Mathematics - 2012-05-07 (page 1 of 9)

@BenjaminLim Well, I've forgotten all the math I've studied. But if I ever apply to grad school I will start studying again. I have gotten my book list ready.

Benjamin Lim

@JasperLoy where did you do undergrad?

user19161

12:08 AM

@BenjaminLim locally

Benjamin Lim

NUS?

user19161

@BenjaminLim Yes. Some of the profs there know some of my secrets...

Benjamin Lim

like what

user19161

@BenjaminLim Well, they are secrets for now like I said.

Benjamin Lim

ok

N3buchadnezzar

12:09 AM

ok

user19161

Don't worry, I am not working on the millenium problems, so that's not the secret!

Benjamin Lim

@JasperLoy have ya been down under

user19161

@BenjaminLim Yes, I told you I have a serious problem remember?

Benjamin Lim

what is it???

user19161

@BenjaminLim Not now, maybe I'll tell you in a couple of years.

Peter Tamaroff

12:12 AM

@JasperLoy I got 16,100 being english my second language.

user19161

@PeterTamaroff Wow, that's about the same as me. The people on ELU have like twice or thrice our vocab!

Peter Tamaroff

What's ELU?

user19161

@PeterTamaroff English SE.

Peter Tamaroff

Oh, why not ESE? (Sounds contradicting, right?)

user19161

@PeterTamaroff ELU=English Language and Usage. QED.

Benjamin Lim

12:14 AM

ok

Peter Tamaroff

@JasperLoy Alright. No need to get so formal.,

user19161

Hey @ben so you are Chinese too right?

user19161

@PeterTamaroff No, formal proof is writing the proof in logical symbols only, haha!

user19161

In that sense, almost all proofs are informal!

user19161

In practice, nobody writes proofs like that, we just need to know that it can be done.

ymar

12:16 AM

Has anyone seen this comment by Asaf? What a nice gesture.

user19161

@ymar Wow, Asaf is like a superhero!

ymar

:)

OK, just wanted to show you this. Exam tomorrow, gotta go. :)

user19161

I only recently learnt that our autogenerated avatar was based on our email address. I thought it was completely random.

N3buchadnezzar

Peter Tamaroff

@JasperLoy INteresting! How does it work?

@N3buchadnezzar HAHAHAH WHAT?!

user19161

12:19 AM

@PeterTamaroff I am not sure. Some algorithm or something. Someone on StackOverflow made one showing unicorns instead. You may see at unicornify.appspot.com.

N3buchadnezzar

@PeterTamaroff Just eading a blog about some of wolframs earlier blunders.

Like typing Guinea Pigs, would get you the pig population on Guinea and so forth.

Like this one

Peter Tamaroff

LOL

afk

user19161

So I will cast my votes in about 20 hours...

Antonio Vargas

@JasperLoy This is amazing.

user19161

@AntonioVargas Yeah, at first I was wondering why so many people use unicorn avatars.

user19161

12:27 AM

OK actually it's not that many unicorns we have on SE.

robjohn

@JasperLoy Yes, it is based on the md5 digest of the email address

user19161

@robjohn md5 is beyong my pay grade, even though I use Debian!

Antonio Vargas

My unicorn is pink too. My email address is cursed.

user19161

@AntonioVargas Pink is sweet.

robjohn

@AntonioVargas generate your own gravatar

user19161

12:28 AM

I have been thinking for a long time whether to use pgf or pstricks for graphics. Right now I am with pstricks.

Antonio Vargas

N3buchadnezzar

@JasperLoy <3<3<3 tkz euclide

user19161

@N3buchadnezzar pst-eucl

user19161

Also, there is no equivalent of what pst-solides3d can do. It's the most amazing LaTeX graphics package to me!

N3buchadnezzar

12:55 AM

@JasperLoy huh?

Jordan

man e is a weird number, if I am using l'hospitals rule what do I do with e^x? when x is infinity?

Brian M. Scott

What's the whole expression whose limit you're taking?

Jordan

$$\lim_{x^{-\inf}} (x^2 - x^3)e^{2x}$$

Peter Tamaroff

Write it as $$\lim_{x \to {-\infty}} \frac{x^2 - x^3}{e^{-2x}}$$

Brian M. Scott

Let's make that $$\lim_{x\to-\infty}(x^2-x^3)e^{2x}=\lim_{x\to-\infty}\frac{x^2-x^3}{e^{-2x}}$$

Peter Tamaroff

12:58 AM

Use Lhopitals for $\infty / \infty$.

$$\lim_{x \to {-\infty}} \frac{x^2 - x^3}{e^{-2x}}=\lim_{x \to {-\infty}} \frac{2x - 3x^2}{-2e^{-2x}}$$

Brian M. Scott

Now this is an $\frac{\infty}{\infty}$ form.

Peter Tamaroff

We still have $\infty / \infty$

$$\lim_{x \to {-\infty}} \frac{2x - 3x^2}{-2e^{-2x}}=\lim_{x \to {-\infty}} \frac{2 - 6x}{4e^{-2x}}$$

Jordan

I rewrote as infinity minus infinity

Peter Tamaroff

It is the same.
$$\lim_{x \to {-\infty}} \frac{2 - 6x}{4e^{-2x}}=\lim_{x \to {-\infty}} \frac{-6}{-8e^{-2x}}$$

Now we can see the limit is $0$.

Jordan

how?

Peter Tamaroff

1:01 AM

Think.

Jordan

e^-inf is -inf

Is it okay to let one side go to infinity?

robjohn

I'm off to the park with Lilly. be back in a bit.

Peter Tamaroff

@Jordan BUt you have $e^{-(-\infty)}$

Antonio Vargas

@Jordan a visual aid

Jordan

I get it

how do I know what is considered an indeterminate form?

Peter Tamaroff

1:09 AM

Reading the theory.

Brian M. Scott

@Jordan Pragmatically speaking, I'd just about bet that your text has a list of them.

The two basic ones are $\frac00$ and $\frac{\infty}{\infty}$.

Peter Tamaroff

Here, here you have two more examples.

Jordan

what about 6/0? that is just undefined right?

Brian M. Scott

Then you have $0\cdot\infty$, $1^\infty$, $\infty^0$, and $\infty-\infty$.

@Jordan Right.

The first three of these can be reduced to one of the two basic forms by standard techniques. The $\infty-\infty$ form is the nasty one.

Jordan

0/0 isnt just undefined?

Brian M. Scott

1:14 AM

@Jordan The fraction $0/0$ is undefined, but it's possible for $f(x)/g(x)$ to have a limit as $x$ approaches a point where they're both $0$.

Jordan

so then why is that not true for any undefined number like 6x/0?

Brian M. Scott

Because if $f(x)\to 6$ and $g(x)\to 0$, it's guaranteed that $f(x)/g(x)$ does not approach a finite limit.

Jordan

I understand now

N3buchadnezzar

1:29 AM

There is something terrible wrong with people creating 3d images of shells in latex.

Mariano Suárez-Alvarez

@BillDubuque BTW, I would personally appreciate it very much if you made precise statements: «some mods have acted far too impulsively»... Which mods? They have done what exactly? When? Communication online is prone to problems, as we all know, and vagueness does not help in the least.

Peter Tamaroff

@MarianoSuárezAlvarez Hey Mariano!

Can we speak in Spanish for a while?

Mariano Suárez-Alvarez

let me deal with flags and other fun stuff, and I'll be back :D

Peter Tamaroff

@MarianoSuárezAlvarez =)

Brian M. Scott

@Mariano: If I delete the comment, I'll replace it with something along these lines: Bluntly, I consider that indefensible. It ill serves the people asking the questions (and their teachers, for that matter). Is that preferable?

Mariano Suárez-Alvarez

1:39 AM

I wish people simply ignored Wolfgang Mueckenheim and his many puppets... He's already contributed enormously to turning several other fora into wasteland, and he only feeds on attention :(

2

There is not much that can be done to stop him from creating new user accounts, but at least regular users should pick up his main lines, recognize them and ignore him :(

@BrianMScott, much better :) It's getting flagged as it is: making it clear that it is your position will at least make that clear :D

Peter Tamaroff

@MarianoSuárezAlvarez How can I identify him.?

Brian M. Scott

@MarianoSuárezAlvarez I thought it pretty obvious that it was just my position!

Mariano Suárez-Alvarez

he rants about Cantor, actual infinity, the diagonal argument, etc

@BrianMScott, being explicit online is always a plus

Peter Tamaroff

@BrianMScott DId he post here at SE?

Mariano Suárez-Alvarez

Brian is talking about something else

Brian M. Scott

1:43 AM

@MarianoSuárezAlvarez True, true. I'm afraid that his comment really rubbed me the wrong way $-$ much more than the actual answer did.

Peter Tamaroff

@MarianoSuárezAlvarez And what are you talking about? We were talkig about him in the chat, but I presume he wasn't here in SE:

Mariano Suárez-Alvarez

you people need to learn how to produce a real — :D saying $-$ is Just Wrong™ :)

Brian M. Scott

@PeterTamaroff We were talking about a comment that I made to an answer, one that some apparently found a little too strongly-worded for comfort.

Peter Tamaroff

@BrianMScott Mind if I see the comment in context?

Brian M. Scott

You can't: it's been replaced by a less abrupt version.

Mariano Suárez-Alvarez

1:46 AM

Flags which tell mods that some answer is wrong or not really an answer always leave me wondering...

At most, what we mods could do is leave a message saying the answer is wrong

but the flagger apparently already noticed this... so the comment could well be left by him/her

Peter Tamaroff

Well, if it really isn't an answer, it should be deleted right?

Mariano Suárez-Alvarez

it is not an answer in formal temrs —for example, if it is someone askign a question, or commenting on someone else's answer (not uncommon) then yes

and in those cases we turn them into comments or, inextreme cases, delete them

Peter Tamaroff

That's my point.

Mariano Suárez-Alvarez

but if the answer is wrong, then it is not our job to fix it or delete it

the set of candidates for mods would need to be significantly cut down if we had the requirement that mods should be able to judge correctness!

as would the number of current mods, in fact

Peter Tamaroff

@MarianoSuárezAlvarez That's so true. Definitely. Down votes should be used there.

Brian M. Scott

1:50 AM

Comments pointing out the error(s) are more useful.

Peter Tamaroff

@MarianoSuárezAlvarez Did you see Carrió @LaCornisa today?

Mariano Suárez-Alvarez

@BrianMScott, indeed

@PeterTamaroff, nop

Similarly, often users vote to close and then flag the question with an explanation of their vote

Peter Tamaroff

I usually do that.

Mariano Suárez-Alvarez

This is common with duplicates

Peter Tamaroff

I haven't seen bad answers recently which is good.

Mariano Suárez-Alvarez

1:54 AM

but we are not experts in all subjects, so we are rarely the best to judge if two different questions are really the same

Peter Tamaroff

@MarianoSuárezAlvarez Should I be checkig my mail? :P

Brian M. Scott

@MarianoSuárezAlvarez You'd have loved my first dean: he maintained that since he was a physicist, he was capable of judging the quality of publications by members of the math department! (In some ways he was a very good dean, but not that one.)

Peter Tamaroff

@BrianMScott Maybe in Soviet RUssia he was a physicist.

Mariano Suárez-Alvarez

@PeterTamaroff, sadly no: I spent most of my weekend babysitting my nephew so I have done exactly none of the items in my to do list :/

I am going to bed late tonight!

Brian M. Scott

He really was a member of the physics department, and I'm sure that his math background was reasonably good, but there were about two dozen people in the math department, and I don't think that any one of them would have claimed to be able to judge the work of all of their colleagues in the department.

How old is your nephew?

Peter Tamaroff

2:01 AM

@BrianMScott I confused dean with janitor, XD

Brian M. Scott

Ah, now it makes sense. :-)

Mariano Suárez-Alvarez

3 years, @BrianMScott

Brian M. Scott

So you've been busy.

Mariano Suárez-Alvarez

yeah!

Brian M. Scott

Is he a pretty good-natured kid?

Mariano Suárez-Alvarez

2:02 AM

I think that my sister makes him drink coffee before leaving him with me :)

yeah, but he is 3 years old :)

Peter Tamaroff

@MarianoSuárezAlvarez LOL, I think sugar would suffice.

Brian M. Scott

Yes, but active and difficult would be a lot worse.

Peter Tamaroff

@MarianoSuárezAlvarez If he was older you could entertain him with math stuff.

Mariano Suárez-Alvarez

haha

well, we spent a lot of time with numbers and letters :)

but he's not gotten to summing yet

Brian M. Scott

@MarianoSuárezAlvarez My youngest brother wasn't much older than that $-$ four, I think $-$ when he was told that he could have two strawberries from the neighbors' garden and interpreted that as $2+2+2+\ldots$.

Peter Tamaroff

2:09 AM

@MarianoSuárezAlvarez I'm still confused about Mueckenheim. Where does he participate with fake ids?

Brian M. Scott

He's done so both here and on MO.

Peter Tamaroff

@BrianMScott And where was he taught how to sum?

@BrianMScott But now we can be sure he's out irhgt?

Brian M. Scott

@PeterTamaroff He didn't have to know what the sum was; he just kept on adding. :-)

Peter Tamaroff

@BrianMScott Oh, I see. Funny.

Brian M. Scott

@PeterTamaroff Not really: he can always register under yet another pseudonym.

It now occurs to me that some of the loons on de.sci.mathematik may be sock puppets of his, too.

Peter Tamaroff

2:12 AM

Well, if we see anthing contradicting cantor we can flag it =)

@MarianoSuárezAlvarez What is out policy on these type of questions? I like the pic personally.

@BrianMScott What is your opinion on the above?

mixedmath

I have no problem with the pic, personally. But nor do I have any attachment to it

Brian M. Scott

It's cute, but I don't really care either way. I'd be annoyed if people started doing such things frequently, though.

Dylan Moreland

2:27 AM

Right. I don't want this place to look like, shudder, reddit.

mixedmath

I agree

Peter Tamaroff

@mixedmath Democracy calls then. Let's delete it.

Dylan Moreland

Nah. Isolated incident. And it has a dog.

Peter Tamaroff

Or state that it shouldn't be repeated

Dylan Moreland

Special provisions apply to pictures of dogs.

Brian M. Scott

2:28 AM

@PeterTamaroff Don't borrow trouble.

@DylanMoreland I prefer cats, m'self. Or a platypus.

Peter Tamaroff

@BrianMScott You're right. But maybe I can write something asking for that not to be done again.

Brian M. Scott

@PeterTamaroff Wait for it actually to happen; otherwise you may simply give people ideas!

Peter Tamaroff

@BrianMScott In what sense, ideas?

Brian M. Scott

Telling people not to do something often pushes some contrary folks to do that thing, or something similar.

2

robjohn

Back from the park. I haven't seen any word about the town hall yet.

Peter Tamaroff

2:32 AM

@robjohn Context

??

Dylan Moreland

There's supposed to be a big chat featuring moderator candidates.

robjohn

@PeterTamaroff There is a town hall being scheduled to talk to those running for mod

Dylan Moreland

Here we go.

Bill Dubuque

@MarianoSuárezAlvarez I plan to post a (constructive!) meta thread on this. But it hasn't yet percolated to the top of my priority list. It does not involve you as I recall.

robjohn

@DylanMoreland But no word on when? Tomorrow was to be a possibility

mixedmath

2:34 AM

Yes - I was even hoping for tomorrow

apparently, that's not to be the case

Peter Tamaroff

@DylanMoreland OH, that! Town halll chat.

robjohn

@mixedmath who knows?

@PeterTamaroff Yes :-)

Dylan Moreland

@PeterTamaroff Yes, I noticed that you were mentioned in that thread, so it seemed curious that you wouldn't know about it :)

Peter Tamaroff

@DylanMoreland BRB. I can do Wednesday 8, 9 PM UTC-3.00. If you happen to do something tomorrow it will have to be for a short while. and on tuesday night, I have to study, so there's no possibility there.

Dylan Moreland

I'm certainly not running it. That would be a disaster.

Alex Youcis

2:50 AM

@DylanMoreland Working with Matthew Emerton, eh?

Dylan Moreland

The one and only.

Alex Youcis

How is that?

Dylan Moreland

Ask me in a few years. It's great, more or less. I spend a decent amount of time wondering what I've gotten myself into. But the stuff he's doing and how he's doing are is so incredibly cool. And he has more insight than anyone I've ever met, or at the very least he's freer with it.

Good at wasting his time on our meetings every week, I like my project, etc.

Alex Youcis

I am extremely jealous. I assume you're at Chicago with him? It says on your website that you're at Northwestern but I assume you made the move with him.

Dylan Moreland

Nah. I split time.

Alex Youcis

2:58 AM

Oh, so you're still in Evanston?

I guess that it's not that much of a commute!

What are you currently working on?

Dylan Moreland

It's about 1:20 each way. I do a lot of grading on the train.

Alex Youcis

Hey, let me ask you something. If I was going to come visit Northwestern, who would I talk to? Who's the grad chair?

(also, who would give me a good impression of the department).

Dylan Moreland

I only make the trip if he's teaching a course. He lives closer, so I go visit him there otherwise.

Paul Goerss. He's a good guy.

Alex Youcis

Cool, cool.

I know you have a bias, but how do you like it there?

Dylan Moreland

Hard to say. I split time so I'm not as involved in the department itself as I once was.

And they have a lot of hires to make.

Alex Youcis

3:04 AM

What do you mean?

Dylan Moreland

But it's a good place. I say that at something of a distance, so maybe it counts for something. We're treated well, in the sense that our teaching load is low, our offices are nice, we get enough money, your advisor can buy you out of teaching, etc.

Alex Youcis

I see you were at Michigan for undergraduate. Any opinion of there? NW and Michigan are definitely two big places I'm thinking about

Dylan Moreland

Department culture is pretty good. Always lots of stuff going on. Particularly if you're into anything involving mathematical physics or analysis. Friendly place, daily tea, etc. Decent selection of courses that I don't go to, unfortunately.

It isn't some unhappy competition, and people have been getting good jobs out of here recently, etc. And Michigan is great too. Depends on what you're looking for and what you're interested in.

Michigan is much larger.

Alex Youcis

I mean, algebraic number theory and algebraic geometry are the things that interest me most. Complex geometry is up there too.

Dylan Moreland

Michigan is really strong at algebraic geometry. Rob Lazarsfeld is a good person to talk to.

Alex Youcis

3:12 AM

Maybe I'll go to Chicago and work with Emerton too :)

Dylan Moreland

Perhaps you will. That's a different place.

Alex Youcis

Different in what regard?

Dylan Moreland

What little caution I can muster regarding Matt is that he only has one gear and that gear is very high.

Alex Youcis

Sounds like heaven.

Dylan Moreland

It depends. I think you have to give up on understanding everything he says and for me that was really hard.

Alex Youcis

3:16 AM

Ah, I see what you mean. Yes, I've had fleeting experiences like that, and they always suck. But, I guess that just means that you're with a guy who's the real deal--and eventually you'll be like that.

Dylan Moreland

But Chicago is one of those places that you just go to, unless you've got some other outrageous offer. They have a lot of rock stars.

Alex Youcis

Haha, of course. I am going to go out there this summer and talk to a few people--apparently Peter May's the guy to see.

Dylan Moreland

I guess there's the theory that it's better to be a top person at Michigan than the worst person at Harvard. I don't know. I haven't met many people who selected in that way.

I guess. I would talk to Benson Farb, if it were you.

[Nothing against Peter May.]

Alex Youcis

Hmm, I'll be sure to see him.

Is Kottowitz still there?

Dylan Moreland

He's emeritus. Still around at times, but I only know this because Ngo says they talk.

John Smith

3:23 AM

How many ways are there to create a subset of distinct integers from a set S to sum up to all possible sums 1 to max(S)?

Alex Youcis

lololol Ngo, huh? No big deal.

Brian M. Scott

@DylanMoreland Rock stars aren't always a good thing. I knew two very good grad students who left Berkeley for Madison because too much revolved around the rock stars at Berkeley at the time. They were much happier at Madison.

Alex Youcis

I assume you, him, and Drinfeld eat cookies and chat :)

Dylan Moreland

I just wanted to make it clear that I'd only heard he was around still. I don't see him.

Alex Youcis

No, no. I wasn't calling attention to it, that's just awesome that you talk to him.

John Smith

3:28 AM

does anyone know about subsets

Brian M. Scott

What about them?

John Smith

number of ways to break up a given number X into distinct, specific numbers

J. M.

@JohnSmith is this still about the PE problem you're doing?

Benjamin Lim

Hi all

Alex Youcis

YO

Benjamin Lim

3:30 AM

@AlexYoucis wassup man

J. M.

@JohnSmith You mean partitions I guess.

John Smith

yes, been working at it for a few more days straight. i'm going crazy

Alex Youcis

Nothing much dude.

Benjamin Lim

@AlexYoucis I am so tried.

so so tired

Alex Youcis

Then, go to bed.

Benjamin Lim

3:30 AM

you got facebook or somethin?

John Smith

i'm not getting anywhere

Brian M. Scott

@JohnSmith What's the specific question?

Benjamin Lim

@AlexYoucis Stayed up so late yesterday some stupid vector calc stuff

John Smith

i have a main set in the form of [1, 2, 3, 4, 6, 9, 13, 19, 28, 41] for instance and I am trying to find the number of subsets where the max element is less than the sum of the rest of the subset

Benjamin Lim

@AlexYoucis You like Regina Spektor right?

Alex Youcis

3:32 AM

Damn straight I do.

Benjamin Lim

I recommend you the Jezabels

John Smith

it's also the same as 2**n -1 - minus the number of sets adding up to 1 thru max(S)

Benjamin Lim

@AlexYoucis youtube.com/watch?v=IvCr1UAcPc4

Alex Youcis

What makes you think I am not already aware? :F

Benjamin Lim

@AlexYoucis You know about them???They're from sydney and are just up and coming

Brian M. Scott

3:33 AM

@JohnSmith I suspect that that's a fairly nasty problem; it looks awfully close to the knapsack problem.

J. M.

@AlexYoucis Never underestimate a dedicated fan...:)

Benjamin Lim

@JM You know about the jezabels too?????

John Smith

for example if i want to know the number of subsets that have an inner sum of 8: [(2, 6, 9), (2, 6, 13), (2, 6, 19), (2, 6, 28), (2, 6, 41), (1, 3, 4, 9), (1, 3, 4, 13), (1, 3, 4, 19), (1, 3, 4, 28), (1, 3, 4, 41)]

would be the count of valid sets

J. M.

@BenjaminLim Not a fan myself, but people I know talk about them... a lot.

Benjamin Lim

@AlexYoucis youtube.com/watch?v=WvUQ22Itxjw

@JM You know about the tv show Budoy?

John Smith

3:34 AM

yeah i know it's nasty/is reminiscent of the knapsack problem

not quite the same though

J. M.

@BenjaminLim Yes, the show was rather popular a few months ago...

Benjamin Lim

@JM Among several cebuanos here they call me Budoy

@JM I just realised if you say "kayu" in tagalog it means all of you, while "kayo" in bisaya means fire

J. M.

@BenjaminLim Hence you need care if you're talking across different dialects.

Benjamin Lim

exactly.

That's really confusing!!!

ok I need to go, bbl

John Smith

not asking for anyone to solve it for me but just to get me on the right track, anything that can offer any insight that I am glazing over

i'm spinning my wheels hard on this one and about ready to defenestrate myself

David K.

3:41 AM

@JohnSmith defenestrate. Never heard that one before.

Brian M. Scott

@JohnSmith Is this something to which the answer is definitely known, and you're supposed to find it, or is this a problem that you set yourself?

John Smith

answer is definitely known, supposed to find

Brian M. Scott

@DavidK Look up the Defenstration of Prague.

@JohnSmith But in these the maximum element is greater than the sum of the other elements.

John Smith

the negation case

I am not yet sure which way to take it

Brian M. Scott

Okay.

John Smith

3:44 AM

I can either find subsets where the inner sum is greater than the max

or 2^n-1-the sum of sets where the inner sum is <=the max

both yield the same answer

David K.

@BrianMScott Nice!

Brian M. Scott

@JohnSmith Do you have any idea what kinds of parameters are expected in the answer? Presumably it depends on more than the cardinality of the set and the size of the its maximum element.

John Smith

tinyurl.com/cmx7xdg is the full problem statement

J. M.

@John: don't I seem to recall that you said that there was something special about your integers?

David K.

Can someone here help me find the Galois group of $\Bbb{F}_{2^{3}}(x)$ over $\Bbb{F}_{2}(x^{3})$ ? I know it is cyclic and of order 9, but I'm not sure if it is $C_{3}\times C_{3}$ or $C_{9}$. Of course $C_{N}$ is the cyclic group with $N$ elements.

John Smith

3:48 AM

special?

Brian M. Scott

@JohnSmith Yes: the fact that they're generated by the recurrence $s_n=s_{n-1}+s_{n-3}$, with initial values $s_1=1,s_2=2,s_3=3$.

John Smith

yes

pastebin.com/raw.php?i=L8sgCgaK is my output for N=10 case (501 solutions), showing all ways of having subsets where the inner sum exceeds i

J. M.

Sums of numbers defined by recurrences sometimes satisfy recurrence relations of their own. Sadly I don't have my book for these things...

Brian M. Scott

The PE problems that I've seen are distinctly non-trivial; I'd not expect to be able to offer any useful suggestions without spending quite a bit of time thinking about the problem.

John Smith

Correct, JM, that's what I am trying to look for

I am expecting that there will be some sort of pattern to this but nothing I try seems to work, and I expect it's because I am missing something in terms of math knowledge

Dylan Moreland

3:54 AM

@DavidK There are two subfields of index $3$, right? $\mathbb F_2(x)$ is in there, and so is $\mathbb F_8(x^3)$.

David K.

@DylanMoreland Yes.

Dylan Moreland

So how could it be $C_9$?

David K.

I agree. And this is what I was thinking. But

John Smith

for instance if you look at the counts in what i just posted (2, 5, 12, 28, 61, 128, etc) I try to figure out if that follows a pattern but I can't find out one that does

things like that

J. M.

@JohnSmith You have a four-term recurrence (one of the terms has a zero coefficient), in any event; their behavior's not as easy to study as three term ones like Fibonacci, but there are results. Look up things like difference equations.

David K.

3:56 AM

I'm honestly quite lost here. I don't really know what the automorphisms even look like...

John Smith

yes I have tried difference equations

David K.

I've tried to write them out explicitly but I'm not having much luck with that.

J. M.

@JohnSmith I would presume you always check any sequence you get with the OEIS...

John Smith

yes

including sub-pieces of the sequence just in case, and many times i'll offset them by 1 or 2 or lag them by increasing integers just to see if there's another pattern hiding

J. M.

Okay. Sadly that's all I can help you with; sorry if I don't have anything concrete...

Dylan Moreland

3:59 AM

@DavidK You can use your knowledge of the quotients. See something like Prop. 3.20 in Milne.

John Smith

the fact that it is asking for f(10^18) means the main set is 10^18 numbers long, which is huge. it implies that there is a recurrence in some breakdown of the counts that will allow for easy modular matrix exponentiation, which is trivial to do.

the problem is the mathematical intuition behind the recurrence of the counts

nothing i try seems to hold

Dylan Moreland

@DavidK I'm slightly worried about some things I haven't checked for your particular problem. But this is a start, at least.

David K.

@DylanMoreland Worried about what things?

Bill Dubuque

@BrianMScott I didn't see your original comment (presumably here), but I think this is another example where standardized meta comments could help. Such a comment linking to a meta thread discussing the pros and cons of hints vs. complete solutions for homework would help readers to understand other's viewpoints and possibly lead to less tension on the main site. I hope to find some time to take the next step with the proposal.

Brian M. Scott

@BillDubuque Marvis's response to my first comment got under my skin, and I simply said 'Bluntly, that's unacceptable'. Not very diplomatic, though I did expect everyone to realize that I was talking about my own opinion, not site rules.

John Smith

4:08 AM

is anyone willing to help set me on the right path with this problem or am I still out cold? ;-;

Brian M. Scott

I'm willing; I'm just not able, at least not without spending a good deal more time thinking about it.

Bill Dubuque

@BrianMScott Ah, I see. That is definitely one of the most contentious issues on the site. It would be good to have meta threads (and comments) that we could occasionally bump to keep folks constantly informed on such matters. Such meta discussions may help serve to divert meta level discussions from the main site. I too have gotten comments saying please state that is your opinion when, of course, that should have been clear. I'm not sure what motivates remarks like that.

David K.

@DylanMoreland I'm not sure how that Prop will help me here....

Dylan Moreland

I wish it were understood that everything I say is merely my opinion.

2

David K.

Wait, so your word isn't actually verifiable fact?

Dylan Moreland

4:14 AM

Wasting words on little outs and caveats because someone is going to say, "Hey, man, that's not an absolute truth" is tiresome.

David K.

Is this directed at me?

Brian M. Scott

@DylanMoreland Safer, though.

Dylan Moreland

@DavidK Sorry, that had nothing to do with your Galois group.

David K.

Oh good.

John Smith

i suspect there's some recursive relationship here

David K.

4:16 AM

Does it have to do with what you're "worried about" ?

Dylan Moreland

@DavidK What you do know about the extension $\mathbf F_2(x)/\mathbf F_2(x^3)$?

David K.

Umm, nothing. $\Bbb{F}_{3??}$ ??

Bill Dubuque

@DylanMoreland My impression is that some folks say such things because they hope to subtly attack the statement by leaving the impression that it may be an isolated or minority opinion, disingenuous as that might be.

Dylan Moreland

@DavidK Sorry, I've been up for a while.

David K.

@DylanMoreland Ah. Well, I believe that it is the splitting field of $f(y)=y^{3}-x^{3}$ over $\Bbb{F}_{2}(x^{3})[y]$. Man I hate that notation.

Dylan Moreland

4:22 AM

@BrianMScott True. It reminds me of preparing students for an exam I didn't write.

Brian M. Scott

@DylanMoreland :-)

Dylan Moreland

@DavidK This is the part that confuses me. It seems like if you want to split that polynomial, then you need cube roots of $1$. And those are in $\mathbb F_4$.

David K.

@DylanMoreland Yes, this was a concern for me as well. So perhaps not the splitting field. So the cube roots of 1 are not in fact in there.

Peter Tamaroff

@BillDubuque Can I show you something?

@BrianMScott @BrianMScott Are you there?

@DylanMoreland You there?

Dylan Moreland

Knee-deep in commutative diagrams, but here.

J. M.

4:56 AM

I only noticed this just now: the rep gaps between most users in the first page are wider than I remembered them. (Not even counting how Arturo outshines us all.)

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$Mathematics$ Mathematics