12:24 AM
I have only read one textbook cover to cover.

12:46 AM
i faintly remember finishing my highschool textbooks. what a great feeling tossing those books lol

easily the worst thing about my hs was our inability to toss those books. that would have felt great

why couldn't you? @leslietownes

my daughter's watching a documentary about polar bears and just said "maybe we can go to the arctic someday and see the polar bears." pretty sure there aren't gonna be any.
well technically i could have, but then i'd have had to pay for the book. which would be worse than the pleasure i'd get from destroying it.

lol i mean if you're quick im guessing they still do expeditions

she can see the last one, haha
there's a polar bear at the san diego zoo, she can see that one

12:55 AM

one kinda fun thing about our school re-using the same books forever is that sometimes you'd see the name of someone you knew as a previous user of your book. my sister and i used the same 8th grade science book.

they keep a san diego one on a pretty regulated diet with a lot of vegetables so it doesn't build up the fat/fur that it would need in the arctic but would render it miserable in san diego.

my school/country was going through a change in the language used to teach science

it seems like a happy bear

12:57 AM
so my sister learned words i never learned lol

i wonder how the books are now, at my high school. i hope they've moved on to newer books

What if we rewrite the books?

i bet they're using the same ones, haha. nothing has changed
our history book had stuff up through reagan's first term but the class never got past WW2

I wonder if I'll be in a history book one day
a high school history book

i'd personally hope not to make it into the history books
but you do you :)

1:11 AM
why wouldn't you?

people mostly get in there because of the bad stuff they did, i try to keep a low profile

gotcha

i have a relative who is in some history books and i remember reading them with trepidation
thankfully he did nothing to disgrace our name

You might still get thrown out of Wimbledon.

didn't wanna be there anyway. i've been thrown out of better places than wimbledon.

1:27 AM
describe your mathematical style in 3 words. I'll go first

my, mathematical, style

one-on-one in person discussion, curiosity, real world application

if that's 3 words then 1=2pi. Oh wait...

ill relax the conditions to merely 3 phrases
good one Leslie

7 hours later…
8:56 AM
hi, i wanted to ask what is the best method of approximating the principal branch lambert w for x < -e^-1 regarding the speed at which it converges to actual value

1 hour later…
10:41 AM
I wish there was a community where people point grammatical errors in your thesis.

should the second term $o(h)$ in the answer here math.stackexchange.com/questions/1409167/… read $o(\| h \|_{L^2})$, and if so why is is $\int \|\nabla h\|^2= o(\| h \|_{L^2})$

11:07 AM
No way it could be L2. Should be say H1, and they seem to be considering something like C1 plus sufficient decay for things to make sense

$L^2$ with enough regularity
say $W^{2,2}$

you can’t control gradient in L2 by L2 norm even if h is smooth

yes I meant the right space to use is $W^{2,2}$?

1 derivative is enough though

5 hours later…
4:03 PM
Good Wikipedia article:
The Gudermannian function relates a hyperbolic angle measure ψ {\textstyle \psi } to an associated circular angle measure ϕ {\textstyle \phi } . The circular angle measure is called the gudermannian of the hyperbolic rotation, and is denoted gd ⁡ ψ {\textstyle \operatorname {gd} \psi } . The Gudermannian function reveals a close relationship between the circular functions and hyperbolic functions. It was introduced in the 1760s by Johann Heinrich Lambert...
On the Gudermannian function, which relates the trig and hyperbolic functions to each other
If $\phi=\operatorname{gd}(\psi)$, then:$$\begin{array}{}\sin\phi=\tanh\psi&\csc\phi=\coth\psi\\ \cos\phi=\operatorname{sech}\psi&\sec\phi=\cosh\psi\\ \tan\phi=\sinh\psi&\cot\phi=\operatorname{csch}\psi\end{array}$$
It's defined by $\operatorname{gd}\psi=2\arctan(\tanh\frac12\psi)=\int_0^\psi\operatorname{sech}t~{\rm d}t$
It's inverse is $\operatorname{gd}^{-1}\phi=2\operatorname{artanh}(\tan\frac12\phi)=\int_0^\phi\sec t~{\rm d}t=\log(\sec x+\tan x)$
(Of course from that table you can also define $\operatorname{gd}\phi=\arcsin\tanh\psi$ etc)

4:49 PM
Hello, generally speaking, if we have a mtrix that is in diagonal form, is it true that charpol = minpol? i am thinking of examples like a matrix with zeroes everywhere but a_11 = 2 , a_22 =2 , a_33 = 1 , then the min pol is one degree less than charpol
so i guess its only true, if the matrix is orthogonally diagonalisiable, say every Eigenvalue is different from the other

it is true if and only if the eigenvalues are pairwise distinct
nothing to do with orthogonal diagonalizability

Is this article (investopedia.com/terms/c/cagr.asp) algebraically illiterate, or is there some ghastly convention in Finance where "$*\ 100$" means "multiply everything to the left by $100$% ignoring order of operations"?

5:05 PM
It looks pretty horrendous to me. $a-b\times c$ of course is equal to $(a-b)\times c$. Right. Fire them.

Right, I'd though the site was slightly more reputable than this.
And the article lists an author, peer reviewer, AND fact checker.

5:41 PM
Is there any accepted terminology for the operators arising from weak/variational formulations of PDE?

The simplest example being the dirichlet Laplacian extending to an operator $$\Delta \colon H^1_0 \rightarrow H^{-1}$$
Something like "variational extension"? I looked into some books but just can't find a commonly used term
(Negative Laplacian, not that important though)

1 hour later…
6:59 PM
user10478: there is a grand tradition of not reviewing or fact checking equations.
or symbolic formulas generally. once you enter 'math mode,' you exit the world of things that people pay attention to.

7:34 PM
there is a deeper issue there; maintaining consistency between something and a 'model' of something. (not to suggest that mathematics is just a model.)

8:16 PM
Pretty insane that we have to "remind" people in formulas what percent means, anyhow.

8:52 PM
hey guy any hints on how can i prove this $\lim _{n \rightarrow+\infty}\left(1+\frac{z}{n}\right)^{n}=\mathrm{e}^{z}$ using counting measure and measure theory in general?

how is $e^z$ defined?

As a power series

@AlekMurt use Lebesgue dominated convergence theorem then

that's what i think as well, but it confuses me that i have to use counting measure, how do i use that measure on this problem

9:11 PM
$$\sum_{n=1}^\infty a_n = \int a_n\mathrm{d}\mu(n)$$

srry but i dont get your hint, could u explain me a bit more

2 hours later…
10:59 PM
Suppose we have an $a\times b\times c$ cuboid, oriented so one vertex is lowest. Then the number of ways to stack cubes in it (following gravity) is$$\prod_{i=1}^a\prod_{j=1}^b\prod_{k=1}^c\frac{i+j+k-1}{i+k+j-2}.$$

11:21 PM
the k + j instead of j + k is killing me

11:48 PM
No idea how I didn't notice
Still true, at least

if/when you teach, do not do that to your students
or alternatively, do that to your students while cackling and burning sacrifices to satan