quick question since my book is confusing me, is 90 degrees pi/2 radians or 2pi/2 radians

@WDUK It's pi/2.

pi/2 @WDUK

surely its 2pi/4 so pi/2

okay so my book is wrong

Indeed

glad my brain understood it regardless xD

@KajHansen I think a lot of people goes through this. I haven't yet. I find questioning out existence very crucial and dangerous at the same time; the way we act and the things we believe in depends entirely on the mental image of the person we strive to be. So why strive to be that person and not someone else? These are murky waters I haven't bogged myself down to yet. There's no knowing whatever darkness lies at the pit of our minds; it's so much better to believe in something and move on.

I am sure you'll get better soon.

I have gone through depression, though not quite of this sort, and I have found mathematics helps me get over it. To me mathematics is sometimes a living being, a friend at need, helping you out from your miseries (sometimes the cause too, when you realize you suck at it!)

@Kaj I don't like to talk about this publicly, but feel free to email me.

wow

that was a very fast review

all of my intuition for vector spaces come from modules over a field

Most people might say the reverse, @meow

here's something. I don't claim that's helpful but, there's the man talking whose ideas changed my views about some things, I suspect forever. also whenever he says "art", I include "mathematics" in it.

I myself have never had depression, but I'd like to think that I know some of what you are dealing with, @KajHansen. I was bullied when I was younger for being "different" and "nerdy" and there wasn't much I could do about it. I don't think I was depressed, but I certainly thought a lot about things, and questioned things a bunch. So, all my sympathies to you, and there is a light at the end of the tunnel, and you will reach it.

@heather would i be correct in assuming you are female based on your name?

Thanks so much @heather

@meow-mix, you would indeed be correct

oh, depression, that's a bit close to home of recent, eek

@heather awesome! we need more females in STEM jobs

I was wondering about this kind of question though math.stackexchange.com/questions/2021273/…

If I may be permitted to glom onto the train of support, @Kaj...it's something I've dealt with myself. Both the events of my life and my MO itself have lent themselves to a significant depression. What I've found to be the cures are expression and creativity. Whether that's writing, music, visual art, or mathematics--that queen of creative endeavors--these things will do wonders. And not just as a distraction--they allow you to confront those dark corners of the mind and create beauty.

@meow-mix, from the way you phrased that, just a guess, are you male?

Nothing is more therapeutic than creativity, in my opinion.

I asked that because I didn't have a clue about it - and was interested in seeing a worked solution... I thought perhaps it was interesting enough to be of interest to someone, but i've been down voted on it

well, as you see in my picture, yes :P

@heather loooooooool

@meow-mix, hey, I don't know, I have friends who look male and are female, and vice versa, so I didn't want to guess off your profile photo =P

wonderful, I solved two more "work and integrals" problems correctly

today is a good day =)

:D

good job

did anyone see that post i made?

also how did i power through 200 pages today

geesh, talk about focus @meow-mix

@baxx I am unfortunately not equipped to answer. D:

@baxx, not able to answer, sadly =(

@Fargle no worries - i'm not too sure how hard / easy it is - but the format / post seemed reasonable

@KajHansen I agree.

and moreover

so i was a bit confused about the down votes , and wanted to see if anyone thought i'd done anything inconsiderate or whatever

how did i understand 200 pages of content?

@heather no worries :)

@meow-mix how is anyone meant to answer that?

@meow-mix, what was it about?

rigorous linear algebra

nice

@meow-mix The only true test will be doing the exercises. :)

sounds like an /r/iamverysmart post

indeed it does

perhaps already being somewhat familiar with the content?

@meow-mix i'm going to presume a troll then, gg

troll?

i am no troll.

i just thought of vector spaces as a module over a field of "scalars"

indeed, meow-mix is no troll, rather, an intelligent member of the human race.

and the module consists of the "vectors"

That's exactly what vector spaces are

yes

that's why i didn't have any trouble with it

lol

:P

I guess I have grown spiritual in some sense while dealing with my issues (the details of which are too personal to be of any interest). I am not ashamed of it; I strongly believe human being cannot live with bare, naked logic without emotions. As we progressed, as science progressed, we went through war and blood. Two world wars have passed and perhaps, god forbid, we're on the verge of a third. I am not sure how I feel about any of it.

But now I am digressing.

@baxx i do not understand why you would believe that.

You aren't alone @BalarkaSen

@meow-mix what?

about the post i made?

yes

@meow-mix I'm not sure what you mean - believe what?

I concur 100%

@BalarkaSen I will contend that logical positivism did far more harm than good. Our problems can't be solved by cold logic alone. We must listen to our hearts as much as our minds.

it's just a question

believe that i am a troll

@Kaj @Fargle Glad to know we share similar ideas.

It warms my heart to see @Fargle's comment get starred so quickly.

creativity and our soul/heart is what makes us human. logic is something a computer can do. we can do more than that. a computer cannot empathize, or believe, or hope, or pray, or dream, or any of those things that make life worth the living.

Oh that - just the way you kinda humble bragged then said you'd gone through "200 pages of rigorous LA" in the day sounded like BS, I'm doubting anyone can get through a difficult LA book in a day - axlers ~200 pages I think, I dont' think anyones doing that in a day. Basically

@KajHansen, @Fargle, @BalarkaSen, I agree with all of what you said =)

@KajHansen Yeah, same. Both for altrustic and for self-serving reasons. >_>

hahaha

@baxx, well, he did, so (::drumroll::)

@hea

@heather and the proof is in teh chat

gg

my apologies, what does "gg" stand for?

good game

ah, thank you.

@baxx to be fair the book was kind of

used in chess a lot i think, but sarcastically used towards people trolling online

loaded with examples

TBH most of the time I spend in this chat is trying to milk stars.

Don't we all :P

@Fargle right? =) (::stars::)

i skipped chapter 1 because it was all computational mumbo jumbo, nothing relating to the actual theory that i need

@Fargle ask and ye shall receive

Somehow I knew that would get starred.

Ironically, this post will not be starred.

@baxx "200 pages of rigorous LA" sounds like a hard-boiled detective novel

rigorous language arts

@Semiclassical well sounded like a nice troll set up to me lol

Proof-based literature

@Ted's going to come in here, glance at the starred messages, and smack me. I can feel it.

@baxx er noo.

@KajHansen So, have fun with math, and that's the most important bit IMO. Representation theory is the cool stuff; I know nothing of it.

welp

Except knowing what a representation is I mean :P

projective geometry time

using teddy's book

@Fargle As you should deserve!

well

time to figure out what I did wrong with this problem

@BalarkaSen "All that time you spent getting stars, you could have been doing analysis!"

@meow-mix, Abstract Algebra: A Geometric Approach?

To which I'll have no rebuttal.

@KajHansen nah, his algebra book

If I'd done particle physics instead of condensed matter, I'd probably understand representation theory a lot better

oops

thought that said linear algebra

yes,

chapter 8, on affine and projective geometry

I have been thoroughly acquainted with that one :P

about all I know is stuff like su(2) algebras and their representations

Can't do quantum mechanics without doing at least that much.

okay, so I have to integrate $3x^2+4x$ from 0 to 7, and I got 58

I like Ted's writing style. But I never read his algebra texts.

@Semiclassical, are you into physics?

Yeah, physics grad student

Cool

the book says the right answer is 441

well

@heather What antiderivative did you get?

the integral of $3x^2$ is $x^3$, right?

Indeed

and the other will be 2x^2

and the integral of $4x$ is $2x^2$, hm?

ah, \LaTeX isn't rendering for me :(

so evaluate $x^2+2x^2$ from $0$ to $7$

@meow-mix, wouldn't it be $x^3/2$

@heather why is that?

well, take the derivative of that and check

what's the power rule give when you differentiate x^3?

times by the power to the power minus one... i hate that

I mean, that you would take $3*x^3/3+4*x^2/2$ over the range 7 to 2

excuse me, 0 to 7, can't think today

@baxx what's so bad about it...?

@heather that's what you should end up with, yes.

@heather and simplify those multiplications

@meow-mix idk - the rhyme is sorta too easy to remember :P

to get $x^3 + 2x^2$

if it were x^3/2, then differentiating would give 3*x^2/2 not x^2.

an odd thing to dislike i guess

@Semiclassical, okay, so all of the 0 part cancels out to 0, so you just have to evaluate it for 7

right.

@baxx i always remember it as $ax^n \to nax^{n-1}$

which gives you $3*7^3/3+4*7^2/2$

@heather simplify the fractions lol

@meow-mix that's nicer yeah, and hints at the antiderivative more maybe. Though I guess one could reverse the rhyme , eh...

@meow-mix, right, you get $7^3+4*49/2$

or $7^3+2*49$

if I did that right

@heather Indeed.

and then...oh, darn, just realized what I did.

I mis-multiplied, how did I even do that...

wow

it happens.

yeah

this is the pinnacle of /r/iamverysmart: article title "6 Downsides to Being Extremely Intelligent"

If it makes you feel any better, I've definitely had moments where I've asserted that 7 + 4 = 13 for far longer than I'm proud of.

@meow-mix, I can relate to them all!!

lol, jk

@meow-mix, could you link to that?

...and that was last year.

the main tip-off for me is that the answer should be on the order of 7^3, which is a good deal bigger than 58

that's a simple sanity check

@Semiclassical, yeah, I dunno how I got that

58 I mean

there must have been something else besides the mismultiplying

anyway, I redid the multiplication and I got the right answer. Phew.

neat.

@meow-mix lol... "sometimes when I'm having conversations I have to hold back so I don't confuse people, wears me out!"

@heather businessinsider.com/downsides-of-being-smart-2016-7

oops

why was that in my clipboard

Another one is that the answer should be a multiple of 7--in general $\int_{0}^{b} P(x) dx$ should be divisible by $b$ for any polynomial $P$.

@Fargle, another good point

wow that's a real article, i thought you were joking

Not to drive the point home, just a good thing to remember in the future. Helped me out in AP Calc many years ago.

I should brag about all the times I said pure, unadulterated garbage.

But I don't, because I am a humble person.

@BalarkaSen This is meta enough to hurt my head.

lol

Actually, now that I think about it, I think a stronger result holds: $\int_a^b P(x) dx$ is divisble by $(b-a)$ for any polynomial $P$.

That's true.

@baxx didn't mean to sound like a braggart earlier

That totally makes sense @Fargle, but I've never specifically noted that before.

Would've been a wonderful check for me back in calculus :P

eh. $\int_0^1 x\,dx=\frac{1}{2}$.

@meow-mix no worries ;)

@Semiclassical ...damn it.

It still holds whenever $\int P(x) dx$ has integer coefficients...

never mind, I see your point.

@meow-mix what's the text btw?

@Fargle Not really necessary to even talk about the antiderivative in that case, though

@Semiclassical I suppose not.

just, any integer polynomial $P(x)$ has $(b-a)|(P(b)-P(a))$

@baxx Hefferon's "Linear Algebra"

here's a digital copy: joshua.smcvt.edu/linearalgebra/book.pdf

Ok, it's almost morning, I should get going. See y'all.

@meow-mix have you heard of "linear algebra done right" ?

@BalarkaSen, have a good day!

i'm guessing @BalarkaSen is going to have a drowsy day

@baxx I believe i have.

@meow-mix it's often cited as the best text for it - and if your algebra etc is good then all good I guess

by the way, just to confirm my intuition, the $xy$-plane is a subspace of $\mathbb{R}$ whose basis is $\{\hat{\imath}, \hat{\jmath}\}$?

yep, I believe that is right

subspace of R?

no

i mean

$\mathbb{R}^3$

then sure, if you use i,j,k for the coordinate basis vectors

or, $\mathbb{R}^n$ for that matter, where $n \geq 2$

so with this question, would you write (a) as an integral, like $\int^{29}_0 x^2 + k \, dx$

note that I'm not sure what you would put in for $k$ here

Eh, not really.

Suppose that the square has side length $s$. Then it has perimeter $4s$, so the length leftover for the triangle is $29-4s$.

oh, true.

that's a much better way to do it =)

so then would you integrate that over 0 to 29?

So each side of the triangle has a length $(29-4s)/3$. need to translate that into an area and add that to that of the square $s^2$.

No. There's no need for integration here.

oh

The maximation part is actually easy: the area ends up being a concave-up function of $s$, so the maximum has to occur at a boundary of the domain.

are there any subspaces of $R^2$ that arent $R^2$ itself, a line, or a point?

i assume not

oops, $R$ is supposed to be $\mathbb{R}$

subspaces are linear, so no

Nope @meow-mix

ok then i understand :D

so, an affine subspace is a plane, or line, or whatever, that need not contain the zero vector?

yes