Mathematics - 2014-09-18 (page 3 of 5)

Chris's sis

7:00 PM

@robjohn That was a good idea.

robjohn

@Hippalectryon I will expand on $(3)$ to make it clearer.

Will Hunting

I just submitted 5 edits. Please approve them.

Alizter

@WillHunting done

Will Hunting

I am still waiting for amazon to ship my books. It has been so long.

Hippalectryon

@WillHunting It's a sea sick book

They can't ship it :P

Alizter

7:06 PM

ha

Ice Boy

Ahoy!

Balarka Sen

Arrr. All hands on board.

Chris's sis

@robjohn do you think that there is any school in the world that would give such a problem on an exam? That one is a research level problem.

Will Hunting

Will someone take a look at math.stackexchange.com/questions/936810/… and math.stackexchange.com/questions/936765/… and math.stackexchange.com/questions/889547/… and upvote if they are correct?

Hippalectryon

@Chris'ssis Well wanna look at some French exams ?

@Chris'ssis It's not crazy sums, but... it's tough

@Chris'ssis ens.fr/IMG/file/concours/2014/BCPST/14_sujet_bcpst_math.pdf

Balarka Sen

7:10 PM

Those are just... analysis :/

Hippalectryon

@Chris'ssis And yum yum

Alizter

@BalarkaSen posted something about the french math education earlier...

Hippalectryon

Did i mention you only have 4h to do the exam ?

Balarka Sen

link?

Hippalectryon

@Alizter I'm interested, permalink ?

Alizter

7:11 PM

it is pinned

Balarka Sen

@Alizter oh you mean I did

Hippalectryon

'Having originated in France, this pervertedness quickly spread to teaching of foundations of mathematics, first to university students, then to school pupils of all lines (first in France, then in other countries, including Russia).'

-_________-

'To the question "what is 2 + 3" a French primary school pupil replied: "3 + 2, since addition is commutative". He did not know what the sum was equal to and could not even understand what he was asked about!'

That example is plain dumb

Balarka Sen

@Hippa it was a joke, surely

Alizter

I don't agree with Math $\subset$ Physics

Balarka Sen

and that kid is now a mathematician

he is in MO

Chris's sis

7:13 PM

@Hippalectryon Do you know what is my profound desire to those that put such questions on an exam? I'd like to see them how they perform on my poor questions ... I give them not 4 hours, but 40 hours or 400 hours to play with them.

Hippalectryon

@Chris'ssis Those exams are for people like me (16-20), not older

Balarka Sen

@Alizter me neither.

Alizter

@Chris'ssis I agree. It's not like good mathematics comes from sitting in a room for 3 hours.

Hippalectryon

'For example, these students have never seen a paraboloid and a question on the form of the surface given by the equation xy = z2 puts the mathematicians studying at ENS into a stupor. Drawing a curve given by parametric equations (like x = t3 - 3t, y = t4 - 2t2) on a plane is a totally impossible problem for students (and, probably, even for most French professors of mathematics).'

That's grothendieck for you

Random Variable

@DanielFischer I thought you left the chat like 30 minutes ago because I didn't see your avatar from Stack Overflow.

Balarka Sen

7:15 PM

@Hippalectryon I think it's not completely true, but oh well it was Arnol'd after all.

@Hippalectryon HAHAHA

Hippalectryon

@Chris'ssis Also, we don't specialize in some parts of mathematics, like the computation of sums, series, ...

@Chris'ssis We don't learn all the weird theorems and constants you might have learn or found

eg Stolz Ceràro

Balarka Sen

@Hippa here

robjohn

@Hippalectryon I have added a couple of formulas to hopefully explain that inequality and the next (they are both the same, almost)

Daniel Fischer

@RandomVariable Aha. No idea why the avatar changed.

Hippalectryon

French education in the best in prep schools :D

Ice Boy

7:20 PM

@DanielFischer very strange

Will Hunting

@Hippalectryon French and Germans are the best in everything.

Balarka Sen

"The Arnold Principle. If a notion bears a personal name, then this name is not the name of the discoverer.

The Berry Principle. The Arnold Principle is applicable to itself."

-___________________-

Hippalectryon

@WillHunting Everything ?

Alizter

The Berry Principle is appickable.

Will Hunting

@Hippalectryon Yes, to me. I am biased. I have an obsession with France and Germany.

Chris's sis

7:22 PM

@Hippalectryon I've just received an answer to my question

5

Q: Computing in closed form $\sum_{n=1}^{\infty}\frac{\operatorname{Ci}\left(\frac{3}{4}\zeta(2) \space n\right)}{n^2}$

What tools would you recommend me for computing the series below? $$\sum_{n=1}^{\infty}\frac{\operatorname{\displaystyle Ci\left(\frac{3}{4}\zeta(2) \space n\right)}}{n^2}$$ I lack the starting ideas, I need some. Thanks.

Hippalectryon

@Chris'ssis Useless -__-

Balarka Sen

Seriously? An answer?

Hippalectryon

@BalarkaSen Look at it lol

Balarka Sen

@Hippalectryon Hey that is NOT an answer

Hippalectryon

^

Will Hunting

7:23 PM

I will sleep in 4 hours from now.

Hippalectryon

@robjohn About $(5)$ : since we haven(t set any conditions on $x$, how do you get $xf(nx)\leq \frac{1+\epsilon}n$ ?

Chris's sis

@Hippalectryon Anyway, that question of yours is very weird. I'm curious about the tools of the creator.

Balarka Sen

"For example, not only students but also modern algebro-geometers on the whole do not know about the Jacobi fact mentioned here: an elliptic integral of first kind expresses the time of motion along an elliptic phase curve in the corresponding Hamiltonian system."

who cares?

Hippalectryon

@Chris'ssis The one @robjohn answered ?

Chris's sis

@Hippalectryon aha

Hippalectryon

7:25 PM

@BalarkaSen exactly

@Chris'ssis Or the picture from the ENS test ?

Chris's sis

@Hippalectryon The question involving $A\gamma$ limit ...

robjohn

@Hippalectryon Since $n\le x_\epsilon/x$, we have that $nx\le x_\epsilon$ and therefore $nxf(nx)\le1+\epsilon$

Hippalectryon

@Chris'ssis Look at the full exam then

@Chris'ssis Part III

@robjohn But isn't the inequality $xf(x)\leq\epsilon+1$ ? where does the $\frac{1}n$ come from ?

robjohn

@Hippalectryon did you see the edit to my last comment?

Hippalectryon

@robjohn Oh I see now

Ice Boy

7:31 PM

@DanielFischer only your StackOverflow account avatar is unchanged, very strange...

Daniel Fischer

Vel. It may go back to normal tomorrow. Or maybe not, we shall see.

robjohn

@Hippalectryon I have added that to the line before $(5)$

Balarka Sen

"Attempts to create "pure" deductive-axiomatic mathematics have led to the rejection of the scheme used in physics (observation - model - investigation of the model - conclusions - testing by observations) and its substitution by the scheme: definition - theorem - proof. It is impossible to understand an unmotivated definition but this does not stop the criminal algebraists-axiomatisators."

Hippalectryon

@robjohn thanks

Balarka Sen

"For example, they would readily define the product of natural numbers by means of the long multiplication rule. With this the commutativity of multiplication becomes difficult to prove but it is still possible to deduce it as a theorem from the axioms. It is then possible to force poor students to learn this theorem and its proof "

WAT

Hippalectryon

7:33 PM

sWAT

Balarka Sen

say what?

Ice Boy

His opinions are very old fashion.

Hippalectryon

@robjohn And in $(7)$ what's the link between the two last lines ? (the $\leq$)

Balarka Sen

@IceBoy Some of this is just pure nonsense, but some are true.

like the one about mathematics without geometry

"What is a group? Algebraists teach that this is supposedly a set with two operations that satisfy a load of easily-forgettable axioms. This definition provokes a natural protest: why would any sensible person need such pairs of operations? "Oh, curse this maths" - concludes the student (who, possibly, becomes the Minister for Science in the future).

We get a totally different situation if we start off not with the group but with the concept of a transformation (a one-to-one mapping of a set onto itself) as it was historically. A collection of transformations of a set is called a group if …

Or that^

Ice Boy

@BalarkaSen yes, he is clever with his mixing and matching.

robjohn

7:36 PM

@Hippalectryon each thing in brackets is less than or equal to $\dfrac\epsilon k$

Hippalectryon

Why ? And don't you mean $\dfrac{\epsilon}k$ ?

Daniel Fischer

@IceBoy More bluntly, despite his mathematical brilliance, he's (well, was) a crank when it comes to some things.

Balarka Sen

"I was astonished that all the best and most important in methodical approach mathematical books are almost unknown to students here (and, seems to me, have not been translated into French). Among these are Numbers and figures by Rademacher and Töplitz, Geometry and the imagination by Hilbert and Cohn-Vossen, What is mathematics? by Courant and Robbins, How to solve it and Mathematics and plausible reasoning by Polya, Development of mathematics in the 19th century by F. Klein."

@Hippa did you read any of those ^

Hippalectryon

@robjohn I think I get the first ($xf(kx)\leq \frac{1}k$ for $x\leq x_e$), but not the second

@BalarkaSen Nope

Balarka Sen

-______-

Hippalectryon

7:39 PM

@BalarkaSen But I'm only 16 wink wink @Chris'ssis

Balarka Sen

I'm glad I read Courant-Robbins.

So that's one out of 6.

Chris's sis

@Hippalectryon ;)

Balarka Sen

@DanielFischer But I'd say that his books are pedagogically much easier and good read.

Hippalectryon

@Chris'ssis What if I was really 16 ? :D

Balarka Sen

That guy knew how to teach

Chris's sis

7:42 PM

I wanna see Ted in action one more time

►

Balarka Sen

as the MO post starred says, Bourbaki classics were never meant for textbooks.

Chris's sis

:-)

Hippalectryon

:D

I'm old

Chris's sis

@Hippalectryon :-))))

Hippalectryon

Not me, HE !!

I'm just $\huge16$ :P

robjohn

7:47 PM

@Hippalectryon They are both the same. I have added some explanation before $(7)$

Ice Boy

@DanielFischer it probably lost something in the translation, no?

As do most.

Balarka Sen

(nudge-nudge-wink-wink @Hippa)

Hippalectryon

:D

Insta star

Balarka Sen

@Hippa I liked -_____- better.

Hippalectryon

How old is this hippo ?

Balarka Sen

7:49 PM

@Hippa $\sqrt{a^2+b^2}$ years old.

Hippalectryon

-______________-

a=,b=?

Ice Boy

3-4-5

:D

Hippalectryon

@IceBoy Nuh i'm not 5 :c

Balarka Sen

-____________-

Ice Boy

@Hippalectryon multiply both sides by whatever you want, except 0

Hippalectryon

7:52 PM

@IceBoy I'm not sure @Chris'ssis will agree to multiply by $\dfrac{16}5$ :)

Chris's sis

:-)

Hippalectryon

Ok I lied. I'm 15 so credible

Ice Boy

you lier

when is your birthday?

Hippalectryon

@Chris'ssis Urm. Anyway, sincerely i'm 16. No jokes. it's been funny for a bit, but... uh ...

december 1997 @IceBoy

There was a terrible storm that year

Wrecked Paris's Vincennes forest

Ice Boy

did you skip any grades?

Hippalectryon

7:55 PM

2 @IceBoy

Ice Boy

so you are 3 years ahead?

Hippalectryon

2, but it seems like 3 since I am born in December

Ice Boy

that's what I meant, including the december birthday :-)

robjohn

@Hippalectryon does that make sense?

Hippalectryon

@robjohn For now yes, let me look at the end

robjohn

7:58 PM

@Hippalectryon okay... I was just asking about $(7)$ now

Hippalectryon

Yeah $(7)$ is good thanks

@robjohn If I get it well, you get $(8)$ by adding $(5),(6),(7)$.

robjohn

@Hippalectryon yep

Chris's sis

Kouba finished it -> math.stackexchange.com/questions/936876/…

(that one is the way to go)

Hippalectryon

Then, why $\frac{2+\epsilon}n$ ? Since $|Sf(x)|\leq \frac{1+\epsilon}n+\sum_{k=1}^{n-1}\frac{\epsilon}{k}$ and $|S\phi (x)|\leq \frac{1}n+\sum_{k=1}^{n-1}\frac{\epsilon}{k}$, don't we have $|Sf(x)-S\phi(x)|
\le2\epsilon(\log(n)+1)+\frac{-1+\epsilon}{n}$ ? And why the +1 in $2\epsilon$ ?

Ice Boy

@DanielFischer your avatar is back to its old self :-)

Daniel Fischer

8:05 PM

:D

Ice Boy

@DanielFischer I hope you didn't mind me borrowing it for awhile?

It was a joke.

Daniel Fischer

@IceBoy You didn't do anything indecent or offensive using it, I hope.

Ice Boy

@DanielFischer nah, I'm harmless

Daniel Fischer

Then it's fine.

Ice Boy

:D

Hippalectryon

8:09 PM

@robjohn forgot to ping you, see above

porton

I have 1348 reputation. Is it worth to spend 100 bounties on a question which is important for my research? or should I spend just 50?

robjohn

@Hippalectryon $(5)$ is $\frac{1+\epsilon}{n}$ and $(6)$ is $\frac1n$

Hippalectryon

@robjohn But aren't we subtracting ?

That would make $\dfrac{\epsilon}n$

Not that the end results changes, but I was wondering

robjohn

@Hippalectryon when you are bounding using the triangle inequality, you add. We know the absolute values of things. For example, $|a|\lt1$ and $|b|\lt3$ means $|a-b|\lt4$

Hippalectryon

Oh right :)

@robjohn And for the $+1$ in $\log(n)+1$ ?

robjohn

8:15 PM

@Hippalectryon it is easy to get the bound $\log(n)+1$ for the harmonic series...

porton

How to decide to spend 50 or 100 on a bounty?

robjohn

@porton it's whatever you think the answer is worth to you

Hippalectryon

@robjohn Ah yeah thanks

Ice Boy

@porton It depends on how important it is. Also note, you can spend 50 now and if you are not satisfied spend 100 later, right?

Hippalectryon

@robjohn What about the end of $(10)$ ? all I know about $\gamma$ is that $\gamma=\displaystyle\lim_{n\rightarrow\infty} H_n-\log(n)$

robjohn

8:19 PM

@Hippalectryon look at the sum... at the partial sums in particular

Hippalectryon

I see $H_n-$.. OOH

Telescopes

:D

ALL PRAISE @robjohn :D

@robjohn Thanks very much for your time

porton

I think I should spend 100

robjohn

@Hippalectryon no problem. It was an interesting question that took a bit of thought.

@porton it's not like it will ruin your retirement or anything :-)

Ice Boy

lol

robjohn

@porton what question are you going to add a bounty to?

porton

8:23 PM

@robjohn math.stackexchange.com/questions/934172/…

robjohn

@porton I don't know enough about it to even guess at how much :-)

Ice Boy

@robjohn did you see my latest lhf?

about "belonging to"

robjohn

@IceBoy "belongs to" or "is an element of"

Ice Boy

@robjohn yep

Chris's sis

lol, I've just derived an awesome series in terms of Bessel function of the first kind ... :-)))

Ted Shifrin

8:44 PM

NO wonder it wasn't obvious to me why it should be true @robjohn. Well done!

People are stealing you, @DanielF? Hmm ...

Daniel Fischer

@TedShifrin Not stealing, borrowing.

Ted Shifrin

Well, I suppose that as long as you suffer no bodily harm, it's ok.

@DanielF @skull: What mathematician were you discussing above?

Daniel Fischer

@TedShifrin Vladimir Arnol'd

Ted Shifrin

Ah ... I missed out hearing him lecture (USSR wouldn't let him out to go to Lyon in 1984), but I admire his mathematics a great deal. Several of my papers were in part inspired by work of his and some of his colleagues.

Daniel Fischer

His mathematics are admirable. His rantings against everything vaguely connected to Bourbaki not so much.

Ice Boy

8:53 PM

pauli.uni-muenster.de/~munsteg/arnold.html

Ted Shifrin

Ah, well, Arnol'd is not known for getting all the pedantic details right. Very opposite in spirit to Bourbaki. I'm not a huge Bourbaki fan, either, I guess ...

I'm in the middle, in terms of expositional style, I think.

Ice Boy

balance is nice

Ted Shifrin

I haven't read that carefully, but Arnol'd is on the side of motivating mathematics with interesting questions, but for being formal for formalities' sake. I totally concur.

I'll read it carefully later; thanks, @skull ... I'll bookmark it.

Ice Boy

:D

thank Balarka

Ted Shifrin

I'd never do that.

Balarka Sen

8:56 PM

@TedShifrin It was posted by me, actually. ahem

Ted Shifrin

Well, fine, then. Thanks, @Balarka. I'm still a huge Arnol'd fan, whatever it says :P

I totally agree with him that abstraction for abstraction's sake has been detrimental.