4,833 reputation
1223
bio website quantdec.com
location
age
visits member for 3 years, 10 months
seen 2 days ago

Consultant (environmental stats a specialty) and teacher.


Mar
30
comment Find $\lim\limits_{(x,y) \to(0,0)} \frac{xy^2}{ x^2 + y^4} $
+1 Nice reference. For some illustrations, please see mathematica.stackexchange.com/questions/21544/….
Mar
28
awarded  Pundit
Mar
27
comment Hugely ugly messy determinant - any trick to find it?
If you view the determinant as a function of $a$, evidently it's a polynomial of degree $3$. By inspection--and understanding the basic properties of determinants--you can identify three roots immediately, so you know it up to some multiple that depends only on $b$, $c$, and $d$. Repeating this observation for the other variables pins down the determinant up to a constant. By choosing nice values for $a$, $b$, $c$, and $d$, you can compute that constant--and have thereby reduced the problem to finding the determinant of a single matrix with numerical entries.
Mar
19
comment How to find the trigonometric identities?
Did you really mean to post this on a site about Mathematica software? By the way, there is an infinity of trigonometric identities. They can all be determined from a very small number of them in standard ways, such as a statement of the first order linear ODE satisfied by $\cos(x) + i \sin(x)$ (together with their initial conditions) and the definitions of the other trig functions in terms of them, or the power series definition of $\exp(i x)$, or the definition of $\exp(z)$ as the inverse of $\int_1^z \frac{dz}{z}$, or the infinite product representation of $\csc(z)$, etc.
Mar
1
comment A Cover of an Orientable Manifold is Orientable
You used one more thing that you're not explicitly making note of: the existence of a nowhere vanishing form on $M$.
Feb
28
comment Lagrangian Duality Complementary Slackness solution
This isn't really a data analysis question. Math has agreed to look at it. Cheers!
Feb
6
comment Probability proof and combinatorics
I have rolled this question back to its original form because the corrections added in the edit make it incomprehensible: without the typographical errors, there's no question here at all and the comments make no sense.
Feb
6
revised Probability proof and combinatorics
rolled back to a previous revision
Feb
6
comment Probability proof and combinatorics
@Dilip Sorry; I wasn't trying to imply you weren't aware: your comment showed you understood the issues. My comment was intended to help the OP avoid a possible misunderstanding of your comment, which could cause the reader to focus on the second equality in each line without noticing the blatant typographical errors that occurred at the first equality.
Feb
6
comment Probability proof and combinatorics
@Dilip Actually, the $k!$ in the numerator on the first line and the $(n-k+1)!$ on the second line are typos. Upon removing the extraneous "!", all is well.
Feb
5
comment sum of two random variables
+1 There should be no objections from purists: use of $\delta$ can be made rigorous in the (Schwartz) sense of distributions. Integration by parts of the convolution of the PDFs produces an integral which is the product of the derivative of the Gaussian PDF and the Heaviside function, both of which are integrable (even Riemann integrable).
Jan
13
comment Game with losing and winning a dollar
The probability of winning $n$ dollars is $0$ unless $k=0$, because the most that can be won is $n-k$. Perhaps you mean to ask for the probability of reaching a total of $n$ dollars?
Jan
13
reviewed Close What is gained by computing additional digits of $\pi$?
Jan
13
comment A system of equations of Vietnamese Mathematical Olympiad 2013
Cross-posted at mathematica.stackexchange.com/questions/17621/….
Jan
11
comment A system of equations of Vietnamese Mathematical Olympiad 2013
Hint: add the equations and show that $\sqrt{\sin^2 x + \dfrac{1}{\sin^2 x}} + \sqrt{\cos^2 x + \dfrac{1}{\cos^2 x}}$ is minimized when $\sin^2 x = \cos^2 x = 1/2$. The rest is easy.
Jan
10
comment Can a symmetric matrix always be represented as the sum of a positive-definite and negative-definite matrix?
Intuition: Sylvester's Law of Inertia implies there always exists a basis in which a Real symmetric nondegenerate matrix is diagonal with $p$ ones and $q$ $-1$'s on the diagonal; $(p,q)$ is its signature and is a property of the matrix as an endomorphism of a vector space (that is, it is the same for all such bases). The matrix with the $-1$'s replaced by zeros is obviously positive semidefinite and the matrix with the $1$'s replaced by zeros is obviously negative semidefinite; their sum is the original matrix.
Jan
10
answered Confusion related to the simplification of an equation
Jan
10
comment Confusion related to a convex optimization problem
Closely related: math.stackexchange.com/questions/274837.
Jan
9
comment Confusion related to calculation of Hessian
It's a straightforward calculation. Why don't you try it for the case $n=2$? That will show you why the result is a difference of two terms and where all the pieces are coming from.
Jan
5
revised Optimisation problem; Length of a cable
added 43 characters in body