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1d
comment Books on locally convex topological vector spaces
It seems to me that it's flawed that Rudin uses little categorical language, and maybe viewpoint.
1d
revised Decompose a vector space into invariant subspaces?
added 70 characters in body
Apr
15
asked Decompose a vector space into invariant subspaces?
Mar
28
comment Rigorous pre-calc book with answers
@crash I didn't really understand what's pre-calculus, but I suggested Concrete Mathematics because most part of the book isn't relied on calculus and should prepare readers techniques of manipulating $\sum$, binomial coefficients, etc. Well, on the other hand, I started my first systematic study of calculus from Rudin's Principles of Mathematical Analysis. It's concise but terse and without solutions.
Mar
28
comment Does differentiability have a geometric interpretation for high dimensional functions?
It's still a linear approximation. Instead of a linear function when $m=1$, it's approximated by a linear transformation represented by the matrix.
Mar
28
comment Prove that $Ker(g \otimes k)= Im(f \otimes 1_{N}) + Im (1_{M} \otimes h)$
@LuisVera Edited. Hope it's clearer now.
Mar
28
revised Prove that $Ker(g \otimes k)= Im(f \otimes 1_{N}) + Im (1_{M} \otimes h)$
added 409 characters in body
Mar
28
comment Rigorous pre-calc book with answers
Take a look at Knuth's Concrete Mathematics to see whether it's what you like?
Mar
28
comment If $N$ divides $a$ and $N$ divides $b$ then
But either $N\vert a$ or $N\vert b$ implies $N\vert ab$.
Mar
28
revised Trouble finding the limits of integration for polar coordinates
LaTeX
Mar
28
comment Oscillating essential discontinuities exist?
In your example $f(1/n)=(-1)^n$, the limit doesn't exist. It follows directly from $\epsilon$-$\delta$ definition. If you want to see a continuous example, try $f(x)=\sin(1/x)$ for $x\neq0$ and study $\lim_{x\to0}f(x)$.
Mar
28
revised Can anyone check if this correct?
LaTeX
Mar
28
comment Does there exist an entire function such that $f\left(n+\frac{1}{n}\right)=0$
See wiki.
Mar
28
comment Does there exist an entire function such that $f\left(n+\frac{1}{n}\right)=0$
In general, look for Weierstrass factorization.
Mar
28
asked Local normal form of a (several complex variable) holomorphic map at a point?
Mar
28
revised Proving that the tensor product is right exact
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Mar
28
answered Prove that $Ker(g \otimes k)= Im(f \otimes 1_{N}) + Im (1_{M} \otimes h)$
Mar
28
accepted The hyper-derived functors $\mathbb L_\bullet F$ are just derived functors of $H_0F$?
Mar
21
revised Homomorphism of local rings
added 12 characters in body
Mar
20
comment A quasi-isomorphism between the total complex of a Cartan-Eilenberg resolution and the complex per se.
@AndreaGagna I just skimmed G&M and found that they assume that the double complex is bounded. It's a different story. But the spectral sequence with filtration by rows works (assuming AB5), since it's upper half-plane therefore the spectral sequence converges to $\operatorname{Tot}^\oplus$.