Mathematics - 2013-03-28 (page 1 of 3)

@κρανίοπεριπολία Don’t know; it’s been a number of years since I last looked at what was available, and it would also depend a bit on the kind of students I could expect.

vzn

12:59 AM

hi all. looking for anyone interested in a new attack on the collatz conjecture. algorithm-driven. experimental math. plz reply on my blog

Collatz conjecture

The Collatz conjecture is a conjecture in mathematics named after Lothar Collatz, who first proposed it in 1937. The conjecture is also known as the 3n + 1 conjecture, the Ulam conjecture (after Stanislaw Ulam), Kakutani's problem (after Shizuo Kakutani), the Thwaites conjecture (after Sir Bryan Thwaites), Hasse's algorithm (after Helmut Hasse), or the Syracuse problem; the sequence of numbers involved is referred to as the hailstone sequence or hailstone numbers, or as wondrous numbers. Take any natural number n. If n is even, divide it by 2 to get n / 2. If n is odd...

turing machine blog

user19161

@vzn You need to copy your profile to all accounts so that we know where your blog is.

amWhy

@Jasper Nice factoring problem/solution! here

vzn

more bkg on the collatz attack from cs.se chat

robjohn

1:32 AM

@vzn I like to say that if $n$ is odd, the next term is $\frac{3n-1}{2}$

Amzoti

2:00 AM

@robjohn: You have such a distinct and cool graphic. May I ask what it is from? Also, what are all of the little graphics (are they fractals or something else and what generates them)?

robjohn

@Amzoti by the cool graphic are you talking about my avatar? the mean square

Amzoti

yes - correct -

avatar

robjohn

@Amzoti I made my avatar based on this comment to which there is a link on my profile. It is the mean square >8(

@Amzoti I am not sure what you mean by the little graphics...

Amzoti

@robjohn: excellent!

anorton

@robjohn probably referring to the auto-generated gravatar...

(Like mine)

Amzoti

2:05 AM

All of the Avatars look like they are randomly generated when one does select their own

What are those avatar graphics called (they look fractal like) and what generates them?

robjohn

@Amzoti Ah, they are generated based on a hash of the email address

anorton

huh. Another new thing I've learned today!

Amzoti

Very cool! Is that a SHA-1, SHA-2 or maybe the new SHA-3?

robjohn

@Amzoti Check out this question and its answers

The hash is the MD-5 hash of the email address

Amzoti

@robjohn: thanks for that - very interesting

I wonder how much they would change by using a larger hash value? These now have me very curious - thx for that link!

nerdy

2:26 AM

quick and sily question about mathematical formal notation, i took a print screen and uploaded : postimg.org/image/mltdd6kzr

are both representations correct, my folks ?

robjohn

@nerdy They both look the same.

nerdy

thanks robjohn :)

user19161

OK, just did another 5 edits on old posts for today. Tried to do them in quick succession to minimise spread...

user19161

What I do is open up 5 tabs and then click edit in quick succession after rewriting.

user19161

Hey @ethan have you met the prof?

robjohn

3:10 AM

@JasperLoy what class?

user19161

@robjohn I don't know, must ask Ethan lol.

user19161

I think even after I am dead, Ethan will still have not made an appointment, lol.

robjohn

@JasperLoy Does that mean that if Ethan makes an appointment, we can kill you? ;-)

amWhy

@robjohn hahahaha!

user19161

@robjohn My logic is failing since the meds are making me drowsy...

robjohn

3:13 AM

@JasperLoy It's probably not your logic that is failing...

user19161

Er, is 1+1=3?

user19161

Actually, that happens in the trivial ring.

amWhy

I think my avatar makes me "look" silly :-/

user19161

My LaTeX knowledge currently is very minimal. So my posts are not formatted ideally.

amWhy

It's cute, and I like it, sort of, but it seems as though it leaves me subject to not being taken seriously. Perhaps I'll just have to learn to dress for the occasion, and use it when I'm in the mood to be lighthearted.

user19161

3:17 AM

But as long as it looks OK, it is OK. I use a combination of LaTeX and whatever formatting the site offers.

amWhy

@JasperLoy There are times I wish I had the time to remind myself how I can format - I know I've seen it done, but can't quickly find the reference (or I see things I want to remember, but can't, at the time I need them!) so I improvise.

user19161

@amWhy Remember this site is not writing things in LaTeX per se. Writing a LaTeX only document is quite different.

Ethan

@JasperLoy I met with proffesor blasius who suggested I speak with a bill duke, but I am starting to think, I should just study more instead of trying to meet with him

amWhy

@JasperLoy Yes, I do keep that in mind. And I plan to tap your brain, once I get back to my installation (er, once I uninstall what I have, and reinstall what I need).

Ethan

@JasperLoy Also found this yesterday $$\int_{0}^1\frac{e^x-1}{x}\ dx=\sum_{n=0}^\infty\frac{1}{2\binom{n+2}{2}}\frac{1}{n!}(0!+1!+2!+3!+...+n!)$$

lol

user19161

3:22 AM

@Ethan The only number theory I know is gcd and lcm, lol. Don't forget me when you win the Fields medal.

Ethan

I don't really know any number theory either

amWhy

@Ethan Go for it, Ethan. Meet with Bill Duke, and study more. Not mutually exclusive endeavors!

Ethan

only baby stuff

@amWhy I don't want to make a fool of myself, if my stuff is already known or boreing

user19161

@Ethan Glad you know it is baby stuff. Many people don't know that they are doing baby stuff and think they are doing advanced stuff, lol.

Ethan

baby stuff is important tho

amWhy

3:24 AM

@Ethan The fact that you recognize what you don't know says a lot about what you do know! lol, same point as Jasper!

user19161

And then they try to judge me based on the things I say, not knowing that there are many things I know which I don't say, lol.

amWhy

I wouldn't trust anyone who claimed to have mastered any topic, comprehensively and thoroughly!

user19161

This just shows me their flawed reasoning, lol.

awllower

The review queue today is crowding!

user19161

Now I use that reasoning to conclude that they won't be able to do great stuff, lol.

Ethan

3:26 AM

I wish someone here would look at some of my stuff before I show him

amWhy

@JasperLoy Exactly!

Ethan

I don't want to bother eric naslund anymore

awllower

100 first posts...

user19161

@Ethan How are you bothering him?

Ethan

I sent him a bunch of stuff a while back, alot of which now I think is crap lol

user19161

3:32 AM

@Ethan You love using lol like me, lol.

nerdy

can i represent any vectorial subspace as a general vector ? for example, taking the nullspace, can i represent the entire nullspace as a general vector or do i need to represent the nulspace as a set containings vectors ?

user19161

@nerdy A vector subspace is a vector space, and a vector space contains many vectors.

nerdy

i know, but if i treat the vector space as a general vector

like xn = c1.no | c1 is a real number

user19161

@nerdy What do you mean exactly?

nerdy

were both xn and no are vectors

is it wrong ?

user19161

3:34 AM

You can span a vector space using some vectors.

user19161

For example, using (0,1) and (1,0) you can span R^2.

nerdy

my question is only about mathematical notation, in the case i mentioned, my nullspace is 1-dimensional and spanned by no

user19161

Just take all linear combinations.

nerdy

can i represent it by xn = c1.no | c1 is a real number where xn and no are vectors ?

or do i need to represent it as

NullSpace = { c1.no | c1 is a real number }

user19161

If it is 1-dimensional, the basis has exactly 1 vector.

nerdy

3:35 AM

yepp

user19161

That subspace would be the set of all scalar multiples of that vector, end of story.

nerdy

my question is about mathematical notation

how do you represent set of all scalar multiples of that vector, end of story.

the

you need a set ?

user19161

Ah, for notaion, use LaTeX, otherwise not clear...

nerdy

NullSpace = { c1.no | c1 is a real number }

Ethan

what is c1.no

nerdy

3:36 AM

dont know how to use LaTeX :D

c1 = real number

Ethan

.no?

whats that

nerdy

no = basis vector for the nullspace

Ethan

.no

nerdy

.no = times no

scalar multiplication

Jayesh Badwaik

@Ethan Meet Bill. It might be helpful for you. That Prof. Blasius advised you to meet him means his and your time will not be wasted.

user19161

3:37 AM

You can write for example $\{kx:k\in\mathbb R\}$ if it is a real vector space. Here the vector is $x$.

nerdy

latex doesnt work here ;(

Ethan

@jasperloy should I bother learning about linear algebra right now for the kind of math I am interested in

nerdy

linear algebra is so beautiful

khan academy videos in this topic really insightful too

Jasper Loy

user19161

@Ethan It's one of the first courses you will take in university. Eventually you will need to learn many things, and you will become interested in many things, not just NT.

nerdy

can you try to rewrite your notation ?

Ethan

3:38 AM

lol I have watched half of the khan academy vids for linear algebra

nerdy

im finishing them

Ethan

they are incredibly boreing, and the only usefull stuff is when he gets to linear transformations sofar for me

nerdy

while making a summary of linear algebra

user19161

@nerdy You can just copy and paste it onto an answer screen.

user19161

@nerdy I don't watch videos, I read books.

user19161

3:39 AM

Real men read real books.

user19161

Only paper books are real.

Ethan

i am slow at reading

user19161

Ebooks are not real.

nerdy

lol

so

Jayesh Badwaik

@JasperLoy bleh to you..

user19161

3:40 AM

Watching videos are a waste of time to me.

nerdy

you never learned anything from a live lesson

with a teacher

user19161

I mostly watch them for some entertainment.

user19161

I learn most things myself, through reading and thinking.

nerdy

you finished your highschool/college by only reading books

user19161

The world will try to teach you many wrong things about life.

nerdy

3:41 AM

not watching anything

user19161

One must learn to think on his own.

nerdy

ofc

thats why

you can be critical while watching something

or reading something

wheres the answear screen

Jasper /

user19161

Paste onto the main site, just don't click post.

nerdy

got it

user19161

Just a trick, lol.

nerdy

3:44 AM

whats the latex notation for vectors ?

user19161

Depends on context, learn LaTeX yourself by reading lshort. Google lshort, end of story.

Alex Youcis

@amWhy I apologize for this, but I was reading some of the previous conversation and you suggested Ethan talk to Bill Duke. Is there any reason you chose him particularly? Not exactly the first number theorist a lot of people would think of.

user19161

@AlexYoucis Well, just because Ethan has emailed Blasius who suggested he talk to Bill Duke, lol.

amWhy

@AlexYoucis I just responded to Ethan's comment about another professor with whom he met who suggested he speak with Bill Duke. I'm not "up" on who's who in number theory.

user19161

There is a story behind every story, lol.

Alex Youcis

3:49 AM

@JasperLoy Oh? Is Ethan going to UCLA I guess.

user19161

@AlexYoucis Well, that's a long story, lol.

Alex Youcis

Haha, that's fair enough

@Ethan Why did you email Blasius?

Ethan

for advice

Alex Youcis

About what?

Ethan

some stuff i have worked on

user19161

3:53 AM

Ethan is the next Ramanujan.

Ethan

don't say things like that

user19161

Not sarcastic, I have faith in you.

Alex Youcis

Yeah, I see that you do a lot of computations.

Ethan

what do you mean?

user19161

I think he means your HUGE formulas, lol.

Alex Youcis

3:55 AM

Haha, I'm not quite sure what is unclear. You very often ask about some identity or computation in the chat here

Ethan

theres part of my room, lol

user19161

@Ethan OMG!

Ethan

lol I waste alot of paper

user19161

Yeah, these days, I only use toilet paper.

Alex Youcis

I used to do a lot of computations as well.

Ethan

3:56 AM

like 19/20ths of it is crap too, im just to lazy to sort it out

Alex Youcis

Are you interseted in going to UCL?A

user19161

I might be going to grad school in 3 years, if things go as planned.

user19161

UCLA should be one of the places I apply to.

Ethan

not sure, im nearing the end of my junior year, and I have a bad councilor

user19161

@Ethan Just work on your grades for now, and the SATs.

Ethan

4:00 AM

I studied physics for half a year in 9th grade, then studied mathematics over the summer until now, 3 years or so later

user19161

Hey @ethan we might even meet in UCLA in 3 years, lol.

Ethan

lol, I graduate in about a year and a half

user19161

Aha, so what's the problem? Just nice...

user19161

Then we can lol every day in the canteen, lol.

Alex Youcis

What's the canteen?

user19161

4:02 AM

Sorry, wrong choice of words.

Alex Youcis

Are you an undergrad now, Jasper Loy?

user19161

I mean the cafeteria or whatever, you know.

user19161

No, I am an old man.

user19161

I finished undergrad long ago.

user19161

And I am not in the US.

Alex Youcis

4:04 AM

Ok friends, I need to do some studying

Good bye!

user19161

Hey @jayesh you around?

user19161

Ah never mind. Anyway @JayeshBadwaik I am waiting for you to delete that answer, but it is your choice of course.

user19161

I am going to bed, good night @ethan!

Ethan

night

nerdy

4:36 AM

is addition between vectors and sets possible?

Andrew Salmon

Why exactly are there so many "First Posts" right now? I've never seen more than 3, and now there are 88.

amWhy

I saw that, @Andrew just now. The first that popped up was posted 7 days ago? Perhaps a glitch in the screening this past week?

Andrew Salmon

@amWhy hmm...weird.

amWhy

@AndrewSalmon I've never seen so many at one time, either.

κρανίοπεριπολία

6:09 AM

0.999... hours later...

κρανίοπεριπολία

6:39 AM

$\frac{1}{1-0.999...}$ hours later...

κρανίοπεριπολία

7:05 AM

$\therefore \frac{1}{1-0.999...}=(removed)$

QED

;-D

Ethan

hello

hellllllo

κρανίοπεριπολία

nice

wazzup?

Yes, Sir.

Ethan

im bored

what kind of math are you doing

κρανίοπεριπολία

I can see you are bored ;-D

Algebra

Ethan

what kind of algebra

κρανίοπεριπολία

7:14 AM

What kind are you doing?

what kind of what

math

number theory

that is making you so bored

Ethan

yes I found this also yesterday

κρανίοπεριπολία

7:16 AM

cool

Ethan

what have you found in the last week

I need to review :(

lol how old are you

why?

I am currious

7:18 AM

just do math :D

Ethan

how long have you been studying math?

κρανίοπεριπολία

Not long enough because I have to keep going back and reviewing....

:(

Ethan

how long in years

κρανίοπεριπολία

I don't need to know that about you; thank you ;-)

Ethan

Why aren't you currious?

κρανίοπεριπολία

7:24 AM

Because we are strangers chatting on the internet.

Any other questions?

Ethan

yes

do you go to school

Karl's students

7:50 AM

3 years later...

κρανίοπεριπολία

@Karl'sstudents Hi honey, I've been waiting for 3 years for you.

Karl's students

@κρανίοπεριπολία Hi honey! I am solving a mathematics problem now.

A volume of "beheaded" cone.

Ethan

let me see

Karl's students

See the left diagram.

Find the volume of the lower part of the most left diagram.

κρανίοπεριπολία

@Ethan Stay away from my honey, you number theorist ;)

Karl's students

7:59 AM

I am a differential geometer.

Ethan

The volume in terms of what

nerdy

whats special about the particular solution that comes from a system Ax=b with infinitely many solutions when we use rref and solve for the llead variables ?

does it represent any particular shift that the nullspace suffers from the origem ?

Karl's students

@Ethan In terms of constant you defined.

nerdy

who is Karl ?

κρανίοπεριπολία

@nerdy Me.

nerdy

8:04 AM

lol :D

κρανίοπεριπολία

;-D

Ethan

2

Q: $\int_0^{\pi/2}\arctan(1-\sin^2 (x) \cos^2 (x))dx = \pi \left( \frac{\pi}{4}-\pi \arctan \sqrt{\frac{\sqrt{2}-1}{2}}\right)$

In this question sos440 has mentioned about an integral that he computed: $$\int_0^{\pi/2}\arctan(1-\sin^2 (x) \cos^2 (x))dx = \pi \left( \frac{\pi}{4}-\pi \arctan \sqrt{\frac{\sqrt{2}-1}{2}}\right)$$ I would really like to know how this can be proved. I tried using differentiation under the in...

Karl's students

8:28 AM

@nerdy again?

nerdy

lwhat ?

Karl's students

@nerdy Please wait ...

nerdy

lhello

hellol ;)

wait what ?

Karl's students

4

A: What are the advantages of TikZ/PGF over PSTricks?

One good feature of TikZ is that the canvas size is automatically provided. But it is visually not as smart as I think (see question Bounding box is larger than expected when drawing a curved path). In PSTricks, the canvas must be calculated manually to let TeX provide the required space (becaus...

Karl is explained there.

Nimza

Hello!

nerdy

8:31 AM

;(i dont know what is tikz/pgf or pstricks

Dominic Michaelis

huhu

Nimza

If I have two topological subspaces $A,B$ that are homeomorphic to sets in $\mathbb{R}^n$, having interior points, is it true that $A \cup B$ is homeomorphic to such set?

Karl's students

@nerdy Scripting languages for drawing

nerdy

drawing graphs /

Dominic Michaelis

no not only graphs

@Karl'sstudents my TikZ doesn't work like i want it to work :(

\documentclass{standalone}
\usepackage{tikz}
\usetikzlibrary{calc}
\begin{document}
\begin{tikzpicture}
%zuerst ein paar styles definieren
[
help/.style={->,color=gray,very thin},
nodehelp/.style={fill=white,above=1pt,midway},
imp/.style={->,very thick},
pro/.style={color=green!50!blue},
pronode/.style={anchor=south east, fill=white, midway}]
%Basiskoordinaten
\coordinate (null) at (0cm,0cm);
\coordinate (vec) at (-3cm,4cm);
%path für let operator
\path
let
\p1 = (vec),
\n1 = {veclen(\x1,\y1)}
in

@nimza compile it in LaTeX and you see what it is good for

Nimza

8:35 AM

@DominicMichaelis I use tikz, I know)

Dominic Michaelis

@nimza sry i meand @nerdy

nerdy

what are these languages used for ? making math programs ?

writing books ?

Dominic Michaelis

writing books

papers

homework

love letters

all the math on this side is written in $\LaTeX$

Dominic Michaelis

8:55 AM

what is all that removed about? I find it kind of annoying

Karl's students

@DominicMichaelis ask here chat.stackexchange.com/rooms/7828/pstricks-and-pgf-tikz

Dominic Michaelis

@Karl'sstudents thanks

kalpeshmpopat

9:19 AM

Hello

κρανίοπεριπολία

hi

Does anyone have this problem here?

10

Q: Why am I getting disconnects and timeouts in chat?

If I'm chatting in...chat, I'm getting intermittent disconnects, with the following message: There seems to be a problem connecting to the server. Please check your internet connection and reload this page. I usually only get that if chat is down, but it's not: if I wait 30 seconds or do a ...

support bug chat

@robjohn do you know how I can stop this from happening?

Dominic Michaelis

only when my internet is really gone

κρανίοπεριπολία

What do you mean by gone?

...a weak signal...

is it the wifi?

Dominic Michaelis

9:35 AM

jupp

κρανίοπεριπολία

So, I should get the transmitter replaced by the internet service provider?

Dominic Michaelis

i don't know, do you have porblems on other pages ?

κρανίοπεριπολία

jupp

all chat rooms

Dominic Michaelis

are you in a big city? maybe to many wifi signals on the same frequency

κρανίοπεριπολία

I guess I'll have to phone the internet service provider and ask them what is going on?

Dominic Michaelis

9:43 AM

i think its worth a try

κρανίοπεριπολία

thanks :)

robjohn

@κρανίοπεριπολία I've never had that problem. I don't know what might be causing it if your internet connection is fine

κρανίοπεριπολία

@robjohn OK thanks >8(

robjohn

@κρανίοπεριπολία sorry

κρανίοπεριπολία

@robjohn np

Thanks for responding.

:-)

yo @anon wazzup?

pen

9:57 AM

@robjohn I'm completely a newbie at this, but can you tell me how to “save” a script in a browser?

MphLee

hi

robjohn

@pen what kind of script are you talking about?

pen

@robjohn For example, how can I manually just save the ChatJax script for this room so that it automatically starts? There must be some way to input scripts that work on the domain always.

MphLee

someone can help me? in this question math.stackexchange.com/questions/226266/… I noticed that The binary operation $ \# $ must have two values since $39500 \# s= \{ 255\times1.27; 241\times 1.07\} $. maybe that can helpfinding a solution? i don't hink i can writhe this as answer..

but i can't comment the question yet, because i dont have 50 rep.points

robjohn

@pen I have not seen a browser option to load javascript code and run it when a particular page is loaded. I just click on the bookmark bar when I open a chat window

κρανίοπεριπολία

10:05 AM

@pen Do you have all these?

pen

@κρανίοπεριπολία Of course, I click on the bookmarks bar too.

There are some settings that I don't really prefer on some websites, so I'd really love some kind of extension that lets me tweak the HTML, CSS and JS.

MphLee

maybe this isn't the right place for ask, there is a help chat for math.stackechange?

x*

pen

Oh, StackOverflow.

MphLee

there i can ask for this?

κρανίοπεριπολία

"render MathJax" installs MathJax and renders LaTeX once per execution.
This is intended for use on web pages where the contents of the page are static.

MphLee

10:13 AM

@pen : i can find help at stckOverflow or you wasnt talking with me?

pen

@MphLee I was talking to everyone. :-)

I don't know why it doesn't log me in to the chat. Apparently, when I click on "log in", it takes me to the SO main site, but the problem is that I am logged in already on the main SO... not chat.SO

MphLee

i needed to know if i can post in this question math.stackexchange.com/… I noticed that The binary operation $ \# $ must have two values since $39500 \# s= \{ 255\times1.27; 241\times 1.07\} $. maybe that can helpfinding a solution? i don't hink i can writhe this as answer..someone can help me?

MphLee

10:27 AM

up

robjohn

10:44 AM

@pen your chat account is shared among all the Q&A sites. It is a separate account.

Transcript for

$Mathematics$ Mathematics