Mathematics - 2015-10-14

Physicist137

12:11 AM

is there life here?

I'm alive!

oh. That's good.

@Physicist137 Hi

hi

I have a question... :).

You know conic sections right? It has a definition |PF| = e|PD|. How to arrive in this definition from the other conventional ones?

morphic

I don't know conic sections :(

Physicist137

12:21 AM

aww...

Remember me

12:42 AM

Hello@Fargle

Fargle

Hello, @Remember.

Cbjork

So I was looking at this old "ask dr. math" thread. I don't believe his solution. mathforum.org/library/drmath/view/54667.html

is there a solution?

@Anyone? The reason I don't believe it is that when you rotate around B then two points overlap

Remember me

What kind of maths have you been doing @Fargle

Fargle

@Rememberme Mostly just stuff for class. So numerical analysis and probability.

Alias User

Hello @Fargle!

Fargle

12:57 AM

@AliasUser Hi!

Remember me

I know bits of numerical analysis but nothing about probability.

Alias User

I apologize @Fargle, but is there a chance you could answer a couple of questions I had about multivariate normal distributions? I think I may know what I'm doing, but I just want to be sure.

Fargle

@AliasUser I'm probably not equipped to handle such a question. >_>

Couldn't hurt to try, though.

Alias User

@Fargle - thanks anyway!

I'll give it a shot :)

Fargle

...yeah, that's over my head, haha.

Alias User

1:01 AM

No worries! I've had plenty of trouble myself.

I think I solved it by manipulating the expression for Pr(x) to put it in terms of y, then normalizing - it does seem a tad odd that a renormalization would have to take place, though...

Do you have any advice on getting answers to questions like that?

Ted Shifrin

2:29 AM

Hi @Fargle!

morphic

Hi @TedShifrin

Ted Shifrin

Hi, mr eyeglasses.

dREaM

3:20 AM

@anon I invented a new joke

"You make a good $\cdot$ "

@anon Do you get it?

anon

lame

dREaM

so you don't get it?

morphic

3:38 AM

lol

Sanic Hodgeheg

3:54 AM

Hi guys! I'm working on some homework and a multipart question (with each part providing set, S) asks:
"a) find the interior of S; b) the boundary; c) which sets are open; d) which sets are closed"

Do you think it is asking for all sets involved in the question: the set S, its interior, and its boundary? Or just the set S (which'd be a bit weird since it'd use the plural sets to refer to a single set, but it also seems like a reasonable question).

dREaM

@SanicHodgeheg For each problem you have to calculate the four things

Sanic Hodgeheg

@dREaM I know that! Parts (c) and (d) ask whether some sets are open or closed. I was wondering whether that refers to all previously found sets (the original set S, its interior, and its boundary), or just the set S. It seems like the former and I might as well do more practice, so I'll just do that.

morphic

It's better to do the most possible for practice anyway

Sanic Hodgeheg

@morphic seems like we're on the same page!

dREaM

the interior is always open

the boundary is always closed

if you are working in a connected space then open implies not closed and vice-versa

Sanic Hodgeheg

4:15 AM

@dREaM Hmm that does seem correct, thanks!

This isn't a topology class, we haven't talked about connected spaces or anything like that. I'm aware of the fact that a set can be open and closed or neither, and based on what you said it seems a connected space doesn't allow those two possibilities, I'll look into it.

dREaM

sure, no problemo

morphic

I like Sanic

Sanic Hodgeheg

@morphic thanks, gotta go fast.

morphic

I'm listening to Green Hill Zone 10 hours now

Sanic Hodgeheg

@morphic Just wondering since you're from the NYC area, which college do you go to?

morphic

4:29 AM

CUNY

Fargle

@TedShifrin Oops. Woefully belated "hi".

Sanic Hodgeheg

@morphic Cool, I don't go there but have lived around the area for a while. You may have walked by Sanic himself at some point.

morphic

@SanicHodgeheg Not likely as I rarely go outside

Sanic Hodgeheg

4:46 AM

@morphic O, I see.

Ted Shifrin

I still like ya, @Fargle, woeful or not. :)

@Sanic: Connected is equiv to saying that the only sets that are both open and closed are ... .

@dREaM: What you said is not quite right.

Anthony

5:04 AM

yo @TedShifrin

Actually I have a question for you, @TedShifrin. If I have an ideal $\mathfrak{a}\subseteq\mathfrak{o}$, where $\mathfrak{o}$ is a commutative ring, and there is another ideal $\mathfrak{p}\subseteq \mathfrak{a}$, and I know that $\mathfrak{a}^{-1}\mathfrak{p}\subset\mathfrak{p}$, do I know that $\mathfrak{a} = \mathfrak{o}$?

Ted Shifrin

yo @Anthony

Anthony

Where $\mathfrak{a}^{-1}$ exists, because we're actually in a Dedekind domain.

Ted Shifrin

What you said is always true. Do you mean that $\mathfrak a^{-1}\mathfrak p = \mathfrak p$?

Anthony

I don't think that's what I meant, but I'm also very confused.

Ted Shifrin

Oh wait. Maybe I'm not understanding.

$\mathfrak a^{-1}$ is in the field of fractions of $\mathfrak o$.

Anthony

5:14 AM

Indeed.

Ted Shifrin

So it's not even true if $\mathfrak a = \mathfrak o$, is it?

What's your simplest example of a Dedekind domain?

Anthony

I don't have one in my head.

Ted Shifrin

How 'bout $\Bbb Z$?

Anthony

Alright.

Ted Shifrin

So try examples to understand your statement.

Anthony

5:18 AM

It would appear I have no idea what I'm talking about.

Ted Shifrin

Can you give me an $\mathfrak a$ and a $\mathfrak p$ with $\mathfrak o = \Bbb Z$?

This isn't easy stuff. You have to play with examples.

Anthony

Yeah, apparently.

Give me a moment.

Ted Shifrin

In all of mathematics, playing with examples is always a smart thing to do.

Anthony

Take $\mathfrak{p}$ to be like, (10) or something, I guess? And then for it to be contained in $\mathfrak{a}$, we could take $\mathfrak{a}$ to be (5), I guess. I hope that won't make my life more difficult.

Ted Shifrin

OK.

Anthony

5:21 AM

Except this is kind of backwards, I need $\mathfrak{a}^{-1}\mathfrak{p}\subseteq\mathfrak{p}$.

But in any case, it would be educational for me to understand what the inverse of (5) is.

Ted Shifrin

No, you're supposed to start with $\mathfrak p\subset\mathfrak a$.

Anthony

Sure, alright.

I mean, yes, you are correct.

Ted Shifrin

Now think about $\mathfrak a^{-1}\mathfrak p$. (Good grief, having to type all these mathfraks sucks.)

Anthony

I know, I'm sorry, let's just write a and p.

So I'm not really sure what $a^{-1}$ is.

Ted Shifrin

So what's $a^{-1}$ sitting inside $\Bbb Q$?

Anthony

5:23 AM

let me look at the def

Ted Shifrin

Good man.

Anthony

So $a^{-1}$ is a $\mathbb{Z}$ submodule in $\mathbb{Q}$ that is sent back to $\mathbb{Z}$ by some integer., that is there is some $z\in\mathbb{Z}$ such that $za^{-1}\subseteq \mathbb{Z}$

I think.

Ted Shifrin

You better use $a$ in there somewhere.

Shouldn't you be multiplying by things in $a$?

Anthony

Should I be?

Ted Shifrin

Well, we're trying to define the inverse of the ideal $a$ :)

Anthony

5:27 AM

Oh, sorry, I was saying what was meant to be a fractional ideal.

Wait.

Oh, yeah, so $a^{-1}$ is the fractional ideal such that $aa^{-1} = o$

Ted Shifrin

OK, so in our case, what is this?

Anthony

I mean, I said $a$ was $(5)$.

Ted Shifrin

Uh huh.

So what's $(5)^{-1}$?

What sorts of rational numbers are in it?

Anthony

Something like fractions over $5$.

Ted Shifrin

Just over $5$?

Anthony

5:30 AM

Well so it has $\frac{1}{5}$ in it, for sure, that gives us the integers, right?

But then I also need to make sure it's a z module.

Is that right?

Ted Shifrin

Is $3/20$ in there?

Anthony

I'm assuming it is, but at the moment I'm not sure why.

Ted Shifrin

LOL

Anthony

I mean, being a z module it just needs to be closed under linear combinations, and if $\frac{1}{5}$ seems to satisfy the inverse requirements, I feel like it need only be multiples of $\frac{1}{5}$.

Ted Shifrin

I'm suggesting that any element of $a$ can appear as the denominator.

You can't just guess any $\Bbb Z$-module and decide it's right. :)

You have to use the definition you gave me.

Anthony

5:33 AM

I was trying to do that, I thought.

The definition of fractional ideal just tells me that it needs to be closed under the linear combinations right?

Ted Shifrin

You said the fractional ideal.

Anthony

Indeed.

Ted Shifrin

Oh, I guess you're right and I'm wrong. :)

Anthony

Nonononononono

I'm thiiinkniningingigng

Ted Shifrin

So I have to be able to multiply my element of $a^{-1}$ by any element of $a$ and land in $\Bbb Z$, and then close under addition.

No, no, I was being serious.

Anthony

5:36 AM

Oh. phew

Ted Shifrin

You're too defensive. I complained to you about that in person :D

Anthony

Sorry D:

Ted Shifrin

If I multiplied $1/10$ by $5$, I wouldn't land in $\Bbb Z$. So you're right that it's $\Bbb Z[1/5]$.

Anthony

Alright.

Sure.

Ted Shifrin

OK, keep playing with your example now. Put in $p$, etc.

Anthony

5:38 AM

Yeah, so I said $p$ was $(10)$, and I was considering $a^{-1}p$ which would in this case be something gross maybe?

No.

Ted Shifrin

No, stay calm.

Anthony

It's just all multiplies of 2, eh?

$2\mathbb{Z}$?

Ted Shifrin

OK. Looks right to me.

And is that back in $(10)$?

Anthony

No.

So now we cry.

Ted Shifrin

No, now you understand your original statement !

Anthony

5:40 AM

Yeah.

(Tears of joy)

:P

Ted Shifrin

I've never thought about this before.

OK, so now, presumably, armed with the intuition from this example, you can work out an argument.

Just make yourself go through this (with analysis and applied stuff, too) when you learn some new definition/concept.

Anthony

Yeah, I should have started doing this a while ago.

Thanks.

Ted Shifrin

Yup. You should listen to me more often :D

You're welcome :)

Anthony

I do listen to youuuuuu

However, though, as to the original statement, I had some dumber naive thing in mind, that I feel like must be wrong.

If we know that $a^{-1}p\subseteq p$, then don't we know that $a^{-1} \subseteq \mathfrak{o}$? Does this then imply that $\mathfrak{o} \subseteq a$? I was preceding by basically multiplying each side, which feels wrong with set inclusion.

Ted Shifrin

Look at your example, again.

Anthony

5:45 AM

Yeah.

Well actually, now I'm asking for a case where $a^{-1}p \subseteq p$.

So I need new sets, right?

Or rather, i'm saying for some $a^{-1}$.

Ted Shifrin

Well, try to argue your claim by contradiction. Suppose $a^{-1}$ were not in the ring to start with.

Then, separately, you need to understand why $a^{-1}\subset\mathfrak o \implies a = \mathfrak o$.

Anthony

In the case of the integers, if it wasn't in $\mathbb{Z}$, then it would have some fractions, and then it wouldn't land back in $p$.

Ted Shifrin

OK, so write that argument more formally.

You just work with the field of fractions of $\mathfrak o$, just like you work with rational numbers.

Anthony

Sure.

Ted Shifrin

You need to find some particular product that isn't in $p$.

I think you can do this now.

Anthony

5:50 AM

Yeah, alright.

Thanks Ted.

Ted Shifrin

And you taught me some stuff.

You're welcome, kiddo.

Anthony

Ribet's class is very pleasant.

Ted Shifrin

I'm sure it's hard, but he's a good teacher, I think.

Anthony

He seems to be.

Ted Shifrin

Is the department all frazzled about the latest controversy?

Anthony

5:52 AM

I don't know, I haven't really talked to any one in the department that much about it.

Ted Shifrin

I think from what I've read that, as a very dedicated teacher myself, I may have some reservations about Alex Coward.

But I'm never going to pretend the Berkeley math department really cares all that much about high quality teaching.

Anthony

What do you mean by reservations? As in you think he has a case?

(For some reason, I struggle with basic English)

Ted Shifrin

I think that what he and I consider superb teaching may be different.

Anthony

Ah.

I sat in on one of his classes, and wasn't impressed.

Ted Shifrin

I've browsed around on-line and found a number of students who were not impressed.

And if his class is really 100% final exam for grading, I don't like him at all.

But the department is couching it all in the wrong way, or at least what he's quoting makes it seem that way.

Anthony

5:55 AM

It's like, he's available, and amiable, but yeah there seems to be some issues of grading thrown under the bus, and also I feel like he isn't necessarily teaching math in the way it deserves to be taught.

I think both sides could learn something from this.

Ted Shifrin

I won every teaching award I could, but it was by being incredibly demanding and caring.

He clearly cares incredibly much. But is he really pushing students mathematically? And if there's no required homework, can they really be learning?

Anyhow, you have work to do. I'm sorry for derailing you.

Anthony

Oh no it's cool.

I'll keep you updated with any insider info I get. :P

Ted Shifrin

Keep me posted, btw, on the grad school stuff. ... I'm now writing letters of recommendation — I haven't escaped.

Anthony

Haha, alright. Nice talking with you, and thanks again.

Ted Shifrin

One for a grad student on his teaching, one for a high school kid for college, and two for sophomores going up for fellowships. Presumably more to follow soon.

You're welcome. Go write :)

hi @Ramanewb

Anthony

5:58 AM

Good luck with it all.

Ted Shifrin

Thanks.

Ramanewbie

6:15 AM

Hey @ted

Balarka Sen

9:17 AM

@anon ok. I dunno what an order statistics is.

@AndrewG Szamuely might be good.

But fair warning : learning Grothendieck's formality means that you have to know a lot of commutative algebra and algebraic topology and Galois theory.

Alessandro

12:11 PM

Hello everybody is there someone who can help me clarify some extremely basic doubts about $\lambda$-calculus?

anon

1:30 PM

@BalarkaSen statistics with an s at the end is plural

order statistics = knowing how many elts of order k there are for every k

http://groupprops.subwiki.org/wiki/Order_statistics_of_a_finite_group

@Anthony @TedShifrin If $\frak a^{-1}p\subseteq p$ then multiplying by $\frak p^{-1}$ yields $\frak a^{-1}\subseteq o$.

(in a dedekind domain)

Mambo

2:27 PM

Is there any good book to study Amenable groups ?

Balarka Sen

3:28 PM

@anon alright, that's what I thought

Ramanewbie

@hippa Is there an ensemble were you can have negative numbers root

Yes

@hippa Complex ?

yes. Among others.

@hippa Alright. But now is it true that complex allow you to solve equations IN $\mathbb{R}$ that there is no other way to solve them ?

Hippalectryon

3:39 PM

No. There are always alternative ways. It makes some solutions easier though.

Ramanewbie

@hippa So what's the point in such an ensemble

Hippalectryon

What's the 'point' of $\mathbb{R}^{42}$ ?

Ramanewbie

@hippa I don't even know what $\mathbb{R}^2$ means...

Hippalectryon

$R^2$ is just the set of pairs $(x,y)$ where $x,y\in\Bbb{R}$

Ramanewbie

@hippa Why R 'squared' then ?

Hippalectryon

3:44 PM

$R\times R$

Ramanewbie

@hippa I thought it would be sth like every number in R squared

Hippalectryon

No, that's $\Bbb{R}^+$

Ramanewbie

@hippa Whaaat ? I thought R+ was every positive number in R

Hippalectryon

That's the same

Ramanewbie

@hippa Indeed, ok

Khallil

5:18 PM

Must a partition $P$ of a closed bounded interval say $[a,b]$ contain the endpoints of $[a,b]$?

Hippalectryon

@Khallil yes

Huy

5:36 PM

@Khallil: uni started again?

Khallil

Thanks, @Hippa!

Yep, @Huy. In the second week. Pretty chilled out so far.

How's everything on your end, @Huy?

Huy

lots of work even though I don't have to work for high school right now (holidays), so I'll probably drown in work when school starts again

@Khallil: any new courses you're taking?

Ted Shifrin

hi @Huy @Khallil @Hippa

Huy

morning @Ted

Hippalectryon

@TedShifrin o/

Khallil

5:40 PM

Analysis, algebra, vector analysis (multivariable calc) and PDEs are this term, @Huy.

Hey, @Ted!

Huy

cool, you need to teach me about PDEs then! :)

I hardly know anything about them

Ted Shifrin

You can't take PDEs before you've finished vector analysis! You actually need to use stuff from that course in a decent PDE course.

Huy

@Hippalectryon: got a minute to help me out with some French stuff?

non-math related

Hippalectryon

Sure

Tobias Kildetoft

It is kinda fun to reread my old research statement now that I need to update/rewrite it. My main research has become a lot more focused now, even though it has also become more general than it started out (plus, I will need to remove all mention of finite solvable groups as I don't really think about that stuff any longer, but at least I can instead add some stuff about 2-representation theory)

Alec Teal

6:05 PM

A derivation is any map $\alpha:C^\infty(\mathbb{R}^n)\rightarrow\mathbb{R}$ that is linear and satisfies the product rule. So $\alpha(fg)=f(a)\alpha(g)+g(a)\alpha(f)$ - right? Good!

Tobias Kildetoft

@AlecTeal what is $a$?

Alec Teal

What is $fg$ though. How do I multiply $f$ and $g$ - I don't even know what their co-domain is

@TobiasKildetoft $a$ is a point in $\mathbb{R}^n$

If $\alpha$ satisfies the above we call it "a derivation at $a$"

Tobias Kildetoft

hmm, derivation at a point. Not sure I have seen that before. Usually one just looks at derivations

which requires that the codomain has the structure of a module over the domain

Alec Teal

I'm looking for the definition to be clarified.

Oh wait, $C^\infty(\mathbb{R}^n)$ is the set of all functions $:\mathbb{R}^n\rightarrow\mathbb{R}$ which are smooth

It's just piecewise

$(fg)(x)=f(x)g(x)$

Huy

@TobiasKildetoft: smooth functions form an algebra?

Alec Teal

6:10 PM

There is a ring involved.

Tobias Kildetoft

@Huy sure

Huy

so where's the problem with defining derivations at a point?

Tobias Kildetoft

@Huy I have just never seen the term used like that. To me (being an algebraist), being a derivation is a property of the map, not something the map can be at a point

Huy

it's unusual I guess. I've seen it in the context of defining tangent vectors in GR, only later proceeding with vector fields (which are then defined as linear maps from the algebra of smooth functions to itself with Leibniz)

Alec Teal

/me coughs something about derivatives to @TobiasKildetoft

They are derivations.

Chris's sis the artist

6:25 PM

hehe, I found an amazing answer to one of my older problems. :-)

Anthony

@anon Yeah that's what I thought. Thank you, honorable algebra guru.

Khallil

@Huy Will do! If you ever need any help, I'll try my best!

@TedShifrin Yep, I'm taking it in 3 weeks time so I'll have had 5 weeks of VA under my belt by then!

Huy

@Khallil: what are you doing in PDEs right now?

Khallil

Haven't started yet, @Huy.

Huy

ah, ok

Khallil

6:29 PM

It starts in 3 weeks and runs over into the next term :-}

Huy

would be interesting studying some of it simultaneously with functional analysis

Khallil

For sure! I think functional analysis is available to choose in my 3rd/4th year.

(www2.warwick.ac.uk/fac/sci/maths/undergrad/ughandbook/year3/…)

Huy

oh right, you're at warwick. you're not taking any classes from Martin Hairer by any chance?

Khallil

Nope, but his wife taught the linear algebra module to the non-maths students last year and he took one of the lectures as a surprise, @Huy. Wish I was there, haha! I've seen him walking around the department quite a few times.

Huy

:(

Alec Teal

7:03 PM

Another Warwick student.....

@PedroTamaroff

Danu

7:18 PM

Hi all

Huy

hi @Danu

Danu

@DanielFischer or any other mod: Why was my flag on the comments under this answer declined?

I was in here some time ago to ask whether flagging of obsolete exchanges in the comments, including extended back-and-forths between people that did not really have any lasting value for later readers, was appropriate. The answer seemd to be a wholehearted "yes".

There are many comments under this answer that are obsolete, not constructive, or both.

Take, for example, these ones:

"Incorrect", "not right", and "opposite of right" are the same thing, also known as "synonyma". — Luboš Motl Jan 11 '14 at 7:43

@LubošMotl Only in classical topoi, which are quickly becoming passé, even in physics. — Slade Jan 18 '14 at 21:30

OK, you conclude $\sum n \to \epsilon^{-2} - 1 / 12$ for $\epsilon \to 0$... that would be taken as $\infty$ anyway. — vonbrand Feb 10 '14 at 2:59

"As for democratic truth reputation is 100-0 in your favor, but in comment upvotes at the current moment you are losing 17-1, so your advice of relearning applies to you too." Just stumbled across this thread. I have to say, regardless of the details of what was said in hindsight, I've rarely heard of a more absurd notion than "democratic truth", especially when the context is that of mathematics. — user1667423 Aug 1 '14 at 23:47

@Luboš, +1 for connections with physics, -1 for the attitude. Your mathematical arguments remind me of the arguments my mathematics teacher used in proving that 2+2=5 as a joke. Also invoking physics argumentation like "Casimir effect" or "zero point energies in case no metals are bounding the region" to remove uncomfortable terms in expansions would help a lot of first year math students to pass their calculus exam. As for democratic truth reputation is 100-0 in your favor, but in comment upvotes at the current moment you are losing 17-1, so your advice of relearning applies to you too. — mpiktas May 18 '11 at 20:03

I think it would be better to say that both answers are correct. The people that say it converges have an argument, the people that say it diverges have no alternative. This is probably an even more controversial thing to say, but mathematics is inconsistent, we need to learn to deal with that. — Zach466920 Apr 13 at 23:16

I mean... really? Are all of these worthy of preservation?

(note that this is not nearly an exhaustive list of the comments that I think should be deleted; it was just a random selection that I put together in less than a minute)

Alec Teal

@Danu why do people care that comments are around?

I get it if someone is like "you should die" to the other, but in general. but this...?

Danu

@AlecTeal I don't expect you to share my pet peeve. ;-)

ArtOfCode

@Alec Some people are more protective of the comment space than others. Comments can be seen as clutter, or comments can be seen as trivial. SE themselves consider them disposable, though.

Danu

7:28 PM

I personally have a strong dislike of extended comment discussions, and I don't think my habit of going around and trying to get rid of unnecessary ones really disturbs or otherwise inconveniences anyone.

Alec Teal

Thank goodness you were there @Danu but if they were declined, you can still sleep easy knowing you did your duty.

Danu

@AlecTeal I don't see what you're trying to say.

Alec Teal

Here, let me link you to some comments on the matter...

OH WAIT

ArtOfCode

Sarcasm, methink.

Danu

I'm merely asking about an apparent contradiction between what I've heard from the mods and this action.

Alec Teal

7:31 PM

I like the first 3.

I've learned a lot from the comments, if someone is having a discussion like "Hey I see your logic but how do you know X" that's very useful.

Danu

I didn't say that all comments under that answer were devoid of content.

@AlecTeal If there is a valuable clarification/addition in the comments, it's in the wrong place. It should simply be incorporated into the posts (I would, in such a case, leave a comment to that effect).

Alec Teal

So your linked samples were simply samples of "comments" not comments you didn't like?

Danu

@AlecTeal They were comments that I consider worthless, from the perspective of improving the site. They should be deleted (IMO).

Alec Teal

So you want to replace a comment of someone helping another person with a comment noting to the answerer to add something in (and just hope they understand what) rather than someone following the comments along?

Could you not do that? Maybe wait until I get enough rep to see deleted comments.

ArtOfCode

@AlecTeal You can never see deleted comments.

Danu

7:35 PM

@AlecTeal Obviously not. I would monitor the post and delete my comment after the edit, or eventually implement the edit myself.

Alec Teal

@DanielFischer please don't cave.

Thanks for removing the insult there @Danu (although I'd consider the phrase "smart-Alec" as more of a tease)

Hmm... some of my comments have gone missing.

@BalarkaSen good news, you remember that guy who was promoting his own book, comments recommending the book seem to get deleted.

Danu

@AlecTeal Self-promotion (at least without full disclosure) should be flagged as spam :)

Balarka Sen

@AlecTeal that's nice

Alec Teal

@Danu see that's a site-difference thing. Here (IME) self "promotion" (if you can call "being a drain on my server's resources" a promotion) is okay in links it seems. If by "self" you mean "not mentioning who wrote (most) of it"

For example I got bored of typing out (and trying to search) for things later. Now I can just go "listen here n00b, maths.kisogo.com/… click expand" and behold.

ArtOfCode

@AlecTeal And that's the reason you've got a number of suspensions behind you... if you call (perfectly intelligent) people n00bs because they don't understand something, talk condescendingly, etc, then you'll find deleted comments and that people don't like you.

Alec Teal

7:47 PM

Thanks, kind stranger of the internet.

Stop following me.

ArtOfCode

8:12 PM

@AlecTeal I'm not.

Alec Teal

8:38 PM

Can I swear if it's quoting someone?

To quote the immortal Tovalds "Duck you Nvidia"

Daniel Fischer

Thou shalt not swear.

Stan Shunpike

9:13 PM

Hello

Hippalectryon

hi

Stan Shunpike

@Hippalectryon Question: I am given the sequence 32,-16,8,-4,2,-1,... and a system of equations a+b+c = 32, 4a+2b+c =-16, 9a+3b+c = 8, and was told to use matrices to find a quadratic equation that gave me the terms in this sequence.

I did this and got $36n^2-156n+152=t_n$, but it doesn't work except for the first few terms. Do you know what this method of finding explicit formulas for a sequence is called? I can't find more information on how to do this

Hippalectryon

@StanShunpike That's weird, I get the same result as yours. And indeed it doesn't match with the following terms.

Stan Shunpike

Yes, I am not sure how to go about resolving this. I googled quadratic sequence linear matrices and several variants but I found nothing on this

@Hippalectryon ^

Hippalectryon

9:29 PM

I don't know :(

Stan Shunpike

@Hippalectryon ah, well. Thanks for trying! :D

Ramanewbie

@hippa What's the formula to compute such an integral :
$\int_a^b f(x) = mx+p \ dx, \ a, b, m, p\in\mathbb{R}$
?