12,747 reputation
11433
bio website math.brown.edu/~lubinj
location Minnesota
age 78
visits member for 2 years, 10 months
seen 3 hours ago

Aged mathematician


Jul
8
comment Find coefficients of a quadratic by tow points and mimimum value [Monbukagakusho exam 2010]
In this case, “the minimum value” is the $y$-coordinate of the lowest point on the graph.
Jul
8
comment Is $\mathbb{Z}[\sqrt{2} + \sqrt{3}]$ integrally closed?
The units of the full ring of integers of the field have the form $\{\pm1\}$ plus a free $\mathbb Z$-module of rank $3$. And we know, from the quadratic subfields, three independent units, namely $\sqrt2-1$, $2-\sqrt3$, and $5-2\sqrt6$. The group spanned by these three thus has to be of finite index in the full group of units, but I have no idea what that index is, nor how to find a genuine basis. Same goes for the non-integrally closed subring, but in spades.
Jul
7
comment How many (unordered) bases does $\Bbb F_q^n$ have as a vector space over $\Bbb F_q$?
This is precisely the proof I would have given. So I guess I have to say that it looks right to me.
Jul
7
comment Coefficient of x in the expansion of $(2x^2+(x-3))^8$
Certainly it’s the same as the coefficient of $x$ in $(x-3)^8$.
Jul
7
comment Is $\mathbb{Z}[\sqrt{2} + \sqrt{3}]$ integrally closed?
I didn’t say anything about units, but in view of the fact that the ring isn’t integrally closed, I for one find this question less interesting. Others will probably disagree.
Jul
7
answered Is $\mathbb{Z}[\sqrt{2} + \sqrt{3}]$ integrally closed?
Jul
7
comment Is $\mathbb{Z}[\sqrt{2} + \sqrt{3}]$ integrally closed?
It’s likely that OP is not a native speaker of English. We have to be more tolerant.
Jul
7
comment Determine whether the intersection of surfaces is a parabola
The question is whether a nonparabola can project orthogonally onto a parabola. Certainly an ellipse (or circle) can’t, because it is compact, and its image must be compact. So the question is whether a hyperbola can project to a parabola. Consider the minor axis, that’s the axis of symmetry between the two branches. It will project to a line, and the two branches of the hyperbola will project to opposite sides of this line (unless the whole figure is projecting to a single line, which we would want to exclude). So the projection of a hyperbola will be disconnected, and thus not a parabola.
Jul
7
revised Determine whether the intersection of surfaces is a parabola
Corrected an embarrassing slip.
Jul
7
answered Determine whether the intersection of surfaces is a parabola
Jul
7
comment Show that if K is a non-zero ideal of Z/mZ,
It might help you to use the fact that ideals and subgroups of $\mathbb Z/m\mathbb Z$ are the same thing. Prove it for subgroups, and you’re almost done.
Jul
6
comment Who named “Quotient groups”?
@Kcd, indeed, Keith, and I think I still have it somewhere, probably in a carton unopened since the last move.
Jul
6
comment Who named “Quotient groups”?
Indeed, when I was learning algebra a little less than 60 years ago, the term “factor group” was sometimes used.
Jul
5
comment Simplify $\frac{1}{x-2}-\frac{1}{x+2}$
There are some as would say that it’s already simplified.
Jul
4
comment Which powers of a primitive element of a finite field yield a generator of a finite field extension?
Have you looked at examples? Say, the fields with $8$, $16$, $32$, $64$, $9$, $27$, and $81$ elements?
Jul
4
comment can fractions be done on a regular caculator?
You seem to be asking for computations in the field $\mathbb Q$ of rational numbers. To do these, you’d have to be able to handle pairs (num, denom) of integers, and be able to reduce, by finding the greatest common divisor of the pair. Others can tell you whether there’s a calculator now available that will do that for you.
Jul
2
answered $p$-adic numbers and projective coordinates
Jul
2
revised I need a relation which is not reflexive, not symmetric, and not transitive
corrected mathematical error pointed out by amalloy
Jul
2
comment I need a relation which is not reflexive, not symmetric, and not transitive
Whoops, right you are! I’ll add another point.
Jul
2
answered I need a relation which is not reflexive, not symmetric, and not transitive