Mathematics - 2013-04-25 (page 2 of 4)

Mariano Suárez-Alvarez

06:01

the set $\{\partial/\partial x_1,\dots,\partial/\partial x_n\}$ is a basis of $T_xM$

its dual basis is denoted $\{dx_1,\dots,x_n\}$

and $dx_1\wedge\cdots\wedge dx_n$ is a volume form

Eric Gregor

what is $\partial/\partial x_1$?

Mariano Suárez-Alvarez

I am sorry

I don t know what you know

Eric Gregor

the exterior derivative

Mariano Suárez-Alvarez

that notation is explained in textbook on manifolds

Eric Gregor

?

Mariano Suárez-Alvarez

06:02

the best would be for you to read one :-)

Eric Gregor

i will, but would you mind just saying the name of that

Mariano Suárez-Alvarez

standard basis vector associated to the parametrization

or something like that

Eric Gregor

gross

it sounds like this is not an elegant construction

Dominic Michaelis

huhu

Eric Gregor

@MarianoSuárez-Alvarez, your answer looks funny to me. we have a parametrization $\gamma$, so we know what $[D\gamma]$ is. you can name them $\partial/\partial x_i$ if you want

Mariano Suárez-Alvarez

06:06

it is the standard construction

you are free to find my nottation funny

Eric Gregor

but it is explicit, given an explicit $\gamma$

Mariano Suárez-Alvarez

be prepared to laugh at every single book, though

Eric Gregor

so how does that help move to a specific volume form?

Mariano Suárez-Alvarez

i explained that above

Eric Gregor

no, that's not my point @MarianoSuárez-Alvarez

Mariano Suárez-Alvarez

06:08

I suggest you read the chapter on orientation on Lee's book on smooth manifolds

Eric Gregor

so the $\partial/\partial x_i$'s are not just being set equal to the derivatives?

ok, i will

i'd be interested in even the simplest example, btw, if you would indulge me. like getting an orientation form from the parametrization of the circle

$\theta\to (\sin \theta,\cos \theta)$

Mariano Suárez-Alvarez

I refer you to lee

this is very boring to explaineven in person

I spent last semester teaching it

I know, trust me

Eric Gregor

i trust you that it bores you

thanks, anyhow

you've been helpful

Mariano Suárez-Alvarez

in any case, the image of every parametrization has a canonicalorientation

which can be made explict exactly as I explained above

(in the form of a volume form, but then in any other form, because all the forms to give an orientation are equivalent, and it is easy to go from one to the other explicitly)

Eric Gregor

you don't happen to know the relevant page, do you?

i found a copy of the book

or section name, or whatever

skullpatrol

06:19

Have you tried the index?

Dominic Michaelis

gee, i really shouldn't study physics

Eric Gregor

of course, skullpatrol. but mariano didn't give me an easy thing to look up. all the usual suspects don't show it

skullpatrol

Oh, pardon me :-)

@MarianoSuárez-Alvarez Have you read a lot of Wittgenstein?

Mariano Suárez-Alvarez

not really

random pages from the tractatus

and soem other stuff

nothing systematic

skullpatrol

@MarianoSuárez-Alvarez One must accept the concept of "equality" as fundamental, at least in high school, no?

Eric Gregor

06:26

@MarianoSuárez-Alvarez, those are the partials. he calls them the derivations, but they act on a function f as the partials

Dominic Michaelis

gee once again we used that EVERY function is analytic

Mariano Suárez-Alvarez

"the partials" is a very informal name

he does not call them derivations

they are derivations

Eric Gregor

partial derivatives

Dominic Michaelis

What do you think if my prof use that every function is analytic may I use that every matrix commutes ?

Mariano Suárez-Alvarez

Lagrange operated under the assumption that every function is analytic

your prof may just as well

Eric Gregor

06:30

every function you care about is analytic or close to it

Dominic Michaelis

on the other hand every matrix i care about commutes (i only care about the identity and the null matrix)

Eric Gregor

the $\partial/\partial x_i$ are just coming from some local coordinate system. the parametrization gives you a local coordinate system.

man, i just want to sleep

skullpatrol

You can't always get what you want, but if you try sometime, you just might find, you get what you need :-)

Eric Gregor

might

in practice, no

skullpatrol

Ooh yaa...

Eric Gregor

06:37

i think people get so lost in abstractions sometimes they forget how to relate to the real world

Jonas Teuwen

Heh, the treasurer says 'good luck!' with a thing I added to our meeting agenda... 8-)))(((.

Eric Gregor

i know people who study very abstract probability who don't know how to do basic regressions

Jonas Teuwen

I don't.

Eric Gregor

it's shameful

Jonas Teuwen

I do know people that do very abstract probability theory, but can't be fucked to do regressions.

Yes, what kind of Mickey Mouse institutes are they at?

Chris's sister and pals

06:40

Hi

This problem didn't let me sleep well last night. When I fell asleep I had dreams with it.

skullpatrol

hi

Chris's sister and pals

$$\int_0^{\pi}\frac{x\sin x}{5-4\cos x } \ dx$$

It doesn't work to let $x=\pi-y$

Dominic Michaelis

what's the empty cartesian product ?

$$ [0,1] \times \prod_{i=1}^0 [0,1] $$ for example

Jonas Teuwen

Depends where you need it, sometimes the whole set.

You would get 'all sequences on an empty set to the whole space'.

Dominic Michaelis

07:08

It is so annoying that the theoretical physics prof can't handle linear algebra for dummies how shall i know if he can theoretical physics at all ?

skullpatrol

(removed)

Chris's sister and pals

@JonasTeuwen what would a mathematician try above?

Vrouvrou

hi

how are you ?

Chris's sister and pals

@Vrouvrou hi

@Vrouvrou I'm not just fine. The above integral gives me some headache.

Vrouvrou

me too i have 2 theorems which i did not understand the proof and i must find the Green's function of a third order BVP

-_-

Lord_Farin

07:48

A good morning (replace with applicable time of day) to all of you.

skullpatrol

Hi

Chris's sister and pals

@Lord_Farin hi. How are you? :-)

Lord_Farin

@Chris'ssisterandpals I haven't wasted all of my day (yet), so I'm quite fine atm.

Chris's sister and pals

That's good.

@Lord_Farin have you seen this? $$\int_0^{\pi}\frac{x\sin x}{5-4\cos x } \ dx$$

Lord_Farin

@Chris'ssisterandpals Hadn't before.

I'm currently trying to write a proposed comment template for this.

skullpatrol

08:03

Why?

bother

Lord_Farin

@skullpatrol Because people want to have it. It also allows me to channel my frustration.

Chris's sister and pals

Honestly, I wouldn't close/downvote any question. It's up to each user to decide if he wants or not to answer a question.

Jayesh Badwaik

@Chris'ssisterandpals Try integration by parts with $x$ as the first term and the rest of it as second.

Chris's sister and pals

@JayeshBadwaik this leads nowhere I think. You het some ugly logarithm.

skullpatrol

@Lord_Farin Ooh, so you want to waste more of your time on MetaDrama.SE :D

Chris's sister and pals

08:08

One may show effort or not, but to close a question just because of that is too much. In the end, you're not obliged to answer these questions, but if you like it you do it.

Lord_Farin

@Chris'ssisterandpals The other options seem to not have the desired effect. This one surely will.

In principle, I would agree but these questions overwhelm the well-phrased, well-thought-out and interesting ones.

Chris's sister and pals

@Lord_Farin and there are people that really have no idea about what to try. For some problems it's even hard to see a starting point.

skullpatrol

@JayeshBadwaik Hiyoooo! birthday boy, how are you?

Lord_Farin

@Chris'ssisterandpals Even if "showing your work" comes down to result in "I have worked on this for two hours but I can't even get started", that is an improvement over just posting the question. Namely, it shows that highbrow answers are likely not the way to go. It also shows persistence.

Jayesh Badwaik

@Chris'ssisterandpals Its not ugly. Its basically just integral of log(t)

Chris's sister and pals

08:12

@Lord_Farin yeah, but new users need some time to learn how to properly ask questions.

Jayesh Badwaik

@skullpatrol Thank You. :-) I am good.

Chris's sister and pals

@JayeshBadwaik it's $$\int_0^{\pi}\ \log(5-4\cos(x)) \ dx$$

Lord_Farin

@Chris'ssisterandpals My view on this is contained in this comment (on a different thread).

Chris's sister and pals

@Lord_Farin that could be a solution. I respect any point of view.

skullpatrol

@Lord_Farin If you have worked on a question for two hours and can't even get started; you need to reread the book...

Lord_Farin

08:15

@Chris'ssisterandpals I agree it's not optimal. But doing nothing is even less optimal.

@skullpatrol This probably useful tip wouldn't have come to mind if the question were just placed without context. This supports my point.

Chris's sister and pals

@skullpatrol you mean you looked at it for 2 hours ... :D I don't agree that a kid should spend 2 hours of his time on a single problem. Not even half an hour. If you do this every day you're simply ruined and depressed.

Jayesh Badwaik

@Chris'ssisterandpals I disagree about how much time should be spent on a problem.

Chris's sister and pals

@JayeshBadwaik I say that because in high school, for example, you don't learn mathematics only. I mean you have a lot of homeworks.

skullpatrol

@Lord_Farin Then the OP needs a reading lesson :D

Jayesh Badwaik

@Chris'ssisterandpals Hmm. I see.

Jonas Teuwen

08:20

@Chris'ssisterandpals I don't know? Have you tried asking one?

Chris's sister and pals

@JonasTeuwen $x=\pi-y$ seemed a good option, but it doesn't work. On the other hand, integration by parts leads nowhere.

sos440 has something somewhat similar here sos440.tistory.com/83

skullpatrol

@Chris'ssisterandpals I agree in high school Algebra they should teach reading skills that avoid such 2 hour wastes of time.

Chris's sister and pals

@skullpatrol I'm trying to say that it would be great if things were done much faster. On the other hand, the homework should be like a Putnam exam.

I mean the homework !shouldn't! be like a Putnam exam. :D

Our teacher used to give us very hard problems, like those you meet at Putnam contest or other math competitions.

I think he wouldn't be that proud of me to see that I fail to evaluate $\int_0^{\pi}\frac{x\sin x}{5-4\cos x } \ dx$ :-(

skullpatrol

@Chris'ssisterandpals Ok, "should not" makes more sense :D

genepeer

Anyone have a clue on this math.stackexchange.com/questions/371065/… ?

Lord_Farin

08:52

@Chris'ssisterandpals What about plugging in a geometric series with $\frac45 \cos x$ and doing a term-wise partial integration?

Chris's sister and pals

09:16

@Lord_Farin Back. Do you think this works? Let me ckeck it.

Lord_Farin

@Chris'ssisterandpals Mh. I get uglier stuff when integrating $\int_0^\pi \cos^n x \,\mathrm dx$ than I was expecting.

Viz $\dfrac{(-2)^n \pi ^2}{\Gamma\left(\frac{1}{2}-\frac{n}{2}\right)^2 \Gamma(1+n)}$.

Now this can be expanded using the values of the $\Gamma$ function at half-integers, but it isn't really nice.

Chris's sister and pals

I see.

blob

Hello, if i have a loaded die {1, 1, 2, 3, 4, 5} is the probability to get 1 2/6?

Charlie

@skull @Lord_F hello

Lord_Farin

@blob Presuming that you didn't alter the probabilities as well, you are correct.

@Charlie Hello.

Charlie

09:26

@Lord_Farin how are you feeling?

Lord_Farin

2 hours ago, by Lord_Farin

@Chris'ssisterandpals I haven't wasted all of my day (yet), so I'm quite fine atm.

Charlie

@Lord_Farin ah

skullpatrol

Hi @Charlie how are you?

Charlie

@skullpatrol same thing if always, and you?

skullpatrol

@Charlie Fine thanks.

Charlie

09:30

Of

Jayesh Badwaik

@Charlie Thank You. :-)

Charlie

@JayeshBadwaik Happy Birthday, again :D

@skullpatrol you got the idea

skullpatrol

@Charlie Ok I won't do it again :(

Jonas Teuwen

09:46

Where is the rest of my head?

Charlie

@skullpatrol it's okay, skull , thanks

Jonas Teuwen

(Other ones are of the board of another university's PhD association)

Charlie

It's not even 7h... So....

@JonasTeuwen hehehehe

Jonas Teuwen

My pie hole is still there.

Chris's sister and pals

@JonasTeuwen nice girl :D

Charlie

09:49

@JonasTeuwen I like your shirts, Jonas

Jonas Teuwen

@Charlie Thanks.

I removed some pens as I need less in a party.

Charlie

@JonasTeuwen I saw :)

Jayesh Badwaik

@JonasTeuwen Cool pic.

Charlie

@JayeshBadwaik if I were in the pic only my head would appear

Jayesh Badwaik

@Charlie HAHAHAHA.

Jonas Teuwen

10:03

Half of it.

Chris's sister and pals

@Charlie I think in my case only my forehead would appear. :-)

Charlie

@JonasTeuwen haha yes!

Charlie

10:18

@bugbusters hi Buggy

Bugbusters

@Charlie: Hey Charly!

I have created a new package pst-sex here: tex.stackexchange.com/a/110627/19356

skullpatrol

@Bugbusters Hi Honey!!!

Charlie

@Bugbusters cool!

Bugbusters

@Charlie Thank you honey!

@skullpatrol I am fine honey!

skullpatrol

@Bugbusters Are you anticipating my next question honey?

Charlie

10:23

:)

skullpatrol

(removed)

Bugbusters

@skullpatrol Math question honey?

This message was posted 3 years ago.

Charlie

Who's the apple?

skullpatrol

@Bugbusters No, I said "Hi Honey!!!" and you said "I'm fine honey!" :P

Bugbusters

@skullpatrol Oh I see. :-) How are you?

skullpatrol

10:27

@Bugbusters Fine, thanks for asking honey :D

Bugbusters

@skullpatrol Where is JL?

skullpatrol

@Bugbusters Is a Bugbuster like a Ghostbuster?

Bugbusters

@skullpatrol Yes. It is equivalent.

Vrouvrou

hi, please help me for this question

if

w >0 on [q,1) and non decressing

what i can say about $\int_q^1 w(s) (2as+b) ds=0$

i must find a and b

skullpatrol

@Bugbusters Aren't bugbusters called exterminators?

Bugbusters

10:33

@skullpatrol I don't know this. :D

Charlie

@skull I think bugbusters as in computer bugs

Vrouvrou

????

skullpatrol

These are not program bugs in this avatar.

Git Gud

Hey oh.

skullpatrol

Hey

Lord_Farin

10:47

@GitGud Hello @GitGud.

skullpatrol

:-)

Charlie

Hi @git

Vrouvrou

someone can help me ?

skullpatrol

@Vrouvrou Have you posted on main?

Vrouvrou

no

skullpatrol

11:02

@Vrouvrou Provide as much context as you can, where here context also includes what you have tried so far :-)

Charlie

@skull what do you think : we're here for a long time, maybe a good time, so try to have a good time, sun will shine some day

skullpatrol

@Charlie What are you asking for?

Git Gud

@skullpatrol I'd guess she writting a poem or something and she's asking for your opinion. Say you like it to increase your chances of success.

skullpatrol

@GitGud It is actually a play on the lyrics of a song :-)

Charlie

@skullpatrol that's how I see things

skullpatrol

11:15

@Charlie Everybody see's "time" in their own way...

Charlie

Yes

skullpatrol

good time, not a long time, etc, etc...

I prefer to dig in my heels and raise a little hell of MY OWN

Lord_Farin

@skullpatrol After 20 secs I was tricked into believing that the lyrics comprised only one line. I am pleasantly surprised.

Eric

@Lord_Farin Hey

Lord_Farin

@Eric Hello @Eric.

Eric

11:26

@Lord_Farin I ended up getting an 81 on my algebra final

And ended up with a B in the calls

which is great considering I was close to a C

Lord_Farin

@Eric Satisfied?

Eric

Yes!

Lord_Farin

Ah, great!

Vrouvrou

@skullpatrol this a part of a proof and i have w>0 on [q,1) and nondecreasing i want to find a and b such that \int_q^1 w(s) (2as+b) ds =0

Eric

I was really scared of that course. It was harder for me than analysis

Lord_Farin

11:28

@Eric Different trains of thought :)

Eric

@Lord_Farin Yeah

Also i had way to little time. This semester. I am sure I could have gotten an A if I had more time.

but, thats life.

skullpatrol

@Lord_Farin Most of what they call "classic rock" is that way :D

Lord_Farin

There's always the trade-off between quality and quantity.

@skullpatrol I know. Classic rock is awesome!

Charlie

@Lord_Farin what do you like to listen?

Lord_Farin

@Charlie I'll look up some YT stuff for you.

skullpatrol

11:38

@Lord_Farin There must be a trade-off because of limited resources.

Charlie

@Lord_Farin :)

Lord_Farin

@Charlie E.g. this, this, this, this and this.

(In no particular order.)

@Charlie Does that suffice for an impression?

(Although I realise that there's easily over 30 minutes of music behind those five links.)

Charlie

@Lord_Farin interesting

@Lord_Farin I'll listen carefully to each one.of them, later, because I have to go now :) see you later

Lord_Farin

@Charlie Bye!

Charlie

see you @skull :)

skullpatrol

11:52

later

Charlie

@skullpatrol bye bye

skullpatrol

@Charlie }B-)

Charlie

Hahahaha

skullpatrol

:D :D :D :D

shobon

12:08

hello

skullpatrol

hello

Chewbacca.

Lord_Farin

;O

@skull, could you do me a favour?

skullpatrol

12:24

@Lord_Farin Hiyoooo! what?

Lord_Farin

Just say something along the lines of "LF, get off your lazy ass and do something for a change!"

skullpatrol

@Lord_Farin I tried earlier but you wouldn't listen.

Lord_Farin

@skullpatrol Try again.

skullpatrol

@Lord_Farin Do you remember what I said earlier?

Lord_Farin

@skullpatrol Well, no. shame

skullpatrol

12:30

4 hours ago, by skullpatrol

@Lord_Farin Ooh, so you want to waste more of your time on MetaDrama.SE :D

So get up off your lazy ass and stop wasting your time
and do something productive for a change!

2

Lord_Farin

@skullpatrol Thank you. I will be back later today.

skullpatrol

@Lord_Farin How was that?

Lord_Farin

@skullpatrol Yes, that's excellent :)

skullpatrol

Mission accomplished :D

Lord_Farin

@skull Just throw it at me again if I'm back within 3 hours.

Thanks again, bye.

computer.nerd

12:37

I'm wondering if it's possible to learn basic combinatorics and real analysis in less than 5 days.

skullpatrol

later

computer.nerd

?

Dominic Michaelis

basic combinatorics yes real analysis absolutetly no

computer.nerd

Basic Combinatorics: Counting, permutation, combinations, binomial theorem, partitions, cycles in permutations, generating functions, graph theory, trees

so you think it's no problem to learn all these in 5 days?

skullpatrol

How strong is your math background?

computer.nerd

12:39

Well, everything up to basic number theory

calc 1,2

and few math competitions

skullpatrol

Straight A's?

computer.nerd

almost

Tobias Kildetoft

Depends on what level of understanding you are looking for in those topics

Dominic Michaelis

@skullpatrol i know straight A's which are totally retarted ...

computer.nerd

just to cope an exam

lmao

Dominic Michaelis

12:41

@computer.nerd to pass an exam absolutly no problem both

Tobias Kildetoft

there is no way to get a proper understanding of even a small part of either of those topics in 5 days

computer.nerd

both combinatorics and analysis?

@dominic

skullpatrol

My next question was if you have taken enriched or honors math?

computer.nerd

yes

Dominic Michaelis

@computer.nerd with the exams i saw thats no problem

computer.nerd

12:42

@Dominic but that means I will have to study straight for all 5 day right?

@dominic like I need to do well too ...

skullpatrol

I have to agree with Tobias, 5 days is not long enough.

Even for a straight A honors student.

herpderp

I think that really depends on how strong your math background is

skullpatrol

6 mins ago, by skullpatrol

How strong is your math background?

herpderp

Ops didn't see that

Dominic Michaelis

@computer.nerd that depends on how stupid the others are who make the exam

computer.nerd

12:46

he's a professor with respected reputation in the combinatorics field ...

shobon

@computer.nerd, why do you have 5 days

computer.nerd

Actually 4, my exam is on monday

user1

@computer.nerd Definitely not both (you have not given the topics to expect on a real analysis exam).

shobon

that doesnt answer my question

Dominic Michaelis

@computer.nerd no no i mean you won't be the only student which writes the exam ?

computer.nerd

12:48

@shobon I meant I have 5 days because my exam is on next Monday

shobon

what are you even talking about

you have questions about those topics on this site

user1

@computer.nerd So, let me get this straight, you have not encountered any real analysis/combinatorics, but you have an exam in 4/5 days?

shobon

I think hes just trolling

computer.nerd

@user1 Yes that's right

user1

lol

shobon

12:49

that's a blatant lie, look at his profile

computer.nerd

I meant I don't really understand the concepts

shobon

really

skullpatrol

:-)

computer.nerd

@skullpartol omg I'm being serious dude

shobon

lol

user1

12:50

@computer.nerd What the hell are you doing here? You should be studying.

computer.nerd

@user1 but I don't know if I can really make all these topics in 4 days

user1

@computer.nerd Well, try.

That much should be obvious...

skullpatrol

Can you live that long without sleep?

computer.nerd

@user1 well ... 4 hours sleep is all I need

@skullpartol probably 3

herpderp

@computer.nerd It's impossible drop the class

computer.nerd

12:53

@herpderp too late ...

skullpatrol

People literally spend years on each one of those topics.

herpderp

@skullpartol but it's just basic combinatorics right?

@computer.nerd wait what is this topic about?

let me read the top

computer.nerd

...

skullpatrol

@computer.nerd What level of textbook are you using?

computer.nerd

Introductory Combinatorics, by Brualdi

and for analysis,
Elementary Analysis: The Theory of Calculus by ross

not like the whole book ... just few chapters for combinatorics, and like 2/3 of a book for analysis

skullpatrol

12:57

Any lectures?

computer.nerd

Yes but the professor sucks at teaching

@skullpartol so you think it's do-able or not?

Tobias Kildetoft

@computer.nerd is this one course or two?

computer.nerd

two

Tobias Kildetoft

same lecturer?

computer.nerd

yes unfortunately

Transcript for

$Mathematics$ Mathematics