Mathematics - 2015-12-21 (page 2 of 6)

Axoren

06:00

@TedShifrin Right, that works better. I'll need "all sequences", "finite sequences", and "infinite sequences" for my purposes, so it's good to have one for all three. $A^\mathbb N$ for infinite, $\bigcup_n^\mathbb N A^n$ for finite, and I'd like a shorthand notation one for the union of both.

$A^\mathbb N \cup \bigcup_n^\mathbb N A^n$ looks silly and it's fairly wide for use in expressions.

Also, I just realized, it uses the symbols $\{A, n, \mathbb N, \cup\}$ exactly twice each.

It's a lovely, silly, wide, and even expression.

Michael

@Axoren How good are you at statistics, sir?

Axoren

@Michael Fairly comfortable with it, but I'm about to go to sleep in a few moments. Is it a quick question?

Michael

Suppose I have a pearsons correlations coefficient of r=0.99 for a set of data , can I use deltay/delta x instead of least squares method for modelling a function?

Axoren

That's a bit above my expertise, I'm sorry to say.

I wish you luck with that, and I'm off for the night.

Michael

thanks for trying

Portali5t

06:09

@Michael what is your plan for mathematics next year, will you be taking calc 3/4?

Michael

Since I am in grade 11, I plan to focus on bio/chem

I will learn them independently in the summer

Portali5t

oh have you not taken bio or chem yet

Michael

I am a fairly good self learner, so I don't forsee any problems.

Yah, I focused mainly on math history and french

Portali5t

interesting

so was there not a mandated science course this year

for us we have to take a science class every year

Michael

Well, next semester

so do we

I finish my math this semester

but I have 3 more bio courses and 2 more chem. Ib is hardcore

Portali5t

06:12

I was in IB a long time ago, it was intense

Michael

oh really?

IB or pre-ib

Portali5t

I believe IB mathematics

it was analogous to an algebra 2 class

Michael

oh

that class was free marks

Portali5t

as it was 5 years ago I don't recall exactly what the course was called

Kinson Chan

I'm doing IB right now

Michael

06:14

^the struggle is real. :/

Portali5t

wow another high schooler :)

we are everywhere

Kinson Chan

There doesnt seem much to do right now :/

maybe im not working hard enough...

what subjects do you guys take?

Michael

I have to do HL history

HL math

sl french

and HL english

fml

Kinson Chan

WOW

Portali5t

AP chem

AP bio

AP lit

Kinson Chan

06:16

whats AP?

Portali5t

AP calc BC

advanced placement

Kinson Chan

so is that higher?

Portali5t

analogous to IB

yes

Kinson Chan

no wonder u guys say its intense

Portali5t

it allows students to get college credit for classes

Kinson Chan

06:16

HL Econ

HL Business

HL Bio

Standard eng litlang, math, chinese

Portali5t

so if I pass calc bc AP exam I can take calc 3 at uni in 12th grade

Michael

well your courses are pretty easy

except chinese

Kinson Chan

im chinese myself

Michael

IB is wider than AP, ap goes into more detail

Kinson Chan

so thats not a problem lol

Michael

06:18

it is

Like I know too much stats

So my calc isnt as speciic as it should be

Kinson Chan

how old are you?

Portali5t

interesting

so how is the calc too general

is it non canonical

@KinsonChan I am 16

Michael

We skipped too many limiits

we dont know l'hopitals rule

Portali5t

that would be a problem

Michael

we only know proof by induction

Portali5t

06:20

limits are crucia;

not delta epsilon

Kinson Chan

@Portali5t I feel dumb being at the same age..

Michael

we know limits, but we don't know enough

Portali5t

@KinsonChan why is that

Kinson Chan

I have no idea what you guys are talking about

Michael

We don't know multi variable calculus (excluding partial differentiation)

Portali5t

06:21

well that's calc 3 anyway

Michael

We skipped 3 of the 5 integrating techniques

ok I gtg

cya

Portali5t

@KinsonChan don't feel dumb, just feel like you haven't taken calc yet

cya

Kinson Chan

I dont have to take calc if its not in my courses right?

I mean i do standard math

Portali5t

there are many smarter people than me who are 16 and have not taken a calc class

Kinson Chan

would that be covered in that too?

Portali5t

06:22

and I don't know, not familiar with IB

Kinson Chan

ok

Chantry Cargill

@KinsonChan Any math you haven't been exposed to will look alien. Just keep learning and exploring at your level.

Kinson Chan

^^ yea

Portali5t

also it is a lot simpler than it looks to the uninitiated

you'll realize that the integrand means something fairly simple

and leibniz notation (d/dx) etc. is also very straightforward

Kinson Chan

i hope i do understand it if i ever come up to it

Portali5t

06:24

you will, you care enough about math to be on math.se

Kinson Chan

btw is there no business section in stackexchange?

no im just asking questions from my textbook that i dont understand

lol

currently learning trigonometry

Portali5t

that's a good place to get a solid understanding in preparation for calc

Swapnil Das

Which grade you are? @KinsonChan

Kinson Chan

12

Portali5t

I wish I payed more attention in trig, stuff would be easier now if I had

Kinson Chan

06:26

calc is all about trig?

Swapnil Das

Not really

Portali5t

not all about it but there is a fair bit of it

Chantry Cargill

No, but it's certainly involved.

Portali5t

trig functions are important

Swapnil Das

Even beyond Calc, in many elements of Higher Math

Portali5t

06:27

parametric equations depend upon trig

Swapnil Das

Which grade u r @Portali5t?

Portali5t

11th

Swapnil Das

Oh, I'm the youngest here

Portali5t

what grade are you

Swapnil Das

9th

Kinson Chan

06:28

WTF

Swapnil Das

lol

Portali5t

lol

Kinson Chan

everyone here are like einsteins

Portali5t

definitely not

Swapnil Das

except me

Portali5t

06:29

I like math

I am not inherently good at it

Kinson Chan

back when i was in grade 9 i was still playing minecraft and learning algebra

Portali5t

I was playing minecraft in grade 9

Swapnil Das

I haven't played it at all

Chantry Cargill

I can't remember grade 9 too well.

Swapnil Das

:P

Portali5t

06:30

different people enjoy math at different ages or never

I didn't like math until I took pre calc

Swapnil Das

Oh

BTW Kinson U even need Calculus in Studying Complex numbers :P

Lol Trig*

Can anyone answer this question?

Why is zeta(2) = Pi^2/6?

Or can anyone link its derivation?

BTW zeta(s) here refers to the riemann zeta function

Chantry Cargill

@SwapnilDas There are many proofs on this site.

Swapnil Das

Oh, really?

I must check it out

Chantry Cargill

352

Q: Different methods to compute $\sum\limits_{k=1}^\infty \frac{1}{k^2}$

As I have heard people did not trust Euler when he first discovered the formula (solution of the Basel problem) $$\zeta(2)=\sum_{k=1}^\infty \frac{1}{k^2}=\frac{\pi^2}{6}.$$ However, Euler was Euler and he gave other proofs. I believe many of you know some nice proofs of this, can you please sh...

Swapnil Das

Thanks :)

Chantry Cargill

06:38

De rien :).

Swapnil Das

That meant, Welcome?

Kinson Chan

@SwapnilDas translate.google.com/#auto/en/De%20rien

Swapnil Das

Yay, Correct!

Kinson which country do u hail from?

My guess : China? ( As per Jackie Chan)

:P

Kinson Chan

yea

Hong Kong

Swapnil Das

Cool! I love it

Kinson Chan

06:41

crowded city here

Swapnil Das

Second crowded here :P

Guess from where I'm?

Kinson Chan

new york?

Swapnil Das

Nope :p

Kinson Chan

give me a country

Swapnil Das

ANother hint

Chantry Cargill

06:42

India

user174558

I am getting fed up over downvotes. People downvote for no good reason, lol.

Swapnil Das

:P

Ya !

user174558

Hi @ChantryCargill, lol. J here.

Kinson Chan

india right?

Swapnil Das

Ya

My second hint was from the land of Ramanujan'

Chantry Cargill

06:43

@JohnNash I recognized the avy.

@JohnNash How's it going?

user174558

@ChantryCargill So so. My impression of SE is changing over time. I no longer take this site as seriously as I used to 4 years ago.

Swapnil Das

4 years ago!

Chantry Cargill

The point system kind of undermines it a little bit.

Saw someone answer a 2 year old question today with the same answer that was already posted.

Swapnil Das

I recently got to this site after getting fed up from others

user174558

Also, sometimes there is a lot of conflict in this chat room.

Swapnil Das

06:45

For what, conflict?

user174558

I am only here because I am taking a long break from real life.

Chantry Cargill

I always seem to miss the conflict, but I get a good laugh at the starred messages when I return.

2

user174558

@SwapnilDas Arguments between users.

Swapnil Das

Oh, that's bad

Chantry Cargill

Unavoidable in online communities though. You just can't let it affect you.

Kinson Chan

06:47

math arguments are just general trashtalking/hate

?

or*

user174558

Even though you don't meet users in person, by chatting over many months or years, you know them quite a bit.

Swapnil Das

True that

Chantry Cargill

Mostly the latter @KinsonChan .

user174558

@KinsonChan I answered your trig question that day. Your algebra is very weak, you should work on that first before trig.

Swapnil Das

Math arguments are rare, math is so certain :P

Kinson Chan

06:48

yea :/

user174558

@SwapnilDas We don't just talk math here, if you realise.

Swapnil Das

Yah, I c

@KinsonChan DO u use your school textbooks?

Kinson Chan

@swa

yea

oops

Swapnil Das

:P Oh

I don't, they get me bored :(. Use SL Loney, If available

user174558

I no longer cast downvotes because they are useless.

user174558

06:50

Better to leave a specific comment to a wrong answer.

user174558

Sometimes, it is the downvoter who is wrong.

user174558

I think downvotes are useless for the site and harm the friendly atmosphere

Swapnil Das

Just Curious: How does one become a moderator here?

user174558

Moderator elections take place whenever there is a shortage.

Swapnil Das

Oh, I c

I've started liking this site, It has lot of good probs

Chantry Cargill

06:52

While I agree, it would be strange to see wrong answers upvoted.

Swapnil Das

Oh, really?

user174558

Better than correct answers downvoted though, lol.

Swapnil Das

At least it is not like Brilliant.org

user174558

I am not a fan of studying math online.

Swapnil Das

I am :P

user174558

06:54

I think one should study books on his own, and consult peers and professors in real life.

Swapnil Das

It is not possible in India

There's shortage of all of the things u mentioned in yr comment

user174558

Certainly there are books, peers and professors in India.

Swapnil Das

But not available to a given age group

user174558

India is a large country with great mathematicians.

Swapnil Das

is should be was

Chantry Cargill

06:55

True. When I was starting real analysis awhile back, I wanted to start posting all my proofs on stackexchange, but I thought it would be overkill. It's much easier to consult someone irl.

Swapnil Das

In reality?

If I do

Then my teachers would discourage me

user174558

China too, many articles written in Chinese now.

Swapnil Das

@JohnNash Which country do u hail from?

Chantry Cargill

You have irresponsible teachers then.

user174558

You know something? I am just thinking to myself how some arrogant people look humble and some humble people look arrogant on the surface...

Swapnil Das

06:57

Haha

user174558

@SwapnilDas I prefer to keep it a secret. =)

Swapnil Das

NP

(no problem)

user174558

P vs NP

Swapnil Das

Lol

Millenium Prize prob

Chantry Cargill

@JohnNash Example?

user174558

06:58

@ChantryCargill Such things should not be mentioned. =)

Chantry Cargill

Oh, I think I might know some of what you're talking about lol.

Swapnil Das

India is the worst place for math study

user174558

@ChantryCargill Hehehe.

Swapnil Das

Here we are asked to cram up math :(

user174558

There are some very brilliant people on this site. I do not understand why they are wasting time here.

Swapnil Das

07:01

Like?

(Brilliant people)

Chantry Cargill

In the sense of participating in the chat? or answering questions?

user174558

@SwapnilDas Better not to mention also. =)

Swapnil Das

lol

user174558

@ChantryCargill Answering questions.

Kinson Chan

isnt that a good thing?

helping others out

user174558

07:02

Note that brilliant not = high rep

Swapnil Das

Of course

Reputation has nothing to do with brillianc

user174558

Are you both in high school @KinsonChan and @SwapnilDas?

Chantry Cargill

@JohnNash I imagine they simply enjoy doing math, even if it is elementary.

Kinson Chan

yes

Swapnil Das

Me in grade 9 ,

Tup

Yup*

Kinson Chan

07:04

im in 12

user174558

What exams do you guys take before university? I took the A level exams.

Kinson Chan

im taking IB

user174558

Hi @AlexClark I missed you, J here.

Swapnil Das

JEE for engg'

I won't take that

user147690

@JohnNash I'd recognise that blue square anywhere :P.

user147690

07:05

@JohnNash Still planning for starting 1st jan?

user174558

@AlexClark John Nash is my inspiration.

user174558

@AlexClark Yes, next Friday.

user147690

@JohnNash Awesome, what is the current textbook list looking like?

Swapnil Das

@JohnNash Why can't everyone enjoy math?

user174558

@AlexClark I have 12 books on the list, which is not complete yet.

Swapnil Das

07:06

Also @ChantryCargill

user174558

@SwapnilDas Different people like different things.

Swapnil Das

Oh, I thought Math becomes unenjoyable after a level

user174558

@AlexClark How is your exams?

Swapnil Das

Alex, are you an aspiring Mathematician?

user147690

@JohnNash Exams were last month, they were fine. I had family related issues distracting me after that, so I've been away from maths for pretty much a month.

Chantry Cargill

07:08

I'm curious, what's starting January 1st?

user174558

@ChantryCargill My self study.

Chantry Cargill

Oh, good to hear. I'm starting in February.

user174558

@AlexClark Too bad. You can talk to me over email if you want.

Chantry Cargill

@SwapnilDas Did you ask me a question?

Swapnil Das

Yup,

user147690

07:09

@JohnNash Nah it's alright, thanks though, they seem to be resolved.

user174558

@AlexClark My head keeps jerking when I sleep at night.

user147690

@JohnNash That's not good, do you know the cause?

user174558

@AlexClark Nope. I will ask another doctor again.

Chantry Cargill

Why can't everyone enjoy math? I'd say anyone can. However, you could say that about anything, whether it be poker or hulahooping. You either enjoy something or you don't.

Swapnil Das

Ohk

user174558

07:12

Some like apples, some like bananas, as simple as that.

user147690

@JohnNash I probably won't come by here as frequently, I think it is a big distraction normally.

Swapnil Das

Understood, Thanks

user174558

@AlexClark Yeah, I won't come here when I start studying either.

user147690

@JohnNash I'll be going to the non-main rooms I guess. I want to get into that DG reading group & maybe some of the other subrooms.

user174558

@AlexClark I see. I only need the bathroom, lol.

user147690

07:14

@JohnNash Haha :P.

Chantry Cargill

Get a bedpan.

user174558

Frying pan better, for frying eggs.

Chantry Cargill

Your diet is very important.

user174558

Xmas is this Fri, time flies.

Chantry Cargill

It was 42 degrees a few days ago. It doesn't feel like Christmas here.

user174558

07:20

I am not sure if mankind will survive my lifetime, there might be another war or some natural disaster.

Kinson Chan

@JohnNash so true

but lets hope for the best

Agawa001

07:46

@JohnNash ?

Swapnil Das

@KinsonChan You still doing trig?

Kinson Chan

@SwapnilDas yea doing exercises rn

working on double angle formula

Swapnil Das

Oh, great

If U get time after the exercises, be sure to revise at this site : Brilliant.org

It has DAMN HELL hard problems

Kinson Chan

@SwapnilDas looks like a very nice site

Swapnil Das

Yup. Just for the beginners of Higher Math

Haha, Thanks and Welcome by following :P

Kinson Chan

08:00

@SwapnilDas you managed to find me xD

Swapnil Das

I'm very regular to that site

search Trigonometry in the search tab

Kinson Chan

very useful

thanks for the site

Swapnil Das

You are welcome :)

Just speaking, sometimes get an hour or two free and try a Level 5 problem

@KinsonChan

Kinson Chan

alright, ill try

Swapnil Das

Sure, especially trig :P

Trig is damn hard on Brilliant. BTW U can read Trig on Brilliant Wikis

They are better than book and have challenging additional exercises

Kinson Chan

08:11

@SwapnilDas is it not possible to receive "solutions" without subscribing?

Swapnil Das

It is

Just click on Discuss Solution

Which problem are you talking about? Can you link?

Kinson Chan

brilliant.org/practice/degrees-radian/?p=4

Swapnil Das

BTW, you can't to all quizzes without upgrading to B^2

So try to do challenges instead

Kinson Chan

ok

Swapnil Das

They are a lil different from other questions

brilliant.org/problems/basic-trigonometry-2

Here's one I had posted

Kinson Chan

08:16

howd u do your question?

i've done these before

Kinson Chan

08:49

anyone here?

i need help

Kinson Chan

09:10

Why does 2cos^2(x)-1 = -cos2(x) but not cos2(x)

Karl Kronenfeld

09:20

Answering why something false holds is rather difficult.

I guess I could state a false premise of my own and go from there.

Kinson Chan

that is the double triangle formula

Karl Kronenfeld

I have a feeling it is not the double angle formula, since if you set x=0 the equation reduces to 1=-1.

L33ter

09:40

Hi @KarlKronenfeld

L33ter

10:01

would someone like to discuss algebra

maybe you @iwriteonbananas ?

iwriteonbananas

Sorry but I suck at algebra.

What's it about?

L33ter

Suppose M is finitely generated F[x] module for some field F

I want to show for all non-zero $m \in M$ $ann_{F[x]}(m) = g(x)F[x]$ for some g(x) $\in F[x]$

so, let us first type the definition

$ann_{F[x]}(m) = \{ s(x) \in F[x] : s(x)m = 0\}$

iwriteonbananas

Sorry I'm not acquainted with those definitions, you'll have to ask someone else I'm afraid.

L33ter

alright

everybody is asleep now I guess

:S

Swapnil Das

10:32

I'm not :)

Kinson Chan

10:48

anyone here?

L33ter

10:59

@TobiasKildetoft hi

Swapnil Das

Hi :)

L33ter

are you tobias?

Swapnil Das

I'm here @KinsonChan

Tobias??

L33ter

anyway hi @SwapnilDas

Swapnil Das

Urm.. Hi, Sup?

Huh, Anyone there?

L33ter

11:05

yes

nothing much just solving some stuff

evinda

Hello @DanielFischer !!!
I am looking at the following:
The nodes $A,B,C,D,E,F,G,H,I$ are given and are related as follows:
http://www.directupload.net/file/d/4209/fiinaajz_png.htm
The nodes $B,C,D,E,F,G,H,I$ are tasks that are done so that a work is completed , for example a building, and the cost $p(a,b)$ are the days that are needed so that the work $b$ finishes if the work $a$ has already finished.
For example, $p(A,B)=22$: 22 days are needed so that the work B is done.
$p(B,E)$: 16 days are needed so that the work E is done if the work B has finished.

Daniel Fischer

11:28

@evinda Sorry, not my department. What is it, linear programming?

evinda

@DanielFischer A ok... It is dynamic programming...

Karl Kronenfeld

@L33ter As you saw in your question, it is easy to construct a counterexample. What are you really trying to ask?

L33ter

hmmm

I thought that question was correct

Huy

12:16

@FrankScience I defined the exponential function via power series. Why?

@DanielFischer: I'm looking at this proof. Does this implicitly assume anything apart from $C$-linearity of differentiation?

Mary Star

12:29

Hello!!

We have $\sigma =(\sinh u \cosh v, \sinh u \sinh v, 0)$. Do we not get then $\|\sigma \|^2=\sinh^2 u (\cosh^2 v + \sinh^2 v)$ ?

According to my book the answer is $\|\sigma\|^2=\sinh^2 u \cosh^2 v$.

How do we get that?

Lembik

the entropy of multivariate gaussian is given at en.wikipedia.org/wiki/Multivariate_normal_distribution . Does anyone know where one can find the entropy of multivariate binomial?

I feel it should be similar

Daniel Fischer

12:48

@Huy No, except of course that one knows the derivatives of $\sin$ and $\cos$, that $\frac{d}{dt} e^{\alpha t} = \alpha e^{\alpha t}$, and that a differentiable function on an interval whose derivative is identically $0$ is constant.

Oh, and the product rule ;)

Transcript for

$Mathematics$ Mathematics