@Lord_Farin FYI: When you catch this: you'll see our friend Doug Spoonwood has been at work again: I suspect we were each dealt a down-vote by said user, for various reasons.

@Jonn_Underwood Have you googled for it?

Can anyone recommend some good introductory books on elliptic functions?

On what level?

Ahlfors's complex analysis book has lots of nice information

as does Lang's

@MarianoSuárez-Alvarez Helloes.

hi hi hi

@MarianoSuárez-Alvarez, thanks.

@MarianoSuárez-Alvarez How is the weather treating you?

@MarianoSuárez-Alvarez I didn't know that Alexander Beilinson is Russian until I opened a video of him lecturing

If $F\implies G$ is a tautology then $G\models F$ right

nvm i think i have it backwards

$F\implies G$ being a tautology doesn't necessarily mean $G\models F$, but it must happen if in fact $G\models F$

nvm I was correct originally

$A\models \neg F\vee G$, if for any A, $A\models F$ then $A \models G$

@MarianoSuárez-Alvarez Estas?

How would I read $\models$ syntactically?

like outloud

@Ethan "models"?

Or does it mean "is a model of"?

That wouldn't be right, say I want to say $F$ is a tautology

I wouldn't say models F,

"x ⊨ y means x semantically entails y"

?

Are $x$ and $y$ automic formulae

I can give you a definition in terms of propositional logic

If $x$ is an assignment of bits to the atomic formula in $y$, then $x\models y$ means that the truth value of $y$ under those bits is true

If $x$ and $y$ are both atomic formula it means $y$ is a consequence of $x$

Hello chat, I'm somewhat new here and have a question.

@JacobMayle OK. What is it?

It was a meta-type question, but figured it out. Thakns anyways

What is the approrpiate thing to do when a new user is repeatedly posting low-quality (and no-effort) homework problems?

Hey does anyone know how to simplify square root equations? Or know of an example I could look at somewhere? :/ 2 part equation with fractions...

I might

what is the question?

2/3√63-3/2√28

I have no idea where to start... Do I simplify both square roots first? Then I wouldn't know how to cross multiply them though... :/

Try simplifying the square roots first

Note that sqrt(63) = 3sqrt(7)

and that sqrt(28)=2sqrt(7)

How did you get that?

Bingo

$63 = 9 \cdot 7$, $28 = 4\cdot 7$

sqrt(63)=sqrt(7*3^2)=sqrt(7)*sqrt(3^2)=sqrt(7)*3=3sqrt(7)

sqrt(28) simplifies in the same way

Define simplify

I'm so confused! :(

Does latex work in the chat?

So that the question looks something like 2√5 or whatever, @Ethan

Who are you to say the latter is more simplified it really depends on the scenario sometimes it is better to make things look a certain way

If I wanted to show $(2\sqrt{5})^2=20$

@Amzoti Hello!

The notation $\sqrt{20}$ would be more simplified in my oppinion

as it would clearly show that its square is 20

@JacobMayle so how do I add in 2√7 and 3√7 with the fractions...?

You need a common denominator to add the two fractons

I think the answer that he or @Shayna is looking for is -19sqrt(7)/252

yes...so it's 4/6√7?

@Shayna $$\frac{a}{b}+\frac{c}{d}=\frac{da+bc}{bd}$$

Listen to @Ethan.

@Shayna here shayna is this just homework

I have no idea what any of that means- math n00b!

You know how to do this for 2/7 + 3/5 = (2*5+3*7)/(5*7).

This is the same thing, but with square roots.

@Shayna Just type in your stuff here

wolframalpha.com/http://www.wolframalpha.com

wolframalpha.com/input/?i=2%2F(3sqrt(63))+-+3%2F(2sqrt(28))

@Ethan Yes, it is homework... Another of those problems without anything similar in the text :/

Thank you very much- I'll try that!

If you just want to finish it, and you don't want to actually learn how to do it, use that

To expereinced users: Is there a way to report a new user that keeps posting low quality/no effort problems

I do want to learn it though! I'll need it for the final LOL

@Shayna how old are you?

I am not refering to you, @Shayna

@JacobMayle Who?

This user: math.stackexchange.com/users/76459/user76459

keeps posting bad questions

He is plagarising "his attempt" from the best answer on yahoo answers, then asking for explanations

What do you mean by 'bad'?

@JacobMayle Just keep hit flag under each of their questions and ask others to as well.

He also posted the same question twice

I wouldn't reccomend that lol, you do need to give a reason for flaging questions, also you have a limited number of flags

@JacobMayle then flag it as a duplicate

@Ethan I'm 24... Just finished a BA majoring in both psychology and sociology... Now taking math for teachers to get into a BEd program... Just terrible at math.

It already was taken care of as a dup

and closed, but its generally bad behavior

Oh, thats cool

@JacobMayle post a comment, flag as a duplicate. Others with more rep can vote to close. In your comment, link the duplicate (repeated question).

Ok, thanks for the advice

@Shayna I will type up a more detailed soln

@Shayna youtube.com/watch?v=MEo0rSZ4O3w

@Ethan Thank you very much! I've been stumbling through this course, trying to find help on this site- as it seems to be more reputable than yahoo answers... I've had pretty good luck getting people to explain things here rather than just giving me answers. :D

@Ethan Oh I know how to add fractions - and multiply, divide, subtract... Where I am confused is how to solve the equation with the square roots and fractions.

Keywords are 'adding fractions' 'simplifying radicals'

@Shayna what do you mean can you give me an example?

2/3√63-3/2√28 is the question

it asks me to simplify it

What are you being asked to do?

Simplify is kind of vague, but I assume they want you to get a common denominator

And factor out perfect squares under each radicals

can do fractions and square roots... just the two compounded is confusing for me :/

Yep, she wants answers like 4√5... or in the case of 15/√2 she wants (15/√2)/2

(15√2)/5 sorry

errrr one more try... (15√2)/2 LOL typing fail!

@Shayna You may/may not find this useful: udacity.com/course/ma006

If you multiply the numerator and denominator of a fraction by any non zero number the value of the original fraction does not change

Yes, so do I tackle the fractions first? And give them a common denominator?

no, multiply the numerator and denominator by somthing, but find somthing that will cause the square root on the bottom to go away

Say I have $3/sqrt{2}$

If I multiply the numerator and denominator by sqrt{2}

I get $3sqrt{2}/2$

the way it's written it doesn't have a square root on the bottom... unless you want me to put them over 63 and 28 respectively

okay so do that?

nvm

ok

Look at the two fractions

you are taking the diference of

2/3√63

and

3/2√28

Multiply the numerator and denominator of each by the radical appearing in the denominator

So we multiply the top and bottom of the first one by √63

okay LOL

can you do that for me, and tell me what you get

@Shayna Thats what you want to do

126126/189

How so?

126/189**

Is there any way to display latex in the chat?

@JacobMayle yes

Awh, that would have saved some time

how?

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

I am sorry I am to busy and to lazy to help you shayna

Hopefully jacob can

It's all good Ethan. I think you helped me last time :D

@Shayna Did you look at the image I uploaded?

@amWhy: Hello ...

@JacobMayle click start chatjax and reload the page

@Amzoti Hey there, busy beaver!

How do you respond to this?

Give me the general mathematical formula for NURBS curves, with special cases (B-spline and Bézier curves)

@JacobMayle $$\text{ok}$$

Doesn't seem to be working

click render

@amWhy: Am I tired - looks like a slow night

Is this compatible with chrome?

i am using google chrome

it works

Hmm, I clicked on"start ChatJx", then "render MathJax"

then refreshed the chat

but it isnt working

drag it to your book marks

start chatjax

@Amzoti It is indeed a slow night...re: how to respond to "give me..."? Hmmm, I get turned off and walk away. If it's not late in the day, I might comment (if user is genuinely new).

@JacobMayle Yes I did, I'm just trying to solve using it now :D

@Shayna Pl

OK

I just did a very poor attempt at typing "OK"

LOL

Okay, so is it... -√7? :D

Is what -sqrt(7)?

(2/3)√63-(3/2)√28 simplified lol

No

I got -19sqrt(7)/252

Which is not equal to -sqrt(7)

Alright, I'll keep working at it... Back to the drawing board LOL

If I do the question just for an answer... I get -2.645... -√7 is the same thing :/

Negatory

-sqrt(7) = -2.645

but that is not the right answer

The right answer is something like -.19948

Wait

Do you mean:

A: wolframalpha.com/input/…

B: wolframalpha.com/input/?i=2%2F(3sqrt(63))+-+3%2F(2sqrt(28))

Everyone on the chat has been taking what you asked as (B)

Although What you wrote a few lines ago is (A)

in which case, -sqrt(7) is 100% correct!

A LOL

Well, then you have it correct

Yayy thank you! Sorry for being confusing LOL!

$$\prod_{n=1}^\infty(1-\frac{x^2}{n^2})=\sum_{n=0}^\infty\frac{(-1)^n\pi^{2n}x^{2n}}{(2n+1)!}$$

If $d_k(n)$ counts how many ways $n$ can be written as a product of $k$ distinct integers

$$\sum_{n=1}^\infty\frac{d_k(n)}{n^2}=\frac{\pi^{2k}}{(2k+1)!}$$

$d_1(n)=1$

$$\sum_{n=1}^\infty\frac{1}{n^2}=\frac{\pi^2}{6}$$

This math class is terrible- she hasn't even told us how many significant figures to simplify to sigh

I spot the Basel Problem!

$$d_2(n)=\sum_{d\mid n}_{d<\sqrt{n}}1$$

^ Likes that kind of math better! :D

@JacobMayle do you have latex working?

Negatory

aww

I don't know how to add those links to a bookmark

$$d_2(n)=\frac{d(n)-1_{n^2}}{2}$$

Just drag it to book marks

The star thing in the top right

along the URL bar?

yes I think

Also, if anyone ever needs help with stats- I'm very good at that, but terrible at elementary math apparently snickers

I took stats years ago in high school, and probably will be of no use

and by probably, I mean probability = 1

I have to use it for research for soci and psyc... other than that LOL not so much

Although I do use some of the computations to count cards ;)

Probability and combination mostly

Do you mean enumerative combinatorics

@JacobMayle

no

I haven't taken any combinatorics

yet

Are you an undergrad?

Who Jacob?

@Ethan

If you remove the constraint there distinct its just higher dirichlet convolutions of $1$

$$\sum_{n=1}^\infty\frac{d_k(n)}{n^s}=\zeta(s)^k$$

Though the particularity nice form it takes at integers when its distinct I thought was worth noting lol

Lol I was wondering why you even posted that... I was like so what does he want to know ahahaha!

@jacob It is just eulers argument for the basel problem extended to the higher coefficients appearing in the maclaurin series for the sine function

Hmm

@Ethan are you an undergrad?

@JacobMayle lol no I am in high school

Wow, what year?

LOL what! @Ethan you're only in high school?

I am on summer break right now will be a senior next year

Ok

I hope you're going to be a math major in University!

I'm thinking that he will

What schools are you looking at?

Not sure lol

I just finished up my first year at Colgate

Apply to the ivies if your other grades are good

Colgate?

Agreed

Its a LAC in upstate NY

@JacobMayle what kind of math have you studied?

calculus, complex analysis, linear algebra

@JacobMayle do you know any number theory?

yes

read an analytic proof of the pnt?

no

I've read some popular books on the subect

apostol?

So I have a bit of background, but not yet

for number theory?

yes

We didn't have a textbook

nvm, if you had you would have done the latter lol

Our textbook was a three page list of theorems

@JacobMayle Do you self study?

A bit, but not as much as I should

Why are you studying mathematics? Have you written anything identities etc other crap?

Im going over spivak calc this summer

I enjoy math

I've done a bit of CS and physics, but I love math the most

Do you know any propositional logic?

I'm signed up for geometry, diffyQ, and real analysis next semester

I know how to make a truth table, but thats about it

and of course demorgans laws

What math have you studied?

@JacobMayle some analysis (very little nothing really formal) some number theory, and I am studying model theory/logic now

very cool

have you gone through spivak or apostol calculus?

nope

what did you do for calc/analysis?

I used khan academy/ read wikipedia/wolfram alpha/mathworld etc articles and some other course wear I found online

OCW?

and did you use apostols text for number theory?

Often teachers leave up assignments or course wear for there students to do long after the course is over

@JacobMayle A little bit not really I read about half a book on number theory by silverman but never finished it

it was a very bad book lol

really?

I have a copy of Dudley and a copy of Hardy's text

Dudley's is fantastic at a very introductory level

I dont have any exerpeince with that at all

Nope

mm

Have you ever written any identities or anything

@JacobMayle here is a nice telescoping sum

Im not quite sure what you mean

Here 1 sec

I haven't done any analytic number theory

ok

@JacobMayle just like random algebraic identities or series relations, special values of functions etc

No, I haven't studied any of that

Have you tried any putnam problems?

No, I don't like competition math I think its pretty boreing

Solving problems that have already been solved

ok

@JacobMayle I mean like after you learn a subject don't you experiment with the knowledge you have just learned

Of course

Try to write up identities or stuff you find interesting

Yes, I was just wondering if you had and experience with them.

With what?

The putnam

No, lol I don't really like math competitions, time you could spend studying or exploring with the tools you already have

ok

I mean have you written anything?

I've written notes while going through texts, and the solutions to the problems

but nothing original

@MarianoSuárez-Alvarez How would I read $\models$ syntactically

dunnoez

yields, or models

But If I said $\models F$, like as in $F$ is a tautology, models $F$ wouldn't make sense would it?

I would read that "F is a tautology"

my two suggestions work when you have both sides, obviously

And If $A$ was an assignment how would you read $A\models F$

yields

You wouldn't say $A$ models $F$?

I would use 'models" in a context when on the left hand side you have a model, again obviously :-)

k thx

Hi everybody. :-)

hi

How do you do @Ethan?

@BabakS. Hello. :-)

@JayeshBadwaik: Hiiiiii

@JayeshBadwaik: Not at the FB these days?

@BabakS. Hi. Not much. Only in evenings mostly, that half an hour or so.

How do you do?

@JayeshBadwaik: May I ask you to give me a hand? :-)

Great! thanks

@BabakS. Hmm, relating too?

@JayeshBadwaik: I want to propose a sentence in English but not sure how to assemble them. It is easy.

@BabakS. Ohh, I can help...

Thanks @JayeshBadwaik.

Hello

@JacobMayle hi

Assume you have a finite set of things which is partitioned into A U B U C of its subsets. And every of A,B, or C has a presentation. Exactly when you work with $2$ in even integers, or $3$ when you work with $3\mathbb Z$. Ok? @JayeshBadwaik

@BabakS. Hmm, let me ask. You have a set with finite number of elements. And now you create a partition consisting of three subsets, say A,B,C. And every subset of A,B,C has a presentation. Is this what you wanted to say? (Also, since you say partitions, A,B,C are disjoint I suppose?)

what is a "presentation" of a subset?

Now, I want to employ $x$ to be one of these subsets' presentations. How can I say in English this process? Can I say "We choose the general presentation of each partitions as x"? Of course the partitions are disjoint. Yes you found my aim correctly. :-) @JayeshBadwaik

presumably you mean representative of a coset of a coset partition

@anon: Maybe. My bad, sorry.

for example, the partition {{orange, apple}, {dog, cat}, {one}} doesn't have representatives, nor is it a coset partition, nor does the set it partitions have any algebraic structure. this is very much specific to group theory.

or perhaps the cells in the partition are viewed as equivalence classes, and you're looking at representatives of these classes ...

I think @Babak is referring to equivalence classes of $\mathbb{Z}/n\mathbb{Z}$ and their representative?

@anon: Let $S={b}∪\{a^i}∪\{a^j b\}$ in which $i,j$ varies finitely. I want to employ the variable $x$ to be one of those representatives. How can I say this in English?

$S=\{b\}\cup\{a^i\}\cup\{a^j b\}$

what if $b=a^i$ or $a^i=a^jb$ or $a^jb=b$? it wouldn't be a partition then. what are $a,b$ exactly?

@anon: Yes. and $a$ and $b$ are just like fixed elements like the generators.

Should we assume there is a group, $b$ is an element of order two, $a$ is an element of infinite order, and $a$ and $b$ commute? Did you say this somewhere above?

@amWhy sigh.

@anon: I am working on a semigroup

unless you provide more information I'm just going to have to say that "$S=\{b\}\cup\{a^i\}\cup\{a^j b\}$" is the best description

@anon I found something that we can do

fancy steganography ?

sounds cool

Well, you will have to help me with the Math

@anon: I wanna let the variable, say $x$, be $b$, $a^ib$ or $a^jb$. Is it enough saying: "Let the variable $x$ be one of the representatives of one of the partitions". I s it good to say in English?

I don't feel I truly know what you want, so I'm going to go with "sure."

@anon: Thanks for your consideration.

@JayeshBadwaik: Thanks

@anon Wanna know the best part ?

sure

You can get all the pixels as an array of integers

in one function cal

loadPixels()

and viola.. You are ready to go !

I was just reading up on it so that we can do steganography :-)

@anon You should really start learning Processing. You are quite good at Math. You can do stuff way better than us programmers without Math knowledge

you could plan ahead and stage a real-world demonstration. take a collection of "standard files" (very well-known and easy to obtain ones - for instance, popular meme templates, infamous photos, popular youtube videos even), make multiple variants of each file with inserted hidden data, then upload them over the internet

I like your idea of using memes

put innocent-looking hashes or even odd plaintext modifications to the filenames and titles as a tacit "file system" to keep all of the files organized without having to keep any record of them down anywhere.

I will start with Grumpy Cat

All we have to do is bit-wise operation

And some boolean algebra

@anon I also thought over your idea of the infinite image-ception you told me

We can easily make a Kaleidoscope

for fun, make it layered encryption

like truecrypt

Encryption is different from steganography :)

@anon Since we will only hide text in image

there has to be a good Math function as to where to hide it

in what pixel exactly

@anon Here is another one-- making a graph of the red , green and blue channels of each pixel in the image :-)

Found out how to blur an image :)

@anon You there ?

@anon I finished my last exam today that was measure theory

Woohoo ! Successfully performed stegnography !

Now I can hide ASCII text without it being seen

@robjohn Have a minute?

I want to see a deleted answer to my question, could you help me please?