12,747 reputation
11433
bio website math.brown.edu/~lubinj
location Minnesota
age 78
visits member for 2 years, 10 months
seen 2 hours ago

Aged mathematician


1d
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.
Aug
11
comment Finding the matrix of a rotation.
Yeah, it’s associative, but not commutative! This is a real important fact about matrices.
Aug
11
answered Unsure about infinite continued fraction
Aug
11
answered Finding the matrix of a rotation.
Aug
10
comment Could one make a ring of matrices of uncountable size?
I always get confused here. You want your vectors to have only finitely many nonzero entries as well, don’t you?
Aug
10
comment Exponential function, multivariable calculus
Right. No calculus necessary in this case, since both the function and the domain are radially symmetric, the function in the exponent is decreasing along radii, and the exponential part is an increasing function.
Aug
10
comment Suppose that $\beta$ is a zero of $f(x)=x^4+x+1$ in some field extensions of $E$ of $Z_2$.Write $f(x)$ as a product of linear factors in $E[x]$
I like the Galois-theoretical treatment, as @JyrkiLahtonen has guided OP to, namely that the roots are $\beta^{2^m}$, $0\le m<4$. But your answer was really very efficient.
Aug
10
comment Complex Numbers - Finding Roots
I don’t understand. You’re taking an equation of form $T^2+2z+3=0$ and saying it’s quadratic in ?
Aug
9
comment If a function $f$ is decreasing on its domain then would its inverse be increasing or decreasing?
The issue has little to do with derivatives—your answer here is just what I would have said.
Aug
7
answered Eisenstein´s Irreducibility Criterion
Aug
6
comment Find an irreducible polynomial with zero $\cos(2\pi/7)$
Indeed, this is a computation that everyone should do. It’s most satisfying.
Aug
6
comment Minimal polynomial for $\zeta+\zeta^5$ for a primitive seventh root of unity $\zeta$
You’ve got a couple of typos in your expression for the $X^2$-term of $g$. I got $g(X)=1 - 3X + 2X^2 + X^3 + 4X^4 + 2X^5 + X^6$