Dair

03:26

they have those boxes in math as well. I'm just suprised a closed form for the sum is not listed as a problem.

Semiclassical

Eh, it's pretty specialized.

Plus it's a fact that relies on picking a particular base-b representation and a particular string of avoided digits.

By contrast, they do have "Is $\pi$ a normal number" listed there.

Dair

i must admit i'm rather confused about the choice of importance for math problems...

not saying I disagree with you are anything, but it is hard for me to judge whether a problem is valuable or not.

Semiclassical

I've no insight there either.

Fawad

How to solve it? I only know $X^T=-X,Y^T=-Y,Z^T=Z$

Semiclassical

You'll need to compute the transposes of each of those combinations

Note that $(A+B)^T=A^T+B^T$ and $(AB)^T=B^T A^T$.

Fawad

03:33

Ok. Nice

Dair

i wonder how many important problems of the era have disapeared in importance in the next era of math.

Semiclassical

Yeah.

I imagine there are quite a few old conjectures which motivated some work but were ultimately left by the wayside

Dair

in my math history (for specifically calculus) it seemed like there were rather 3 phases:

1. Calculation
2. Proving a lot of stuff
3. Reflection / formalization

Semiclassical

Depends on the subject, but yeah.

My comment here is a bit silly, but I always like pointing out how to use units in order to check an answer

Dair

Units are sooo valuable. I wish I payed more attention to them in chem during highschool.

Semiclassical

03:45

Yeah.

When I'm grading, wrong units are like alarm bells

Dair

it's like a test taking strategy, but also a conceptual check all at the same time.

Semiclassical

Quite.

Of course, there are limits to that. It's less helpful in electrodynamics due to the number of units involved

Not many people remember that a tesla-meters^2 is the same as a volt-second.

And if you do atomic physics you end up using different scale of units (mostly eV and angstroms)

Dair

oh geez that sounds mildly infuriating.

Semiclassical

tbh, it actually makes things easier than with SI units.

for instance, for atomic stuff you measure energy in units of eV. for mass, you really only care about doing $E=mc^2$ stuff, so the natural unit of mass is eV/c^2.

For Planck's constant, the combination I've got memorized is $hc=1240 $nm-eV$=12.4 $keV-angstrom$

Dair

you have 1240 memorized?

Semiclassical

03:53

yeah.

Dair

that's some dedication.

Semiclassical

it reaaally comes in handy when you're doing the Physics GRE

Dair

are you a physics major?

Semiclassical

Physics grad student :)

Daminark

Kek

Dair

03:54

Ahh. That's cool!

Semiclassical

I've also got the masses of various particles in my head, e.g. an electron is about 1/2 MeV and a proton/neutron is about 1 GeV

Daminark

On the subject of units: when my professor in mechanics was doing an intro to SR, he used units of feet and seconds so that $c$ would be almost $1$ :P

Semiclassical

(it's also common to say eV instead of eV/c^2 when talking about mass)

also, to be fair I've got the charge/mass of an electron stuck in my memory pretty well

but that's from TAing intro physics a few times

m=9.11e-31 kg is rather cumbersome compared to "oh, about half a million eV"

also, the e from the electron charge is built right into eV

so you don't have to remember e=1.6e-19 coulombs

Dair

@Semiclassical i feel like there is a relavent SMBC comic for this...

Semiclassical

lol, probably

Daminark

03:57

Is there ever not a relevant SMBC comic?

Semiclassical

The main advantage of eV-type units is that the numbers tend to not require scientific notation

Dair

something along the lines of:

What is Pi?
Enthusiast: 3.14159
Engineer: 3.14
Physicist: 5 is good enough
Math: $\pi$

Semiclassical

this one, probably: smbc-comics.com/?id=1777

Dair

shamefully I have 3.14159 memorized...

Semiclassical

I've got 3.1415926(3)

(3) because I don't know for sure if that's right :P

Speaking of dimensionless constants, one that you see a lot in atomic physics is the so-called fine structure constant

Dair

04:01

2653

Semiclassical

nuts.

Dair

oeis.org/…

Semiclassical

which...I'm forgetting how it's defined. hang on while I quickly rederive it using the relevant mnemonic

Daminark

I memorized 80 digits one time in high school since I was bored :P

Semiclassical

roll

okay, $\alpha=ke^2/\hbar c$

what's fun is that, to a decent approximation, $\alpha=1/137.$

Dair

04:04

what is a fine structure? what is an ugly one?

Semiclassical

ask an atomic physicist :P

(I think it's mostly a historical thing)

I should note, though, that factors of $\pi$ can be a big deal in QFT calculations

$\pi^2\approx 10$, so if you have a few powers of $\pi$ in your calculation for reasons then that can shift the order of magnitude significantly

Dair

$4πε_0ħcα = e^2$ what is the epsilon?

Semiclassical

permittivity of free space

I honestly never remember what number that is :/

Dair

so $k$ is $4\pi\epsilon_0$?

wait no...

Semiclassical

1/k is

Dair

04:08

yeah.

Semiclassical

k is easy to remember. i think it's 9e-9 in SI units?

nuts, 9e9.

but, I mean, I also have it in my brain that $\epsilon_0\mu_0=1/c^2$ where $\mu_0$ is the permeability of free space

and $\mu_0=4\pi\times 10^{-6}$ in SI units (might be wrong about the exponent)

nuts, 10^-7

and, well, I know what $c$ is.

so from that getting $\epsilon_0$ is easy as well.

Daminark

06:34

o lawd we done it

Liad

hi, easy question that i think i missed something. is there 16 ways to write 4 as a sum of 3 non negative integers? i found 15 :/

0 1 3
0 3 1
0 2 2
0 0 4
0 4 0
1 3 0
1 0 3
1 1 2
1 2 1
2 2 0
2 0 2
2 1 1
3 1 0
3 0 1
4 0 0

Fargle

15 should be correct.

There are 4 ways to split 4 into 3 or fewer non-zero pieces: 1+3, 2+2, 1+1+2, 4.

For the latter 3, there are 3 possible reorderings when you introduce 0; for 1+3, there are 6 reorderings. 6 + 3 + 3 + 3 = 15.

Liad

so i guess there is a mistake in the question , thanks.

Fargle

Yeah I'd say so.

What are you doing awake @Daminark?

Daminark

06:49

shrugs

Fargle

Tru

Abdullah UYU

hi guys do you think this question is bad, math.stackexchange.com/questions/2293979/… , why it has downvote?

SteamyRoot

07:32

Morning chat (how many flags/bans did I miss?)

SoumyoB

09:01

wait... Someone got banned from the chat?!! grabs pop corn where? Someone please give me the permalink???

ah found it

well guys I have my VISA interview tomorrow, wish me luck

Sha Vuklia

10:24

Hey @Steamy. I think I understand now what the separation constant is. We have separated our variables to the left and right sight. We introduce this constant, such that we can solve the the two sides separately (in terms of the constant), and then in the end we can combine the results.

Rajesh Dachiraju

10:50

0

Q: Is this product of 8 quaternions a real value?

I'd like to know the product of 8 quaternions $$(a+bi+cj+dk)(a-bi+cj+dk)(a+bi-cj+dk)(a+bi+cj-dk)(a+bi-cj-dk)(a-bi-cj+dk)(a-bi+cj-dk)(a-bi-cj-dk)$$ I'd like to know if it is real? PS : $a,b,c,d \in \mathbb{R}$

Sha Vuklia

11:42

Guys, when normalising the solution to the Schrödinger equation in the case of the infinite square well, we do the following:
$$
\int_0^a\vert A\vert^2\sin^2(kx)\,dx=\vert A\vert^2\frac{a}{2}=1,
$$
so $\vert A\vert^2=2/a$. Now Griffiths says that "it's simplest to pick the positive real root: $A=\sqrt{2/a}$ (the phase of $A$ cassies no physical significance anyway)." I don't understand where the phase comes into play, if we were to consider $A=-\sqrt{2/a}$. Any ideas?

Manolis Lyviakis

why integrating on a closed curve say a circle with a function that is defined well inside that circle except a point say $z_o$ we have a problem? im integrating along a path why do we care what is inside the path?

why do we care about points that are not along the path * especially the ones inside since if our problematic points are outside nothing changes

SteamyRoot

12:04

@ShaVuklia The phase of $A$? Sure this isn't about the phase of some wave?

Because, if you pick $A$ with the negative sign, you can move that sign inside the sine/cosine to get a phase of $\pi$.

Sha Vuklia

@Steamy yea, I just double-checked, and they really talk about the phase of $A$

and you're talking about the phase of $\pi$; what do you mean by that actually?

oh wait

I think I understand what they mean with the phase of $A$

they don't care if $A$ is half a cycle behind or not, because apparently it carries no physical significance anyway

LegionMammal978

Hmm

Given a graph, is there a way to order its elements such that all other isomorphic graphs follow the same ordering?

Balarka Sen

12:39

@Daminark ¯\ _(ツ)_/¯

Alessandro Codenotti

we created a monster @Balarka

Balarka Sen

@Alessandro an $\infty, n$-frankenstein?

Alessandro Codenotti

13:01

lol

Danu

13:38

Hey Balarka

Balarka Sen

Hi @Danu

Danu

Is it right to say that an isometric immersion is completely described by the second fundamental form?

The Gauss equation gives the curvature

The Codazzi equation does... what exactly? :P

It gives the perpendicular component of the ambient curvature

Balarka Sen

@Danu Well, if your immersed surfaces have the same $\Bbb{I}$ (which is the isometry condition) and $\Bbb{II}$, then one can be taken to another by rigid motion.

Astyx

Hi chat

Balarka Sen

It's an extrinsic geometry thing.

Danu

13:41

@BalarkaSen You're talking about surfaces in $\Bbb R^3$?

Balarka Sen

Yeah.

Danu

What about general isometrically immersed submanifolds in any Riemannian manifold?

(you can still think of them as immersed into $\Bbb R^n$ I guess; though that will give a different notion of extrinsic geometry than the original immersion)

Balarka Sen

Err, I don't really know the story for other ambient spaces than R^3.

The 2nd fundamental form is a bundle-valued tensor in higher dimensions, isn't it?

Danu

Hmm.

Yeah, just normal bundle valued

The generalization of the Gauss equation and Codazzi equation is sort of trivial/obvious

(depending strongly on what notation you're using in the surfaces-in-$\Bbb R^3$ case, I should say)

Balarka Sen

I think it should still be true.

That is to say, if two isometric immersions have the same 2nd fundamental form, there should be an isometry of the ambient space which takes one to the another.

But I think you should ask Ted about this.

Danu

13:45

I was just about to ping him

SteamyRoot

Yes, the second fundamental form completely determines the isometric immersion

Danu

@SteamyRoot So is this hard to prove?

Actually

what is the precise statement

is what Balarka said the precise statement?

Balarka Sen

@Soham Hey man.

SteamyRoot

Hmmm.. I don't know the precise formulation.

Soham Chowdhury

o/

SteamyRoot

13:50

The idea is that, using the formulas of Gauss and Weingarten, you can prove the Gauss-Codazzi-Ricci equations

Danu

@SteamyRoot I don't know all those names. But I see that the Weingarten equation is just the Gauss equation for the normal bundle, fine. What are the G-C-R equations, and how does this help us get an ambient isometry?

Balarka Sen

@SohamChowdhury How're you doin'

Soham Chowdhury

real life is determined on sucking very hard at the moment

Danu

@TedShifrin Oh master geometer, any help? I'm looking for the precise sense in which the second fundamental form of an (arbitrary codimension) isometrically immersed submanifold determines the immersion (see above discussion for what we already figured out).

Soham Chowdhury

the whole college admissions thing is not going too well. upside: after a loooong time, I can do math again

I mean, it's been ~6 months since I did any serious math.

Balarka Sen

13:56

i'm very scared about the admission business

where are you going

Soham Chowdhury

I don't know. :(

The ISI/CMI entrances weren't amazing. CMI was okay.

Balarka Sen

I need to take those man, and I'm bad at this sort of math

Soham Chowdhury

Unless something really bad happens, my ISC marks will be good enough to make the IISER cutoff. Pune is full of arithmetic geometry/NT people.

Balarka Sen

um, what's isc again?

Soham Chowdhury

class 12

Balarka Sen

14:00

oh. IISER takes people based on boards?

Soham Chowdhury

HS, I think you call it

They have a low-ish cutoff, yes. Then you have to give a test.

It's like JEE Main, but a bit easier and with biology.

Balarka Sen

Oh yeah I haven't taken biology so

Soham Chowdhury

neither have I

but what they ask for, it's not too hard. class 10-ish.

went to IISc etc. again?

Balarka Sen

Ah ok

nah haven't been to anywhere

Soham Chowdhury

you talked about writing papers and stuff, too

i see you've been doing the diffgeo thing pretty hard ^_^

Balarka Sen

14:03

did i? maybe that was balarka 1.0

yeah i'm still learning stuff at sluggish rate but

more foliations than geometry

Soham Chowdhury

soham 2.0: now with crippling depression

foliations are like the Hopf fibration?

Balarka Sen

Yeah fibrations are good examples of foliations. You break up a manifold into a union of "parallel" submanifolds

Hopf fibration foliates S^3 by S^1's

Akiva Weinberger

Oh hi, Soham!

Balarka Sen

but there are foliations which are not fiber bundles (eg Reeb foliation)

Soham Chowdhury

btw, I got into this

link

but I can't go

I turned down Mathcamp, too, this year. :(

hello, @Akiva

Balarka Sen

14:06

the admission thing is a big wild goose chase

in India

Akiva Weinberger

@SohamChowdhury …so that you can focus on your true love, ballet

Soham Chowdhury

seriously, college admissions has ruined my year pretty well

@Akiva s/ballet/salsa/

Akiva Weinberger

:D

Soham Chowdhury

I will not be trifled with

Balarka Sen

it also doesn't help that there are like 5 university in all of india that truly has good math course syllabus

Soham Chowdhury

14:08

I just discovered that somewhere in my 300 tabs, there are five long-gone-bad nLab pages

I'm definitely going to hell

Balarka Sen

cancel tab immediately

Soham Chowdhury

"Hegel was actually working in a higher topos, that's all"

metaphysics level 3000 unlocked

@Akiva so what's going on rn with you?

Alessandro Codenotti

@BalarkaSen Will you consider studying outside of India as well?

Balarka Sen

Kierkegaard did talk about existential topoi

Soham Chowdhury

mhm, for me, US admissions was a dumpster fire

Balarka Sen

14:10

@Alessandro I don't really want to go outside... it just seems like a huge pain in the neck + i'm homesick

Soham Chowdhury

NYU accepted me, but, y'know, it's expensive

and theoretically I'm still on the Columbia waitlist

Alessandro Codenotti

I'll probably try to move abroad for my master, but those are good points

Soham Chowdhury

Balarka 1.0 also talked about HRI/IMSc iirc

are those out for you?

Balarka Sen

do those really have undergrad

idts

Soham Chowdhury

no

I said so then

Balarka Sen

14:13

yeah balarka 1.0 was an ignorant ass

Hi @PaulPlummer

Soham Chowdhury

soham 1.0 didn't know he was one, so

wow, all the old familiar faces

Alessandro Codenotti

Hi @Paul

Soham Chowdhury

well, identicons more like

Paul Plummer

@BalarkaSen Hello

Balarka Sen

"welcome home, @Soham"

Paul Plummer

14:14

@AlessandroCodenotti Hello

Been a while @SohamChowdhury

Soham Chowdhury

@Balarka do you still meet up with any of your old profs?

yeah, I only got to talk to Mike outside of chat since

indeed, @Paul

Balarka Sen

i met with MM a while ago, he came to the city for a few days. the RKMVU crew is currently on ISI

Soham Chowdhury

ISIB?

Balarka Sen

i talk to all of 'em once in a while

ISICal

Soham Chowdhury

oh

anything else you've been working on since?

Balarka Sen

14:17

currently i'm busy locking myself up in my room and burning a hole through reality using existential angst

Soham Chowdhury

soham 2.0 also has a bit less fomo, which is really liberating

same

Balarka Sen

on a serious note, nah, just trying to work on some foliations and riemannian geometry but i have learnt epsilon > 0 in a few months on either of both

Paul Plummer

@AlessandroCodenotti If you plan on moving to the US for school, just go for the phd, not the masters (if you are thinking "pure" math)

Alessandro Codenotti

@PaulPlummer nah, I'm thinking about Germany at the moment

I don't think I want to leave Europe

Paul Plummer

@AlessandroCodenotti Good idea

Captain Bohemian

14:27

hunger is the main trouble hindering thinking

morbidCode

Hi guys, I'd like to ask you for some advice. I am currently reading a programming book. One section is fully devoted to symbolic algebra. Here are the topics
https://mitpress.mit.edu/sicp/full-text/sicp/book/node49.html
as you can see, it has some sections on doing system on polynomials and rational functions. I am very bad at math and so it seems very difficult for me. I'd like to ask you, are there any real world applications of the topics described in this particularl chapter? Thanks all!

Balarka Sen

meh i have to do calculus but i want to watch a movie

Akiva Weinberger

@Daminark @EricSilva I finally solved the prime-exponents polynomial puzzle

Edlothiad

14:46

I don't mean to interrupt, but I'm wondering if I can ask about the Marshal Problem on this site?

The Marshal Problem is a problem (I think I've come up with but who knows) where I'd like to know how many days it would take me to reach 100 flags, if I start at 10, can only use all my flags once a day and get a new flag every 10 flags I use.

would that be ok to ask?

Soham Chowdhury

@morbidCode: google "automatic differentiation" (assuming that is SICP)

$\Bbb R[x]/(x^2)$ is useful in the real world

morbidCode

@SohamChowdhury yes. chapter 2.5. I am honestly a little borred by it because I have no idea what they are used for. I'd like to know because the earlier sections has some topics that are very very useful (E.G. miller-rabin primality test, newton's method, successive squaring) even though I don't understand all the maths behind them.

Soham Chowdhury

AD is useful for neural nets

to a first approximation, a lot of machine learning is just weaponized chain rules

see how the error depends on your weights and biases ("backpropagation"), change them a bit to reduce the error, repeat

AD is symbolic algebra of a sort and can be very helpful

of a sort, mind you. it's not actually symbolic differentiation. that is slow.

Automatic differentiation

In mathematics and computer algebra, automatic differentiation (AD), also called algorithmic differentiation or computational differentiation, is a set of techniques to numerically evaluate the derivative of a function specified by a computer program. AD exploits the fact that every computer program, no matter how complicated, executes a sequence of elementary arithmetic operations (addition, subtraction, multiplication, division, etc.) and elementary functions (exp, log, sin, cos, etc.). By applying the chain rule repeatedly to these operations, derivatives of arbitrary order can be comput...

22 hours ago, by Zee

I should be doing math right now...

Balarka Sen

15:02

math is 2hard

Akiva Weinberger

Machine learning is, "Here's this formula with a ton of parameters and a spot for an input" "How many parameters?" "I dunno, thousands probably" "Your formula's not giving the right answers" "Hm, maybe the parameters are a bit off"

nudges the parameters "OK, should be better now" (repeat ad infinitum)

Machine learning is less about knowing the right formula than about knowing how to nudge the parameters the right way, I think

SteamyRoot

The answer to "why do these parameters work" is "because they do". :P

Akiva Weinberger

Strictly speaking, the machine isn't even necessary. It's just there to actually calculate the formula and the nudges, but you could theoretically do it by hand if you had enough time

(That would probably be a completely unreasonable amount of time)

But, like, if you were to do it by hand… What did the learning?

morbidCode

@SohamChowdhury um, I think you are referring to section 2.3 (symbolic deferentiation). I think this one is different. It talks about arithmetic on polynomials (no factoring though), long division, rational functions and stuff like that.

Akiva Weinberger

You wouldn't be able to say that "The machine learned blah blah blah" anymore.

On an unrelated note: Does the projective plane on $\Bbb F_p$ have $p^2+p+1$ points?

$|\Bbb F_p{\rm P}^2|=p^2+p+1$?

Mike Miller

15:08

Yeah

Akiva Weinberger

Cool, thanks

Mike Miller

this follows from the usual stratification as a union of affine spaces

Akiva Weinberger

Should help with #14 then

I'm guessing it'd just be the lines

Zee

@MikeMiller hey mike

Mike Miller

theonion.com/article/…

doesn't look like my taste

Soham Chowdhury

15:20

you called?

Mike Miller

no I was just picking on you

I wanted to say hi

Soham Chowdhury

well, hi then

I'm doing math again.

Mike Miller

that's good

as opposed to before?

Soham Chowdhury

as opposed to spending the last couple months barely keeping my head above the water

what do you call a category where you have tensor products?

(something like "parallel composition")

Balarka Sen

symmetric monoidal?

Soham Chowdhury

15:25

monoidal is existence, and symmetric is comm. of tensor?

Balarka Sen

oh yeah I guess monoidal is the right notion of category w/ a tensor product

symmetric means the tensor product functor is symmetric upto isomorphism

Soham Chowdhury

given $f_i : M_i \to N_i$, want $\otimes_i f_i : \otimes_i M_i \to \otimes_i N_i$

Mike Miller

that's too bad

Soham Chowdhury

it was

Mike Miller

what was the water for the past 2 mo

Soham Chowdhury

15:30

finals, college admissions, misc. entrance exams, somewhat Costanzian parents

Mike Miller

where you gojng

your parents are like George costanza or his parents?

Soham Chowdhury

the latter

I don't know yet.

1 hour ago, by Soham Chowdhury

mhm, for me, US admissions was a dumpster fire

Mike Miller

Ah, sorry. :(

Zee

Education is such a scam

Soham Chowdhury

and back home I won't know for about a month

Mike Miller

15:33

But in most likelihood you'll be staying home for your Bachelors?

Soham Chowdhury

approximately yes

Mike Miller

fair enough, crush em boo

you don't need to go to one of those schools all your countrymen are freaked out about exams for right?

the JEE and all that

Soham Chowdhury

well, there are exams and they are worth freaking out about. just different ones.

Mike Miller

I see

Soham Chowdhury

2 hours ago, by Balarka Sen

I need to take those man, and I'm bad at this sort of math

Mike Miller

15:35

I don't miss this pressure

I mean, it just becomes a different flavor of pressure

But still

Have you seen one-punch man?

Balarka Sen

I just thing the bad thing is there are only a few universities in the country which has a reasonable math syllabus

Soham Chowdhury

is that Bruce Lee?

oh, anime

non

Mike Miller

I think you might like it

Balarka Sen

if we had 100 such uni and all with super hard exams i probably would be less freaked out

most of the stuff are the engineering shit

Mike Miller

It's a satire of the sort of fighting anime I think you used to be (still are?) really into

Soham Chowdhury

15:38

although there's the whole point about non-independent random variables. "if you apply to 20 hyperselective colleges you have a 99.<arbitrary digits> chance of making it into at least one"

Mike: you meant me? I don't recalling watching anime, much less telling you about it

Mike Miller

hmmmm

Zee

@BalarkaSen are you in the USA?

Balarka Sen

no

Mike Miller

Maybe I confuse you with some of your friends from when you used to hang out here

Soham Chowdhury

oh, that's the CMI guy

who used to do those integrals with Chris's sis

Zee

15:40

One punch man is awsommmme

Mike Miller

r9m? I wasn't thinking of him

But in any case it doesn't matter

SteamyRoot

You should read the original OPM webcomic. The awful drawing style is half of the fun, really.

Mike Miller

too much work

Zee

Link?

Mike Miller

not a communal experience like TV either

SteamyRoot

15:45

I don't really have a link. It's probably translated on MangaFox or something like that.

Dodsy

Hello

Alex K Chen

Any ideas on this question of mine ?

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Q: Painless introduction to polynomials

While reading through this betterexplained article, I suddenly realised my understanding or mental model of polynomials is no better than this: Put in random value of $x$ in the equation $ f(x) = \sum_i a_ix^i $ and chug out the solution, or just blindly shuffle symbols around ( which is called D...

algebra-precalculus polynomials intuition visualization

Mike Miller

I think 50% of it is how much I love his stupid face

Dodsy

Weird

I didn't learn polynomial like that

Damn autocorrect

A polynomial is a group of variables

With plus and minus signs

Alex K Chen

Huh ?

Dodsy

15:51

You heard me

But precalulus you basically learn how to factor polynomials and find the roots

I never did sums in precalc

Alex K Chen

And I know how to do it, but I can say my mental model sux.

Zee

Sometimes you should treat a polynomial as just a polynomial

Dodsy

Well then you should learn what the different exponentials do to a polynomial

When it goes to infinity or negative infinity

Wether it goes from increasing to decreasing etc

Functions (or precalc) is mostly about graphing.

also there's some memorization about when a graph is stretched or compressed or vertically or horizontally shifted...

Secret

IMO it is very hard to visualise polynomials since you cannot figure out what the coefficients of each term are on the graph

Soham Chowdhury

@Mike the only other, um, visual media I remember you ever talking about is The Seventh Seal

Dodsy

15:58

The seventh seal put me to sleep man

Alex K Chen

Then the only sensible way is symbol pudding @Secret ?

*pushing

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