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bio website supermath.info
location Virgina USA
age 36
visits member for 2 years, 3 months
seen 17 hours ago

I'm interested in mathematics which is used to frame physical theory. I guess that means I'm at least a little interested in just about anything.

Currently I'm trying to understand Cartan's Method of moving frames as it applies to various classification questions of low-dimensional geometry.

I also have interest in superanalysis and certain problems of hypercomplex analysis.

More generally, I'm just looking for interested students who want to exceed the status-quo of undergraduate mathematics. Ideally, our interests overlap.


21h
comment Tensor product of two linear map and its matrix representation
see problem 20 on page 408 of Roman's Advanced Linear Algebra, 3rd ed.
2d
comment Torsion vs Curvature of a curve
This is a good start, but, perhaps the OP in interested in the meaning of the higher $n-1$-curvatures in $n$-dimensions? For $n=3$ we have curvature and torsion and the vanishing torsion insures planar motion. Is this still true in $\mathbb{R}^4$. What is the meaning of vanishing $2$nd and $3$rd curvatures? (see the wiki for the definition)
Oct
20
comment Converting from Polar to Cartesian Equation
This gives $r^2=2r\cos \theta$ aka $x^2+y^2=2x$. Etc.
Oct
20
answered Converting from Polar to Cartesian Equation
Oct
18
comment Isometric Operators: Common Core
If the common core included the content of this question it would really be something.
Oct
17
comment Will computers one day start creating and proving math for us?
@user46944 only in as much as it is a projection of the real artist who programmed it.
Oct
17
comment Will computers one day start creating and proving math for us?
there's a difference between a paint-sprayer and an artist.
Oct
12
comment Tensor analog of Matrix Product
I would like for you not to demand the resulting tensor be the same size. Rather, $2n \times 2n \times 2n$ in your terms. Then, we can use the natural tensor product to answer your question.
Oct
12
comment CR Equations using Polar Form
sorry for the delay, I was really sick yesterday, I had hoped I wrote enough to see where to do, but, see the answer, I complete the thought now. That said, it's nasty.
Oct
12
answered CR Equations using Polar Form
Oct
12
comment Ricci scalar algebra
the $;$ is covariant derivative?
Oct
11
comment how to define a circular helix in terms of the Frenet Frame
the question better stated would be: "among all possible helices in euclidean $3$-space, show that the only ones with constant curvature and torsion are circular" Now you worry me about my initial question... maybe we need a definition of a general helix to be logical here!
Oct
11
comment how to define a circular helix in terms of the Frenet Frame
I'm not sure I understand the $T_h$ euclidean motion definition. Would that condition also be true for a line?
Oct
11
comment how to define a circular helix in terms of the Frenet Frame
This is helpful, btw missing an $=$ between $T(s)$ and $\alpha'(s)$.
Oct
11
comment how to define a circular helix in terms of the Frenet Frame
I'm curious what the final formula for $\beta (s)$ would look like in just terms of curvature, torsion, arclength and the Frenet Frame. I hate to say this at this point, but, maybe the larger lesson here is that $\vec{r}(s) = \langle R \cos s, r\sin s, ms \rangle$ is a better definition, provided, we pair that definition with the proper rigid motion concept as in Christian Blatter's answer. (of course, I'm not talking about the question I posed here, just the larger question of how best to define a helix)
Oct
11
comment CR Equations using Polar Form
I haven't finished the calculation, but, my goal was to write $f$ as a function of $r$ and $\theta$ presented as indicated at math.stackexchange.com/a/205698/36530 and I'm working on obtaining real-valued $U(r, \theta), V(r, \theta)$ for which $f=U+iV$ so I can apply CR-equations in polar form, plus the added observation of continuous differentiability (in the real sense) to conclude $f$ is holomorphic. The answer given by @Nimbda gives an alternate argument to show the function is complex differentiable, but, that argument did not use CR-eqns.
Oct
11
comment CR Equations using Polar Form
Notice $z = re^{i \theta}$. So, $z^5-z = r^5e^{5i\theta}-re^{i \theta}$. Note, $$\frac{1}{z^5-z} = \frac{1}{r^5e^{5i\theta}-re^{i \theta}} = \frac{e^{-i\theta}}{r}\frac{1}{r^4e^{i\theta}-1}\frac{r^4e^{-i\theta}-1}{r^4e^{-‌​i\theta}-1}$$
Oct
11
comment How to switch to a Laurent series' next convergence ring?
I think it would be good to work an example where there is a singularity on the edge. Perhaps working on something specific would be enlightening. That said, textbooks are suspiciously void of examples with details and the topic of Monodromy occupied the efforts of mathematicians far my superior the better part of the nineteenth century. I must think on your question.
Oct
11
comment How to switch to a Laurent series' next convergence ring?
this is actually an excellent question. I'm teaching complex analysis at the moment, I'd love to be able to offer even a partial answer to my class. My general idea is rather low-tech. I just replace $z-z_o$ with $(z-z_1)+z_1-z_o$ and work out the arithmetic. If $z_1$ is within the domain of the original expansion then I think this will provide a continuation. But, I'm not so sure this approach is ammenable to your problem.
Oct
10
revised John Lee's Intro to Smooth Manifolds Inverse Function Theorem
changed tags to emphasize the source and context of this question