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I really appreciate it when you take time to answer my questions. Thanks!


Jan
26
comment fundamental group of the Klein bottle minus a point
How would you solve the torus problem, and can you copy that solution to the Klein bottle case?
Jan
26
comment Typo in Marcus' $\textit{Number Fields}$?
@BenjaLim, yes. But if you try to work out the contrapositive (i.e. what you can infer from $m$ being a square mod $p$), it seems natural what he wants to do.
Jan
26
comment Typo in Marcus' $\textit{Number Fields}$?
@BenjaLim, sorry I meant to say $p > 4|m|$.
Jan
26
comment Independence of coordinate charts in the definition of the order of a pole of a meromorphic 1-form on a Riemann surface
@Silencer, sorry for my unclear notation. $\frac{dz}{dz'}$ is by definition $\frac{d\phi}{dz'}$ here. I have edited the answer to replace all of them by $\frac{d\phi}{dz'}$.
Jan
26
revised Independence of coordinate charts in the definition of the order of a pole of a meromorphic 1-form on a Riemann surface
added 114 characters in body
Jan
25
comment Inequality: $(a^3+a+1)(b^3+b+1)(c^3+c+1) \leq 27$
How is this different from Lagrange multiplier? This is just phrased in a tone-down way I suppose.
Jan
25
comment Symmetric inequality on positive numbers whose product is one
@EwanDelanoy, I don't understand what you are saying. If we multiply as you said, we get $(n-2) + t^{n-1} \ge (n-1)t$, apparently true by AMGM. In fact, eventually I didn't use $t \ge 1$ in the whole proof.
Jan
25
answered Symmetric inequality on positive numbers whose product is one
Jan
25
comment If $H\unlhd G$ with $(|H|,[G:H])=1$ then $H$ is the unique such subgroup in $G$.
Hint: let $K$ be another subgroup of this order. What can you say about $HK$?
Jan
25
awarded  Citizen Patrol
Jan
25
comment How can I prove that “If $M$ is contractible differentiable manifold, then $M$ is orientable?”
@Jaivir Baweja, I don't understand your hint about Poincare lemma. What homology groups are you computing?
Jan
24
asked $l^1$ norm estimate for inverse of Vandermonde matrix
Jan
24
comment Multiple choice question about a $3\times3$ invertible matrix $A$ such that $\det(A)=1$ and $\mathrm{tr}(A)=\mathrm{tr}(A^2)=0$
Do you know the Cayley Hamilton theorem? What are the coefficients in the characteristic polynomial, and how are they related to trace?
Jan
24
answered Independence of coordinate charts in the definition of the order of a pole of a meromorphic 1-form on a Riemann surface
Jan
24
comment Is multivariable calculus synonymous with differential geometry?
(Multvariable) calculus is the tool to study geometry in differential geometry. So yes, they are two different things.
Jan
22
comment Showing that for $f(z)=\frac{1}{z^2+1}$ an upper estimate is $|f(z)|\leq \frac{1}{\rho^2-1}$ for $|z|=\rho$.
No need to use complex analysis - just triangle inequality.
Jan
22
comment Serge Lang and categories
@amWhy, it did not appear in later editions indeed :(
Jan
22
comment Does $d(x+u, y + v) \le d(x, y) + d(u,v)$ holds for every metric?
What is the underlying space here?
Jan
22
comment Inequality involving partial sums of $\frac{|\sin{kx}|}{k}$
I'm not quite certain, since I guess that the phase problem is the main issue here. If you plot the graph of LHS - RHS, you can see that on $[0, \pi/n]$ it's quite positive, while there are troughs that are quite a bit smaller as we wade through $[\pi/n, \pi]$.
Jan
22
comment Inequality: $(a^3+a+1)(b^3+b+1)(c^3+c+1) \leq 27$
@ShaneChern, Are you sure? I don't think that Jensen's inequality tells you exactly what the equality cases are.