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Sep
15
comment Historical basis and mathematical significance of Riemann surfaces
Right. IMO for those who are interested in quick applications of the Abel-Jacobi theorem and are not prepared/motivated to study homology and cohomology theories, a classical exposition of the theory might work just fine.
Sep
15
comment Historical basis and mathematical significance of Riemann surfaces
What is the existing way of presenting the theory of Riemann surfaces? Thanks.
May
10
comment Immunization and Sensitivity Analysis
You are likely to get some answers on the sister StackExchange site devoted to Quantitative Finance: quant.stackexchange.com
May
10
comment Black Scholes PDE and its many solutions
You are likely to get more answers on the sister StackExchange site devoted to Quantitative Finance: quant.stackexchange.com
Mar
31
comment Stochastic/finance monte carlo question
You may want to consider reposting your question on quant.stackexchange.com which is specifically devoted to Quantitative Finance.
Feb
8
comment Are continuous self-bijections of connected spaces homeomorphisms?
There is a thread on Mathoverflow devoted to a similar question: mathoverflow.net/questions/30661/…
Jan
1
comment How can I find the derivative of $y = \ln [\ln(\ln(x^2 +1))]$?
Are you familiar with the chain rule?
Dec
27
comment Axiom of Choice Examples
@Jason DeVito: I have checked this experimentally.
Dec
27
comment Volumes of n-balls: what is so special about n=5?
Yes, this is an analytic argument I referred to implicitly. I'd like to know if there is any geometry behind that.
Dec
27
comment Volumes of n-balls: what is so special about n=5?
Well, for an $n$-dimensional ball of radius $R$ we can consider the ratio $$\frac{V_n(R)}{R^n}.$$ This is a "dimensionless" quantity.
Dec
14
comment Constructing a Cantor-like set by subtracting closed intervals
Alternatively, the measure of the set will not depend on whether you subtract closed or open intervals since the difference is a countable sequence of endpoints, i.e. a measure zero set.
Dec
14
comment Constructing a Cantor-like set by subtracting closed intervals
You will end up with a set of measure $1-\alpha$ because the Lebesgue measure is $\sigma$-additive (countably additive).
Dec
11
comment Domain of the Gamma function
$t^{z-1}e^{-t}$ has a non-integrable singularity at $t=0$ when $\Re z\leq 0$.
Dec
9
comment An orthonormal set cannot be a basis in an infinite dimension vector space?
Thanks to everyone for the comments. I implicitly assumed that the space is complete.
Dec
8
comment Proving that the sequence $F_{n}(x)=\sum\limits_{k=1}^{n} \frac{\sin{kx}}{k}$ is boundedly convergent on $\mathbb{R}$
The argument works for $x\neq 2\pi m$.
Dec
7
comment Proof of $\int_0^\infty \left(\frac{\sin x}{x}\right)^2 \mathrm dx=\frac{\pi}{2}.$
@J. M.: Thank you for linking to the paper.
Dec
7
comment Doubts on Mutually exclusive and Independent events
The events are independent but not mutually exclusive.
Dec
7
comment Proof of $\int_0^\infty \left(\frac{\sin x}{x}\right)^2 \mathrm dx=\frac{\pi}{2}.$
@Raskolnikov: Stand corrected, thanks!
Nov
21
comment Proving $\int_{0}^{\infty} \mathrm{e}^{-x^2} dx = \dfrac{\sqrt \pi}{2}$
@ J. M.: That's it! Thanks.
Nov
9
comment Suggesting closed-form representations of mathematical constants by means of experimental mathematics?
@Max Muller: You're welcome.