Mathematics

Mhm. Quite.

Kaj Hansen

Yes, I was absolutely wrong.

12:27 AM

No, ach, I should've done the question a lot earlier, but my brain's fried from revision. And I can't afford to waste more time on it.

But basically, what I think is, if Z is closed in X \times Y.

Can anyone tell me why -lnx < y implies x > -y ?

Then, well, I want to use X's compactness somehow, so I'm going to look for an open cover of it.

I know that the projection of an open set in the product topology is open.

wait, never mind.

Hmm.

Any ideas, guys?

@Newb - ln x <y implies ln x > -y.

@AlpArslan what's the question?

12:44 AM

So, if X and Y are topological spaces. X is compact. Let Z be closed in X x Y, with the product topology. Let f be projection onto Y. Show that f(Z) is closed.

@AlpArslan use the contains-its-limit-points definition of closed

How do you define limit points?

We're not in a metric space.

have you tried googling limit point?

Hmm. Ach.

consider a more fundamental exercise proving the limit-point definition is equivalent to the complement-of-an-open-set definition

12:52 AM

Fair.

Will do.

Is there not a direct way?

iunno

just the first thing that came to mind that worked

Considering points in the complement, finding products of open sets around them, projecting these down and finding a cover of some sort?

That's what I'd try intuitively.

1:41 AM

Hey, I'm working through a proof about the log uniform distribution

I'm puzzled by a particular detail

The proof can be found at mathforum.org/library/drmath/view/70362.html

I'm curious about the "Now differentiate both sides with respect to y." step

it is not obvious to me that d/dy 1- F_X(e^-y) = f_X[e(-y)]e(-y)

Hello friends. :)

happy retirement, @AlexW :)

Thank you, @Ted! :) Let's hope it's not this early yet...

Huh? :D

Haha, that is, my retirement from any job, as opposed to just this one. ;)

1:49 AM

Oh, you'll have many decades of work ...

Haha, that's my hope! How has your evening been?

Lazy.

Hey guys, do you think one of you could explain to me a step in a proof that I'm uncertain about?

That's not so bad, @Ted. I'm looking forward to a (somewhat) lazy weekend before rolling up my sleeves again.

If it's what you asked above, @Newb, it's just chain rule.

1:52 AM

I know it's an application of the chain rule

So where are you stuck?

but what's special is that it implies

31415926

Why doesn't the differential of the volume of a cube equal it's area? Is it because I should express the cube in terms of it's "radius", not it's "diameter"?

Hiya all.

Correct, @31415926.

heya @nsanger !

1:52 AM

d/dy -F_X = f_X

note the d/dy

no, @Newb: d/dy F_X(y) = f_X(y).

oooh

or d/du F_X(u) = f_X(u)

yes, of course.

thanks! that's clear now.

Glad to be of service.

31415926

1:53 AM

hehe

BTW, @31415926, that very same question bothered me many years ago.

I (used to) make a point to discuss it when I (used to) teach calculus. :P

You're not teaching it anymore?

nope, @nsanger ... Presumably, I've taught my last class and given my last final.

How does it feel @Ted? Did the diff geo students come out alright?

Oh, they finally fired you, huh :D?

1:56 AM

no, @AlexW, it came out pretty disappointing. Out of 21, 5 didn't pass.

Yup, @nsanger.

Oh jeez. That's no good. :(

But most of them made very little effort. It seems to me that when homework counts 40% of the grade, you put 200% effort into getting a high homework score ... not to mention my 8 office hours a week.

They finally realized how incompetent I've been, @nsanger.

Well that's silly. What is homework for but good practice to master material?

Well, especially when I told them the required problem each week was likely to appear on tests/final.

Four of the final exam problems were among those problems.

Besides, working hard on the homework and then slacking off for the test feels like running a mile and stopping short 100m from the finish line.

1:58 AM

What year were most of the people in the class?

Wow, that's a real shame.

One high school junior, a few sophomores, a bunch of juniors, a few seniors, three grad students.

BTW, the high school junior had the second highest score on the final.

Without even coming to the review session.

Damn, that makes me feel bad!

I'm done in just a few weeks.

Still waiting on taking diff geo....

LOL, congrats, @nsanger.

Good for that kid, though.

1:59 AM

Wow. That must be one talented high schooler.

You can read my notes any time you want, @nsanger, after you learn multivariable and linear algebra.

I'm not sure he's even that much into math, @AlexW, but ...

Anyhow, see you all a bit later.

Hehe, I met someone this summer who helped a few professors write a textbook on real analysis his freshman year of high school.

That's crazy!

Take care, @Ted :)

Later @Ted.

Yeah, he took graduate algebraic geometry at Harvard his freshman year.

Whatever :/

ᴇʏᴇs

There's a chem major in my real analysis class and today we were discussing Lesbesgue measure and he was very knowledgeable in the subject

Clarinetist

2:03 AM

Hello Math SErs

Two things:

1) I got accepted to a top-20 M.S. stats program. Excited!

2) I got an interview with Mayo Clinic today and am HOPING on an offer.

ᴇʏᴇs

Congrats @Clarinetist

pjs36

Good for you on both counts!

ᴇʏᴇs

Mayo Clinic is that self-diagnosis website I always see on Google search results when I look up symptoms that I have

Clarinetist

And if 2 doesn't work out, I have another offer waiting for me :)

user147690

@Clarinetist Awesome man