14,557 reputation
11938
bio website math.brown.edu/~lubinj
location Minnesota
age 78
visits member for 3 years, 1 month
seen 13 hours ago

Aged mathematician


13h
comment $t$-adic topology (on $\mathbb F_p(1/t)$)
But of course that’s wrong. Both are gotten by adjoining a single element; and it’s immaterial in a field whether you’re adjoining an element or its reciprocal. If they had been talking about the rings $k[t]$ and $k[1/t]$, there would be something to say. However, the ring $k[1/t]$ can not bear a $(t)$-adic topology, but a $(1/t)$-adic.
17h
comment Angle of intersection between a plane and sphere.
Don’t you have a right triangle, spherical triangle, that is? To save yourself trouble, just look up Napier’s rules, which relate all parts of a triangle.
1d
comment Angle of intersection between a plane and sphere.
Well, your circle is a great circle on the sphere going through $(0,\pm1,0)$, isn’t it? Seems to me you should be able to find the intersection point with your semimeridian easily enough. Make sure you have an accurate picture, in your mind at least.
1d
comment Angle of intersection between a plane and sphere.
What are $u$ and $v$? Did you mean $\phi$ and $\theta$? Why are you calling this function $x$, when this is the name of one of your Cartesian coordinates? Why did you bother with a parametrization, when the sphere is just the unit sphere centered at the origin?
2d
comment why this formula doesn't work?
You’ve got to learn basic TeX, as painful as your first experiences will surely be. You ask, “Why doesn’t the first formula work?”, and I’m not sure what “the first formula” is.
2d
comment When do you drop the absolute value from ln|x| + C when integrating $\frac{1}{u}du$
For a mathematician, the problem is not well formulated. But the wording “increasing at a rate proportional to $800-p$” gives me the slightest hope that $800-p$ is positive.
2d
comment given a point cloud of n points, create a convex shape that defines their outer limits
As a total outsider to the field, I’d say that this is one of the core problems of linear programming. But in what format is your set going to be described? By a bunch of linear inequalities, perhaps?
2d
comment The property a(bc)=(ab)c for linear operators
Indeed. For matrices of finite size at least, it’s easier to use this obviously true principle to show associativity of matrix multiplication, than to get yourself tangled up in the mess of indices.
Nov
24
comment Find a complex number for the splitting field
e-mail me if you’d like to discuss this further.
Nov
23
comment Factorize x^3+3
GF(7) is $\mathbb F_7=\mathbb Z/(7)$
Nov
23
comment Solve $z^{1+i}=4$
This is certainly the right method, just take account of the many-valuedness.
Nov
23
comment Find a complex number for the splitting field
Well, almost any combination of the two separate things will give you a primitive element. My guess is that your process gets only some of these.
Nov
22
comment Find a complex number for the splitting field
Yes, in the sense that for $c$ equal to either of the quoted elements, $E = \mathbb Q(c)$. But not via the procedure you were following!
Nov
22
comment Find a complex number for the splitting field
Both are primitive elements. That is, either of them will generate your sextic extension of $\mathbb Q$
Nov
22
comment Find a complex number for the splitting field
I made a comment that the sum $\root3\of2+\omega$ should work, but that was based on experience, not on using the method you were told to use. With the knowledge of the special properties of this field, though, I found that $(2\omega+1)/(\root3\of2+1)$ has $\mathbb Q$-polynomial $X^6-3X^4+3X^2+3$, a very pretty Eisenstein sextic, more in line with the kind of thing you were looking for.
Nov
21
comment Cyclotomic polynomial identity
This comes from the Möbius Inversion Theorem, which you should look up. Also, in your exponent, you really just wanted ordinary division: $X^{n/d}$.
Nov
21
comment How do I get the expansion of $(2x-1)^{-1} $ to the $x^3$ term
@ClaudeLeibovici, I wish long division of power series was taught in all US schools…
Nov
21
comment Ratio of an isosceles triangle to its altitude is 3:4. find the measures of the angles
When you say, “ratio of an isosceles triangle to its altitude”, are you talking about the base of the triangle versus the altitude? If so, could you edit?
Nov
21
comment How to evaluate $(0.9)^4$ without calculator
Just a matter of terminology: one solves an equation, here you want to evaluate your expression.
Nov
20
comment Is the map, $ f:(0,1)⊂ \mathbb{R}$ → $(1,∞)⊂ \mathbb{R}$ : $x ↦ 1/x $continuous?
If there were a point of discontinuity, what would it be? And what is the inverse function of $f(x)=1/x$?