Mathematics - 2016-08-22 (page 2 of 2)

user 1618033

9:00 PM

@Huy you could have avoided this example which sounds horribly.

Balarka Sen

@Danu I found an example, with help from Mike.

Huy

@Krijn: not exactly a cat person

user 1618033

@Huy My opinion, and maybe I sound somehow cinical: you don't need anyone to become a great mathematician, neither Balarka, nor Mike, nor anyone else.

Huy

@user1618033: sure, I just said the chat was dead, as in "not a lot of people talking like there used to"

user 1618033

OK

Balarka Sen

9:09 PM

@Krijn 2-person class sounds fun

Krijn

@BalarkaSen I had a three person class last year that was awesome

Agawa001

@user1618033 are yu still in clash with ted and some persons here ?

Balarka Sen

nice

Krijn

But that was together with two very hard working bright students

So they raise me up.

I'm hoping this time would be the same

Balarka Sen

It wouldn't be that bad of an experience to raise a not too bright student yourself, either, I don't think ;)

Huy

9:11 PM

anyone know any cool real life applications of derivatives as in "people actually differentiate or used to differentiate to solve this problem"

ktm5124

I have five equations

5 + x = c

6 + y = c

7+ z = c

8 + a = c

9 + b = c

Balarka Sen

@Huy minimizing/maximizing stuff.

ktm5124

Can I solve for x,y,z,a,b in terms of c?

Huy

@BalarkaSen: can you give an example?

Agawa001

5 vars 5 eqs no equivalence you can !

Huy

9:13 PM

most of the problems in math textbooks are not really problems where I think someone actually did use a derivative to do this

user 1618033

@Huy In the beginning of the movie The Man Who Knew Infinity, Hardy says, talking about Ramanujan, He was, in a way, my discovery. I did not invent him. Like other great men he invented himself.

ktm5124

@Agawa001 Can you clarify?

user 1618033

It's not bad to ponder well over these words.

@Agawa001 I'm only a peace dove these days.

Agawa001

dove ? doer ? lover ?

ktm5124

@Agawa001 You said 5 vars 5 eqs you can!

Agawa001

9:16 PM

oh k'

user 1618033

ktm5124

@Agawa001 That would seem to say, "yes".

Am I right?

Agawa001

@ktm5124 yes but c is the sixth

ktm5124

So I have 6 variables, 5 equations, you're saying.

Thus it's impossible. Correct?

Balarka Sen

@Huy What kind of problems are you looking for? Depending on that, I can tell you an example.

Huy

9:16 PM

@BalarkaSen: any that is not eco101

Agawa001

@ktm5124 is c known ?

ktm5124

@Agawa001 No. I only know that "c" can be anything from 9 to 27

Agawa001

if c is supposed to be a known parameter, then it is fine

ktm5124

@Agawa001 This actually pertains to a programming challenge, so I could input all possible "c" values and solve that way. It just wouldn't be elegant.

Agawa001

@ktm5124 all possible c's can solve ur equation somehow

i seem to be lacking some context

ktm5124

9:19 PM

It's a programming challenge, where "c" will assume at least a few values between 9 and 27.

But I don't know what values it will assume until I solve the problem.

Agawa001

@user1618033 i also like peace, but u know, people like peace when they begn to lose benifits, they do refer to war when they want more benifits

@ktm5124 another equation is required for ur system to be solved

user 1618033

@Agawa001 It's not my case. There is no benefit for me coming here, perhaps I'm pretty irrational doing that. I saw enough in this chat, and what is enough is enough.

As I said in the past I still come since robjohn comes around (but we are both pretty busy to talk much).

Danu

@BalarkaSen So what is it?

Balarka Sen

@Huy A basic problem: I am sure you teach how to minimize quadratic formula using completing the square? Do them using differentiation. A project (based on the same idea): prove the Euclidean geometry fact about perpendicular dist. being minimum using differentiation. A physics problem: tell them about infinitisimal velocities and infinitisimal accelerations. Justify the equations of motion using differentiation (justify, not prove: 'cause you need integration on that). A math problem: give them an informal introduction to Taylor series (write $f$ as $a_0 + a_1 x + a_2 x^2 + \cdots$ and the…

On the minimization note, you can add the proof of Snell's law. That's one of my favorite applications. But maybe I am overestimating how much your students are capable of grasping on an introduction to derivatives.

Krijn

I feel terrible, but thanks to that last problem Taylor-series made a lot more sense suddenly.

ktm5124

9:30 PM

@Agawa001 Ah, thanks for your tip!

Huy

@BalarkaSen: I know those examples already, but thanks for the input anyways :)

ktm5124

@Agawa001 I just figured out a sixth equation, getting c = ?

Huy

no, Snell's law is also one of my favourites

ktm5124

@Agawa001 (I put a ? because I don't know the value of c off the top of my head, but my program can find out.)

Agawa001

@ktm5124 some inequalities and domain maybe ?

ktm5124

9:31 PM

@Agawa001 So now I have 6 eqs and 6 unknowns. What's the best way to solve them programmatically?

Err, 5 eqs and 5 unknowns. Sorry.

Balarka Sen

@Huy Ah, well.

How about the Schroedinger equation? :P

duck

@Danu Take e.g. $S^5$.

Agawa001

@ktm5124 by substitution

Balarka Sen

Look at it's tangent bundle. That's not trivial.

Compactify it. A normal bundle of the zero section is still the tangent bundle.

ktm5124

@Agawa001 But programmatically. In a Java program. Would matrices be the best way?

Huy

I'm basically looking for easier things, like the standard "this is some rectangular shape, I want to fit some other shape inside it, how do I need to choose [...] for maximal area", but not so artificial, because let's face it, not a lot of people in the world actually do the maths to solve that problem

Balarka Sen

9:33 PM

But there exists a nonzero tangent vector field on $S^5$: that's because it has zero Euler characteristic, so Poincare-Hopf pushes through! That gives a nowhere zero section.

Krijn

@Balarka (or anyone else, really) Could you recommend me a movie (90 - 100 mins)?

user 1618033

@Agawa001 about Ted, letting the part with Ted's math, it's about the attitude toward top perfomance which I don't agree with. I'm against any act of discouraging the very top performance. For me wanting to know math as the great figures of mathematics is something one should dream of and do somehting to achieve that, to turn it into reality.

Huy

genre ?

Balarka Sen

Did you watch Pather Panchali though?

It's 180 minutes IIRC so maybe too long.

Krijn

@BalarkaSen Not yet, although I did watch some Xavier Dolan movies

Balarka Sen

9:35 PM

Hmm, never heard of him

Huy

@Danu: what are your favourite examples of Taylor in physics that you think a high schooler could grasp?

Danu

@Huy The perturbative expansions in QFT

(jk)

Balarka Sen

:)

Huy

I thought you're Danu, not 0celo7

Danu

I'd surely hope not

Balarka Sen

9:38 PM

I also noted something similar yesterday

Agawa001

@user1618033 i deeply wondered what makes u in disageement with ted because both of yu are nice persons

Danu

Anyways, I'm not a big expert.

Balarka Sen

Maybe Danu is converting into 0celo7.

Huy

you surely know basic physics

Danu

As with linear algebra, I never learned calculus rigorously

Agawa001

9:39 PM

@ktm5124 belike ?

Krijn

@Danu How? What? Who are you?

Huy

speak of the devil

ktm5124

@Agawa001 I think linear algebra is the way to go.

Balarka Sen

lol

0celo7

What

Balarka Sen

9:39 PM

Standard entry.

Agawa001

@ktm5124 if java can help yu solving linear systems so it is a way to go

ktm5124

@Agawa001 There are some libraries like JAMA that help. math.nist.gov/javanumerics/jama

0celo7

@Danu Mr. Danu my single hope in life is to become like you

Danu

@0celo7 No, it's not.

0celo7

Can you read my mind

Danu

9:41 PM

@Krijn A physics bachelor's degree holder

@0celo7 Yes, comes with the mod power.

0celo7

@Huy All forces act like harmonic oscillators for small displacements

user 1618033

@Agawa001 Thanks. Well, it's a rare adjective here to be called nice, I take that as a great compliment, of course. Well, we have totally different visions on mathematics, hence the apparently fight.

Balarka Sen

@Danu I think you should not be underestimating what you know just because you studied physics and not math in undergrad. I think you're fine in linear algebra and calculus.

LeGrandDODOM

12 upvotes for this math.stackexchange.com/questions/1899291/… really ?

Danu

@BalarkaSen Sure, I'm just fine.

Huy

9:43 PM

@0celo7 doesn't it have to be conservative?

Danu

I just don't know any interesting applications of Taylor's theorem :P

@Huy yup

But all forces are conservative deep down :P

Huy

:(

Balarka Sen

Locally conservative.

Always.

0celo7

@Huy what kind of maniac works with nonconservative forces in high school

Huy

:D

just correcting you

0celo7

9:44 PM

there's what, the magnetic force

Agawa001

@ktm5124 if the virtual judge permits yu to use these libraries it is fine, however a manual approach can be great and time sparing

0celo7

@Huy Yes, the potential should be a function of $x$ alone.

Huy

well I think they even do learn about that

yea

0celo7

But I think it's a good example

Huy

but thanks for the example

I do too

0celo7

9:45 PM

yw

Huy

I'm surprised I got a useful example from you, no offense

0celo7

@Huy Don't know why.

Danu

@0celo7 Just shift frames lel

Balarka Sen

Friction is an easier example. But maybe not good.

Huy

@0celo7 because of your interesting input on how I should teach geometry

0celo7

9:46 PM

@Huy That was clearly a joke.

Huy

no

Balarka Sen

@Huy i forgot, did he suggest to teach Riemannian geometry and then do Euclidean geometry as a special case?

0celo7

@BalarkaSen Hmm, that's true. (friction)

@BalarkaSen Yes.

Huy

he wants to prove that Euclidean follows from 0 curvature and topology of R^2

0celo7

@Huy But using variational techniques

Huy

9:47 PM

ah, then it's ok

0celo7

I'm sure you could just show that geodesics are lines and do analytic geometry

but I want a calc. of var. proof of the 5th postulate

I know it has to exist

Huy

ok

Balarka Sen

talk about maniacs

0celo7

My prof removed the "show $\ell^p$ is Banach" problem from the homework...

Huy

lol

0celo7

9:49 PM

I already did it

I'll turn it in anyway

Huy

:(

0celo7

He can read it if he wants

Huy

I liked when I had actual numbers from Mendel for my statistics part

I like using examples that actually happened

0celo7

@BalarkaSen Do you know if "A map from the union of all faces of a cube into a contractible space can be extended to the entire cube" is in Hatcher?

Balarka Sen

Yes, it's an exercise in chapter 0 in a more general case, IIRC.

Any map to a contractible space is nullhomotopic.

Danu

9:55 PM

and nullhomotopic iff extends to the cone

(which is just the disk $\cong$ cube)

Balarka Sen

Which is more or less definitional.

0celo7

Hmm, ok.

@Huy You need a Taylor series to do stuff with pendulums.

Huy

yes, I know that one

that's like the first one most students see, no?

0celo7

Yes.

Just making sure.

Balarka Sen

I haven't seen it. What's that?

Huy

9:57 PM

the sin(x) ~ x to solve the DE?

0celo7

@BalarkaSen Do you know what a pendulum is

Balarka Sen

@Huy oic

@0celo7 da

user 1618033

@Agawa001 now if Ted sees my message above where I said the integral Ramanujan is asked to calculate in The Man Who Knew Infinity movie is ought to be done mentally, perhaps another fight starts.

@Agawa001 there is no doubt if I were a professor I asked my students to do it without pen and paper (after teaching them my mathematics).

0celo7

@user1618033 I don't even know what an elliptic integral is

I've never seen one used

Huy

I know there was a really cool one in one of my basic physics courses but can't remember which one

0celo7

9:59 PM

The only time I ever hear about them is when people are talking about scary integrals

Huy

but maybe I'm mistaking it for a cool application of Lagrange multipliers -_-

Danu

@user1618033 Do you have the impression that there are any professors that specialize in doing integrals?

user 1618033

@Danu I think there are professors that also specialize in doing integrals and series. Yes.

Balarka Sen

@Krijn Have you decided on watching any movie?

Agawa001

@user1618033 whos that man who does infinity or whatever ?

Danu

10:01 PM

@user1618033 Do you know any?

user 1618033

@Danu Sure. I know some.

Krijn

@BalarkaSen Gonna rewatch Requiem for a Dream

user 1618033

@Agawa001 imdb.com/title/tt0787524

Danu

@user1618033 Could you point me to a paper?

Agawa001

@Krijn i know this as a song

Balarka Sen

10:02 PM

@Krijn OK. Have fun.

Krijn

@BalarkaSen Have you ever seen the movie? "Have fun"...

user 1618033

@Danu What that paper should be about to convince you about this little fact? There are tons of papers on integrals, series and limits.

Balarka Sen

No, I haven't. The "have fun" was a general comment, in which I assume people enjoy watching most movies.

Agawa001

a very rush-emotion song that gives yu waves of euphoriaaa

Krijn

@BalarkaSen Requiem for a Dream is one of the most depressing movies I know, haha.

Danu

10:03 PM

@user1618033 Just a paper dedicated to solving some integral (say, from this year)!

Balarka Sen

I enjoy certain kinds of depression.

Agawa001

wait i think it is rather a sad symphony, well i know it is good

user 1618033

@Danu Victor Moll wrote more books on integrals, you can find them on internet.

Krijn

Oh, you masochist.

Balarka Sen

:P

Danu

10:04 PM

@user1618033 But I'd like to see a research paper (from 2016)

Agawa001

@user1618033 ramanujan again ?

i dont think a movie about a man who mistook infinity for -1/12 is worth to be seen

user 1618033

@Danu it takes some time to look after them, and now I don't intend to do that.

@Danu Victor Moll has both books and articles, but I'm not aware where he is publishing his last stuff.

Danu

@user1618033 OK. You see, I'm rather skeptical that this is an active field of research, but I'd like to be proven wrong. I found some papers by Moll, but he's just reproducing integrals from the book by Gradschteyn and Ryzhik, which I don't really consider original research.

user 1618033

@Agawa001 I think you are kidding. ;)

@Danu It is an active field, even not that active as other fields, but I'm not interested in any comparison. Then I'm not affilitated to any university I do the math I like, without considering how active the field is.

Danu

OK, fair enough.

Agawa001

10:13 PM

@user1618033 how is ur progress

user 1618033

@Agawa001 Things are pretty OK these days, can't complain, thanks.

Krijn

@user1618033 If you are not affiliated to any university, how do you support yourself then?

user 1618033

@Danu arxiv.org/pdf/1603.03765v1.pdf

Agawa001

@user1618033 about the movie there is some people who pass thru same or worse than this circumstances then never see light, about the infinity thing

Balarka Sen

It's mentioned in the abstract that it's a note, not a research paper.

user 1618033

10:19 PM

In general often reducing the integrals to series is one of the most desirable things you want for briefly finishing the job.

Krijn

It's also written by a student :/

user 1618033

@Krijn Not sure what you mean by that. Ramanujan was self-educated, not even a student.

Agawa001

ok i have some job to do i must stay awake this night have nice convo by

user 1618033

@Agawa001 hehe, bye.

Balarka Sen

I gotta head to bed. G'night.

user 1618033

10:30 PM

@Danu one of the reasons I didn't have in mind some articles right now is that even if I had access to all these papers I would refuse to access them. I prefer to work on my original ideas and use only the tools I obtained in my research, I don't wanna by pushed in a way or other by the ideas spread in other papers. It's not that I won't do it, but for now I consider very important to work and fully develop only my own ideas.

I prefer to work hard and remark myself by originality, an unique style of solving the problems, to bring my personal style and spirit in the art of creating and solving problems.

I would be exactly the same in any mathematical field. I need originality in all I do, my existance there to have a well-shaped meaning.

(which defines an unique author with an unique style - and with a good impact in the mathemtical progress)

Forever Mozart

10:52 PM

that proof of the Riemann Hypothesis is not really a proof

flaws were found

although it would have been nice

0celo7

Link?

Forever Mozart

see the post by Winther math.stackexchange.com/questions/1896371/…

0celo7

wow what a bad error

Forever Mozart

yes

but the author is a non-expert in that area, so it's understandable

quid

11:42 PM

@ForeverMozart just to hammer this home, though it is in an answer by now: most well informed person should be able to decide in about 30 seconds that paper is virtually certainly not relevant and little is gained in studying it. It was not even among the better false attempts.

0celo7

@quid why?

Is it really unimaginable that no one thought to use Sturm-Liouville to analyze the problem

quid

@0celo7 it's dreamed of since 100 years to get the zeroes as eigenvalues.

Hilbert–Pólya conjecture

In mathematics, the Hilbert–Pólya conjecture is a possible approach to the Riemann hypothesis, by means of spectral theory. == History == In a letter to Andrew Odlyzko, dated January 3, 1982, George Pólya said that while he was in Göttingen around 1912 to 1914 he was asked by Edmund Landau for a physical reason that the Riemann hypothesis should be true, and suggested that this would be the case if the imaginary parts t of the zeros 1 2 + i t ...

user227867

@user1618033 I now have 20 videos and will retire from making videos, lol.

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$Mathematics$ Mathematics