14,557 reputation
11938
bio website math.brown.edu/~lubinj
location Minnesota
age 78
visits member for 3 years, 1 month
seen 20 hours ago

Aged mathematician


Nov
21
comment How do I get the expansion of $(2x-1)^{-1} $ to the $x^3$ term
@ClaudeLeibovici, I wish long division of power series was taught in all US schools…
Nov
21
comment Ratio of an isosceles triangle to its altitude is 3:4. find the measures of the angles
When you say, “ratio of an isosceles triangle to its altitude”, are you talking about the base of the triangle versus the altitude? If so, could you edit?
Nov
21
comment How to evaluate $(0.9)^4$ without calculator
Just a matter of terminology: one solves an equation, here you want to evaluate your expression.
Nov
20
comment Is the map, $ f:(0,1)⊂ \mathbb{R}$ → $(1,∞)⊂ \mathbb{R}$ : $x ↦ 1/x $continuous?
If there were a point of discontinuity, what would it be? And what is the inverse function of $f(x)=1/x$?
Nov
20
comment Can $\pi$ be a ratio of angles?
Any real number can be the ratio between two angles.
Nov
20
comment Is there a formula for calculating the area of 2d shapes on a sphere?
multiply by $r^2$
Nov
20
comment Is there a formula for calculating the area of 2d shapes on a sphere?
For a spherical triangle (bounded by arcs of great circles: these are the geodesics on the sphere), it’s easy, and has been known for centuries: the area is proportional to the “spherical excess”, the amount by which the sum of the angles exceeds a straight angle (of $180^\circ$). So, for a sphere of unit radius, if the sum of the angles is $S$ radians, the area is precisely $S-\pi$.
Nov
20
comment Fixed fields,cyclic groups and Galois theory
Much of this is covered in the Fundamental /theorem of Galois Theory, which you should look into. For your question on $\mathbb Z$, this group is not a Galois group as this is ordinarily defined. Galois groups are profinite: compact topological groups with a neighborhood basis of open subgroups.
Nov
19
answered $\sum_{\zeta^p=1}(\zeta-1)^n$
Nov
19
comment Polynominal odd function
What is $y$? If it’s a variable, I don’t see how $x-y$ can divide a polynomial without any $y$’s in it.
Nov
19
comment Questions about poles
This is my way of doing it, but it’s really “power-series division”, ’cause you write the terms in ascending order of degree rather than descending.
Nov
19
comment Questions about poles
Surely $g(z)=1/z$ has a pole of order one at the origin. So “our definition” is clearly wrong.
Nov
19
comment a question about integration $\int_{0}^{1} \int_{0}^{1} \sqrt{x dx - dx dy}$
Doesn’t look grammatical to me.
Nov
18
comment gcd of polynomials over Z_7
I was about to say the same thing as @Crostul, but in more words. Your error, if any, was to pay too much attention to the quotients. It’s just the remainders that count, here.
Nov
17
comment Implicit differentiation: $\ln(1+xy) = xy$
This is how I saw the problem, too.
Nov
17
answered Proving that the Gaussian integers have no zero divisors
Nov
15
comment Find all the values of $w$ ∈ C that satisfy the equation.
Yes I did. $a=1$, $b=-4i$, $c=-1$.
Nov
15
comment is $f(x)=x^4 +x^3 +x^2 +x +1$ irreducible in $R=(\mathbb Z/7\mathbb Z)[x]$?
This is kind of sketchy. At first I thought it was the way to go, now I’m not so sure.
Nov
15
answered Find all the values of $w$ ∈ C that satisfy the equation.
Nov
14
comment having trouble saying this in a rigorous way
One way is to go by contradiction. Suppose the negative of what you want to show, i.e. that $f(x)\ge0$ throughout some neighborhood of the form $[0,a\rangle$. Then the difference quotient is $f(x)/x$, quotient of a nonnegative by a positive, result being nonnegative. But nonnegative numbers can not have a negative limit $f'(0)$.