12,747 reputation
11433
bio website math.brown.edu/~lubinj
location Minnesota
age 78
visits member for 2 years, 10 months
seen 13 hours ago

Aged mathematician


Aug
3
awarded  Enlightened
Aug
3
comment On the conjugates of $1-e^{\frac{2\pi i}m}$
Maybe just a little clearer to consider the minimal polynomial of $\omega-1$. It should be manifest that $f(X)\in\mathbb Q[X]$ is irreducible if and only if $f(X+1)$ is irreducible.
Aug
3
awarded  Nice Answer
Aug
3
answered Generating all the Pythagorean triples by factorizing using complex numbers
Aug
3
answered Converting between exchange rates
Aug
1
comment Raising to the power over finite fields ??
A close examination of the process shows that the precise sequence of operations is determined by the binary expansion of $m$.
Aug
1
comment Is floor function an algebraic function?
No. if it were algebriac, then so would $\lfloor x\rfloor -x$ be algebraic, so a nonzero polynomial with infinitely many roots.
Jul
31
comment Examples of continuous non-transitive group actions
Similarly, the circle group acting on the plane. Or: the additive group $\mathbb R$ acting on the plane, by $a*(x,y)=(x+a,y)$
Jul
31
answered finding “exp(1)” in the p-adic numbers
Jul
29
comment For all $x$ in $[0,90]$ show that $\cos(\sin x ) >\sin(\cos x )$
You have to use the fact that the cosine is a decreasing function, and so reverses all inequalities.
Jul
29
comment For all $x$ in $[0,90]$ show that $\cos(\sin x ) >\sin(\cos x )$
Foolish me, I just realized that the same proof works for showing the inequality with radian measure. You start with $\sin(x)+\cos(x)\le\sqrt2 < 3/2<\pi/2$, then you write $\sin(x) < \pi/2 - \cos(x)$ and pull the same trick.
Jul
29
comment Can Hilbert spaces generalize non-Euclidean geometry by having the sum of the angles of a triangle not be equal to pi?
@RandomExcess, I’m with you. Isn’t a finite-dimensional subspace of a Hilbert space Euclidean?
Jul
29
answered For all $x$ in $[0,90]$ show that $\cos(\sin x ) >\sin(\cos x )$
Jul
28
comment For all $x$ in $[0,90]$ show that $\cos(\sin x ) >\sin(\cos x )$
Is that really composition of functions you’re talking about? If so, are you measuring angles in radians or degrees?
Jul
28
comment Dimension of $\dim_{\mathbb C}\mathbb C[X,Y]/I(Y^2-X^2,Y^2+X^2)$
You’re intersecting two sets in the plane, each of degree two. You should hope that there are four points of intersection, counting multiplicity, and that should be the same as the $\mathbb C$-dimension of your quotient ring.
Jul
28
comment How to find an angle (in degrees) in a right triangle, given its sides?
You got the first one right, it’s $.64350$ radians. But the formula for cosine is adjacent-over-hypotenuse. The opposite-over-adjacent is the tangent formula. Don’t forget that one radian is a big angle just less than sixty degrees.
Jul
27
comment Why is it that if I count years from 2011 to 2014 as intervals I get 3 years, but if I count each year separately I get 4 years?
Have you drawn the picture?
Jul
27
answered If $x^n = f(x)g(x)$ as complex polynomials, must $f,g$ be of the form $x^m$?
Jul
27
comment Isn't $x^2+1 $ irreducible in $\mathbb Z$, then why is $\langle x^2+1 \rangle$ not a maximal ideal in $\mathbb Z[x]?$
For the same reason that $(x)$ isn’t a maximal ideal.
Jul
26
comment Usage of capital and small letters
The important word here is “often”.