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14h
comment Method for proving polynomial inequalities
There is a fair bit of literature on efficient algorithms for deciding on positive definiteness, and semidefiniteness, for polynomials in $n$ variables. The old stuff in one variable was based on Sturm sequences.
14h
comment Method for proving polynomial inequalities
I was not attempting to answer the general question, except for in a highly indirect way advocating a "problem solving" approach in which we look at specific features of our object. From a logician's point of view, by a result of Tarski there is an algorithm for deciding whether a first order sentence in the usual language of ring theory is true in the reals.
15h
answered Method for proving polynomial inequalities
15h
revised if I have a Poisson random variable $X$, how do I find the constant 'k' that makes $P(X=k)$ be max?
added 123 characters in body
15h
answered if I have a Poisson random variable $X$, how do I find the constant 'k' that makes $P(X=k)$ be max?
15h
comment Countable infinite support of probabilistic measure
"Countable" technically includes finite, and for finite non-empty $E$ it is certainly possible. For countably infinite, it is not, because of countable additivity.
18h
comment How to prove the elementary inequality?
This is very much an answer, a very good answer.
21h
comment How to prove the elementary inequality?
@ClaudeLeibovici: Interesting. Maybe I can think of something simple. But certainly not now, it is the middle of the night. The question has received insufficient attention.
1d
comment Show that if for $a \in \mathbb{Q}$ with $0 = f(a) $ for a monic polynomial $f(x)\in \mathbb{Z}[x] $, then $a \in \mathbb{Z}$
You are welcome. As to the proof (of either) it has much the same flavour as the standard proof that $\sqrt{2}$ is irrational.
1d
comment Counting clarification
Yes, counting the complement is good.
1d
comment Show that if for $a \in \mathbb{Q}$ with $0 = f(a) $ for a monic polynomial $f(x)\in \mathbb{Z}[x] $, then $a \in \mathbb{Z}$
They say the same thing.
1d
comment Revolving an unknown equation around the x and y axes
Rotate about the $x$-axis. That should be routine. Rotate about the $y$-axis. I suggest using cylindrical shells. Set the answers equal, and solve for $a$.
1d
comment How do we find the minimal polynomial of $\alpha = a + b \sqrt{d}$ over $\mathbb{Q}$?
Yes, but OP also said "in the field" $\mathbb{Q}(\sqrt{d})$ and I interpreted "in" as meaning "over". Maybe mine was a feeble joke.
1d
comment How do we find the minimal polynomial of $\alpha = a + b \sqrt{d}$ over $\mathbb{Q}$?
$x-(a+b\sqrt{d})$.
1d
comment If $ x=\frac{\sin^3 t}{\sqrt{\cos 2t}}$ and $y = \frac{\cos^3 t}{\sqrt{\cos 2t}}\;,$ Then $\displaystyle \frac{dy}{dx}$ in terms of $t$
There is some simplification if you write $\cos 2t=2\cos^2 t-1$. And one needs to differentiate correctly.
1d
comment Why is $\frac{4k -1}{2} \equiv 1 \pmod 4$?
Stretching the congruence notation a bit, we could say when $\frac{2z}{\pi}\equiv 1 \pmod{4}$. But there is no point to putting it that way, it makes things look more mysterious than they are. Less mysteriously we could say when $2z=n\pi$, where $n$ is an integer congruent to $1$ modulo $4$.
1d
revised How to prove the elementary inequality?
added 68 characters in body
1d
revised How to prove the elementary inequality?
added 68 characters in body
1d
answered How to prove the elementary inequality?
1d
comment Determine whether the given pair of statements are contrary, contradictory, or neither.
My comment above said that the pair (1) are not contradictory. The pair (2) are contradictory, as are (3).