8,061 reputation
21036
bio website supermath.info
location Virgina USA
age 36
visits member for 2 years, 4 months
seen 5 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.


Jul
13
answered What exactly is a number?
Jul
13
reviewed Approve prime numbers and some conjectures
Jul
12
comment Are vectors and covectors the same thing?
Perhaps in physics the difference between a vector and a covector are best emphasized by the terms contravariance and covariance. For example, a generalized coordinate transforms contravariantly (ok, essentially by defininition) whereas a generalized momentum transforms covariantly. These transformation laws are not the same.
Jul
11
comment Pair of PDEs to be solved together
Thanks for this answer and the physical insight.
Jul
11
comment Pair of PDEs to be solved together
I usually wait a week before awarding a bounty, but, after reading this answer it seems quite unlikely it will be improved upon, so thanks. I should have had enough sense to tinker at the level of $\nabla$ notation.
Jul
11
reviewed Approve shortest distance between the point $(0,-3)$ and the curve $y=1+a_{1}x^2 + a_{2}x^4 + …+a_{n}x^{2n}$
Jul
11
reviewed Approve Find the sum of the 10th and 11th terms of the G.P.
Jul
10
reviewed Approve The best way to factorize?
Jul
8
reviewed Approve About a specific argument purporting to show $0.999\dots = 1.0$.
Jul
8
answered The Best of Dover Books (a.k.a the best cheap mathematical texts)
Jul
8
reviewed Reject How find the matrix $K$ such $AKB=C$
Jul
7
comment all complex solutions of $z\sin(z)=1$?
Lambert $W$ functions? en.wikipedia.org/wiki/Lambert_W_function
Jul
7
reviewed Approve Square Root in inequalities
Jul
7
comment Pair of PDEs to be solved together
I'll put a bounty on this question when I can.
Jul
6
comment Soviet Russian Mathematical Books
somewhat related, you ought to look at Love and Math by Frenkel. I suspect, Gelfand, Krillov, Arnold, but, I'm no Russian so I'll leave it at that.
Jul
6
comment Background for 2 differential geometry questions
interesting questions, however, you might do better to ask one at a time.
Jul
6
comment Linear dual of vector fields
@InTransit indeed, this is why I made the comment, I saw the question refer to "$\mathbb{R}$-dual without qualification, as we see in studiosus' answer and the surrounding materials, the dual used is not the $\mathbb{R}$-dual, but rather some suitably restricted subset which is not hopelessly infinite in the manner you indicate.
Jul
6
comment Linear dual of vector fields
@mathematician surely some analysis can be done across multiple topologies at once, in fact, this might make an interesting question. Perhaps I'll ask it later today.
Jul
6
comment Linear dual of vector fields
A related question, why do we not look at the full dual to infinite dimensional vector spaces in the usual functional analysis course? As I recall, the set of linear functionals is bigger than the set of bounded linear functionals... but, I second @WillJagy's comment.
Jul
6
comment Integrate $\tan^4(\theta)$
@Joshhw you can use as many different substitutions as you wish. Remember the integral has the linearity properties $\int f+g = \int f+\int g$ and $\int cf = c \int f$ so we can divide and conquer by disparate methods. I'm sure amWhy's answer cleared it up for you.