12,554 reputation
11332
bio website math.brown.edu/~lubinj
location Minnesota
age 77
visits member for 2 years, 9 months
seen 4 hours ago

Aged mathematician


Jul
11
answered Is $4x^2-4x+2$ surjective?
Jul
11
comment Completion of Complex Numbers
This answer seems very satisfying, to me.
Jul
11
comment Real Analysis: Showing $f: \Bbb Q \to \Bbb Q$ is continuous
For the case that $U$ contains $1$ but not $-1$, isn’t $-2$ in $f^{-1}(U)$?
Jul
10
comment What is the meaning of “fix” in field theory?
It’s not a specially mathematical term. One speaks of the “fixed stars” (as opposed to the planets): they don’t move. Or one can say “I am fixed in my opinion” to indicate that the opinion hasn’t changed.
Jul
10
comment names in a quadratic field extension
As an old-fashioned guy, I rebel against the use of “abscissa” and “ordinate”; I would use the terms first and second coordinates, or first and second entries, thinking of an $n$-tuple of things in the base as column matrices.
Jul
10
comment Triangle problem - finding the angle
Yes, but what method did you use for computing that algebraic number? Was it just a repeated application of Law of Cosines, or something else?
Jul
10
answered Real Analysis: Showing $f: \Bbb Q \to \Bbb Q$ is continuous
Jul
10
comment Triangle problem - finding the angle
You didn’t say how you got your sextic equation in cosine, did you?
Jul
10
answered Triangle problem - finding the angle
Jul
10
comment Triangle problem - finding the angle
Yes, you seem to have used the Cubic Formula, which I have never been comfortable with.
Jul
9
comment Triangle problem - finding the angle
Preliminarily, I don’t believe it’s necessary to solve any polynomial equations. I think I have a method of expressing $\tan(x)$ rationally in terms of $\sqrt3$ and the trig functions of $80^\circ$. But I have some chores and a meeting to get out of the way. Perhaps I’ll have something written up in six hours.
Jul
9
comment Sketching the graph of a function with three real roots
What about $x=0$?
Jul
8
comment Help with Monbukagakusho mathematics exams questions.
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.