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visits member for 3 years, 8 months
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May
14
comment Multiplication of very Large Diagonal Matrix
In the absence of structure on the diagonal entries, even reading the data takes $O(N)$ time, so I don't see how you expect a substantial improvement.
Apr
30
comment Does the pullback of a covering space correspond to the pullback of the corresponding representation of $\pi_1$?
You also want to equip your spaces with distinguished base points.
Apr
23
comment Proof that a product of two quasi-compact spaces is quasi-compact without Axiom of Choice
It looks like you are claiming that the $U$ you construct in the second paragraph is adequate, but I don't see it very clearly. In particular, there seems to be an implicit claim that $U \times X \subset W_1 \cup \cdots \cup W_n$.
Mar
12
comment On $\int_{-\infty}^{+\infty} {\frac{\tan(t-t_0)}{\cosh^2(t-t_0)} \cos(\omega t) \,\mathrm{d}t}$
How did this question arise? What have you tried?
Jan
23
comment In the history of mathematics, has there ever been a mistake?
@Zarrax Ken Perko vehemently denies having a PhD in math.
Sep
22
comment On a abelian representation of galois group
It might help to think of the Galois group as a projective limit of finite groups coming from finite Galois extensions, instead of some abstract group of automorphisms of an algebraically closed field.
Sep
10
comment Monotonic log det function?
What is $\sigma$?
Sep
10
comment Why Euler-Lagrange equation does not depend on the second derivative of the function?
See en.wikipedia.org/wiki/…
Jun
29
comment Cutting the $2$-dimensional real Projective Space
The projective plane is the quotient of $S^2$ by the antipodal map, and cutting out a non-contractible cycle corresponds to removing the equator in the sphere.
Feb
13
comment How to bound the maximal consecutive length in a random subset of [n] as function of n?
Concerning the usual reasons: On MathOverflow, we're getting flags claiming that this user's questions come from a take-home exam that is in progress.
Jun
10
comment Guaranteed Checkmate with Rooks in High-Dimensional Chess
@George: Your strategy sounds good, but I'm pretty sure you don't need more than 7 at each corner. The extra shrinking piece also seems unnecessary, so I have a tentative upper bound of 44.
Feb
10
comment The definition of the logarithm.
There is also the lemma-definition that log is the unique continuous homomorphism from $(\mathbb{R}^\times, \times)$ to $(\mathbb{R}, +)$ that has unit slope at 1.
Aug
1
comment Why the moduli space of complex structure in a compact complex manifold is of finite dimension
By Kodaira-Spencer theory, you can compute the space of first-order deformations of the complex structure as a cohomology group. For a fixed choice of complex structure, this space is (more or less) the tangent space of the moduli space of complex structures at the point that describes the chosen complex. structure.
Jul
23
comment Can an algorithm be faster than O(1)?
Your analog computation is still $O(1)$ due to relativistic considerations. From a physical perspective, since the observable universe has finite usable energy, it will always take time bounded away from zero to output the result of a non-null algorithm.
Jul
23
comment Should I write out stuff?
@Alex J: I interpret the quote as follows: For each theorem that Bourgain proved, he did not need to do a computation to convince himself that it was true. Often, there are structural methods outside computation that you can use to make guesses.
Jul
21
comment Why is it “easier” to work with function fields than with algebraic number fields?
Incidentally, there's nothing formal about the derivative of a polynomial. Given a polynomial map, the derivative is the canonical map from the tangent bundle of the source to the pullback of the tangent bundle of the target.
Jul
10
comment What it takes to a mathematician
I got UASHed when I was 19. Does that count as doing something?
Jun
27
comment Banach spaces over fields other than $\mathbb{C}$?
Hahn-Banach in general requires "spherical completeness", not just completeness.
Jun
20
comment Characterizations of Prüfer Group
You can also define it to be the group of complex numbers which when raised to some $p$-power-th power yield 1.
Jun
20
comment Alternative to imaginary numbers?
Make that $J^2 = -\text{Id}_V$.