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Jun
18
reviewed Approve If $x_i \gt 0$ for $1\leq i\leq n$ and $x_1+…+x_n=\pi$ Then the greatest value of $\sin x_1+…+\sin x_n$ is $n \sin \left(\frac{\pi}{n}\right)$.
Jun
18
reviewed Reject Functional completeness for a ternary operator
Jun
18
answered The exterior algebra is a superalgebra?
Jun
18
answered Is there any published research on the value of finding new proofs for old theorems?
Jun
18
comment Prequisites for a PDE course (Strauss)
While it's difficult to be sure without knowing more particulars of your institution, I think you'll be ok provided you have some time to fill in gaps in your knowledge. Beware Chapter 7 in Strauss, perhaps you have not seen Green's theorems yet...
Jun
17
comment Derivatives and solving a system of linear ODEs
see page 142 of supermath.info/DifferentialEqns.pdf
Jun
17
comment Applications of Principal Bundle Construction: Vague Question
I think what you want to look into is associated bundles of the frame bundle. As I recall this is the way to naturally generate all manner of tensors. But, I think the frame bundle is also a principal bundle with respect to $G = GL(n)$ so, my comment is not so far off your idea... This math.stackexchange.com/questions/649142/… might be helpful, more to the point see en.wikipedia.org/wiki/Frame_bundle
Jun
17
comment What fraction of a sphere can an external observer see?
Are there any mirrors?
Jun
17
reviewed Approve Game Theory: Prisoners Dilemma
Jun
17
comment What are some of the iconic mathematical images ever done in 2D, 3D and 4D? I've mentioned just a few
if you were not already aware... check out mathoverflow.net/questions/1714/best-online-mathematics-videos !
Jun
17
comment What are some of the iconic mathematical images ever done in 2D, 3D and 4D? I've mentioned just a few
Reeb folitations of torus are worth a look
Jun
16
comment Visual approach to abstract algebra
Ted Shifrin wrote Abstract Algebra: A Geometric Approach (see books.google.com/books/about/… ). It might have some of what you're looking for. His section on Gaussian integers was helpful to me recently.
Jun
16
comment Rewriting a integral using a pullback between manifolds with different dimensions
interesting question, I'm not sure I know, but, for the standard concept of integration of a form we'd need $f^* \omega$ is an $dim(M)$-form. So, how can we naturally add degree? If $M$ and $N$ were related by Hodge duality perhaps? I can trade two-forms on surfaces for one-forms along curves in three dimensions. I hope somebody answers your question.
Jun
15
answered Intuition of multivariable chain rule
Jun
15
comment Is SU(2) a subgroup of the exceptional lie group $G_2$?
seems like math.ucr.edu/home/baez/octonions/oct.pdf will be worth a glance.
Jun
15
comment How to prove that $\cos^2(z)+\sin^2(z)=1$, where $z$ is a complex variable (if it is true)?
@salimmath15 his answer is not complicated and it is very helpful for you as you learn more about complex variables. That is part of the beauty of this website. You don't just get answers at your level, you get a spectrum of understanding.
Jun
14
answered Need some help understanding the condition of the implicit function theorem
Jun
14
comment How do I find a basis for the null space?
$T$ is surjective but far from injective. The null space is $3$ dimensional.
Jun
13
reviewed Approve Differentials - Area of a circle from its diameter
Jun
13
comment How do the components of a cross product transform?
@Uldreth yes, but, I think the usage has more to do with how various vectors are defined and how the equations of physics change as we transform coordinates.