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bio website math.brown.edu/~lubinj
location Minnesota
age 77
visits member for 2 years, 6 months
seen 36 mins ago

Aged mathematician


Apr
15
comment Finding the value of trigonometric functions
The important thing, beyond @Seth’s suggestion, is to remember that in view of the periodicity of $\tan$ and $cos$, you can add or subtract multiples of $\pi$ from the argument of $\tan$ without changing the value, similarly, you can add or subtract multiples of $2\pi$ from the argument of $\cos$.
Apr
15
comment Is the reasoning/algebra for my proof correct? (musical tuning theory proof)
That would have been my proof, but you got there first! (I would have pointed out that @SanathDevalpurkar’s proof was perfectly fine, but that this argument is much more basic.)
Apr
15
comment how to find congruence class modulo a polynomial
The unspoken requirement is to represent each expression in $\alpha$ as a linear combination of $1$ and $\alpha$, via Euclidean division. The standard, mindless, way to find the inverse of $2\alpha+1$ would be to work through the Euclidean Algorithm for gcd. In a case like this, it’s far easier to write down the successive powers of $\alpha$ (I’m assuming that there are $8$ distinct ones here), and pick out the exponent for $\alpha+1$, and then you know the reciprocal of $\alpha+1$, presto pronto.
Apr
15
comment Characterizing the Galois group using permutations of roots
I think that for this, one must be very careful with quantifications. I’d want to see a precise statement, with all quantifiers before the various clauses.
Apr
15
answered Characterizing the Galois group using permutations of roots
Apr
15
comment What does root of unity in $\mathbb{Z}_p$ look like?
Other than $1$ and $-1$, the roots of unity are not rational numbers. You can prove that.
Apr
15
comment In $Z/3Z[x]$ find the GCD of $x^5+2x^3+x^2+x+1$ and $x^4+2x^3+x+1$
Books are sometimes wrong. Your teachers are sometimes wrong. It’s an imperfect world, populated by imperfect human beings.
Apr
14
revised $2$-adic inverse of $3$
Expanded considerably on my answewr, explaining a technique for $p$-adic hand computation.
Apr
14
answered $2$-adic inverse of $3$
Apr
14
comment Philosophical question in real analysis
Yes. It’s not the compactness of the interval that’s important, but the fact that it’s a connected set with more than one point.
Apr
14
comment Criterion that $R[\sqrt{D}]$ be a Dedekind ring.
Sorry, sorry, sorry, I meant to say $D\equiv1\pmod4$. And as all too often happens, I managed to skip over your essential hypothesis that $2$ should be a unit. My deepest apologies.
Apr
13
comment Criterion that $R[\sqrt{D}]$ be a Dedekind ring.
I suppose you mean that $D$ is not divisible by the square of a prime idea of $R$. The test cases are $\mathbb Z[\sqrt D\>]$ with $D\equiv3\pmod4$. Have you examined these?
Apr
13
comment Maximal Ideal of $\mathbb{Z}[i]$
And you may find it helpful to use the Euclidean Division that you have in $\mathbb Z[i]$.
Apr
13
answered What does root of unity in $\mathbb{Z}_p$ look like?
Apr
13
comment The number of rational solutions to the cubic analogue of Pell's equation
Well, I was supposing that the first two you found would span a rank-two free-abelian group ($\mathbb Z$-module), and that the third would be dependent on those (with respect to multiplication, of course!). I didn’t check my guess out, though.
Apr
11
comment Degree of closure of $\mathbb{Q}_p$
You might as well make things easier for yourself by looking not at all $p^{1/n}$ but at a subset: all $p^{1/2^m}$. The corresponding fields clearly form a totally ordered chain, and since $[\mathbb Q_p(p^{1/2^m})\colon\mathbb Q_p]=2^m$, you’re home free.
Apr
11
answered Is convex hull of a finite set of points in $\mathbb R^2$ closed?
Apr
11
comment Is convex hull of a finite set of points in $\mathbb R^2$ closed?
What have you tried? How have you used the description of the convex hull, or maybe of an arbitrary element of the hull?
Apr
11
answered The number of rational solutions to the cubic analogue of Pell's equation
Apr
11
comment What are elements of a field called
In my opinion, this is very sloppy talk. Please remember, this book was written by The Great Serge Lang, but he was still an ordinary fallible human being, not an infallible deity. There are situations where the constant-field (“scalar-field”) of a vector space does not consist of numbers at all. The moral? Don’t spend any more time worrying about the issue.