bio  website  math.poly.edu/~yang 

location  New York, New York  
age  
visits  member for  5 years 
seen  6 hours ago  
stats  profile views  12,114 
2d

comment 
Why do we teach calculus students the derivative as a limit?
Depends on what you mean. If you need it for your work, you'll learn it properly through what you do. That's always the best way, because you understand why it's needed. If you just want to learn it, you succeed either by having a really good teacher or studying it on your own (and not being satisfied until you understand it inside out). 
2d

comment 
Existence of minimizer in Sobolev space $H^{1,2}(\Omega)$
Sure it does. The functional is nonnegative and equal to zero if $u$ vanishes on the boundary but not in the interior. 
Oct 18 
awarded  Yearling 
Oct 16 
comment 
Regularity of the Minkowski functionnal of a convex
Use polar coordinates. 
Oct 16 
comment 
Source needed (at finalyear undergrad level) for the double cover of SO(3) by SU(2)
Yes, but without discussing the topological aspect. Uses quaternions. 
Oct 16 
answered  Source needed (at finalyear undergrad level) for the double cover of SO(3) by SU(2) 
Oct 15 
comment 
How is this transformation related to the Legendre transform?
If you apply the Legendre transform to $xf(x,y)$ in the $x$ variable and for fixed $y$, then you should get $s$ back. And, yes, it appears that $f$ is concave with respect to $y$ since it's obtained as an infimum over a family of concave functions. 
Oct 15 
comment 
How is this transformation related to the Legendre transform?
It looks to me like that, for each $y$, $xf(x,y)$ is the Legendre transform of $s(t,y)$. 
Oct 11 
awarded  Custodian 
Oct 11 
reviewed  Leave Closed The periodic architecture underlying the natural numbers 
Oct 11 
comment 
MongeAmpere type PDE
I agree with Robert that the question (and not just a comment) should contain an explicit description of how a Riemannian metric is constructed from the function $f$. Also, I don't recognize the PDE as written as an elliptic MongeAmpere equation as it should be. 
Oct 7 
revised 
Variation of curvature with respect to immersion?
deleted 98 characters in body 
Oct 7 
answered  Variation of curvature with respect to immersion? 
Oct 7 
revised 
Variation of curvature with respect to immersion?
deleted 16 characters in body 
Oct 7 
answered  Variation of curvature with respect to immersion? 
Oct 1 
awarded  Favorite Question 
Oct 1 
comment 
The relation between Gromov hausdorff convergence and inverse limit of compact metric spaces
The question could be rephrased as follows: Does there exist a subset of Euclidean space that is isometric to the GromovHausdorff limit? 
Oct 1 
comment 
Is the identification between symmetric tensors and homogeneous polynomials useful?
Sorry. I didn't read the question carefully. Your example is a question about tensors with respect to a single vector space, so it is a purely algebraic question. Differential geometry is effectively the study of tensors with respect to a smooth parameterized family of vector spaces. I don't see any need or use of differential geometry for a question like yours. 
Sep 30 
awarded  Explainer 
Sep 30 
comment 
Is the identification between symmetric tensors and homogeneous polynomials useful?
Arguably, the only point to tensors is as homogeneous polynomials or multilinear functions. A tensor is difficult to interpret geometrically. Typically, it's only when you evaluate it on on the right number of tangent vectors (or cotangent vectors) that you get a number that you can interpret. The most obvious example of this is the Riemann curvature tensor. I don't know any way to explain the full tensor geometrically, but if you evaluate it properly using two tangent vectors (which span a 2d plane), then you get sectional curvature which does mean something geometrically. 