20,866 reputation
33473
bio website
location
age
visits member for 2 years, 7 months
seen 2 hours ago

1d
comment Rational roots of a polynomial with integral coefficients and constant term 1.
You have shown that any possible rational root must be $\pm 1$. You're done, as $1+p_1 + \cdots$ is not zero, nor is $1-p_1+\cdots$, which are the exact expressions you get for using $\pm 1$. That's it.
1d
comment How to select the right books?
Take a book. Read it. Work some problems. If you hate it, make a note of it and set it aside. Find a different book, and iterate until you find one you like. After you have finished the book you like, ask yourself why you hated the other books. Go back to them. See if your newfound knowledge gives you a different opinion.
1d
comment Intuitively, why is the Gaussian the Fourier transform of itself?
Yes, I will update the link. Thanks.
2d
comment Old oxford scholarship question: $a^ab^b \ge a^bb^a$
@TheMathTroll Alas, one must be way of the 200 rep daily upvote cap!
2d
answered Solve $x''(t)-\frac{x^2(t)}{\sin t}=\frac{\sin\left( (t-1)^2\right)}{\sin t}$.
2d
comment Prove ${x:d(x,p) < d(x,q)}$ is open in metric space $X$
Once you do that step, the remainder of the proof will fall out directly from the definition of an interior point.
2d
comment Prove ${x:d(x,p) < d(x,q)}$ is open in metric space $X$
Typically, how is it proved whether a set is a subset of another set?
2d
comment Prove ${x:d(x,p) < d(x,q)}$ is open in metric space $X$
You're skipping over the formality of the set inclusion step. Why is $N_r(x) \subset E$?
Dec
16
comment If $v_1,…,v_r$ are the eigenvectors that correspond to distinct eigenvalues, then they are linearly independent.
I certainly got caught halfway through forgetting what was a hypothesis, and what we were trying to prove.
Dec
16
comment If $v_1,…,v_r$ are the eigenvectors that correspond to distinct eigenvalues, then they are linearly independent.
+1... what I was trying to do until I got caught up in jibberjabber.
Dec
16
comment Solving ODE for x instead of y
You seem to have misplaced a $dy$. I am not sure if that is a typo or the source of your error.
Dec
16
revised When using the Central Limit Theorem, how to scale the mean and variance depending on the number of samples?
added 1 character in body
Dec
16
comment When using the Central Limit Theorem, how to scale the mean and variance depending on the number of samples?
Precisely.${}{}$
Dec
16
comment When using the Central Limit Theorem, how to scale the mean and variance depending on the number of samples?
The Central Limit Theorem states that a sum of i.i.d. random variables can be well approximated by a Gaussian (aka normal) distribution. The cumulative distribution function of a normal distribution is given by the first representation that I wrote. The steps I completed basically showed that multiplying the mean by $N$ and the standard deviation by $\sqrt{N}$ and keeping the mean the same and dividing the standard deviation by $\sqrt{N}$ result in the same distribution.
Dec
16
answered When using the Central Limit Theorem, how to scale the mean and variance depending on the number of samples?
Dec
16
revised how find this polynomial?
Retagged
Dec
16
comment The “sin-cos-maximum” function
I know. I was remarking that the OP wanted a compact expression. This is... decidedly less so ;)
Dec
16
comment The “sin-cos-maximum” function
Well, the intervals are compact.
Dec
16
answered Polynomial Chaos: How are the pdfs calculated from the response surface?
Dec
15
comment Convergence of Newton method under some assumptions
Is the standard proof of quadratic convergence not sufficient here? It does not require that $f''$ be continuous, just bounded.