Mathematics - 2014-09-18 (page 4 of 5)

That info should totally be private. I know the US is ridiculous about privacy rights, but there's no way that should all be public to students, @Hippa.

Studentmath

9:16 PM

Remind me never to change my name to my real name in here.

Ted Shifrin

Some of us know, @Studentmath. Oh, you'll find my probability exam way too easy.

Studentmath

You french are crazy

Will Hunting

It's actually OK that people know your name, unless you killed someone.

Ted Shifrin

d'accord @Studentmath

Notice that I'm using my real name, for worse or for worse glares @Hippa

Studentmath

@Ted only with whom I trust not to share :P

Hippalectryon

9:17 PM

@TedShifrin Here's how it works : for each exam, each school, results are stored on the exam's website. It's not public. But the website's not that secure

Tadaam

Ted Shifrin

Well, @Hippa, act older than you are and don't betray people's private score information.

Anthony

@TedShifrin What's the product topology defined as? A set of projections?

That question made no sense.

Hippalectryon

@TedShifrin Why would anyone mind about his score -__- it's not as if I was saying where he lives

Ted Shifrin

NO, @Anthony. A basis is a product of open sets in the various spaces --- unless you're doing infinite products.

Studentmath

Prof. @Ted when are you doing your tests in the uni? Depends on you, or set dates by the uni?

Ted Shifrin

9:18 PM

@Hippa: Most students don't want everyone knowing their scores.

Hippalectryon

~~Wanna know ?~~

@TedShifrin Barely anyone will remember.

@TedShifrin Oh and

Ted Shifrin

Each professor gives tests according to his own schedule. We write our own exams, except perhaps in large calculus classes.

Hippalectryon

@TedShifrin None of you know the other's scores so you can't even compare it

Anthony

@TedShifrin I don't know what you mean, and also I think we talked about infinite sets.

Ted Shifrin

@Hippa: I'm just recommending you behave better.

Balarka Sen

9:19 PM

That's some logic, @Hippa

Ted Shifrin

It's bad when @Balarka is more mature than you, @Hippa :D

Hippalectryon

@TedShifrin I'll try :)

@TedShifrin :O That's frightening

Will Hunting

@Hippalectryon Are you in high school or university?

Ted Shifrin

Fais attention, @Hippa.

Balarka Sen

~~throws a table at @TedShifrin~~

Ted Shifrin

9:20 PM

is that your version of smack, @Balarka?

Studentmath

That's nice. It's set dates here, and they have to hand to exams the semester before - so sometimes they write the exams before they write the homeworks.

robjohn

@Chris'ssis You've escaped being downvoted until now?

Ted Shifrin

That's nuts, @Studentmath.

Balarka Sen

Yep, @TedShifrin. A worded version of Hippa emoticons.

Anthony

Oh, the elements of a product are indexed projections into the sets being multiplied.

Studentmath

9:20 PM

Yeah, they aren't too happy about it either. Trying to change it.

Will Hunting

@TedShifrin When are you retiring?

Hippalectryon

@WillHunting en.wikipedia.org/wiki/…

Ted Shifrin

You're still confused, @Anthony.

The plan is May 2015, Jasper.

Balarka Sen

@TedShifrin What will you do after that?

Stick to this chat 24/7?

Ted Shifrin

become a bum

Chris's sis

9:21 PM

@robjohn lol, no. I was downvoted once. :-) (maybe it's @Hippalectryon from a secret account)

Anthony

I am? I recall we talked about something being made from projection maps when we talked about infinite products.

Ted Shifrin

NO @Balarka

Balarka Sen

droops ears

Will Hunting

@TedShifrin You can spend all your time on MSE after that.

robjohn

@Chris'ssis Ah... I thought you were just downvoted.

Hippalectryon

9:21 PM

@Chris'ssis My only other account is dead

Ted Shifrin

Sure, the projection maps $\pi_\alpha\colon\prod X_\beta \to X_\alpha$ are all continuous.

Chris's sis

@robjohn lol, no. Do you think my question is wrongly posed?

Ted Shifrin

You understand what the product space is, @Anthony?

robjohn

@Chris'ssis which question?

Chris's sis

3

Q: Closed form of $\sum_{n=1}^{\infty} \frac{J_0(2n)}{n^2}$

I'm new in the area of the series involving Bessel function of the first kind. What are the usual tools you would recommend me for computing such a series? Thanks. $$\sum_{n=1}^{\infty} \frac{J_0(2n)}{n^2}$$

@robjohn The one above. I'm really new in that area of Bessel functions.

Balarka Sen

9:23 PM

@TedShifrin I have searched for references of the group theoretic form of galois theory I have dug up, but there weren't any.

Anthony

When I think product space, I just think of like $\mathbb{R^2}$ @TedShifrin. I mean, ordered tuplets, but not necessarily ordered?

Ted Shifrin

Well, you can think of them as ordered. When you have an uncountable product, this gets a bit crazy, but don't obsess over that. So a point $x=(x_\alpha)$ has a coordinate for each of the $\alpha$ indexing the product.

Anthony

Yeah.

Sab ಠ_ಠ

Hallo everybody :D

Balarka Sen

Haven't seen Mike for some days.

Ice Boy

9:29 PM

hi

Balarka Sen

Preparing for his quals, I guess?

Ted Shifrin

salut, @Sab

Alizter

gee chemistry.se is lifeless

Sab ಠ_ಠ

Salut, @Ted :)

robjohn

@Chris'ssis are they defined by $$J_\alpha(x) = \sum_{m=0}^\infty \frac{(-1)^m}{m!\Gamma(m+\alpha+1)} \left(\frac x2\right)^{2m+\alpha}$$

Anthony

9:30 PM

@TedShifrin But so you said "a basis is a product of open sets in the various spaces --- unless you're doing infinite products."

robjohn

@Chris'ssis where $\alpha=0$

Anthony

What is it for infinite products?

Ted Shifrin

@Sab, let me know when I should send you my second-semester Spivak exams :D

Sab ಠ_ಠ

:O

Send them all. :D

Ted Shifrin

@Anthony: In all but finitely many slots, you must take the entire space.

Chris's sis

9:30 PM

@robjohn I was looking at that right now. Let me check that.

Sab ಠ_ಠ

My finals are in 36 days exactly

and I got a test in 12 days

Ted Shifrin

In second calculus, @Sab? What are you doing in it now?

Sab ಠ_ಠ

we finished D.Es

Complex

Taylor series

Alizter

@Chris'ssis how to find $\displaystyle \int^{1/e}_0x^x\mathrm dx?$

Sab ಠ_ಠ

we are now doing vectors

Alizter

9:31 PM

is it better than sophomore?

Sab ಠ_ಠ

and there will be some linear algebra as well.

Ted Shifrin

oh, rather different from our course. I do several days of simple differential equations. Vectors are not in our course.

Balarka Sen

It presumably doesn't have a closed form.

Anthony

@TedShifrin I don't follow. sigh I thought we defined the elements of a product, which I'm guessing is an element of the product space, as being projection operators, indexed by from indexing set, mapping from that index into one of the sets making up the product.

Ted Shifrin

No, no, @Anthony, you're confusing elements and maps.

Sab ಠ_ಠ

9:32 PM

vectors are quite easy when you grasp them.

just need to be able to visualize what's happening and it's all good :)

Balarka Sen

Vector analysis is fun.

Alizter

i agree

Sab ಠ_ಠ

my problem is the basics

Chris's sis

@Alizter How could I know that? hmmm, no idea

Balarka Sen

It takes some of that to cope up with complex analysis, actually.

Sab ಠ_ಠ

9:33 PM

I need to get my concepts right

robjohn

@Hippalectryon: If the downvoter doesn't remove their downvote, I may get to the rep 123456

Ted Shifrin

A typical basis element for the product topology is of the form $$\pi_{\alpha_1}^{-1}(U_{\alpha_1})\cap\dots \cap \pi_{\alpha_k}^{-1}(U_{\alpha_k})$$ for some choice of $k$ and $\alpha_1,\dots,\alpha_k$, and, of course, of respective open sets.

Sab ಠ_ಠ

and be able to put my derivatives, integrals into practice

if I get these 2 right I'm all set

:)

Ted Shifrin

I love vector stuff, but that's my multivariable math class (linear algebra + multivariable, done right) :D

Sab ಠ_ಠ

Anyone read What is Mathematics (Courant)?

Balarka Sen

9:34 PM

@TedShifrin polynomial algebras. polynomial algebras everywhere.

Sab ಠ_ಠ

@Ted this will be second year :

Ice Boy

@robjohn that is a 6 figure income if I've ever seen one :D

Balarka Sen

commutative algebra is addictive.

@Sabಠ_ಠ yep

Sab ಠ_ಠ

When you mention Done Right, it's like Axler Linear Algebra Done right :P

Balarka Sen

Courant-Robbins.

Ted Shifrin

9:35 PM

@Sab, did you do applications of integrals (volumes, work, surface area, etc.) ? And methods of integration? Integration by parts, trig substitution, etc.

Sab ಠ_ಠ

@BalarkaSen what's it about? I read it's a really good book

Ted Shifrin

no, no, not like Axler at all ... I don't like his approach except for advanced math majors.

Sab ಠ_ಠ

@Ted Yep all of them.

Will Hunting

@Sabಠ_ಠ There is a book called Linear Algebra Done Wrong.

Balarka Sen

@Sabಠ_ಠ it's a survey of modern and classical mathematics

very cool book

Anthony

9:35 PM

@TedShifrin But I thought that's what I was told. :(

Sab ಠ_ಠ

Cool, I'll get it then :)

Ted Shifrin

What textbook are you using, @Anthony?

Sab ಠ_ಠ

There is one called Linear Algebra by Hoffman

Anthony

No textbook... :(

Sab ಠ_ಠ

I got the book for 2$ in my country :D I'm sure it will be useful next year

Ted Shifrin

9:36 PM

Hoffman/Kunze ... It's very advanced, @Sab.

Will Hunting

I like Petersen's Linear Algebra.

Ted Shifrin

Great @Anthony.

Sab ಠ_ಠ

@Ted it is I barely understand stuff in that. But some stuff make sense.

Ted Shifrin

You should look at a standard text, like Munkres.

Anthony

Mmkay.

Balarka Sen

9:36 PM

you like all the hipster books, @Will

Will Hunting

@BalarkaSen It is a very new and awesome book.

Ted Shifrin

What I wrote above is the definition of the basis elements for the product topology, @Anthony. Trust me.

Sab ಠ_ಠ

I like hard books. They make me sweat but in the end I'm sure I know more than what I was looking for. :)

Balarka Sen

that's what i meant by hipster @Will

Will Hunting

@Anthony Munkres is terrible. You should read Bredon's Topology and Geometry, lol.

Anthony

9:37 PM

No, I trust you. I just don't know what I was told.

Balarka Sen

@Will Prepare for a smack

Ted Shifrin

Jasper: Please refrain from saying books that some of us respect deeply are terrible.

2

You may say that you don't like them or that you are unable to learn from them, but they may still be excellent books.

Will Hunting

That is what terrible means, ain't it?

Ted Shifrin

No, you're making a universal judgment.

Ice Boy

no

Balarka Sen

9:39 PM

i don't believe so, no

Ted Shifrin

If you say my books are terrible, I might not argue.

Will Hunting

OK OK, all of you win.

Ice Boy

terrible means extremely bad

Sab ಠ_ಠ

Given 2 sets X and Y, a function is a correspondence which associates to each element of X one and only 1 element of set Y.

Now let's say 1 element of set X is not associated to anything in Y, is it still a function?

Anthony

@TedShifrin I was told that the elements of this product (this meaning the product of $(X_n,T_n)$) are functions from the index set into the union of the $X_n$'s, such that $x(n) \in X_n \subseteq \cup X_n$.

I think.

Balarka Sen

9:40 PM

nothing about winning @Will. you can prefer your Cohn over Artin, but Artin is a universally accepted and respected book

Will Hunting

@BalarkaSen How did you know my favourite is Cohn?

Ice Boy

extremely or distressingly bad or serious.
"a terrible crime"
synonyms: dreadful, awful, appalling, horrific, horrifying, horrible, horrendous, atrocious, abominable, deplorable, egregious, abhorrent, frightful, shocking, hideous, ghastly, grim, dire, unspeakable, gruesome, monstrous, sickening, heinous, vile; More
antonyms: minor, negligible, slight, brilliant, excellent
extremely unpleasant or disagreeable.
"the weather was terrible"
informal
used to emphasize the extent of something unpleasant or bad.

Balarka Sen

@Will you have posted your 12 holy books for like 100 times before?

Ted Shifrin

Yes, @Anthony. I suspect your teacher is over the heads of most of the students. That's a very formal description. Note that's different from what you were saying earlier. You only mentioned projection maps.

Will Hunting

@BalarkaSen I see. LOL

Chris's sis

9:42 PM

@robjohn can you tell me if someone is preparing an answer to my question?

(if it's not against the rules)

Ted Shifrin

shakes his head: Things are really bad here when @Balarka is, several times over, the voice of reason.

Will Hunting

@TedShifrin I thought he is 41 years old, not 14?

Ted Shifrin

perhaps so

Ice Boy

come'on he's a good hearted kid

Anthony

@TedShifrin It's 202a if that means anything, it's a grad course, but basically only undergrads take it. I'm actually confused on how what I said was different. By projection map I was thinking of the $x(n)$'s, is that wrong?

Ted Shifrin

9:43 PM

wow, @Anthony: When I was in grad school, it was mostly grad students, except for a handful of undergrads who planned to go get Ph.D.'s.

Balarka Sen

I am interchangeably 14 and 41, @Will.

Will Hunting

@BalarkaSen Maybe you are 55, lol.

Anthony

@TedShifrin lol really? I don't know if there are any grads in my class.

Sab ಠ_ಠ

@Balarka is 69.

Ted Shifrin

$x_\alpha = \pi_\alpha(x)$, @Anthony.

@Sab: I can't easily find your email address, so email me again if you want the exams.

Balarka Sen

9:45 PM

@TedShifrin Hmm, I think I missed something. Didn't get what you were trying to say in that statement.

Sab ಠ_ಠ

Okay @Ted :)

Anthony

The function $x_{\alpha}$ mapping from an index into a set is the same a projection that eats the function and... does what?

Ted Shifrin

No, I mean $x_\alpha$ as the $\alpha$-coordinate of the point $x$. You're writing that as $x(\alpha)$.

Sab ಠ_ಠ

I sent u a blank mail @Ted

Balarka Sen

not black mail, @Sabಠ_ಠ?

ducks and runs

Will Hunting

9:46 PM

So can I say a movie is terrible then?

Ice Boy

yes (ref. above def.)

Sab ಠ_ಠ

@BalarkaSen This is a fail pun.

Balarka Sen

droops ears

Anthony

Oh. So some point's $\alpha ^{th}$ element is a projection map that eats the point and gives the element.

Ted Shifrin

right.

Sab ಠ_ಠ

9:48 PM

@Ted Now that I'm realizing your papers are quite hard given the time frame :O

Anthony

Gracias.

Ted Shifrin

@Sab: Your course is just far removed from a Spivak sort of course, @Sab.

Sab ಠ_ಠ

Yeah.

Ted Shifrin

I don't have the email. Perhaps the blank thing got it tossed in the spam folder.

Sab ಠ_ಠ

prolly.

Will Hunting

9:49 PM

I am going to sleep. I will see all of you in my dreams.

Dream well, Jasper.

Sent a Hi

later

LOL @Sab

I'm lazy to type xD

9:49 PM

@TedShifrin If I want to go about find an embedding of a flat donut into $\mathbb{R^3}$, how do I even begin to think about it...

Ted Shifrin

You cannot do so, @Anthony. Gauss explained why.

Anthony

I probably said something wrong.

And what do you mean, Gauss?

Ted Shifrin

You need $\Bbb R^4$ to get a flat doughnut.

Sab ಠ_ಠ

@Ted I always had this question. How do you read a math textbook to get most out of it?

Balarka Sen

@TedShifrin That's news to me. Why though?

Chris's sis

9:50 PM

@robjohn I asked that because I was preparing to delete the question.

Anthony

I didn't mean a flat doughnut, I don't think.

Ted Shifrin

Because any compact surface in $\Bbb R^3$ must have a point where it's positively curved.

Anthony

Someone used that word, I assumed that's the word I wanted.

I was talking about the unit square, properly defined with equivalence classes such that it's a torus in $\mathbb{R^3}$.

robjohn

@Chris'ssis I would try to apply that formula with $\alpha=0$ and see if that leads anywhere

Ted Shifrin

Gauss understood that you can't have a faithful representation of a sphere on a plane, because a plane is flat and a sphere isn't. "Faithful" means distance-preserving.

Balarka Sen

9:52 PM

@Anthony You're identifying the sides of the parallelogram, then.

Chris's sis

@robjohn OK

Ted Shifrin

Oh, @Anthony. You know how to put the surface of a torus in $\Bbb R^3$.

Balarka Sen

@TedShifrin mhmm.

Anthony

I do?

Ted Shifrin