8,311 reputation
21037
bio website supermath.info
location Virgina USA
age 36
visits member for 2 years, 6 months
seen 9 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.


Dec
17
answered How to select the right books?
Dec
15
answered Manifold Orientability Definition
Dec
15
comment Reference request for studying on Fiber bundles
what have you already studied?
Dec
13
comment Manifold Orientability Definition
My copy of Morita seems to be at school, I'll try to give some better comment once I get a chance to look it over. Of course, it is entirely possible someone will beat me to it!
Dec
13
comment Manifold Orientability Definition
When I think of the orientation of an $n$-manifold, I think of a non-vanishing $n$-form which exists over the whole space. That said, perhaps the idea is to frame the curve?
Dec
13
awarded  Nice Question
Dec
12
comment Divergence Theorem to calculate flux
The divergence is a scalar. Why does your divergence have a "k" in it? Also, you're missing a nontrivial term from the coefficient of $j$ which has $y$-dependence. That said, the answer is the same with that mistake...
Dec
12
awarded  Enlightened
Dec
9
awarded  Caucus
Dec
7
comment How does algebra on differential forms work?
for a more clumsy account (but free) see Chapter 7 (page 155...) of my supermath.info/AdvancedCalculus2011.pdf
Dec
7
answered How does algebra on differential forms work?
Dec
6
comment How can I prove a formula for integration by parts for matrix functions?
Next, integrate the expression above, do we want a definite or indefinite integral? I'm not sure from your question thus far...
Dec
6
comment How can I prove a formula for integration by parts for matrix functions?
Yep, I wrote it out a bit more in an answer, these comments only go so far.
Dec
6
answered How can I prove a formula for integration by parts for matrix functions?
Dec
6
comment How can I prove a formula for integration by parts for matrix functions?
Hint: integration by parts is about reverse-engineering the product rule. What product rule do you have for matrix-valued functions of a real variable?
Dec
4
comment A tough question on meromorphic functions- Conway
this seems like an extension of Casoriti Weierstrauss, for each pole you can find a sequence which limits to $w$. I suppose you just need to link those together somehow... unfortunately, I have not proved Casoriti Weirestrauss so that is as far as I can go here.
Nov
30
comment What quantity does a line integral represent?
@Irongrave Sorry about that, CCW = Counter-Clock-Wise
Nov
30
comment What quantity does a line integral represent?
to be clear, I don't think the question "what does the line integral mean geometrically?" is the correct question. It has some meaning, but, it is in a higher dimensional context where the vector field and curve both appear as objects. Otherwise, in the three dimensional context, the line-integral says something about the pair $(C, \vec{F})$ and how they relate.
Nov
30
answered What quantity does a line integral represent?
Nov
30
comment In war with exercise, any future for me?
given any mathematical arena one can typically play two games. One, how can I weaken the theory and still retain essential features. Two, how can I specialize the theory and what new features appear. These are interesting exercises.