Lubin

5,946 reputation

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bio	website	math.brown.edu/~lubinj
	location	Minnesota
	age	76
visits	member for	1 year, 7 months
	seen	16 hours ago
stats	profile views	1,167

Aged mathematician

	5,946 reputation	bio	website	math.brown.edu/~lubinj	visits	member for	1 year, 7 months
620 badges		location	Minnesota		seen	16 hours ago

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Apr 12	comment	Show set of all differentiable functions $f\colon [0,1]\to\mathbb R$ is uncountable. It seems to me that the problem that was posed did not ask you to show that there were (continuum) many differentiable functions but just uncountably many. So showing that there are at least (continuum) many differentiable functions should do it.
Apr 12	answered	Finding root using Hensel's Lemma
Apr 12	comment	Finding root using Hensel's Lemma The version of Hensel that I learned is exactly the one you mention in your second paragraph, and I think people who are under the impression that Hensel is a root-finding theorem have been cheated.
Apr 12	answered	projective cubic curve to complex projectie space
Apr 12	answered	Finding $x$, where $\int_{r-x}^r \sqrt{r^2 - t^2} dt = A$
Apr 11	answered	Finding irreducible factors of a polynomial over $\mathbb{F}_3$
Apr 10	answered	Can a ring of positive characteristic have infinite number of elements?
Apr 8	comment	Finding the certain angle at the intersection point The most naive approach to this problem points out that a pair of intersecting lines divides the plane up into four V-shaped regions. Which one of these do you measure for its vertex angle?
Apr 8	answered	Complex numbers $z$ such that $\|z\|= 1$
Apr 8	comment	Does $\mathbb{F}_p((X))$ has only finitely many extension of a given degree? The local class field theory makes it clear that there are infinitely many cyclic extensions of degree $p$.
Apr 8	comment	Does $\mathbb{F}_p((X))$ has only finitely many extension of a given degree? Sorry, not right, 3.19 is for $\mathbb Q_p$ only.
Apr 7	comment	Lef $f \colon \mathbb{R}→ \mathbb{R}$ be a continuous function.Which of the following is always true? I would have used the sine function for my counterexample for 3 and 4.
Apr 4	comment	Number of irreducible polynomials of degree $3$ over $\mathbb{F}_3$ and $\mathbb{F}_5$. This is such a neat result, I always tried to slip it in when I was teaching abstract algebra.
Apr 4	comment	Number of irreducible polynomials of degree $3$ over $\mathbb{F}_3$ and $\mathbb{F}_5$. Because if $\alpha$, $\beta$, and $\gamma$ make up a set of conjugates, then $(x-\alpha)(x-\beta)(x-\gamma)$ is a polynomial with coeffs in $\mathbb F_p$, necessarily irreducible. So the set of all conj. triples can be looked at as the same as the set of monic irreds of deg $3$, and there are $N/3$ triples, if $N$ is the number of cubic irrationalities in the $\mathbb F(p^3)$
Apr 4	comment	How to prove $\left(\frac{a}{(a,b)}, \frac{b}{(a,b)}\right) = 1$? What do you know? An answer will depend on what stage you’re at in number theory.
Apr 4	answered	Number of irreducible polynomials of degree $3$ over $\mathbb{F}_3$ and $\mathbb{F}_5$.
Apr 4	comment	Number of irreducible polynomials of degree $3$ over $\mathbb{F}_3$ and $\mathbb{F}_5$. Uniqueness of factorization is always described or defined up to units of the ring in question. Here, the units of $k[x]$ are the constants of $k$. So God’s in his heaven, all’s right with the world.
Apr 4	comment	Number of irreducible polynomials of degree $3$ over $\mathbb{F}_3$ and $\mathbb{F}_5$. Ordinarily, people count monic polynomials. Is that what you have in mind?
Apr 2	comment	Fixed field of automorphisms determined by $t\mapsto at+b$. Another hint: often you can find the fixed field of a group by taking a nice thing upstairs and calculating its norm down to the fixed field. It’s surprising how often this works.
Apr 2	comment	Fixed field of automorphisms determined by $t\mapsto at+b$. Good, and the subgroup you found was normal, right? So the intermediate field you found is normal over the fixed field, of degree $p-1$, and you have the $p-1$-th roots of unity in all fields, so the intermediate field is gotten from the fixed field by adjoining a $p-1$-th root of something or other, right? This ought to lead to the fixed field itself...