Mathematics - 2015-07-19 (page 1 of 3)

Karl Kronenfeld

00:00

@Math is Life: maybe you can elaborate?

Agawa001

00:24

oeis rejected a new formula i introduced there

maybe i shouldnt use % operation

Alec Teal

I hate to do this but math.stackexchange.com/questions/1365990/… bump. It's not needed in a timely manner, just don't want it to die!

user240033

00:54

Why does the operation $(k,x) \mapsto k \cdot x$, $x \in F$ make a $\text{GF}(p)$-vector space?

anon

what's F?

David Wheeler

@AlecTeal it's been decades since I looked at stuff like that, but I believe it's a theorem, that if $\kappa$ is a transfinite cardinal, and $\lambda < \kappa$, that $\kappa^{\lambda} = \kappa$

user240033

$F$ is finite field with $\text{char}(F) = p$

David Wheeler

It certainly holds if $\kappa$ is infinite, and $\lambda$ is not.

anon

@user240033 then F contains what you call GF(p) no?

whenever a field F contains a subfield K, we can say F is a vector space over K

Alec Teal

00:58

@DavidWheeler I'm pretty confident with the set theory there being valid, it's the writing that $C$ function I'm iffy on!

user240033

why the explicit operation $(k,x)$ though? I assume it means $k$ copies of $x$.

anon

um, what?

Alec Teal

I think you need to check your operations

anon

for instance, if $V$ is a real vector space, there is a map $\Bbb R\times V\to V$ given by $(\lambda,v)\mapsto\lambda\cdot v$. That's scalar multiplication.

user240033

The wiki article said $n \cdot 1$ a sentence earlier.

anon

01:00

your point being?

user240033

but okay lol, that makes more sense.

Alec Teal

Some tit has voted to close that question, WTF is missing?

anon

I suppose if k is an element of Z/pZ, it can be represented by an integer, in which case kx=x+x+...+x (k times) is true.

David Wheeler

@AlecTeal I don't think anyone ever actually explicitly calculates the bijections on "repeated cartesian products"...it's enough to know that if $|A| = |\Bbb N| = \aleph_0$, that $|A^n| = |A \times A \times \cdots \times A| = |A|\cdot|A|\cdots|A| = |A|^n = \aleph_0^n = \aleph_0$.

@Alec it's an "off-topic" close, those are suspect, in my opinion.

@user240033 you need to be careful about what you mean by "copies"...$(x,x)$ and $x+x$ might both be so construed.

Mike Miller

morning

pjs36

01:06

Hello hello, Mike

Alec Teal

@DavidWheeler I was quite happy with $|Q^n\times Q^n|$ being countable and stuff. But I think it is important that I /could/ form the bijection (more importantly, surjection)

Although what you've just said shows I don't need to...

You should submit that as an answer.

David Wheeler

Have you seen a proof of the Cantor-Bernstein-Schroeder theorem? It gives a way to construct a bijection explicitly given two injections.

Sigh I'm not sure what cardinality arguments are, if not set theory, but I don't want to get in a shouting match with a mod.

pjs36

I think the difference is that MSE set-theory looks like complete gibberish, orders of magnitude worse than "abstract nonsense". Alec's post is somewhat intelligible, and is therefore elementary set theory :P

Dave

Can some one point me to a decent online guide with how you calculate a scale factor for a given equation?

anon

huh?

"scale factor for a given equation" does not mean anything to me

user240033

01:19

Scale factor

A scale factor is a number which scales, or multiplies, some quantity. In the equation y = Cx, C is the scale factor for x. C is also the coefficient of x, and may be called the constant of proportionality of y to x. For example, doubling distances corresponds to a scale factor of two for distance, while cutting a cake in half results in pieces with a scale factor of one half. The basic equation for it is image over preimage. In the field of measurements, the scale factor of an instrument is sometimes referred to as sensitivity. The ratio of any two corresponding lengths in two similar geometric...

is this what you mean dave?

David Wheeler

Pick a scalar, any scalar.

Dave

well i have an equation of y = a*b^x, where x is between 1 and 40

David Wheeler

@anon who owns this room now?

I'm very happy for you, Dave.

anon

me and robjohn. I think mixedmath and some employee guy are also on the list.

you can click "info" in the upper right corner BTW to see that.

David Wheeler

I recall it changing hands for a while, a while back.

Dave

01:21

thanks i think ?

anon

you mean all the way back with asaf?

David Wheeler

Mhm

anon

yes, I think he gave it to robjohn, and then robjohn added me to the list at the time. that was around the time he quit chat foreverz.

David Wheeler

@Dave If your equation is $y = a(b^x)$, $a$ might reasonably be called the scaling factor, and $b$ the "base".

pjs36

@Dave, if I had to guess, you're talking about things like "$y = x^2$ can be scaled, by a factor of 3, to $y = 3x^2$". If this is what you mean, then the "scale factor" is whatever your "parent function" needs to be multiplied by, to get what you have.

Dave

01:25

Ah okay, i was for some reason thinking it was to do with ^x

David Wheeler

@pjs36 I think you and I are on the same page. Web coding these days...

pjs36

Yeah, @DavidWheeler, woohoo! Haven't seen you in a while, by the way

David Wheeler

Do I know you?

Dave

so could m in y= mx+c also be considered simply the scale factor?

pjs36

Oh, not really, I just remember seeing you around a few months ago, when I first entered chat, that's all.

David Wheeler

01:28

@Dave That's....a bit different. It would be if you wrote it like this: $y = m(x + \frac{c}{m})$ (provided $m \neq 0$)

Dave

Good point !

David Wheeler

@Dave I don't know if there's a "standard terminology" but if $f(x) =$ something in $x$ + constant, the trailing constant is often called a $y$-shift, or vertical shift, or something similar.

An $x$-shift (called a "phase shift" in trig functions) is something like $f(x - x_0)$ for a known function $f$.

Dave

Hmm i haven't heard those terms before - at least not yet anyway

David Wheeler

So the "point-slope" form of a line $y = m(x - x_0) + y_0$ employs all of these.

You can think of it as the line $y = mx$ shifted from the origin to the point $(x_0,y_0)$.

I see the term "scaling factor" used in two scenarios a lot: $y = A\sin(Bx + C) + D$ (here, the "scaling factor" is also called amplitude), and $y = Ae^{kx}$, for exponential problems.

Dave

if you have y=ab^x im wondering if b is the scale factor, because if b > 1 y grows exponentially and if b < 1 and > 0 it decays exponentially

David Wheeler

01:43

The scale factor should be $a$, it's the base that affects the growth/decay phenomenon. One caveat, however: Note $b^x = e^{\log (b)\cdot x}$.

El'endia Starman

And if b < 0, turn on the lights and spin the disco ball, because dem curves start dancing!

(For $(-1.5)^x$.)

David Wheeler

So, we can regard $b$ as being "up in the exponent" $k$ in $e^{kx}$.

We have two axes, so it's logical to ask whether we mean to "scale the $x$" (input) or "the $y$" (output).

It's quite possible for $f(ax)$ to behave very differently than $af(x)$.

and disco balls, tee-hee.

David Wheeler

02:13

This room isn't as fun as it used to be. We used to have deep conversations about important things. Like scotch. And beards. Beards!

Dave

Plenty beard physics talks in game development channel some times!

Soham Chowdhury

@AlecTeal probably some kind of an I

@DavidWheeler I have one in a pdf, if you'd like

Dave

Well i finished my assignment, hopefully i didn't balls it up. Now to do my computer science.

Soham Chowdhury

@Dave, don't mind Alec. Sometimes he forgets that we all used to struggle with algebra and graphing once upon a time :)

good luck. :)

Dave

Well im teaching my self before i go on to calculus in winter

using these books

David Wheeler

02:21

one what?

Dave

Don't know if any one else knows, harvard university has a free introductory online course for computer science if it interests any of you : courses.edx.org/courses/HarvardX/CS50x3/2015

Suits me for my game programming interests ^_^

Soham Chowdhury

02:34

I suggest you give yourself a real algebra workout before hitting logs and stuff, btw.

@Balarka, @Alex: really good question in Aluffi.

6

Q: $\mathbb Q$ is not the direct product of two non-trivial groups.

I know this has been asked before, in a bunch of places, so I expect it to be closed as a duplicate at some point, but I'd like to know if my own proof works. If the proof is incorrect, please limit answers to pointing out the errors. If the proof is correct, then thoughts on improving it would b...

group-theory

Dave

@SohamChowdhury do you know good website that can help with it.. besides kahn academy as i use that one already

One thing i found using logs, was the calculator rounded off the numbers which gave issues with my answers so i don't know if i should leave me answer as is or not =/ i hope the mark sheet takes that into account

Soham Chowdhury

03:08

whoa. total mindf**k.
the modular group $\cong C_2 * C_3$?!

r9m

anyone wants to upvote and gimmie a silver badge? :P

Soham Chowdhury

there ya go.

r9m

hee!! Thanks! :D

Remember me

03:37

Hello@SohamChowdhury

Soham Chowdhury

03:53

woo, redoing Aluffi with all the exercises feels great.

hey, @Rem.

my internet is going off every five minutes :(

@Dave did you check out BetterExplained?

Remember me

@Soham check if my reasoning is right or not...

UserX

Is there a math-heavy book that lays out the basics of online stores?

Soham Chowdhury

@Rememberme for what?

UserX

I'm interested in opening one but I want to learn some finance rules first

r9m

@UserX hey there! :)

user147690

04:01

How did your (requested) ban go @UserX? Did you regret it?

Remember me

A set in the order topology is a linear continuum.. So there will exist an least upper bound for it . Also between two elements there always exist an element ... This means that if I take two open sets around the points there will always exist a point coming in between. Hence the union of the two open sets can be equal to the full set but the two open sets will never be disjoint . Hence the set will be connected @SohamChowdhury

Is this reasoning fine ?

Hey @AlexClark following the ashes ?

thanasissdr

Hello to all. How can I strikethrough a part of a text?

Remember me

~~blah~~ just put three dashes on both sides @thanasissdr

UserX

Oh hey

No I didn't regret it, just missed MSE for a week or so

thanasissdr

Thank you, @Rememberme .

Soham Chowdhury

04:11

hey, Alex.

I've been revising the first two chapters. they kid you not, doing this book properly will leave you with rock-solid ideas.

also, pushouts and pullbacks are cool.

r9m

~~CUT~~ didn't know that ..

Soham Chowdhury

?

@Rememberme what is the question?

UserX

Does @Sawarnik and the abstract algebra guy still visit the chat?

r9m

@UserX @Sawarnik rarely .. and Idk who is the Abstract algebra guy?!

Remember me

I have to show that a set in the ordered topology which is connected is a linear continuum . So I have assumed it is a linear continuum and not connected @SohamChowdhury

UserX

04:14

He should be 15 y/o by now

Remember me

You mean Balarka @UserX

UserX

Yea

Soham Chowdhury

@Rememberme oh. well, I can't be of any help. I suck at topology.

thanasissdr

@Rememberme I want to strikethrough a part in a post of mine, but it's not rendering. Does it have to do without the browser? ~~test~~

Remember me

Oh... nvm

thanasissdr

04:16

@Rememberme Ok, it works here, but what about in a post?

Remember me

@userX Balarka is a frequent MSE'r here

@thanasissdr I have never tried it in a post ... But it should be same...

UserX

The strikethrough required a command at the start of your post @thanasissdr but my memory might be fooling me. Haven't texted in like 7months

thanasissdr

@UserX @Rememberme Never mind. No big deal.

UserX

I think you had to use a usepackage command like a real tex doc, I remember this distinctively because it was the only time I saw it on MSE

Thanasi what are you studying? In what city?

thanasissdr

I 've been studying Maths, as most of all the members here, I suppose.

UserX

04:24

Nah, many are engineers or just enthusiasts

thanasissdr

I see. Wrong guess! :p

I' m on my way to finish my MSc.

UserX

City? Also, \require{cancel} \cancel{text to strike through here} might work on mse

But that's not a horizontal strike, it's a diagonal

thanasissdr

Karditsa, Greece.

Yeap, I am aware of that package.

UserX

I'm pretty sure karditsa has no math schools lol

thanasissdr

Ahahahaha. If you mean a math faculty, you are right indeed. :p

UserX

04:27

By math I mean the departments like the ones at ΑΠΘ, ΕΜΠ, Γιάννενα etc

thanasissdr

I 've graduated in AUTH.

Mike Miller

@thanasissdr What do you study?

thanasissdr

Correction: at

@MikeMiller Mathematics.

UserX

Might start there at Septmber :)

Mike Miller

@thanasissdr Sure, I mean more specifically.

user147690

04:30

@SohamChowdhury First two chapters of aluffi?

Soham Chowdhury

yes.

UserX

Mike, have you studied any applied maths? Finance in particular?

thanasissdr

@UserX MikeMiller Currently I'm registered on Hellenic Open University (HOU), in order to get my MSc.

user147690

@SohamChowdhury I'll do it xD

Soham Chowdhury

I just left out a few of the ultra-abstract CT things from the first chapter, which I'm doing now. But the exercises in the groups chapter are fun.

Mike Miller

04:31

OK, I see. I was just curious if you were interested in some particular area.

@UserX I dropped out of a financial mathematics course, too soon to be able to tell you anything interesting about it. Sorry.

UserX

@thanasissdr I'm guessing he wants to know the specfic area of math you're studying

thanasissdr

Applied Mathematics. Specifically, PDE's (wave equation, heat equation)...

Soham Chowdhury

@AlexClark I learned today morning that the modular group $\cong C_2*C_3$.

thanasissdr

But my thesis is about Google's PageRank (that means a lot of linear algebra and Markov Chains)

Mike Miller

OK, very cool.

thanasissdr

04:33

@MikeMiller What about you?

Mike Miller

Topology.

thanasissdr

MSc in Topology?

user147690

@SohamChowdhury I haven't worked with the modular group, so I'll have to look at aluffi xD

UserX

@thanasissdr Great, how do you bug the pagerank so you appear first page? :P

user147690

@UserX Was it you who user Alec teal got really annoyed at first having a girl in your profile picture with you(and ranted about being a clingy guy)

Soham Chowdhury

04:34

@AlexClark you had complex analysis right? o.O

thanasissdr

@UserX Google "link farms" or even better try "SEO". :p

Mike Miller

@thanasissdr: I'm a PhD student.

user147690

@SohamChowdhury Yes, but they don't look at it from a group perspective ever

UserX

@AlexClark probably. Had a lot of talk about that by many users though

Soham Chowdhury

@Alex, it's the group of $2\times 2$ matrices with integer elements and det $1$.

thanasissdr

04:35

@MikeMiller That's terrific! Country?

Mike Miller

USA. I'm at UCLA.

user147690

@SohamChowdhury Oh I see on wiki

thanasissdr

@MikeMiller I see! Is it on top 5?

UserX

@AlexClark I got a pic with a different girl now, I should change to that haha

@thanasissdr I think it's ranked 8th if you take all departments into account. Maybe Mike knows the math dept ranking

Dave

@SohamChowdhury thanks for the suggestion will check it out :)

user147690

04:39

No @Rememberme I don't follow any sports really

Mike Miller

Not quite, @thanasissdr. That's Harvard/Princeton/Stanford/Berkeley/MIT on any ranking list.

user147690

I'll be back later. I'll start on Aluffi for you @SohamChowdhury :P

Mike Miller

I think we're usually top 10. I don't spend much time looking at ranking lists, though.

Soham Chowdhury

@AlexClark good. I'm going back and doing all the group exercises that work with matrices; I skipped those the first time.

I can't wait to get to modules. I'm tired of how many books start with "let $M$ be an $A$-module". :P

user147690

May 28 at 14:35, by Alex Clark

@SohamChowdhury ahahaha. Hey learn all this category theory, but if you don't have time for learning matrix multiplication, dats cool mang

Soham Chowdhury

04:42

star-re-farmer spotted

user147690

Hahaha

Soham Chowdhury

are you gonna study algebraic geometry this sem?

thanasissdr

@MikeMiller. I see. However, it is considered to be among the best ones worldwide.

Soham Chowdhury

and as five-years-younger me would've said: "they have Tao"

Mike Miller

I'm happy here, which is I suppose what matters.

user147690

04:44

@SohamChowdhury Nope, I don't think we even have alg geo

thanasissdr

Yeah, that's for sure!

Soham Chowdhury

@MikeMiller what is your advisor like?

thanasissdr

@UserX What's your affiliation?

Soham Chowdhury

I remember reading about him once. Something about a conjecture he proved on untriangulable (?) manifolds.

Mike Miller

He's kind. He likes movies, which is good, because so do I. Not very relevant to our meetings, though.

Soham Chowdhury

04:45

@AlexClark you were saying you're getting interested in it, iirc

user147690

@SohamChowdhury Yep yep, I was checking it out, since AG comes up when looking at tropical geometry heaps

Soham Chowdhury

I was reading over at Academia.SE about some poor chap whose advisor passed away during the PhD. :(

UserX

@thanasissdr finished HS, applied for schools, waiting for acceptance

Mike Miller

"Every topological $n$-manifold, $n \geq 5$, is triangulable" was a long-standing conjecture. Galewski and Stern proved it was equivalent to a problem in 3-manifolds. He disproved this 3-manifolds conjecture (and as a corollary proving the existence of non-triangulable $n$-manifolds for all dimensions $n \geq 5$).

thanasissdr

"HS" stands for high - school?

Soham Chowdhury

04:47

ah. sorry if this is a stupid question, Mike, but can you understand the proof?

Mike Miller

Can I? Hypothetically.

I haven't read it.

UserX

@thanasissdr yes

thanasissdr

@UserX Interesting you are involved in this site - forum.

And certainly good for you!

Soham Chowdhury

@Alex, did you look at the proof that $\Bbb Q$ is not a direct product of two nontrivial groups? (I didn't; I want to have a go at it)

UserX

Why is it so strange?

Soham Chowdhury

04:50

@thanasissdr there's a bunch of school students on here.

user147690

@SohamChowdhury I have it open on my - to.look.at browser window, but not yet

user147690

Still not 100% after food poisoning, but after food comes I should be + first coffee in days <3( a heart)!

thanasissdr

@Soham, I had the impression it was a site for more advanced math questions.

Soham Chowdhury

that'd be MathOverflow

@AlexClark <6?

user147690

What the heck is <6 lol

Soham Chowdhury

04:53

<3!

crappy attempt at humor

thanasissdr

Ahahahhahaha!

UserX

@thanasissdr advanced math $\not \implies$ advanced age. You'll meet many exeptional 12-18 y/o s here.

Dunno if that rendered correctly

user147690

Yes we have a few prodigies here

Soham Chowdhury

one* prodigy

@UserX $\not\hskip -0.095in \implies$?

UserX

@SohamChowdhury yup

thanasissdr

04:55

@UserX Yeap, I am to confirm that (about the geniuses)! Nope, it's not rendered, but ok, I am a LaTeX user. :Ρ

user147690

$\not\!\!\!\!\implies$

user147690

I win @SohamChowdhury

Soham Chowdhury

:( :(

user147690

Okay I must actually leave now haha, be back later

Soham Chowdhury

do Aluffi.

All hail the $$\huge{\not\hskip -0.14in \implies}$$

UserX

04:56

It should be rendered to you assuming you're on your PC/Laptop. I'm on my tablet, so I just read the codes

Soham Chowdhury

yours didn't render properly.

thanasissdr

Nope, I 'm currently on Safari/Mac. I dunno if that matters.

Soham Chowdhury

doesn't, but I suck at math so I have to pass the time somehow

:P

UserX

I guess the line didn't cross the implies sign

Soham Chowdhury

heya, @Clarinet

@UserX indeed

Clarinetist

04:58

Hi @Soham

Soham Chowdhury

I have been overdosing on Segovia's version of the Chaconne.

Have you heard it, perchance?

UserX

@thanasissdr it has js so you can copy Rob's code (stickied) to render tex in chat

Clarinetist

Nope, haven't. Been watching movies with the gf and am now doing stats

Soham Chowdhury

And I heard a bunch of Ravel.

Clarinetist

Ravel FTW :)

Soham Chowdhury

04:59

oh, you're busy lol.

internet high five

Clarinetist

@Soham Yeah, the movie repertoire was quite strange. Fifty Shades of Gray (it was a free rental! and we couldn't think of anything else) and Sleeping Beauty (gf never saw it, we're going to watch Maleficent tomorrow)

Soham Chowdhury

Grey*, puny American.

thanasissdr

@UserX Where's that code? If you could provide a link.

Clarinetist

Btw, for the record, Fifty Shades of Gray has moneygrab all over it

Lol @Soham

Soham Chowdhury

@thanasissdr it's on the sidebar

UserX

05:01

math.ucla.edu/~robjohn/math/mathjax.html

Soham Chowdhury

oops. @UserX use \centernot

Clarinetist

Whoever wrote the script for Fifty Shades must've been quite uninspired

It was like Twilight with the strange shock every so often that wouldn't add anything to the plot

UserX

We're having an existencial crisis over a bar not crossing half a centimeter to the right in LaTeX. This reminds me why I love this place

Remember me

Hello@MikeMiller

UserX

Anyway it's past bedtime, I'll head to sleep. See you guys later.

Clarinetist

05:06

Btw, can any of you solve the final IMO problem?

Soham Chowdhury

has something to do with juggling, I heard

can you?

Clarinetist

i.guim.co.uk/img/static/sys-images/Guardian/Pix/pictures/2015/7/…

Nope

Soham Chowdhury

05:21

@Rem, since you were looking for interesting things about the center: if $|G| = p^3$ for prime $p$ and noncommutative $G$, $Z(G)\cong\Bbb Z/p\Bbb Z$. ;)

@Balarka, did you know that? ^

Remember me

@SohamChowdhury how do you prove that..?

Soham Chowdhury

oh, I can't yet.

The Substitute

off topic algebra - If $G$ is a group, is there a difference between $Aut(G)$ and $S_G$? I believe they are the same since they are both the set of permutations of $G$, but I am not sure why we use two different notations.

Soham Chowdhury

@TheSubstitute yes

Remember me

What are its prerequisites?@Soham

Soham Chowdhury

05:24

it takes Sylow theory and the classification of finite abelian groups. chapter 4 of Aluffi. I accidentally reached that page in my pdf reader.

Mike Miller

oops

Soham Chowdhury

@TheSubstitute $S_G$ is the symmetric group of the underlying set. ${\rm Aut}(G)$ is the set of those which are homomorphisms. not all set-functions $G\to G$ are homs. :)

(am I wrong?)

Mike Miller

that's correct

The Substitute

Ah, so we just have $Aut(G)\le S_G$, thanks.

Remember me

@Mike I had this question : Does path connectedness have a relation with compactness?

Mike Miller

05:28

they're both important

Remember me

I mean to say that a set under a given topology if pathconnected implies something about its compactness ?

Mike Miller

no

Transcript for

$Mathematics$ Mathematics