13,222 reputation
11533
bio website math.brown.edu/~lubinj
location Minnesota
age 78
visits member for 2 years, 11 months
seen 23 hours ago

Aged mathematician


Aug
25
comment Disproving an “almost true” trigonometric identity
@MarianoSuárez-Alvarez, thanks for that. I’ll look it up.
Aug
25
revised Disproving an “almost true” trigonometric identity
Gave an alternate, longer, less magical, proof.
Aug
25
comment Disproving an “almost true” trigonometric identity
The idea is that in addition to the field extension degree there’s something called the ramification index (or degree), locally at each prime of the extended field. It’s traditionally called $e$, and the property of the ram. index is that it’s multiplicative. Since this degree (above $17$ and above $37$) is $1$ for the extension $\mathbb Q(\sqrt2)\supset\mathbb Q$, the problems arise.
Aug
25
comment Disproving an “almost true” trigonometric identity
I’m looking for a more direct way of understanding the problem. Maybe by the end of the day today (140825)
Aug
25
revised Disproving an “almost true” trigonometric identity
deleted 14 characters in body
Aug
25
revised Disproving an “almost true” trigonometric identity
Correct two even more embarrassing careless errors
Aug
25
comment Disproving an “almost true” trigonometric identity
Will I ever get this right? Sorry!
Aug
24
revised Disproving an “almost true” trigonometric identity
corrected an embarrassing error of elementary-school arithmetic.
Aug
24
comment Disproving an “almost true” trigonometric identity
I never was so good at that kind of arithmetic, @WimC. Thanks!
Aug
24
answered Disproving an “almost true” trigonometric identity
Aug
24
comment Mathematical writing: why should we not use the phrase “we have that”?
We’ll just have to disagree on this.
Aug
21
comment Calculate the area of the ellipsoid that rotates around the $x$-axis
At first glance, this does not look like a valid method of calculating area. Are you sure it’s right?
Aug
19
comment Taylor series of an analytic function that maps the unit disk surjectively onto the upper half plane
To answer this, it helps to know what the automorphisms of the unit disk are.
Aug
18
comment Is there any way to express $\theta=c$ as some function of $r$?
The whole point is that $r$ is not a function of $\theta$.
Aug
18
comment Is there any way to express $\theta=c$ as some function of $r$?
Indeed, that was the reason for my comment.
Aug
18
comment Is there any way to express $\theta=c$ as some function of $r$?
Is there any way to express $x=c$ as a function of $y$?
Aug
17
comment Can the cube of 2 different complex numbers be the same?
@PeterWoolfitt, perhaps easier to write $\omega$ out as $-1/2 +\sqrt{-3}/2$
Aug
11
comment Compact closure in $C([0,2])$
The way you’ve stated your problem, your sets do not seem to be subsets of $[0,2]$ at all. Unless “$([0,2])$” means something I’m not expecting.
Aug
11
comment Laurent series for $1/(e^z-1)$
This is the answer I would have given, too, but I would have given a different method of finding the coefficients. You set up a long division problem à la high-school math, but run the terms in the opposite direction, that is, increasing degrees as you go left to right. You’re dividing the standard series for $e^x-1$ into $1$, and do your thing. Of course it gets messy after a while, but there are no undetermined coefficients.
Aug
11
comment $2 {\mathbb Z}$ is flat
The module $2\mathbb Z$ is free (basis is $\{2\}$) and thus projective, thus flat.