Mathematics - 2014-06-21 (page 4 of 5)

9:00 PM

Link to your books?

I don't much care that the definitions are wishy-washy. It's just poorly organized and poorly written, and far too focused on computation.

I bet one can teach a calculus course that's not computation-based without it being proof-based. Somewhere in the middle.

Ted Shifrin

I challenge you to teach that course, @Mike.

Sab ಠ_ಠ

My high school "calculus" had barely no proofs @Mike

Ted Shifrin

I don't think you have any idea of what you'd actually do.

Studentmath

My high-school math had barely no proofs, @Sab

Ted Shifrin

9:01 PM

@Sab: You can find my books on Amazon (overpriced, totally).

Sab ಠ_ಠ

A-levels they call it xD

skullpatrol

@MikeMiller was that the gamble bet?

Mike Miller

No.

Sab ಠ_ಠ

@Ted I'm sure I'll find them in the library :D

Mike Miller

@TedShifrin I have no idea what I'd actually do. I think it would combust.

I think a better person than me could do it.

Sab ಠ_ಠ

9:02 PM

If I don't I will tell them to order it and I'll borrow it xD That;s what I did with Apostol second edition. When I'm going to uni next semester they will have it by them and I'll borrow it since noone does xD

Mike Miller

Chern's book will be here next Friday.

Ted Shifrin

I've taught medium courses (where I don't expect students to write much in the way of proofs), @Mike. But there was still emphasis on computation/applications ... more interesting, challenging ones. I also like Simmons' Calculus (and diff eq) books.

AH, cool, @Mike.

Good planning, @Sab. I like your style.

Daniel Fischer

I totally don't get the concept of teaching maths without proofs.

skullpatrol

prove it

Sab ಠ_ಠ

I have had some nice books on my shelf for months

Naive Set Theory by Halmos

I loved that book

Chris's sis

9:04 PM

@robjohn are you around?

Sab ಠ_ಠ

Wanted to keep it lol

Ted Shifrin

For teachers who don't want to invest a lot of time with their students, it's the way to go, @DanielF. In Europe, students aren't as whiney (or at least they didn't used to be) and parents don't butt in the way they do in the US.

It takes hard work on the teacher's part to be demanding. Just reciting proofs in dull fashion doesn't get anyone much of anywhere.

Sab ಠ_ಠ

@Ted I;m not really sure why the first page of google is showing a site with your book on it for like Free to View

Ted Shifrin

LOL ... some people here mentioned that, @Sab. There are illegal copies all over the web, apparently.

I'm not sure if the Multivariable Mathematics book can be found that way. I know the Linear Algebra one can.

Sab ಠ_ಠ

Did you think of taking any action? Like a DMCA complaint?

Daniel Fischer

9:06 PM

True, @Ted, just reciting isn't anything good. That's why you let the students prove stuff in exercises.

Ted Shifrin

which one is it, @Sab?

Sab ಠ_ಠ

I just googled "Linear Algebra by Ted Shifrin"

doc88.com/p-318767553838.html

Ted Shifrin

But then you have to spend hours coaxing them in office hours, @DanielF, and most faculty don't want to do that. They get promoted/raises for publishing research, not raising students' levels.

Right, @Sab, I reported that one to the publisher, and they're supposed to be working on it. THat's not the book I was talking about. Look for Multivariable Mathematics.

Sab ಠ_ಠ

Books should not be typed on a computer. They should be done on a typing machine.

Ted Shifrin

Ugh, NO ...

Daniel Fischer

9:08 PM

And I thought teaching was an important part of a Professor's job.

Ted Shifrin

Silly you @DanielF ...

Daniel Fischer

I'm an old-fashioned guy.

Chris's sis

@TedShifrin What do you think about the theory that says that some students excel when they learn on their own?

Ted Shifrin

Most go through the motions, but unless we actually base promotions and raises on serious quality of teaching (not just being easy to get high evaluations from students), it won't happen at most universities. Small colleges, yes.

Some students, for sure, @Chris'ssis. But I think very, very few.

Sab ಠ_ಠ

This one is really famous @Ted :D

Ted Shifrin

9:09 PM

In the classes I teach, with the best students at our university, I might have one a year who would excel that way. No more.

Sab ಠ_ಠ

At least there is nothing like a pirate version on the first 3 pages on google(I don't go past page 1 normally lol)

Daniel Fischer

haa!! suppose $K$ is not closed, and $\alpha$ is a limit of $K$ while not being in $K$. Then $f:K \to \mathbb R$, $f(x)=\frac{1}{|x-\alpha |}$ is not bounded! so indeed, if every continuous real valued function is bounded, then $K$ is compact. — Oria Gruber 1 min ago

:D

skullpatrol

@TedShifrin 1/1000

Ted Shifrin

My denominator is small, @skull, but I'm talking about the top .5% of the students.

Sab ಠ_ಠ

@Chris'ssis I know someone who excelled like that.

Ted Shifrin

9:11 PM

Well, @DanielF, $K$ has to be closed. 50% done.

Chris's sis

@Sabಠ_ಠ I'm sure of it. :-)

Sab ಠ_ಠ

Guy never came to maths lectures he aced it with 100% on the first test.

He self-learned it all.

Chris's sis

@Sabಠ_ಠ like me :-)

Daniel Fischer

@TedShifrin That part was in the question, $K$ bounded but not closed was the missing part.

G.T.R

@r9m Vladimir posted your proof :/

Sab ಠ_ಠ

9:12 PM

@Chris'ssis like me in high school xD But uni is different. I took it lightly lol

Ted Shifrin

So @r9m lost his rep points by being stubborn and lazy :D

r9m

@G.T.R great :D !! .. I'll hit it with something else then .. =P (I think I have another ace up me sleeves :P )

Chris's sis

@TedShifrin Don't understand me wrongly, I'm sure the professors may teach you a lot of things, but some are built to learn alone, especially those with social phobia. It's hard to imagine what difficult is for those students with social phobia to stay focused on things. It's a hell!

skullpatrol

@TedShifrin to be an independent researcher you must be in that .5%

r9m

@TedShifrin XD .. happens a lot :)

Mike Miller

9:17 PM

@TedShifrin That's what I meant. E.g., asking calc students not to write a proof, but still to explain why something's true. (A proof in disguise.) Do computations, but don't spend the course doing them.

I told you someone better than me could pull it off!

Ted Shifrin

I just think that doing proofs that are formal and give little insight (what I call "mathematical masturbation") does little good in a standard course. I'm not talking about a theory course or one for majors. And I do do proofs when they impart understanding/insight.

Mike Miller

Right. I agree.

Ted Shifrin

So I insist on a proof of the Fundamental Theorems of Calculus, for example. And for why conservative force fields have potential functions, etc.

Mike Miller

Right.

skullpatrol

even physics courses require proofs

Ted Shifrin

9:22 PM

they call them derivations, not proofs :)

r9m

Now I'm onto disturbing/annoying Vladimir with the doubts/questions I faced while proving it ... =P

Ted Shifrin

You enjoy being a pest, @r9m? :D

Oh, wait, you're here. Of course, you do.

skullpatrol

lol

r9m

@TedShifrin pestering is my second nature :P .. especially when I think I have a chance to learn sth :D

Ted Shifrin

What's your first?

Ilan Aizelman WS

9:25 PM

boo

skullpatrol

learning is the first

Ted Shifrin

Heya @Ilan :)

G.T.R

I like Vladimir's witty comment "How to guess this proof? It is easy enough: $\frac13$ can only come from $\int t^2 dt$ in this context, so we need to estimate $f$ somehow via the integral of $tf'(t)$.". Good insight

Ted Shifrin

Yes, I love it when people give insight. (See above.)

r9m

@G.T.R I envy your questions :P ... they get a lot of attention :-)

Ted Shifrin

9:28 PM

I don't recall paying attention to any of @GTR's questions!

Mike Miller

Sonny Corleone Would Still Be Alive Today If He Had E-ZPass

r9m

I mean they always have a decent number of upvotes and views :)

Ilan Aizelman WS

@TedShifrin You know, I wish I would invest more time in studying. Sometimes, I feel kinda wasting my time. Although I do study atleast 3 hours a day. But I always think it's not enough and I can push myself more and more and thus I can study more and understand more. But I don't know when I studied enough to succeed in the test - it's not high-school anymore which I studied like 2hours before the exam and got 100 mark..

G.T.R

@r9m I've been posting a streak of non-trivial questions (mostly oral exams) but go back earlier in time, they're less numerous

Ted Shifrin

Well, @Ilan, you're right. It's not high school any more. But give yourself a break. It's impossible to work a full-time job and be a serious college student. Being in the full-time military is even more onerous!

Maybe I should post an occasional question on main for you, @GTR :D

Mike Miller

9:32 PM

Surely you have things you'd like to know, @Ted?

Ilan Aizelman WS

@TedShifrin Well, I'm not going to give up anyways. I'm just not that kind of a person to give up. and I hate being defeated (Like: getting a bad mark after I sweat alot for the exam). Do you have an insight to make me less misreable than I am now?

Ted Shifrin

@Ilan: I would tell you to do the best you can do and stop beating yourself up.

I also would comment that I've taught plenty of students who, with 3 hours a week of my lectures and numerous office hours, probably aren't understanding things as well as you do. So you should appreciate that you're learning a lot.

Mike Miller

I'll second that advice

Ted Shifrin

Part of what I do as a teacher is act like a cheerleader. (I recognize that that is not the European model.) You have no cheerleader other than yourself, @Ilan.

skullpatrol

why the big difference?

Ted Shifrin

9:35 PM

There's now a business model of education in the US, @skull. After all, the students and their parents are the consumers. We have to please them. ... But I felt like I had to cheerlead and encourage students to work hard/learn even before that.

Ilan Aizelman WS

@TedShifrin I see, well, then I need to keep working on my discipline, because sometimes I decide something and I don't eventually do it. For e.g., planning to study for 3hours, but I scroll facebook sometimes, answer to unimportant calls, chatting, etc.

Ted Shifrin

Not to mention spending time talking to worthless people like us, @Ilan :D

Ilan Aizelman WS

Exactly. although sometimes I find you useful ;)

haha. @TedShifrin

Ted Shifrin

Illusory.

We're just cute and charming :D

skullpatrol

I asked you to not mention that :D

r9m

9:38 PM

@Ted would you mind if the pestering me follows you to fb ? :D xD

Ilan Aizelman WS

Well, I'm off to bed now. Going to manage my time more efficiently now for studying. Need to get off the things the distract me while studying.

Ted Shifrin

LOL @r9m

Glad to help, @Ilan :) Good night.

Ilan Aizelman WS

You got fb Ted? :O

r9m

@TedShifrin I'll take that as an affirmative :D

Ted Shifrin

Some of you people may not like what you find on FB ... :D

Ilan Aizelman WS

9:40 PM

gimme! :)

G.T.R

@Ted ah, I have another non-trivial question. Find all $n\times n$ square matrices such that $\exp(M)=I_n\$.

Ted Shifrin

What field, @GTR?

G.T.R

$\mathbb R$

Ted Shifrin

Ah, ok. Well, I still have some answers.

We just need the "realified" Jordan form.

G.T.R

NO!

Ted Shifrin

9:43 PM

Don't yell at me.

G.T.R

please not Jordan :P

Ted Shifrin

Well, I need to use that to prove I've got everything.

Daniel Fischer

@G.T.R You don't need to prove it, just to use it. That's nice, actually.

Ted Shifrin

@Ilan: You're welcome to submit a friend request if you so desire.

runs fast and hides from @hippa

Hippalectryon

@TedShifrin :D

@TedShifrin I created a new meme :P

not showing it tho

Lol

Ted Shifrin

9:45 PM

Oy vey.

Hippalectryon

It's not for you don't worry

Ted Shifrin

You may send it to me privately, @Hippa. :D

Oh, good.

Hippalectryon

Some friend of mine just made a http gui generator

Ted Shifrin

For whom is it?

oh lord

Hippalectryon

And i needed an image to test it

:D

Pedro Tamaroff

9:46 PM

@DanielFischer Daaaaaaaaaaaaaniel.

Hippalectryon

@TedShifrin einsteink.freezoy.com/Result.png

Ted Shifrin

not saying hello to @Pedro

Daniel Fischer

@PedroTamaroff Yeeeeeeeeeeeeeeeeeeeeeeeeeeeees?

Pedro Tamaroff

=(

Ted Shifrin

What do you mean, it's not for me, @Hippa? Oy.

Pedro Tamaroff

9:47 PM

@DanielFischer Do you know the name "Carothers"?

Ted Shifrin

@Daniel: Did she figure out your hint?

Hippalectryon

@TedShifrin I mean, even though you're in it, it's not because it's you

Daniel Fischer

@TedShifrin Not yet, it seems.

Hippalectryon

It's because it was what i had right when I did it

Ted Shifrin

frappe @Hippa très fort

Hippalectryon

9:47 PM

ewwww that hurts

Daniel Fischer

@PedroTamaroff I know the name, yes. But hardly more. What is it about?

Ted Shifrin

@DanielF: Perhaps the next hint would be: does $f$ have a primitive?

Pedro Tamaroff

@DanielFischer I am reading a book written by him, but his name has a certain ring, like he's famous or something.

Ted Shifrin

so, @GTR, are you asking this question to test me, or do you not know the answer?

Pedro Tamaroff

It's a cool surname.

Ted Shifrin

9:49 PM

much cooler sounding than us Russian types, @Pedro.

Pedro Tamaroff

@TedShifrin No way!

Ted Shifrin

LOL

Pedro Tamaroff

Kolmogorov is the mathiest surname ever.

Chevoratev.

Ted Shifrin

So you don't like the British school?

Pedro Tamaroff

Shilov.

Tychonov.

All sound cool.

@TedShifrin What's the British school?

Ted Shifrin

9:50 PM

Шифрин и Таморов

r9m

@Chris'ssis Is there no end to this tail ? ;)

G.T.R

@Ted no I do not :(

Ted Shifrin

Carothers sounds English or Irish ...

Pedro Tamaroff

@TedShifrin Yes, Tamarov would be a nice addition. Hehe.

@TedShifrin The book is by the CUP.

Mike Miller

Naptime.

Chris's sis

9:51 PM

@r9m It's a surprise! :-) I'll create a lot of questions of this type, maybe some hundreds (I wanna explore each type of family as much as I can).

Ted Shifrin

oh fine, @Pedro ... you like you but scorn me ...

no, @Mike, dinnertime.

So, @GTR, what do you surmise is the answer?

Pedro Tamaroff

@TedShifrin WAT.

Ted please.

Ted Shifrin

LOL ... I put both our names in Cyrillic

Pedro Tamaroff

Oh, I only recognized mine I don't know Cyrillic.

Ted Shifrin

ah :)

Pedro Tamaroff

9:53 PM

Trivia. Huey rejected an offer to compose for the Ghostbusters movie.

r9m

@Chris'ssis Yessss !!! put them in a book .. all the charts and details of your exploration .. Marco Polo :D !

G.T.R

$0$, but unsure @Ted

Hippalectryon

@G.T.R :O trouvé :D :D :D prntscr.com/3v6702

Ted Shifrin

Think about $2\times 2$ rotations, @GTR.

robjohn

@chris'ssis I am at lunch. I hate the mobile interface. I will be back in a while.

Chris's sis

9:54 PM

@robjohn I wanted to send you something privately (in case you have an e-mail for that you use on MSE).

@robjohn OK

Ted Shifrin

lunch at 3 PM? Oy ...

Pedro Tamaroff

@DanielFischer Do you recall the proof of the open mapping theorem off the top of your head?

Ted Shifrin

In complex analysis or in functional analysis, @Pedro?

Pedro Tamaroff

Functional analysis.

I didn't know there was one for CA.

Ted Shifrin

I'm out ... :P

Daniel Fischer

9:56 PM

@PedroTamaroff Not all details, but I could reconstruct them, given a little time.

Ted Shifrin

Yup, all complex differentiable maps are open maps (except for constants).

r9m

@Chris'ssis why so secretive ? :D

Daniel Fischer

@PedroTamaroff Though, if you're asking about the version for webbed spaces, reconstructing that would take more than a little time ;)

Ted Shifrin

WTF are webbed spaces?

Pedro Tamaroff

What on earth is a webbed space?

Ted Shifrin

9:58 PM

ROFL

Pedro Tamaroff

I heard about barreled spaces once.

Ted Shifrin

me too

@GTR: Tu es toujours là?

Hippalectryon

@TedShifrin Spider webbed space ? :D

Daniel Fischer

Do you guys want me to look up what a webbed space was? I forgot the details, I have to admit.

G.T.R

@Ted yes

Ted Shifrin

10:01 PM

So think about what you exponentiate (in $2\times 2$ matrices) to get a rotation through angle $\theta$ @GTR

G.T.R

@Ted are you referring to the identification with complex numbers ?

Daniel Fischer

Wow, they even got their wikipedia page

Ted Shifrin

sure, @GTR, but you still need the exponential.

Pedro Tamaroff

@DanielFischer Weesh.

Ted Shifrin

Well, @DanielF, I've lived a long time without knowing about these things. I reckon I can survive longer ...

Spider webs in mathematics ... We had sheaf theory with all the agronomical vocabulary :P

Chris's sis

10:05 PM

@r9m Well, it's nothing secretive there (or it is a bit?) ... :D

Daniel Fischer

@PedroTamaroff Well, unless you're going in really deep, you won't need to go beyond LF spaces, I guess. Probably not even beyond Fréchet spaces.

Okay, @Pedro, so what was the question?

Ted Shifrin

I was assuming @Pedro meant Banach spaces.

r9m

@Chris'ssis I just wanted to sound like 'Why so serious ?' there ! .. :P

Pedro Tamaroff

@DanielFischer That was my question. =P

I am a bit surprised that Carothers' book doesn't prove any of the major theorems though.

Ted Shifrin

Why reprove stuff that's in tons of textbooks?

Daniel Fischer

10:09 PM

@PedroTamaroff What major theorems?

Pedro Tamaroff

@DanielFischer Open mapping, closed graph, uniform boundedness.

Ted Shifrin

So what is Carothers's book?

Chris's sis

@r9m Do you know there is a soundtrack with this name? 'Why so serious?' -> youtube.com/watch?v=t6wrZ6P6-wU :-))))))

Daniel Fischer

@PedroTamaroff And is it supposed to be a textbook on Functional Analysis?

Pedro Tamaroff

"A short course on Banach Space Theory"

Daniel Fischer

10:10 PM

Erm, that should prove such things, IMO.

Pedro Tamaroff

Sorry $\uparrow$

Daniel Fischer

Well. So after a glimpse of what it doesn't contain, what does it contain?

r9m

@Chris'ssis (y) this sound track (Joker's theme) sounds awesome with HD surround sounds !! :)

Hippalectryon

What do you put when you have no idea what tag to write ? :/

Ted Shifrin

Give me a hint, @Hippa.

Hippalectryon

10:13 PM

It's about a weird think i remarked when applying $\ln$ to the pascal triangle

Pedro Tamaroff

worldstarhiphop.com/videos/video.php?v=wshh7UQ5Uo0xZU3a5tK6

WHOA.

Daniel Fischer

@TedShifrin math.stackexchange.com/questions/842942/… She found Morera :D

Ted Shifrin

Oh, that is weird. Do you have it typed in, @Hippa?

Hippalectryon

@TedShifrin Yep

Pedro Tamaroff

Chris's sis

10:14 PM

@r9m Yes, I know. :-) Don't miss this one -> youtube.com/watch?v=tZXBvJnPx3A

Ted Shifrin

Yeah @DanielF: I gave her an upvote on that comment.

Pedro Tamaroff

Ted Shifrin

Link me, @Hippa.

Hippalectryon

@TedShifrin It's written, but not asked yet

Ted Shifrin

So, what does he say in his introduction, @Pedro?

Hippalectryon

10:15 PM

@TedShifrin i need to enter a tag

r9m

@Chris'ssis YA .. :D .. I have 'em all in lossless audio :)

Ted Shifrin

combinatorics, precalculus [I got censored for removing a precalculus tag and putting combinatorics a week ago] ... I have to see @Hippa

Hippalectryon

0

Q: What is that curve that appears when i use $\ln$ on Pascal's triangle?

I made a little program that generates pascal triangle as images : I first tried it associating to each pixel a color which's intensity was proportional to the number in the pascal triangle The colors being 0-255, i used the following function to convert value to colors: $$f(x)=\frac{x-m}{M-m}2...

Daniel Fischer

@PedroTamaroff The section headers in chapter 6 are a little, how shall I say. But looks not bad. Presumably, it presupposes the basics like OMT, CGT etc.

Pedro Tamaroff

Yes, that's what Carothers says.

@DanielFischer A little what...? =P

Ah, yes. They strike me as funny.

Ted Shifrin

10:19 PM

@Hippa: Maybe something like $(\log x)/x$? I'm not truly understanding the relevance of Pascal here. What's on the $x$-axis?

Chris's sis

@r9m Good! :-)

Hippalectryon

@TedShifrin i'm basically drawing the pscal triangle

Ted Shifrin

I don't get it yet. How does $\binom nk$ enter in here?

Hippalectryon

@TedShifrin mathman.biz/images/pastri.gif <-> i.stack.imgur.com/oDBD7.png

Swadhin

Someone please help on this one math.stackexchange.com/questions/843018/…

Ted Shifrin

10:20 PM

I know what Pascal's triangle is, @Hippa. :) How is it related — precisely — to your curve?

@Swadhin: You do know that you can find all the solutions to Putnam problems on the web?

Swadhin

@TedShifrin The web solution seems beyond my understanding, so I am asking here.

Hippalectryon

@TedShifrin You see how the pictures are pascal's triangles ?

Ted Shifrin

@DanielF: Kudos to you on the restraint and guidance of that OP. :)

Well, @Swadhin: I would recommend that you say what precisely you do not understand in the web solution as part of your question.

Swadhin

@TedShifrin And moreover, they are using too much of intuition and assumption.

Studentmath

Hmm. If I am looking at a configuration with a ring length 4, there is a lobe outside and a lobe inside. I look at the subgraph induced by the lobe outside together with the ring itself, call it O, and I define a proper 4 colouring of it $f:O\to [1,2,3,4]$ so that, if $R=\{v_1,v_2,v_3,v_4\}$, $f(v_i)=i$ for $i=1,2,3,4$. Why is it so that either $v_2,v_4$ are at different components of the subgraph of O induced by the colours 2,4.

Or that $v_1,v_3$ are at different components of the subgraph of O induced by the colours 1,3 - but both isn't possible?

Daniel Fischer

10:23 PM

@TedShifrin Kudos to claire for looking over her notes.

Swadhin

@TedShifrin and I cannot find the intuition in that, is the solution only possible by intuition?

Ted Shifrin

Well, I'm just applauding your patience and guidance, @DanielF.

Daniel Fischer

Well, thanks.

Pedro Tamaroff

@DanielFischer Did you like the contents, tough?

It has lots of references, for one.

Ted Shifrin

@Swadhin: I have not worked that problem or looked at the solution. But undoubtedly people will tell you to read it. So you should say explicitly what you follow and what you don't in that solution.

@Hippa: No, I really don't.

Daniel Fischer

10:24 PM

@PedroTamaroff I said: "But looks not bad".

Hippalectryon

@TedShifrin Higher intensity => higher number

Pedro Tamaroff

@DanielFischer Does not bad = good?

Ted Shifrin

So, if the commenter is correct, you should look at Stirling's formula and see if it fits (more or less what I said just guessing). Do you know Stirling? @Hippa

@Pedro: No, "not bad" = "not bad" :D

Hippalectryon

@TedShifrin I think so

Ted Shifrin

$\log(n!) \sim n\log n - n$ @Hippa

Hippalectryon

10:26 PM

@TedShifrin $\binom{n,k}$'s equivalent right ?

Daniel Fischer

@PedroTamaroff Meet my good friend

Ted Shifrin

So what is the estimate on $\log\left(\binom yx\right)$?

Swadhin

@TedShifrin I have seen one solution, where they say, it seems that $-1,0$ are crucial points, so one can assume $F(x)=a|x+1|+b|x|+cx+d$ , now, there are quite a few things I do not understand here, why should the sum need to be linear, second, why should we consider this?

Ted Shifrin

bows @DanielF

@Swadhin: I'm not going to think about the problem. I suggest you incorporate all of these comments into your question.

Swadhin

@TedShifrin Ok, I asked for help here anyway.

Pedro Tamaroff

10:28 PM

@DanielFischer OH HO HO!

Ted Shifrin

The more specific and focused you make your question, the more likely you'll get helpful answers, @Swadhin. Just sayin'.

Hippalectryon

@TedShifrin $\ln\binom{y}{x}\sim y\ln(y)-x\ln(x)-(y-x)\ln(y-x)$

heya @Kaj

Hello everyone

10:29 PM

@TedShifrin ok, thanks.

Ted Shifrin

OK, @Hippa ... I suggest you graph level curves of that, as that commenter suggested. :)

is that for @DanielF, @Pedro?

Hippalectryon

@TedShifrin Ok done :) i added something at the end

Pedro Tamaroff

@TedShifrin Hehe, yes.

Hippalectryon

@TedShifrin Btw is the english correct at the beginning ? I'm not sure

Ted Shifrin

no, @Hippa, "which's" should be "whose"

The least I can do for your reteaching me French :D :)

Hippalectryon

10:31 PM

Thanks

:)

Kaj Hansen

@TedShifrin, according to the little tracker, my rep in the diff geo section is no longer 0 as of today :P

Swadhin

Can anyone please explain: if $r(x)$ and $s(x)$ are any two functions, then $\max\{r,x\}=\dfrac{r+s+|r-s|}{2}$?

Ted Shifrin

LOL @Kaj ... You mean you deserved to pass the class? :D

@Hippa: Based on mathematica, these are not level sets of that function. I'm not quite sure.

Chris's sis

llollllllllll, I just cracked another tough series!!! :-))))

3

Hippalectryon

@TedShifrin Well maybe if I tried with huge numbers i wouldn't have that anymore, but i can't do it on my computer

@Chris'ssis :D Congrats

Chris's sis

10:36 PM

@Hippalectryon Thanks! I have so fun here now! :-))))))

Kaj Hansen

Well, perhaps I wouldn't go that far @Ted. Just trying to even out a little bit, ya know? Total score of 145 under the abstract algebra tag, and the next highest subject is elementary number theory with a total score of 41, LOL

Ted Shifrin

ugh ... @Kaj: Robert Lewis with his damn fiat lux ... has to always publish complete solutions when I'm trying to get the student to figure something out. I abhor him.

Hippalectryon

@Chris'ssis Write down a correction of one of the monster integrals once a month and send it to me :D

Ted Shifrin

You don't need huge numbers, @Hippa. That conjecture is just wrong. I don't think it's level curves at all. I think it's the graph of the function.

Hippalectryon

@TedShifrin But

hehe i did 'but' him

Kaj Hansen

10:38 PM

@TedShifrin, I've been trying to work on that because I've been bad about that in the past. It's surprisingly difficult to give just enough so that someone is no longer stuck, but avoiding giving too much at the same time.

Chris's sis

@Hippalectryon It is possible you may find it soon in one of the American monthly magazines ... :-)

Hippalectryon

@Chris'ssis I live in France :/

Ted Shifrin

Well, @Kaj, keep trying. We have to win this battle. :)

Maybe I've rubbed off on you :D

Hippalectryon

@TedShifrin Why is the pattern still the same for 50*50 and 150*150 ?

Ted Shifrin

@Hippa, what I said doesn't make sense either. Agh.

Hippalectryon

10:39 PM

@TedShifrin Don't worry i didn't even see it xD

Ted Shifrin

Ask @Kaj to look at it :P

Hippalectryon

I can't believe this question is getting so many upvotes :/

Ted Shifrin

It's interesting, @Hippa. I just don't quite understand it yet.

Kaj Hansen

haha, what are you looking at @Hippa?

Hippalectryon

10

Q: What is that curve that appears when i use $\ln$ on Pascal's triangle?

I made a little program that generates pascal triangles as images : I first tried it associating to each pixel a color whose intensity was proportional to the number in the pascal triangle The colors being 0-255, i used the following function to convert value to colors: $$f(x)=\frac{x-m}{M-m}25...

combinatorics algebra-precalculus

Kaj Hansen

10:41 PM

That's pretty interesting @Hippa. +1 as well, because it's refreshing to see questions with originality and effort from the OP from time to time.

Ted Shifrin

@Kaj: You'll find most of the young'uns who hang out in this chatroom are seriously vested in mathematics. :)

I still say the graph looks like $y=(\log x)/x^k$ for some $k$.

Well, translated ... $y=(\log (x-c))/x^k$ for some $c,k$.

Kaj Hansen

You know what bugs me about SE is not that people will post asking about their homework, even if that question may have been asked before. No. It's those users who will post either a list of problems, or will post 10 questions in a single night that are obviously coming from problem sets (and invariably end up with downvotes on each one).

Ted Shifrin

Not to mention take-home exam questions which then 100+K rep users obligingly post solutions to, even when asked NOT to. I'm so pissed off, @Kaj.

r9m

@Chris'ssis Awesome !! but how will I know that it is you (or is it that you are planning to publish under the name Chris'ssis -_-) ? :D

Ted Shifrin

If people would stop answering these questions, the 1-100 rep users would desist. But all these guys have to show off how great they are.

LOL @r9m

Hippalectryon

10:44 PM

Well i should thank @Alister, he gave me the diea with his dihedral groups :D

Ted Shifrin

@Hippa: I feel like we should be able to figure this out. I'm just being too dumb.

Please don't meme that.

Hippalectryon

I won't :)

Chris's sis

@r9m Is it a bad idea to use the name Chris'ssis? :-)))

Kaj Hansen

@TedShifrin, I remember seeing someone posting about a question that was apparently on their in-class midterm as they were taking the exam! Flagged/voted to close as soon as I saw it. Nevertheless, SE has a lot to offer when it's used correctly.

Ted Shifrin

I agree, @Kaj. So these guys in here are on the good side :)

Chris's sis

10:47 PM

@r9m btw, this is such a great day to me, a blessed day! Really! :-)

Ted Shifrin

Congrats @Chris'ssis.

Pedro Tamaroff

@DanielFischer OK, now I do have a question.

r9m

@Chris'ssis Great :D

Chris's sis

@TedShifrin Thanks Ted! :-)

Ted Shifrin

@Hippa: So I'm still confuzled. I'm muddled by what the axes are and what the intensity is. What are we looking at?

$y$ and $x$ are what? Intensity is what?

We are looking at level curves of intensity. I grant that.

So intensity is something like $\binom y{\log x}$?

Kaj Hansen

10:50 PM

Also, what does the color "0" look like, and likewise for 255?

Pedro Tamaroff

@DanielFischer Nevermind got it.

Daniel Fischer

@PedroTamaroff Got what, out of curiosity?

Ted Shifrin

LOL @Pedro @DanielF

r9m

@Chris'ssis Who is Chris and his sis ? :{ any idea for a meme @Hippa ? :P

Ted Shifrin

Oh, you answer my questions at the very beginning. $x$ is the entry of the triangle, $M$ is the max, so we're rescaling (since $m=1$ which is basically $0$) to $y=\log (x/M)$. But where do the various rows come in, @Hippa? I'm still confuzled.

Hippalectryon

10:54 PM

@KajHansen 0 is black, 255 is white

Chris's sis

@r9m That wording sounded like Bonnie and Clyde :-)))

Hippalectryon

@TedShifrin $x,y$ (left->right and up->down) are the rows, columns of the pascal triangle

Ted Shifrin

Wait, that's not what you wrote.

Hippalectryon

?

Uuuh mea

horizontal is the colums

vertical is rows

That's still unclear-_-

@TedShifrin It's exactly as in i.stack.imgur.com/HQ7wX.gif

Ted Shifrin

You put $x$ is the entry. So you mean Intensity at $(x,y)$ is the ratio of the $y$th entry of the $x$ row to the max in the whole thing.

r9m

10:57 PM

@Chris'ssis you mean the 1967 movie ? I haven't seen it yet :-)

Ted Shifrin

Or vice-versa. What does the top line represent (with slope approximately $-1$)?

Hippalectryon

@TedShifrin It's the line of 1s (cf i.stack.imgur.com/HQ7wX.gif)

Pedro Tamaroff

@DanielFischer Suppose that $B_1(0)\subseteq \overline{M \varphi(B_1(0))}$ for some map $\varphi:X\to Y$. Then for any $y\in Y$ we can find $x\in X$ so that $\lVert x\rVert < M\lVert y\rVert$ and $\lVert y-\varphi x\rVert <\varepsilon$.

r9m

@Chris'ssis no ! :]

Chris's sis

@r9m OK :-)

Ted Shifrin

10:59 PM

OK, so the intensity is the ratio at $(x,y)$, where $x$ is the column and $x-y$ is the row.

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$Mathematics$ Mathematics