listening to the house of the rising sun...

make him redder than leslie's daughter's hair?

@robjohn Yeah, no problem pushing forward by diffeos, but with fibers you need invariance along the fiber

my offspring have no discernible visible irish traits...

But we require evidence @robjohn

@TedShifrin yeah, I needed a wake up call :-)

@TedShifrin Let's get some!

OK, let's!

@copper.hat my son is as pale skinned as I am. No red hair though. Of course, I'm only 1/4 Irish.

and it's Scots Irish, so maybe doesn't even count.

of course, the reality is that irish is quite the conglomeration of genes...

only one real redhead in our broad family tree, and he has greyed with age...

small country, travel is encouraged (island crazy), need that variance...

variance has something to do with mean squares...

groan

most squares?

square packing. That's about my speed.

my midterm is over!

Congrats :)

my daughter's collections are over

@copper.hat collections?

an term for some exams in oxford :-)

she was happy today, it was sunny outside, she misses the california sun

It's ok, @love_sodam. You'll have more to learn now!

@copper I almost swore like you here.

@TedShifrin :-). it would help to have some context (age, educational background, etc.) in order to let loose properly...

Well, this is a beginning exercise in virtually every differential geometry text. Surely the OP knows the basics of multivariable calculus (e.g., the product rule) and linear algebra. It's impossible to tell since there is 0 effort and the OP claims the other solutions go differently (they don't).

I don't think there's much chance of this OP being 7 or 12. But we'll find that many college-aged participants here don't actually understand fractions, either.

@TedShifrin Thank you for you consolation

You're welcome.

Morning MSE friends

hello

@TedShifrin Putting in effort to learn is hard. (I have put zero effort into trying to solve the OP's problem, but reading it the intuition that the surface must be a sphere popped into my mind...is that going in the right direction?)

I'm not sure what this means $f : U \to R, z = f(u, v)$ is $U$ a subset of real numbers?

I read that as the function $f$ maps $U$ to $R$, and $z$ is the output of $f$ with inputs $u$, and $v$

@TedShifrin i did lose it once with an OP interaction, thankfully Daniel F. was gracious and 'guided' me.

Andrew, an open subset of the plane.

Any tips to solve $\displaystyle \sum_{y=0}^{\lfloor k/2\rfloor}2^{(k-2y)z}\binom{k}{k-2y,y,y}$?

dare i ask what $\binom{a}{b,c,d}$ is.

that is the problem...

haha, i did that exercise in beginning differential geometry.

the thing about exercises is you have to do them to learn anything.

its the number of ways you can chose $b$ blue socks, $c$ cream socks and $d$ dead bolts from $k$ garage sales.

clearly i never learned any real maths

i can see from the starred comment that i am going to be one of those people that meta mse discusses in hushed tones after being unceremoniously dismissed.

he used to copy underage answers for himself.

he's just some guy running around in platform shoes and bell bottoms responsible for a number of bombings. let's ignore him.

his abbreviations were entirely inappropriate...

what are those flashing lights at my door???

are friends in the defense side of business?

@leslietownes multinomial coefficient: $\binom{k}{k-2y,y,y}=\frac{k!}{(k-2y)!\,y!\,y!}$

i only know lawyer who is involved in the criminal side of things and she has not taken the bar in ca.

i was afraid of that.

count on her. i don't handle criminal incidents, only civil stuff. i would answer your phone call but pretend not to know who you are.

i did have a notion, sorry. those pde days are gone, along with prof. quinlan the nose cone prof.

but the call would be coming from inside your house...