Mathematics - 2014-06-21 (page 3 of 5)

7:00 PM

@TedShifrin Yes, but that doesn't affect my idea, as far as I can see. But, as insinuated, I think making the idea precise (if it can be made precise) would be unheimlich difficult.

robjohn

@Chris'ssis Ah... without the earlier one, it is hard to follow the later one.

Ted Shifrin

Heinrich Unheimlich?

Pedro Tamaroff

@robjohn I see DonAntonio has been suspended for voting irregularities.

3

Hm....

Daniel Fischer

@TedShifrin Heinrich MirGrautVorDir

Ted Shifrin

I wonder who could have caused that, @Pedro ...

robjohn

7:02 PM

@PedroTamaroff it would appear so...

Studentmath

@Pedro hm, go on

Pedro Tamaroff

@Studentmath Well, now I need to show we actually have a $K_{n,n}$.

The point now is to argue again like before, using the "maximization".

Studentmath

Yes

Pedro Tamaroff

Well, and that's that.

Studentmath

You have to be rigirious regarding the maximization, as it is intutive but not obvious

But as you explained it before, it seems without fault

But wait, if you get to $K_{l,k}$, and afterwards to $l=k=n$, you don't have to go further.

Ted Shifrin

7:07 PM

mr @Pedro, you ignoring me today?

G.T.R

@r9m how do you derive $x^2+y^2+z^2 \ge xy+yz+zx$ without diff calculus ?

Pedro Tamaroff

@TedShifrin Sorry, I was a bit caught up with this combinatorics stuff.

I need to pass the next midterm and make up for the first.

skullpatrol

Oooh noo failure?

r9m

@G.T.R well $x^2+y^2+z^2- xy-yz-zx = \frac{1}{2}((x-y)^2+(y-z)^2+(z-x)^2) \ge 0$ :-)

Ted Shifrin

No problem, @Pedro ... Just checking ...

Mike Miller

7:10 PM

@DanielFischer Not pleasant for his customees...

G.T.R

@r9m ah

Mike Miller

@Studentmath I know of it, but I don't know it

Studentmath

@Mike 6.3.9 here (page 329) holds a small part of the proof, most is made by computers though. I don't ge the proof there too well still.. toihoctap.wordpress.com/2013/02/13/…

Ted Shifrin

Talk about chutzpah!!!

Mike Miller

I own West's book. Let me check.

Someone commented on my answer from 2 weeks ago saying he wants help with complex analysis.

G.T.R

7:12 PM

@r9m I switched the answer check to your answer because you taught me something :P

Ted Shifrin

@Mike: I figured in summer the amount of homework begging would decline, but it seems to be getting worser and worser.

Wow, someone taught @GTR something? :D

Mike Miller

@TedShifrin Ah, no, this is not a student. It's just someone with a poor grasp on english and manners.

@Studentmath That must be a new edition. 6.3.9 for me is the definition of thickness.

Ted Shifrin

You talking about yours or the one I just referred to above? @Mike

skullpatrol

The worsest is yet to come...

Mike Miller

@TedShifrin Mine. Yours is terrible.

Studentmath

7:14 PM

@Mike yes, it's the second edition

Ted Shifrin

I'm sure I'll be accosted for being rude to him with my comment.

Studentmath

Quite new.

Mike Miller

@Studentmath I don't want to look at copyrighted stuff online (bad!), so can you guide me towards the page?

@Studentmath Hm, I have the second edition.

Ted Shifrin

LOL ... duelling second editions.

Studentmath

Oh it's illegal?!

The question itself is on page 270.

Ted Shifrin

7:15 PM

covers eyes and ears yet again

Mike Miller

Wow.

Studentmath

Has an hint at 514.

skullpatrol

@TedShifrin Ya, why are you being rude to him?

Mike Miller

@Studentmath Oh, I thought you were having trouble reading one of West's proofs.

Daniel Fischer

yes.but it is a topology homework.pls help me in writing this solution. — user115608 4 hours ago

Studentmath

7:15 PM

@Pedro I still don't get why you are not done when l=k=n, since you have shown it to be $K_{l,k}$.

Pedro Tamaroff

@MikeMiller Holy shit. This will be good.

Ted Shifrin

Hmm @Mike: Martin is pretty accomplished.

Studentmath

@Mike ah sadly not that simple, trying to practice up for the test so doing few 'hard' questions.

Pedro Tamaroff

@Studentmath Did I show that?

=P

Mike Miller

Yeah, I can't help with this. I don't know what a lobe is, for instance. I also haven't thought seriously about graphs for a long time.

I probably never thought seriously about graphs.

r9m

7:16 PM

@G.T.R irk .. there is something in math110's answer too :P .. do you know weighted am-gm inequality ? he used it and later balanced weights by solving a system of liner equations that are necessary to get to the final expression ... :P its definitely not out of thr blue (he just hid his machinations) :P

Studentmath

@Pedro - ah, the maximilization part comes at the end

My bad

Mike Miller

@TedShifrin Hence the wow. That guy's condescension is definitely not deserved.

Ted Shifrin

@DanielF: This guy is acting a lot like B11b, whom I got suspended a while ago. He may be back with a new persona.

user105491

Does anyone in here participate in the homotopy theory chat room?

skullpatrol

or personae :-)

Ted Shifrin

7:18 PM

Well, @Mike, even we relative experts occasionally deserve to be condescended to :P

G.T.R

@r9m I prefer tortuous, enriching solutions to polished gems

Ted Shifrin

Probably right, @skull ... I thought I saw something a few weeks ago.

Mike Miller

This one's my guy. I didn't even properly answer his question, so I don't know why it's me he's asking.

Ted Shifrin

You like turtles, @GTR?

Daniel Fischer

@TedShifrin I don't think so, B11b scanned his/her beautiful handwriting and was generally polite enough to use complete words.

Pedro Tamaroff

7:19 PM

@SanathDevalapurkar I don't think anyone in this room knows too much about homotopy.

r9m

@G.T.R LOL :P

Mike Miller

I know some homotopy at the level of part of Hatcher's chapter (not the supplements!), but that's it. None of the categorical stuff.

Ted Shifrin

@Mike: I've quit answering Rafik. I learned after one answer, if I remember correctly.

Pedro Tamaroff

@MikeMiller Yeah, I know you know some.

user105491

@PedroTamaroff Oh. I had a question regarding infinitesimal thickenings of topoi, so I first decided to check if it could be answered here, and go there if necessary.

Mike Miller

7:20 PM

lol

G.T.R

that's a whole lotta love (music national day in France, and there's a rock band performing right in front of my window (sleep? none!))

Mike Miller

yeah, @Ted, I should have learned earlier - sometimes I don't pay attention to who the poster is

Ted Shifrin

wow, @GTR, which arrondissement are you in?

G.T.R

@Ted Nation 11 ème. I'm gonna take some pictures to show you how crazy it is :P

Ted Shifrin

ah, I was there several times last summer ... one of my friends lives near there

Pedro Tamaroff

7:22 PM

@SanathDevalapurkar What is a topoi?

Mike Miller

topoi is the plural of topos

topos is the romanization of the greek word τόπος, for place

Pedro Tamaroff

What is a topos?

user105491

@PedroTamaroff It's the plural of topos. A topos is a category which looks like a category of spaces.

user105491

That's roughly speaking.

Pedro Tamaroff

What does that even mean?

Isn't there a clear definition?

skullpatrol

7:25 PM

if there was, we wouldn't be talking about it

blue

@TedShifrin wat

user105491

@PedroTamaroff There is, if you want. I work with Grothendieck topoi; let me define that. In $1$-category theory, at least, a Grothendieck topos is a category which is cocomplete and has a small generating set.

user105491

Alternatively, it is the category of sheaves on a small site.

Ted Shifrin

@blue: he said tortuous ...

Pedro Tamaroff

@SanathDevalapurkar What is $1$-category theory?

This looks like super advanced stuff.

user105491

7:27 PM

@PedroTamaroff It's ordinary category theory .

Mike Miller

@PedroTamaroff A 1-category is just a category.

Pedro Tamaroff

OK, what is $n$-category theory.

Mike Miller

Why do you assume $n$ comes after 1?

Maybe next is $\chi$-category theory.

Ted Shifrin

Ugh ... I remember when it used to be fun to be in here ...

skullpatrol

Me too

Mike Miller

7:29 PM

It's always fun in here, @Ted.

Pedro Tamaroff

@TedShifrin I have a joke for you.

What do you call a crocodile in a vest?

Mike Miller

Maybe I should talk about injective $\mathbb Z$-modules instead? To lighten the mood.

user105491

@PedroTamaroff In essence, an $n$-category is a category enriched over $(n-1)\mathbf{Cat}$, where enrichment is defined as follows: the hom-set is an $(n-1)$-category (note - it's an inductive definition). But perhaps I'm getting too technical here!

user105491

@MikeMiller Ah, yes. That's be fun! :-)

Mike Miller

@PedroTamaroff Well, if he's drunk, I call him a cab.

Pedro Tamaroff

7:31 PM

Silly Mike. An investigator.

skullpatrol

lol

Mike Miller

I hate you.

Ted Shifrin

The zoologist will remind us an alligator a crocodile is not.

4

Pedro Tamaroff

@SanathDevalapurkar What is "the hom-set"?

@MikeMiller OK, this one is better.

Mike Miller

@TedShifrin Luckily, we have assassins to take care of the zoologists.

Pedro Tamaroff

7:32 PM

Yesterday I saw a kidnapping.

r9m

@PedroTamaroff That would be Alligator in a vest .. :P

Ted Shifrin

@Pedro has been in a very punny (or puny?) mood of late. It must be that graph theory test.

Pedro Tamaroff

I didn't wake him up.

Sawarnik

@PedroTamaroff :O

@r9m True!

Pedro Tamaroff

@TedShifrin It is not graph theory, it is combinatorics.

G.T.R

7:33 PM

@ted see your facebook messages

Ted Shifrin

Then why are you doing all this graph theory, @Pedro?

Mike Miller

Graph theory $\cap$ combinatorics $\neq \varnothing$

Pedro Tamaroff

@TedShifrin It is part of the course.

Ted Shifrin

Ah, ok.

Studentmath

@Ted he is feeling masochist today

Ted Shifrin

7:33 PM

Oui, monsieur @GTR

Sawarnik

@MikeMiller Luckily, we have law enforcement guys to take care of you.

user105491

@PedroTamaroff Given objects $X,Y$ of the category $\mathcal{C}$, the class of morphisms in $\mathcal{C}$ from $X\to Y$ is called the hom-set. If this is an $(n-1)$-category, then $\mathcal{C}$ is an $n$-category. Inductively, you can define $\infty$-categories, and then define $(\infty,n)$-categories.

Pedro Tamaroff

@SanathDevalapurkar Ah, but do we always require ${\rm Hom}(X,Y)$ to be a set? Why not a class?

user105491

@PedroTamaroff Are you asking why it's called a hom-set?

user105491

@PedroTamaroff Found my mistake, and edited it. Thanks for the clarification.

user105491

7:36 PM

@PedroTamaroff Are you a grad student?

Pedro Tamaroff

@SanathDevalapurkar I am not sure.

user105491

@PedroTamaroff What does that mean?

Daniel Fischer

The I-do-your-homework squad really gets on my nerves lately.

Pedro Tamaroff

I am not sure.

Ted Shifrin

@DanielF: You and I need to lead a revolt.

skullpatrol

7:37 PM

@DanielFischer take a break pal

Ted Shifrin

But most of our colleagues are on their side, not ours.

Mike Miller

I think it's 50/50.

skullpatrol

yep^

Pedro Tamaroff

@TedShifrin "Do you hear the people sing...."

@DanielFischer.

Studentmath

Pedro, you doing planar graph theory?

Mike Miller

7:39 PM

@Ted The same user posted the same question before, and I guess reposted it when it wasn't written as something they could copy paste.

skullpatrol

@PedroTamaroff nice comment :D

Pedro Tamaroff

@Studentmath Why planar?

user105491

@PedroTamaroff +1 for the comment!

skullpatrol

@TedShifrin revolts are for revolutionaries

Alyosha

@TedShifrin Yes.

Studentmath

7:40 PM

Trying to prove something, if it might be on your test you might want to try it too

Otherwise not :P

Ted Shifrin

@Alyosha: I have no recollection of what this refers to :P

Alyosha

Analysis and Abstract Algebra limits.

Mike Miller

Yes to analysis and abstract algebra limits?

Ted Shifrin

ohhh ... right

they are analogous, @Alyosha, but different concepts.

Alyosha

'Can analysis limits be done using abstract algebra limits, or is it just a coincidence of terminology?'

That's what I thought.

user105491

7:42 PM

@Alyosha I think there was an M.SE/MO question regarding that somewhere.

Alyosha

@SanathDevalapurkar Do you recall the name of it?

user105491

@Alyosha Check out mathoverflow.net/questions/9951/…, and math.stackexchange.com/questions/60590/…

Alyosha

@SanathDevalapurkar Thank you. I think the MO one is what I wanted.

user105491

@Alyosha The accepted answer in MO is the same as the accepted answer in M.SE

Alyosha

I meant the question.

But yes.

user105491

7:45 PM

@Alyosha Yeah. So, what's your motivation?

Alyosha

@SanathDevalapurkar I'm learning about limits in category theory, and am not fond of analysis, so wondered whether it was applicable there.

user105491

@Alyosha As the answers say, it could be applicable, but it'd be very hard to do actual computations using CT in Analysis.

G.T.R

@r9m there it is math.stackexchange.com/questions/842913/…

r9m

@G.T.R okay ,, I'm following it :-)

Alyosha

@SanathDevalapurkar I feared as much.

user105491

7:51 PM

@Alyosha Anyhow, have you finished learning about limits or have you just begun?

Alyosha

@SanathDevalapurkar Just begun. Are there any bits of intuition you can offer?

user105491

@Alyosha Yeah, sure! I can't explain it better than these three answers, so check them out: math.stackexchange.com/questions/123883/intuition-for-limits, mathoverflow.net/questions/23268/geometric-intuition-for-limits, math.stackexchange.com/questions/38517/…

Ted Shifrin

Sigh. Another one with attitude. What is going on?

Studentmath

I don't get this step. We assume the graph is planar and has a ring of length 4, $R=\{v_1,v_2,v_3,v_4\}$. We also assume (for contradiction) it is minimal 5-chromatic graph. Now if we observe the outer-lobe+$v_1v_3$ and the inside-lobe+$v_1v_3$, each is four colourable, so far so good. But now they claim that we can assign the colours so that in each the colour given to $v_1,v_2,v_3$ will be the same. But what if in one colouring $v_1,v_3$ have the same colour and in the other not?

Pedro Tamaroff

@TedShifrin I think everyone hates you Ted.

It is settled.

[jk]

Ted Shifrin

8:01 PM

I'm inclined to stop trying to help.

Studentmath

@Ted people are usually ungrateful

Mike Miller

@SanathDevalapurkar @PedroTamaroff We should delete our comments, so as not to clog up the question.

Keep the bit asking about the coefficients, though.

user105491

@MikeMiller OK.

user105491

Done.

Ted Shifrin

It didn't used to feel that way on this site, and I only started about 15 months ago ...

Mike Miller

8:03 PM

@TedShifrin I mainly contribute for my own learning. Answering stuff solidifies my knowledge.

Studentmath

The longer something is/the longer you do anything, the probability to encounter such behaviour increases. On the other hadn the probability to encounter positive behaviour also increases, so..

Mike Miller

Luckily I don't feel a need to solidify my knowledge in some jerk's homework.

Ted Shifrin

No, @Mike, you just want me to help you with yours :D

And pretty much I can't any more ...

Mike Miller

@Ted Hey, it's not homework.

Well, I guess it is. I'm at home and I'm doing these problems.

Ted Shifrin

Are you doing summer school, @Mike? You've already graduated ... So you're just hanging out until you move?

Mike Miller

8:06 PM

@Ted I'm studying and I'm working for a professor on a problem.

I thought I had the problem solved, but I didn't, so now it's interesting again.

Ted Shifrin

Sorta like life ...

Mike Miller

:)

Right now I'm being frustrated by a literature search coming up short, but c'est la vie.

Ted Shifrin

What a twit. Says he knows how to do a volume with a triple integral but cannot do it with a double integral. Do you really know how to do it? :D

Mike Miller

Don't be mean!

I bet you were a twit at some point in your life, too.

Chris's sis

That guy downvoted me a lot in the past -> DonAntonio

Ted Shifrin

8:13 PM

glares

Oh, really, @Chris'ssis? How do you know?

Chris's sis

@TedShifrin Well, I had some quarrel with him in the past and he used to downvote me, but I think he used a different account to do that.

Ted Shifrin

Wow ... Well, he apparently went and downvoted me a bunch after I chewed him out for doing someone's takehome exam problem.

Mike Miller

Hmm. Is gambling allowed on MSE?

skullpatrol

yes

Chris's sis

@TedShifrin I'd like to see his account totally erased. (serial downvoting ...)

Studentmath

8:16 PM

Isn't it against the site rules @Ted?

Ted Shifrin

@GTR: With regard to the problem you posted, do you know Wirtinger's inequality?

G.T.R

@MikeMiller gambling rep ?

Ted Shifrin

It isn't quite there, but it smacks of the right flavor.

Mike Miller

@G.T.R No, I bet someone a quarter.

Ted Shifrin

Isn't what against site rules, @Studentmath?

Studentmath

8:17 PM

Seriel downvoting

Mike Miller

@Studentmath Yes. Hence his suspension.

skullpatrol

poker.SE

G.T.R

@Ted I had the occasion to discuss Wirtinger inequality with @r9m

Ted Shifrin

But, truth be told, I'd like people to be suspended for doing students' exam problems.

Of course, the student should be suspended too for posting them.

But I give up ...

Studentmath

Who gives take-home exams?

Mike Miller

8:17 PM

@skullpatrol Well, it's a gamble about math.

Ted Shifrin

Stupid professors who don't give a **** about what their students are actually learning?

Mike Miller

@Studentmath I had a take-home exam in complex analysis. It allowed the professor to give us better, longer tests. But it also had an in-class portion.

Studentmath

Or maybe they're naive/over-trust the students

Ted Shifrin

@GTR: So? It smacks of that. But I don't see the trick yet.

Chris's sis

True.

Ted Shifrin

8:18 PM

Tests aren't better if students are tempted to cheat. And everyone is.

Mike Miller

It wasn't a big class, though... I think he had good reason to trust the lot of us.

Studentmath

Well, in a small class he could always check the net to see if someone uploaded the question.

Ted Shifrin

Hell, when I took point-set topology from Munkres, he gave problem sets which counted as takehome exams (and in-class midterm and final). This was way before internet or anything else. But we were allowed to use the book. One of his questions was solved many chapters later in the book, and a number of us found that and used it. The problem was then thrown out (legitimately).

Alizter

@Chris'ssis blabhabhabhasb $$\int^1_0\frac{\arcsin(x)}x\;\mathrm dx$$

Studentmath

I was given a few tests to do home in school, was naive and never cheated

Alizter

8:20 PM

maybe you can expand on this family?

Ted Shifrin

Well, @Studentmath, you're all the better for your honesty and your true learning.

Studentmath

I doubt these few tests have advanced me in life, but yeah I don't have any guilty conscience about cheating

skullpatrol

let them cheat themselves out of learning

Ted Shifrin

I remember cheating on a memorization-based history test in 8th grade. I never got caught, but I've always felt horrible about it. I so hated that sort of testing. Always have.

Chris's sis

@Alizter What about that (elementary) integral?

Studentmath

8:22 PM

I cheated on a math-test in 3rd grade or so, I still feel bad about it. It wasn't even intentional

Alizter

@Chris'ssis It looks obvious. Sub then parts but then it diverges. Maybe creating integrals in such a manner can give more evil ones :)

Mike Miller

@TedShifrin Well, at a certain point, there's nothing you can do. One problem on the test had us proving the FTA step-by-step. Certainly someone could google it, but they could do that too if it was a homework... and it's a good experience to actually do the details of the proof.

Alizter

@Chris'ssis Not just for trig..

Chris's sis

@Alizter I see.

Ted Shifrin

You could do that on an in-class exam, quite fairly, @Mike.

@GTR: Someone's posted a solution for you.

Alizter

8:23 PM

@Chris'ssis I am very happy and over my head at the moment. So excuse my if I am being quite random

Mike Miller

@TedShifrin I suppose. But that wasn't the takehome exam, it was one of the six questions, most of which were similarly enlightening.

I've forgotten what they enlightened me of, but I guarantee they did.

Uh huh ...

lol

@Alizter :-)

I don't like Sal Khan's voice, it's too business like. (like a used car salesman)

G.T.R

8:27 PM

@Ted this is the solution I already knew. Wait to see how elegant r9m 's one is

Ted Shifrin

Well, get him to post it. I was trying to think about it. Grr.

G.T.R

@r9m Ted mandates that you post your solution :D

skullpatrol

de-mandates

Ted Shifrin

Oui, je l'ordonne! @GTR @r9m

r9m

@TedShifrin I won't post it now .. (I've sent the outline to GTR on fb) ... I want to learn how others approach it too :-) .. @G.T.R will that be a problem ? :-)

G.T.R

8:32 PM

@r9m well post it here since Ted is very impatient :P I also hope others will come up with something different

Daniel Fischer

I need an idea how to say Morera without actually saying Morera.

Ted Shifrin

Integrate around closed path? @Daniel

Daniel Fischer

@TedShifrin This question. I wonder how to tell the OP to use Morera without naming it.

r9m

Well my idea is $F(x) = \int_0^x f(t) \,dt$, then $F(0)=F(\pi)=0$, and from applying integration by parts to obtain $\pi f(x) = \int_0^x tf'(t)\,ft + \int_x^{\pi} (\pi - t)f'(t)\,dt $ and Cauchy Schwarz inequality after squaring to the RHS :)

Sab ಠ_ಠ

Hello everyone :)

Ted Shifrin

8:36 PM

Yeah, @r9m, that's the sort of trick that shows up in these sorts of problems. I like this better than Fourier series, by far. Plus, the proof that's posted bothers me. How does he know there are no $\sin$ terms?

Sab ಠ_ಠ

Hi Prof. @Ted

Ted Shifrin

Heya @Sab !! Did you pass?

Sab ಠ_ಠ

I guess.

No results yet just got on holidays.

But I know I will pass. Although I will just pass

Ted Shifrin

@DanielF: The OP is trying to differentiate under the integral sign, which is perfectly acceptable. Really, a technique that's needed later, anyhow. But Morera is the slick proof, yes.

Sab ಠ_ಠ

I didn't do well in my test and I'm sure about it.

Ted Shifrin

8:38 PM

Well, @Sab, I don't want to be mean, but the adviser in me (with 35 years' experience) suggests that maybe a career in math isn't necessarily the right path for you ... You should consider that if the exam in first calculus was not good.

Sab ಠ_ಠ

@Ted I'm starting to doubt myself. As you said I'm not sure anymore

Ted Shifrin

P.S. @r9m: I like that argument.

OK, @Sab, as I said, I don't want to be mean, but you should explore some options ... would be my advice ... while you take the next math.

Sab ಠ_ಠ

Thing is I will pass, but that's not what I want. I want to get above 80% minimum

Daniel Fischer

@TedShifrin That part was added later. And for the one with only analyticity in $z$ given for rational $t$, I don't see how differentiating under the integral would be doable without violating the Geneva convention.

Ted Shifrin

Right. If you really want to be serious about studying mathematics, the first year courses should be relatively easy for you. @Sab

r9m

8:39 PM

@TedShifrin Thank you very much !! ^_^ :D (skips in joy)

Sab ಠ_ಠ

Exactly. I realize maybe that my study habits were not good

Or maybe I didn't do enough

or maybe I slacked off somewhere along the way

skullpatrol

too much chat room

Ted Shifrin

Well, @Sab, studying the week before the final doesn't make up for regular hard work. Math is not a subject learned by last-minute cramming.

Sab ಠ_ಠ

That's 1 point

Ted Shifrin

@DanielF: Where am I supposed to see just rational $t$? [goes to look again]

G.T.R

8:41 PM

@Ted yes there's something odd... he should make the symetric of $f$ over $[-\pi,0] and then replicate it by periodicity to make it an even function. But he got the gist

Sab ಠ_ಠ

Thinking about it, I just did all my homeworks and tuts during my first semester

I didn't actually learn/revise before one week

Ted Shifrin

Oh, I see it now, @DanielF. Then we absolutely need Morera.

Sab ಠ_ಠ

So probably this was the case

Ted Shifrin

I find that many of my students are in bludgeon mode to get homework done, but they don't take the time to reflect and absorb what they've learned doing it. @Sab ...

Sab ಠ_ಠ

The funny thing is I can do integrals and derivatives easily

I mostly lose marks on fundamental things

I realized that I focus too much on the hard stuff, master them and don't put time on the very little details(which make me lose marks)

Ted Shifrin

8:43 PM

Wait @DanielF ... If I only know for rational, how do I use Morera? Is it even true?

Sab ಠ_ಠ

we got 5 integration questions worth 20 marks, I did them all in 10 minuts

Ted Shifrin

Yes, @Sab, many of my students do that, too, when I keep reminding them that exams are not about the hardest stuff.

Sab ಠ_ಠ

Yep.

Daniel Fischer

@TedShifrin $F$ is still assumed continuous in both variables, as I understand it. So the integral over $\partial\Delta$ depends continuously on $t$.

Ted Shifrin

Well, @Sab, learn from the experience and see if you can do better the next course with modified learning/studying strategies.

r9m

8:45 PM

@G.T.R @TedShifrin I didn't know the inequality had a name ... its apparently a slight variation of Block's Integral Inequality :-)

Sab ಠ_ಠ

@Ted that's the only thing I should do I guess. It's my first semester and I did some mistakes. I guess I will have to grab the 65% I'm expecting and move on

Ted Shifrin

Wirtinger? @r9m ... also a case of the Poincaré inequality that shows up in diff geo and PDE.

Studentmath

This drives me nuts.

Ted Shifrin

But, @Sab, I would still encourage you to take a course in something else you think you might be interested in ...

Sab ಠ_ಠ

I'm taking applied maths, physics and computer science

Thing is physics is really loads of calculus

I ace it

applied maths is just easy

and so is com. scie

Ted Shifrin

8:47 PM

Well, applied maths is still maths ... :)

r9m

@TedShifrin ya .. all these are bros and sis of Poincare Ineq :)

Ted Shifrin

Well, computer science is a good career choice in this day and age.

Sab ಠ_ಠ

Yeah, but I'm pretty sure I got 95%+

The only thing I'm sure about is I took pure* maths lightly

Ted Shifrin

Well, work on Spivak during your holidays and see if you still enjoy the challenges, @Sab.

Sab ಠ_ಠ

I'm covering the whole thing this month. :)

Ted Shifrin

8:48 PM

I can send you more of my exams, too :D

Sab ಠ_ಠ

Sure :D

Spivak is next to me right now, borrowed it from library for the month

I'm also gonna study stats and take the module next semester

Studentmath

Stats!

Sab ಠ_ಠ

Stats is awesome.

Studentmath

How I wait to finally be at that exam. Though I may be sorry for that waiting.

Ted Shifrin

Did I send you anything with integrals, @Sab, or just derivatives?

Sab ಠ_ಠ

8:49 PM

@Ted You sent some integrals. :)

Ted Shifrin

Oh, yeah, I did send stuff from home, so I see what I sent. OK, I'll send the rest of second semester stuff.

Sab ಠ_ಠ

I would appreciate if you have some questions which makes me apply my proofs

Ted Shifrin

Well, there are a number of proofs in those exams. Did you do them all?

Sab ಠ_ಠ

Not all. I did what was on my syllabus

Ted Shifrin

And Spivak's book has plenty for you ... more than plenty. Some are too hard. But some are appropriate for you.

Sab ಠ_ಠ

8:51 PM

Yeah. I love Spivak's approach

I wish I knew about it wayyy before

Ted Shifrin

OK, sent.

Sab ಠ_ಠ

Got it. Thanks :)

I see Taylor Series

I did that in applied maths.

Ted Shifrin

But I ask for proofs that things are valid :P

Sab ಠ_ಠ

It was fun, but we didn't do it in depth as we will do in pure

Ted Shifrin

As well as applications, of course.

@DanielF: Why not ask the OP if he/she knows some alternative ways to show a function is analytic, rather than just the definition? [Rather than saying what you want.]

Sab ಠ_ಠ

8:54 PM

I love the exam on integrals. 10 points per integration :D

We got 4 points per integration lol

Daniel Fischer

@TedShifrin I guess I'll do that, and see how it evolves.

Ted Shifrin

But I don't mean to butt in, @DanielF ... :)

Sab ಠ_ಠ

@Ted So the book you use for your class is Spivak, right?

Daniel Fischer

@TedShifrin But, didn't you forbid "but"s yesterday?

Ted Shifrin

Yes, @Sab, but I hand out supplementary homeworks on things like volumes, work, differential equations.

Indeed, that was my goal (mon but), @DanielF :D

Sab ಠ_ಠ

8:57 PM

Aha, so I guess Spivak is the way to go. And I'll use Stewart as a supplementary.

I understand better from Spivak, it just makes more sense.

Mike Miller

I wouldn't use Stewart at all, personally

not sure what I would use

I never read Spivak, but any calculus text I've looked at has been terrible

Ted Shifrin

Stewart's an OK standard book. I liked Edwards & Penney a fair amount in their early editions (colleagues of mine here). I like Rogawski (now dead, sadly) from UCLA. Very interesting book. A few non-standard approaches.

Remember, @Mike. Calculus texts are not written for math majors.

Spivak, more or less, was.

Sab ಠ_ಠ

Stewart doesn't give the "real" definitions.

And it omits some proofs.

Ted Shifrin

"Real" definitions are beyond the average calculus student ... in today's world.

Right, if you want proofs, do Spivak or Apostol's Calculus. And do mine for multivariable/linear algebra :D

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$Mathematics$ Mathematics