Mathematics - 2014-09-30 (page 3 of 3)

Chris's sis

5:10 PM

@robjohn nice

user2179021

hi

can anyone work out the answer for n =3 ? math.stackexchange.com/questions/952446/…

The Game

@user2179021 Welcome back !

@user2179021 What was your guess for n=3,k=5 ?

rehband

@robjohn Robjohn, could you please explain to me what's happening in the first step of you answer to Chris's "a cute limit"?

Huy

@BalarkaSen: You said you didn't read.

@rehband: Zwei Räuber werden auf dem Heimweg von Polizisten überrascht und gefangen genommen. Nachdem man die beiden voneinander trennt, werden sie in verschiedene Befragungszimmer gebracht. Dort erklärt man ihnen: „Wir wissen, dass ihr gestern zusammen einen Überfall begangen habt, aber wir brauchen ein Geständnis. Gesteht ihr beide, so müsst ihr für je vier Jahre ins Gefängnis. Wenn du gestehst und dein Partner die Tat leugnet, musst du nur für ein Jahr ins Gefängnis, dein Partner aber für sechs. Wenn ihr die Tat beide abstreitet, so müsst ihr für je zwei Jahre ins Gefängnis. Deinem Partn…

@rehband: Does that sound appealing?

rehband

5:26 PM

@Huy Haha yes. I've heard of that problem before. What is GU?

Huy

@rehband: Short for Gruppenunterricht.

rehband

@Huy Ok, so this is the topic you've settled on?

Huy

@rehband: Yes, I looked at a few examples and they seemed to be very accessible and solvable using some linear algebra, so they have problems they can grasp easily plus learn a bit of matrix multiplication etc.

rehband

@Huy Sounds great!

Huy

@rehband: And there are also a lot more complicated examples for more gifted or dedicated pupils, so I don't have to be scared of them being bored.

rehband

5:28 PM

@Huy Good choice

Huy

@rehband: What have you been up to these days?

Balarka Sen

@Huy I lied. I actually read a lot.

I also lie a lot.

Huy

@BalarkaSen: Why do you lie a lot?

rehband

@Huy Finished all my exams, so I've had a chance to take it a bit easier...just preparing some stuff for next semester and learning fun limit/series/integral stuff

Balarka Sen

Don't know, never read human psychology.

rehband

5:31 PM

How about u?

@BalarkaSen For example about your age? :P

Balarka Sen

Yes, that.

Huy

@rehband: I see. Did you get your results back already?

rehband

@Huy No, it'll take 2-3 weeks..I'm fairly sure I'll get a good grade though :P

user2179021

@TheGame I have changed it to 14

rehband

Have you listened to a lecture called "Numerik" ?

The Game

5:35 PM

@user2179021 That's for k=4

@user2179021 1,2,4,8,14,?

Huy

@rehband: Yes, over here it's usually called Numerische Mathematik 1 / 2.

rehband

@Huy What topics are treated in that lecture?

Huy

@rehband: In the first semester, one would typically start with some computer arithmetic, then talk about direct solving of systems of simultaneous linear equations, then start a new chapter about polynomial interpolation and apply it by means of numerical integration. Then, you would learn about how to solve non-linear equations using fixed-point iteration (e.g. Newton's method) and also a bit about the least square method (normal equations, Householder QR).

@rehband: Eventually, something about splitting methods, Jacobi- and Gauss-Seidel methods, relaxation methods like JOR and SOR and after that depending on the time left maybe some eigenvalue problems and trigonometric interpolation.

@rehband: And in the second semester, typically it's all about ordinary differential equations, at least over here.

rehband

@Huy Ok, I see..Now I know what to expect

Huy

@rehband: I really disliked it because it is rather "dry" to me, but my friend is all about Numerik.

rehband

5:44 PM

@Huy It doesn't sound too great to me either, but I won't knock it until I try it :P

Huy

@rehband: If you want to have a look at what we did, I still have the lecture notes for Numerische Mathematik 1. The part about polynomial interpolation and numerical integration is actually really cool, blew my mind when I actually read it. :D

rehband

@Huy That would be really great, I could prepare a little bit

Huy

@rehband: You can start right at that chapter and don't need anything from the chapters before, in case you're worried.

rehband

Kk

Huy

@rehband: dropbox.com/s/hhygcfjt5lancm0/nm1_merged.pdf?dl=0

@rehband: Chapter 3 and 4 are the ones I liked. The rest, not so much. Some of them a little, but not really. :D

rehband

5:48 PM

@Huy Thank you!

user2179021

@TheGame I don't know!

The Game

@user2179021 Why 14 and not 12 btw ?

user2179021

@TheGame I think you can get it by choosing a hyperplane which cuts more of the regions

Sawarnik

Hello @Huy @TheGame @rehband

The Game

@user2179021 Do you keep the first three planes as in k=3 ?

@Sawarnik Hello

rehband

6:00 PM

@Sawarnik Hi Sawarnik

Hi @Sawarnik

Wow, hi @all

:-)

@Huy I picked up Bartle and Sherbert as I told you, its tough but I am enjoying it :)

@Huy Not at all, he reads a lot. And yes, lies a lot.

@rehband Probably not.

user2179021

@TheGame yes

Will Hunting

6:05 PM

@Sawarnik It is a very expensive book with little content...

Ice Boy

Quality over quantity?

Sawarnik

@WillHunting Haha, that's the only book on that thing which I can get at a little cost, thanks to Wiley India :D

Will Hunting

@Sawarnik OK. But there are tons of books that are cheap in India. Why get that?

@IceBoy It is not exceptional in quality either.

Sawarnik

@WillHunting Its was the cheapest book on it on Flipkart that is recommended, and I don't mind going to the market to search for other books. The quality is not bad anyway, its good enough for me.

Will Hunting

@Sawarnik Interestingly, I used to have a copy of Bartle and Sherbert too. =) It was one of my first math books, lol.

The Game

6:15 PM

@user2179021 and where is the 4th ?

@Chris'ssis ?

@Chris'ssis -__- prevent me before posting soon to be deleted messages

i'm not on the screen all the time :)

Chris's sis

@TheGame OK ;)

Huy

@Sawarnik: Hello to you too.

Sawarnik

@Huy So late :D

Huy

@Sawarnik: Preparing tomorrow's classes.

Sawarnik

@Huy Oh, which topic?

Huy

6:29 PM

@Sawarnik: We're starting to discuss functions.

Sawarnik

@Huy Alright :)

Chris's sis

@TheGame Is it true that Eiffel Tower got married?

3

Ice Boy

@Huy how long will it take to get to two variables?

Huy

@IceBoy: Too long.

Chris's sis

Erika Eiffel

Erika "Aya" Eiffel (née Erika LaBrie), is an American woman who famously "married" the Eiffel Tower in a commitment ceremony in 2007. She is founder of OS Internationale, an organization for those who develop significant relationships with inanimate objects (objectophile). She has been featured as a spokesperson and advocate in a wide variety of publications, and on radio talk shows and television programs. She is a former US military member and archery world champion. She continues to compete at an international level as an archer. She claims that her object relationship with Lance, her competition...

Sawarnik

6:35 PM

Ah!

Chris's sis

It would be interesting to hear one day someone gets married a series or an integral. :-)))

The Game

@Chris'ssis Totally non official :c

robjohn

@rehband Sorry... $$\log(2)=\sum_{k=1}^\infty(-1)^{k-1}\frac1k$$

Chris's sis

@TheGame OK (since you live in France, I was about to ask you if you attended that ceremony) :-)

rehband

@robjohn Got it, thanks :)

The Game

6:39 PM

@Chris'ssis Of course not >:c

I don't have time for that nonsense :D

Too busy with homework

Ice Boy

@Huy some teachers begin with equations with the variable on one side before progressing to equations with the variable on both sides...

...and then move to equations in two variables.

Chris's sis

@TheGame :That thing is important for one reason, it emhasizes that there is no free will in our world, we are just programmed to think in a certain way, and sometimes when that "soft" fails, some things begin to happen as in the case mentioned above.

The Game

@Chris'ssis There is free will

But not as much as one might want

Chris's sis

@TheGame No, there is no such a thing. This is the worst illusion we live.

Anyway.

The Game

@Chris'ssis Arguing about this would be useless anyway :) we'd never agree

Chris's sis

6:45 PM

@TheGame Yeah, I agree with you at this point. ;)

The Game

:)))))

Nope

Sawarnik

Yope

The Game

she smiles as :-))))))))

I smile as :))))))))

I think

Sawarnik

Hmm.

Your point is valid.

Ice Boy

@Huy They also don't introduce the idea of a function until they have covered equations in two variables. But this is all pedagogy as you know :)

Sawarnik

6:50 PM

I found functions interesting when I studied it :)

Ice Boy

Do you recall the first definition they gave of it?

Sawarnik

@IceBoy Maybe.

Ice Boy

students should never want to answer "maybe" to a basic question...this, in my opinion, is a sign of bad teaching

Sawarnik

No.
I have to go anyway, bye.

Ice Boy

later pal

Huy

7:49 PM

@IceBoy: Over here, we introduce the idea of a function in the beginning already, but not enough, imo.

Ice Boy

pedagogy is a very controversial topic

Huy

@IceBoy: Yes, there is not a "best" way, just opinions.

Ice Boy

and we are all different :)

Huy

Of course, that too.

Ice Boy

that's why I suggested to let the kids decide

Huy

7:53 PM

@IceBoy: I would, if I could make a representative poll.

Ice Boy

there must be an overwhelming majority for it to work

say >80% want to study geometry...

Huy

@IceBoy: Yeah, and my class only consists of about 10% of all pupils who have to choose one of the optional courses.

Alizter

8:18 PM

Browsing MSE feels like you are being really productive when in reality you really aren't.

Ice Boy

yep, you can't stay in shape by watching other people exercise

The Game

8:45 PM

'question eligible for bounty in 52 minutes' aww

How many points are usually needed for a good bounty ?

Balarka Sen

@Alizter

Aliztaaaaar.

@Alizter! @Alizter! Dark lord arises! Pronto!

The Game

@BalarkaSen How do you show that $rank(f\circ g)\leq\min\{rank(f),rank(g)\}$ ? I'm pretty sure it's trivial but my mind is messed up tonight

$f,g\in\mathcal{L}(E),E$ a vector space

Balarka Sen

I dunno, forgot all my LA. I'm too busy with some NTs ATM in any case.

The Game

-__-

Now I just have to hope that Ted comes here tonight

Balarka Sen

@Alizter where the heck do you go when I need your help?

The Game

8:53 PM

@BalarkaSen Why don't you ask already ?

Balarka Sen

@TheGame the sentence doesn't make sense.

i have my reasons.

The Game

uh

Balarka Sen

@TheGame Perhaps you can help me with an unrelated silly question : $[a, b]$ be an interval in $\Bbb R$. Given a rational $m/n$ in this interval, can we canonically build up another rational $p/q$ in the same interval with $q < n$?

The Game

canonically ? as in ?

Balarka Sen

Erm, it's kind of vaguely formulated. How about explicitly determining $p$ and $q$ in terms of $m$ and $n$?

The Game

9:02 PM

I'm strongly believe that the answer is yes

Balarka Sen

Heh, oh, I should've asked for a construction rather than a yes or no =P

The Game

:)

I'm thinking about it

Balarka Sen

It's nontrivial, I believe.

Well, not much of a problem (as it can't be rigorously formulated) but a topic.

The Game

We can assume that $b-a<1$

Balarka Sen

yes, sure

otherwise an integer does the trick

$n/1$. $1$ is the smallest one can have.

The Game

9:05 PM

ye

stop reading my mind :P

Balarka Sen

who the hell married the Eiffel Tower, @TheGame?

The Game

Erika Eiffel

Erika "Aya" Eiffel (née Erika LaBrie), is an American woman who famously "married" the Eiffel Tower in a commitment ceremony in 2007. She is founder of OS Internationale, an organization for those who develop significant relationships with inanimate objects (objectophile). She has been featured as a spokesperson and advocate in a wide variety of publications, and on radio talk shows and television programs. She is a former US military member and archery world champion. She continues to compete at an international level as an archer. She claims that her object relationship with Lance, her competition...

Balarka Sen

Puleeeez.

The Game

Moniiiii

Balarka Sen

@TheGame Just in case, are you familiar with continued fractions for $\log$?

The Game

9:11 PM

Nope

question eligible for bounty in 24 minutes

Balarka Sen

what question?

The Game

5

Q: Problem on matrices : $\dim E\leq n^2-(n-r)^2-1$

I have the following problem : Let $E$ be a subspace of $M_n(\mathbb{R})$ that contains no invertible matrix. Let $r=\max\{rank(M)\mid M\in E\}$ Show that $\dim E\leq n^2-(n-r)^2-1$ I don't know how to do this. We have obviously $\dim E=n^2$, and I guess that he $(n-r)^2$ is due to the ran...

Balarka Sen

eh

Alizter

@BalarkaSen

Balarka Sen

@Alizter Meet me at the NT room.

Alizter

9:16 PM

To the ntmobile

Balarka Sen

9:34 PM

i use windowsnt

The Game

NoTopology

If I am putting a bounty to have an answer to a question, should I pick 'Canonical answer required' or 'Draw attention' ?

200 rep bounty put math.stackexchange.com/questions/950166/…

robjohn

10:31 PM

@TheGame: I feel so stupid. I misunderstood your question. My answer can be generalized, but then it would look like Robert Israel's answer, looking at sums of $PAQ$ for some $A\ne0$ where $f(A)=0$. I deleted mine and upvoted his.

nerdy

11:58 PM

Let (X,d) be a metric space and A a subset of X. Does anyone have a characterization of discrete sets A ( which only have isolated points ) ? I'm coming up with A is discrete iff ( A is finite) or (A is infinite and unbounded and ... )

the problem is the "...", don't know how to effectively express it.

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$Mathematics$ Mathematics