7,458 reputation
2731
bio website supermath.info
location Virgina USA
age 36
visits member for 1 year, 11 months
seen 4 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.


Jun
28
comment How to define the disciplines of mathematics
I usually say something glib like "algebra is about equations, but, analysis is about inequalities". I have no place for topology in this slogan. Honestly though, any sentence or even page cannot hope to truly encompass what these things are.
Jun
28
reviewed Approve suggested edit on Finite difference schemes for an ODE
Jun
27
comment Finding the basis of an intersection of subspaces
@GinKin always a problem. Hopefully the added detail at the end helps it gel now.
Jun
27
revised Finding the basis of an intersection of subspaces
added 293 characters in body
Jun
27
comment Finding the basis of an intersection of subspaces
but, the column corresponding to $-u_2$ is $[1,-1,0,1]^T$ and those corresponding to $v_1,v_2$ do the rest. Go back to the original vectors and see if you can see this linear combination there.
Jun
27
comment Finding the basis of an intersection of subspaces
Sorry for adding to the confusion initially, I thought $w_1,w_2$ were sets of vectors in my initial post, I now see the "sp". I put $B_1,B_2$ for the finite sets in my revised answer to distinguish from the infinite sets $w_1,w_2$.
Jun
27
comment Finding the basis of an intersection of subspaces
@GinKin I'm not sure what you can immediately say from placing vectors vertically. The reduction tells us about linear correspondences between columns (not rows, which is what you seem to be doing, reading between the lines in your comment)
Jun
27
revised Finding the basis of an intersection of subspaces
added 1712 characters in body
Jun
27
answered Finding the basis of an intersection of subspaces
Jun
26
reviewed Approve suggested edit on Differentiation tangent line
Jun
25
reviewed Reject suggested edit on Equivalence relations and equivalence classes
Jun
25
reviewed Approve suggested edit on Independence Lemma, is it non-trivial?
Jun
23
comment finding a basis of tensor product of dual space
I haven't shown it, but $T \otimes S$ is bilinear on $U \times V$. We feed a pair $(e_k,a_l)$ to a function on $U \times V$. For the tensor product of maps, $T \otimes S(e_k,a_l) = T(e_k)S(a_l)$ by definition of $\otimes$. I assume you view tensor products as represented by multilinear maps.
Jun
23
revised finding a basis of tensor product of dual space
added 824 characters in body
Jun
23
answered finding a basis of tensor product of dual space
Jun
23
comment Derivatives of equations
It should be noted, the reason implicit differentiation is "ok" is that the Implicit Function Theorem states that given a certain condition we can solve for one variable as a function of the remaining variable. Without that condition, it may or may not be possible to solve for $y$ as a function of $x$ and thus it may not make sense to differentiate w.r.t. $x$ at such a point. However, you can always take the total differential of an equation and that has meaning... but, this is a calculus I question so I leave this as a comment for your future.
Jun
22
reviewed Approve suggested edit on Find an unknown coefficient in a line equation…
Jun
21
comment Inexact Differential Equations: how to know if μ will be a function of x or y instead of guessing?
interesting answer, do you happen to have a link to the paper of Lie you mention? Also, how do you identify the "family of groups" for the given ODE?
Jun
20
comment When is separation of variables possible?
this question is far deeper than it appears. See ima.umn.edu/~miller/sepofvariablestalk.pdf for a sense of why this question must be narrowed to obtain a good answer. I think if you limit it to Hamilton-Jacobi in a reasonable context the linked items shows you what's what.
Jun
20
reviewed Approve suggested edit on Orientation double cover