Mathematics - 2016-11-19 (page 2 of 10)

Brody

02:00

How's it go on your side?

meow-mix

refreshes e-mail inbox

no new e-mails

Ted Shifrin

I've been battling old TeX documents for the past few hours. It's all meow's fault.

smacks @meow anew

meow-mix

my fault?! i have been playing chess this whole time!

Brody

I won't ask

heather

you should learn LaTeX @meow-mix, then you can help @TedShifrin in his struggle against evil =)

meow-mix

02:01

i know LaTeX

you should see my typesetting :D

Ted Shifrin

Yeah?

Brody

test: $\Latex$

Ted Shifrin

OK, sent, finally.

Brody

darn

meow-mix

test "chapter"

a picture of rene descartes in the top for, well

i dont know

heather

02:02

nice

@meow-mix, because rene descartes and cartesian coordinates and analytic geometry =)

Brody

@meow-mix The text body is certainly pretty.

Ted Shifrin

@Brody: Have you done the cool exercise on the three different points associated to a triangle and how they're collinear?

Brody

@TedShifrin Not yet. Is that first chapter?

Ted Shifrin

End of section 2.

meow-mix

oh you guys want to see my visualization of the circle group?

Ted Shifrin

02:05

You mean a circle? Deep.

Snideness begets snideness. :D

meow-mix

displays what multiplication "means" in the circle group

Brody

@TedShifrin I speed-read through the chapter material just to get to the cross product and have Balarka tell me something cool.

meow-mix

and why its closed (specifically due to Euler's formula)

Ted Shifrin

Balarka likes to show off, @Brody :P

What did you get to?

Maks

@TedShifrin I had the test today

Ted Shifrin

02:06

Did you survive, @Maks?

takes pulse

Brody

@TedShifrin If that's true, he layers it with well-intended pedagogical fervor.

meow-mix

@TedShifrin wow, you like large margins dont you?

Ted Shifrin

@Brody ... I think Balarka is great. He's matured a great deal. He's learned a smidgeon from Mike and me, too.

Maks

@TedShifrin Maybe, I dont know

meow-mix

i'd even call them

larg-ins

Ted Shifrin

02:07

@meow: That was for the publishers for the actual book. I didn't reset all the margins.

Maks

@TedShifrin There were 5 exercises, I could only do 4

Ted Shifrin

I actually typeset the book as it appeared in print. They just did the binding.

meow-mix

was that not a good pun?

heather

hilarious (::groans::)

Ted Shifrin

NO.

Fargle

02:08

@meow-mix No pun is good.

DHMO

@meow-mix "$e^{i\theta}$ forms group under multiplication"?

Ted Shifrin

@heather: You're allowed to smack him too.

Fargle

That's what makes them good.

Maks

@TedShifrin i.imgur.com/NYKFd1M.jpg

heather

eh, it was actually kind of funny, for about a picosecond

Ted Shifrin

02:08

Well, @Maks, in my world, if you did 4 well, you did superbly.

Brody

@TedShifrin He has a good "sense of things" imo. I enjoy not only his knowledge and mathematical maturity, but his intellectual and social maturity as well

meow-mix

@DHMO that's called the circle group; the group consisting of all $z \in \mathbb{Z}$ such that $|z| = 1$

Maks

@TedShifrin The problem is, I dont know If I did those 4 in the right way, (the picture is the test)

DHMO

@meow-mix nice

Ted Shifrin

Yup, @Brody. As I say he's a different person now from the one I got to know 2 years ago.

Maks

02:08

Its in spanish tho

meow-mix

so basically, $e^{i\theta}$ for all $\theta \in \mathbb{R}$

Fargle

He's good people, I like Balarka.

DHMO

@meow-mix also known as $\Bbb R /\Bbb Z$

Ted Shifrin

I can read it, @Maks ... and I'm trying to learn Spanish fast, too :)

Maks, the test is quite fair, I think. I am meaner :)

meow-mix

@DHMO the factor group of $\mathbb{R}$ and $\mathbb{Z}$?

Maks

02:10

@TedShifrin Can you help me redo the exercises in a fast way ? Like telling what I did and the answer I got ?

DHMO

@Maks como puedo ayudarte?

@meow-mix yes

meow-mix

@DHMO good thing im wearing my DHMO-resistant gloves

what

Ted Shifrin

@Maks, sure ... but I'll be leaving in a half hour or so. Ask whatever you want.

Maks

@DHMO Quiero rehacer el parcial, no escribirlo sino revisar que lo que hice esta bien

meow-mix

doesn't a factor group have to be with a subgroup?

DHMO

02:11

@meow-mix nice, ban all DHMO!

Ted Shifrin

Yes, with a normal subgroup.

DHMO

@Maks entonces solo numero 4?

Ted Shifrin

I hadn't realized how confusing math would be in Spanish with "and" being $y$. :D

DHMO

@TedShifrin English with "one" being $a$ it's the same thing

meow-mix

well we have "I" being, well "I"

Ted Shifrin

02:12

Yes, in English "a" and $a$ cause difficulties :P

no, because, other than in Mathematica, $i$ isn't "I". :D

meow-mix

good thing we have cute math fonts to make them

differentiable

3

DHMO

but you can resolve it by context, and so can we

meow-mix

ba dum tss

Brody

@TedShifrin Really? Good to hear he's grown so much. It's funny seeing you ~~abusively~~ playfully smack him around, definitely an interesting dynamic lol

Ted Shifrin

I wasn't criticizing Spanish, @DHMO. Don't worry.

DHMO

02:13

never thought so

meow-mix

ok, maybe that one was a bit too far

heather

@meow-mix, you know, $\sum$ people like math puns, and $\sum$ people don't

Ted Shifrin

@Brody: You'll get your turn.

Brody

D:

Ted Shifrin

I miss my office hours with 10 students in them all the time.

(or more)

@Maks: So which question(s) do you want to discuss?

Mike Miller

02:14

h

Ted Shifrin

G'night @MikeM

Fargle

@meow-mix What's the contour integral around western Europe?

meow-mix

ummm is this some residue theorem joke

Fargle

It's zero--all the Poles are in eastern Europe.

Ted Shifrin

Dogs' residues?

Maks

02:15

@TedShifrin @DHMO first exercise, taylor series of $ xe^{-x} $ is $ \dfrac {(-1)^{n+1} x^n} {(n-1)!} $

meow-mix

i knew it

Fargle

Hehehehehehehehe.

Ted Shifrin

OK, @Maks.

Brody

@Maks I struggle enough with conversational Spanish, but with math involved too? Mmm

Ted Shifrin

puts @Fargle on ignore

Fargle

02:16

I've always wanted to be a math professor. I'm told it's one of the Cauchiest jobs in America.

:c

Ted Shifrin

Not when Trump's done with America, @Fargle. Actually, we had lots of problems even before him.

now puts Fargle on ignore

Fargle

That's cold.

DHMO

@Maks and with the constant term being $0$

meow-mix

@TedShifrin not complaining, but your references are bugging out

like it'll say Lemma ?? instead of Lemma 1.1 or something

Ted Shifrin

Huh? @meow

Oh crap.

Fargle

02:17

...he could have just smacked me...oh well. goes back to Rudin

meow-mix

all i do to fix that is just compile it again

Ted Shifrin

Yes, I know that. But I recompiled it several times, I thought. Let me look.

Brody

My high school math team had a shirt that said $$\text{Cow }\pi\text{'s are }\int e^{x}y$$

Maks

Then that one is ok ?

Fargle

@Brody Classy.

meow-mix

02:18

where's his infinitesimal

Ted Shifrin

Sure. Keep going, @Maks.

DHMO

guys, when do you pronounce "integral" as inTEGral and when as INtegral?

Maks

Now, it asks for which values of x does the series equals the function

DHMO

(in normal English context)

@Maks el serie es la foncion

Maks

Is that right DHMO ?

Fargle

02:19

@DHMO When it's inTEGral to the discussion, not an indefinite INtegral.

meow-mix

@DHMO inTEGral i use when stressing it

Maks

So, I just take the interval of x in which the series converges ??

DHMO

@Fargle dictionaries list INtegral as a valid pronunciation also in normal English context

@Maks pienso que si

Maks

@DHMO es lo que unico que se me ocurrio jajaj

Fargle

@DHMO Either way's fine for the former context, but only one is fine for the latter, at least in my opinion.

meow-mix

02:20

@DHMO yo soy zach y me gustaria estudiar mas de matematicas

excuse the missing accents

Ted Shifrin

Well, to do that rigorously, you need to look at the remainder formula for the Taylor polynomials for $e^x$. Or you can just know from class that it converges for all $x$.

Fargle

I'd never say "an indefinite inTEGral", but I could say either "INtegral..." or "inTEGral to the discussion"

DHMO

@meow-mix do i look like i used accents?

heather

@DHMO, I say INTEGRAL when I'm telling my friend(s) overly enthusiastically that calculus is wonderful, and INtegral in all other occasions

meow-mix

@TedShifrin do i have to read the chapter about induction

section*

Maks

02:20

the exercise b, says which order of taylor you have to use to calculate $ f(x) = \sqrt{(36+x)} $

DHMO

@meow-mix nice to meet you

Maks

When a = 0 , x = -1

Ted Shifrin

@meow: You should read what you don't know, and go back to stuff if you don't know it.

Maks

The result was 3

meow-mix

i know induction :P

DHMO

02:21

@Maks que es a?

Ted Shifrin

@Maks: So you wrote down the remainder formula and estimated it?

DHMO

@heather but people do use inTEGral instead

Maks

@DHMO the point $ (x-a)^n $

In the taylor function

DHMO

@Fargle ok

Maks

@TedShifrin I used lagrange

DHMO

02:22

@Maks right

heather

@DHMO, I use inTEGral when I say that something is integral to, say, a conversation

Ted Shifrin

Yes, that's fine. I haven't checked your answer. Do you want me to?

@meow: New version sent.

DHMO

@Maks y que hiciste?

@heather I see

meow-mix

@TedShifrin thank you

Brody

@DHMO integral like integrity, integral like integer :D

Ted Shifrin

02:24

@Brody: Do you know the English word GHOTI?

DHMO

@Brody so integral = pertaining to integers

how did integral come to mean $\int$?

Fargle

Sanity check: The set $\{\frac{1}{n} : n \in \Bbb Z \setminus \{0\}\} \cup \{\frac{n-1}{n}: n \in \Bbb N\} \cup \{\frac{1-n}{n} : n \in \Bbb N\}$ has only three limit points--$0$ and $\pm 1$, right?

Ted Shifrin

Yup.

Brody

@DHMO You're asking the wrong person. The earlier remark was just a handy association

Ted Shifrin

Not that I'm vouching that you're sane.

Brody

02:25

I'm also curious though

DHMO

@Brody ok

Brody

@TedShifrin Huh?

Ted Shifrin

Integrate means to put together.

Fargle

@TedShifrin I don't have to be sane, the result has to be though. ;)

DHMO

@TedShifrin fair enough

Ted Shifrin

02:26

That's a famous one on the irrationalities of English pronunciation, @Brody. George Bernard Shaw came up with it.

It's pronounced FISH. Now figure out why.

Brody

GHOTI looks like the rapper Yo Gotti's name to me

Ted Shifrin

No ... Think about grouping letters and English idiotic pronunciation.

Brody

I'm thinking... @Ted

cough

mmm...

Ted Shifrin

OK ...

Mike Miller

Had my first meeting in a while today in which I had to say i've got nothing new at all

Ted Shifrin

02:28

@MikeM: meeting with your adviser, you mean?

I had zillions of those.

Fargle

@MikeMiller "yeah man, math's pretty hard, turns out"

I'd never keep an adviser.

Semiclassical

"So..." "So..." "..." "..." "...How about that election?"

Ted Shifrin

@Fargle: You're not yet ready for prime time.

Fargle

@TedShifrin You must know how much of my being it's taking not to make a primality pun.

Brody

You can maybe argue lemon @Ted

DHMO

02:30

@Semiclassical hi

Ted Shifrin

Not the right vowel, @Brody.

Semiclassical

hi @DHMO

Fargle

@Brody There's an even more egregious example.

Ted Shifrin

Well, right vowel, but wrong sound.

Brody

I swear some people say it like that though @Ted, but yeah there's certainly a better one out there

Ted Shifrin

02:30

@Fargle: I'm glad you've composed yourself.

@Brody There's no accounting for ...

Fargle

@TedShifrin All I've ever strived for is self-unity.

ducks

Ted Shifrin

I rather thought you were a zero divisor.

Brody

I'm assuming o corresponds to i, and ti to sh

Fargle

@TedShifrin Not only that, I'm practically nilpotent.

Ted Shifrin

Not to mention impotent ... ducks

Mike Miller

02:33

He asked me to explain what I was stuck on. So I did, then asked him to explain something unrelated, then it had been 20 minutes and we were done.

Ted Shifrin

It's OK, @MikeM. Don't beat yourself up.

Maks

@DHMO Perdon, estoy con haciendo otras cosas

Mike Miller

I have excuses, at least. Some more valid than others.

ti as in tion

Maks

@DHMO Aplique lagrange

DHMO

@Maks no hay problema

Maks

02:34

y saque el n

Ted Shifrin

@MikeMiller Yes.

Brody

@MikeMiller Right

Maks

el 3a no se como hacerlo

Brody

I can't do o though

Mike Miller

o as in "oh fuck this"

Ted Shifrin

02:34

@MikeM: I showed up in Chern's office at 8 AM on Friday more than a few times saying I hadn't gotten what I wanted done.

DHMO

@Maks el 3a significando la cuestion "2a"?

Ted Shifrin

@MikeMiller NO.

Fargle

@Brody Many men and women have struggled with this before.

DHMO

si 1b es la 2a cuestion

Ted Shifrin

@Brody: Here's a hint. Whom does Trump hate (other than Muslims, gays, foreigners ...)?

heather

02:35

@TedShifrin, women?

Ted Shifrin

Fargle gave a more blatant hint.

Brody

@Fargle Their sexuality

heather

but that makes no sense...

Ted Shifrin

Perfect, @heather.

How is the "o" in "women" pronounced?

heather

@TedShifrin, but women isn't pronounced that way

Brody

02:36

It is around here

heather

I mean, the o isn't pronounced like an i

Fargle

@heather "wimmen" is how I pronounce it.

Ted Shifrin

Where are you, @heather?

heather

Iowa @TedShifrin

Ted Shifrin

Hmm, how do you pronounce it, then?

Brody

02:36

fish and women

Ted Shifrin

"woman" and "women" are distinctly different

Maks

@DHMO Nono me refiero el apartado a del 3)

Ted Shifrin

English is just a ridiculous language.

Maks

No pude hacer ninguno del 3

heather

I almost pronounce it as a u, like wumen, or woomen, something like that. I pronounce it practically the same as woman.

Maks

02:37

@TedShifrin I couldnt do the number 3

Brody

@TedShifrin Then Spanish should feel relieving

Semiclassical

wuh-men and wih-men

Ted Shifrin

Well, you're totally weird.

heather

=P

Maks

Couldnt figure how

DHMO

02:38

@Maks pronuncialo como "thwee"

Fargle

@TedShifrin As little as I know about German, I do like the consistency of pronunciation.

Ted Shifrin

@Maks: So you need the partial derivatives of $f$ at $(1,3)$.

@Fargle: I know 4 other languages (not all thoroughly), and English is uniquely ridiculous.

Brody

brb, gotta finish an economics assessment

(kill me when I'm gone please)

DHMO

@TedShifrin cuales 4 idiomas?

Maks

@TedShifrin the formula was $<(f_x(1,3),f_y(1,3) , (x,y,z) - (1,3,1) > $ ?

Fargle

02:39

@TedShifrin Surely the other languages have different elements of ridiculousness--I seem to remember words like "doch" in German. However, English is uniquely bad probably because it's such a mutt of a language.

Ted Shifrin

No, @Maks. The normal vector to the plane is $\langle f_x, f_y, -1\rangle$.

@Fargle: "Doch" is totally consistent with all pronunciation in German.

Fargle

A German grammatical structure with some, but very few, relics of conjugation and declension, mixed with a vocabulary borrowed from French, Norse languages, and the many languages in places where the British colonized.

DHMO

@TedShifrin its meaning as the positive response to a negative question is ridiculous to him

Fargle

@TedShifrin I don't mean pronunciation-wise--I mean it's a strange part of the language itself.

meow-mix

what is the latex command for floor?

DHMO

02:40

@meow-mix \lfloor and \rfloor

Ted Shifrin

Oh, I was talking about pronunciation alone. I like "doch." In English, a "yes" or "no" answer to an ambiguous question is completely ununderstandable.

Fargle

@TedShifrin I love the word myself--I just find it an oddity.

Maks

@TedShifrin so (x,y,z-1) ??

Fargle

But that's an oddity relative to my own language, not to the space of languages overall.

meow-mix

seriously guys, should i use a times-like font in my typesetting?

Fargle

02:42

Similarly: "es gibt" for "there is" is very strange.

DHMO

@Fargle what is your language?

Fargle

English.

Ted Shifrin

@Maks: Oh sorry, I put in the brackets wrong. $\langle (f_x,f_y,-1),(x-1,y-3,z-1)\rangle = 0$.

heather

@meow-mix, times new roman is pretty standard in papers in school, at least for me

Fargle

Mayhaps the oddest language, and yet the lingua franca.

Ted Shifrin

02:42

@Fargle: "it gives"

Maks

@TedShifrin ohh, could you explain me why please ?

meow-mix

@heather yeah, but not for math papers

Fargle

@TedShifrin Yeah--it's just kinda weird that a German speaker might say (in German): "It gives a wheelbarrow over there!"

But, in a very strange way, it makes a sort of conceptual sense.

"It" being the universe, I guess.

Ted Shifrin

@Maks: Well, if you look at the curve in the $x$-direction in the surface, its tangent vector is $(1,0,f_x)$. The curve in the $y$-direction has tangent vector $(0,1,f_y)$. If you take the cross product of those two vectors you get the normal vector. Is that OK?

Maks

Ahh right, yes, I forgot about that

Ted Shifrin

02:44

@Fargle: Note that several of our chat denizens say "Does it stand that ..." ... :)

heather

@meow-mix, maybe look at packages written especially for math journals? they have preset everything such that it fits with that journal's requirements.

Maks

Now, what we just got is the equation of the plane tangent to the function

meow-mix

heh, i'm not writing for a journal

Ted Shifrin

plane tangent to the graph of the function, yes

Maks

What's the equation of the line tangent to the plane on that point ?

Ted Shifrin

02:44

which is what the question asks for ... "tangente al gráfico ..."

that doesn't make sense ... you mean line normal to the plane?

Maks

Yes, sorry

Ted Shifrin

the vector $(f_x,f_y,-1)$ is the direction vector of the line.

(evaluated at the point of course)

Fargle

@TedShifrin I mean strange in a sort of "from an alien perspective" kind of way, haha. Language itself strikes me as a strange phenomenon.

heather

@meow-mix, ah, ignore me. =)

Ted Shifrin

@meow has lots to learn now ...

heather

02:46

got to go, see you guys later

Ted Shifrin

g'night, @heather

Fargle

Take care @heather!

Maks

And what about the level curves ? That's my last question

meow-mix

is my statement correct? "The mapping $f: \mathbb{Z} \to \mathbb{R}$ which maps every $n \in \mathbb{Z}$ to $[n, n+1)$ is a bijection. Additionally, the inverse $f^{-1}$ is the floor function, $\lfloor x\rfloor$."

Ted Shifrin

@Maks ... so $e^{3x-y}$ is constant precisely when $3x-y$ is constant. So you just have to think about the graph of $3x-y=c$, and for the question you choose $c$ that will fit the point $(1,3)$.

NOOOOOOO @meow

Fargle

02:48

@meow-mix This isn't a function: to each integer you've mapped an entire set of reals.

Ted Shifrin

You can't have a bijection between $\Bbb Z$ and $\Bbb R$.

meow-mix

oh

Ted Shifrin

Oh, and you can't map a point to an infinite set. :)

@meow: This is why I'm telling you to slow down and learn things well ... Much better than being in a ridiculous hurry.

Fargle

@meow-mix This is a function from $\Bbb Z$ to the power set of $\Bbb R$, however. Though it is still not a bijection.

Ted Shifrin

@Maks: Are we OK with what I said?

Maks

02:49

@TedShifrin so 3(1) - 3 = 0 ?

I dont get the logic of it :(

Ted Shifrin

Right, so the level curve is $3x-y=0$.

meow-mix

i just realized

Ted Shifrin

That's the line $y=3x$.

meow-mix

how stupid i am

[n,n+1) is not an element of $\mathbb{R}$

Ted Shifrin

Well, elements versus subsets is hard for lots of people.

Fargle

02:50

@meow-mix Don't be so hard on yourself. I might have said the same thing but a few years ago.

Ted Shifrin

He can be somewhat hard on himself if it slows him down and makes him learn thoroughly. I went through this with Balarka, too :P

meow-mix

is balarka really 16?

Ted Shifrin

Yeah, I think so. I can't keep track.

DHMO

what?

meow-mix

but wait

Ted Shifrin

02:51

@Maks: Is that OK?

Fargle

Balarka's a young'un, and you know that's true because I'm the one saying it, and by all accounts, I'm a young'un too.

meow-mix

hmm

@Fargle how old are you?

Ted Shifrin

@Fargle: No fair rubbing in how old I am.

Fargle

21, @meow.

meow-mix

oh, ok

Ted Shifrin

02:52

Tern was right when he said I raised the average by 10 or so ... :D

Fargle

Balarka's got me beat in mathematical maturity, however. Maybe because he listened to @Ted and I'm still somehow retaining my impetuousness...

meow-mix

i wish more people my age were interested in maths

Ted Shifrin

Lots are, @meow, truly.

You say "maths," so you're in Europe?

meow-mix

no, America

Ted Shifrin

So stop saying "maths." :P

@Maks: OK?

Maks

02:56

@TedShifrin I'm sorry I'm trying to learn matlab at the same time

Ohh I get it

Ted Shifrin

OK ... Well, I'm leaving. I'll be back later.

Maks

I have to do some examples

Ted Shifrin

Good. Keep up the good work :)

meow-mix

wait @Fargle

Maks

Thanks :) appreciate all the help

Fargle

02:57

Yes?

meow-mix

why can't it be a mapping?

Ted Shifrin

@meow: Enjoy learning algebra and projective geometry.

Mappings send points to points.

meow-mix

@TedShifrin thanks for the resource, have a nice night

Fargle

@meow-mix For something to be a function, it must map each element in the domain to only one element in the codomain.

Ted Shifrin

Bye @Fargle

Fargle

02:57

Your example maps a single integer to many reals.

@TedShifrin Bye!

Ted Shifrin

We could define a function $f\colon A\to \mathscr P(B)$, however, @Fargle :P

meow-mix

but can't mappings send an element to more than one element?

Ted Shifrin

Only if the codomain is a set of sets :)

DHMO

@meow-mix yes, but then it is not surjective

meow-mix

injective, you mean

Fargle

02:58

@meow-mix Not sure what definition of mapping you're using--if by "mapping" you mean "relation", then sure, but usually "mapping" is taken to mean "function".

meow-mix

right?

Ted Shifrin

leaves in a hurry

meow-mix

@Fargle yeah i meant as in a relation

that is, $f: A \to B$ is a subset of $A \times B$.

DHMO

@meow-mix isn't it surjective?

meow-mix

it is surjective

not injective

Fargle

02:59

@meow-mix Then that kind of works, but it fails to have a lot of nice properties.

DHMO

@Fargle is it not sujective?

Transcript for

$Mathematics$ Mathematics