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Dec
24
comment Proving that $\left(1+\frac{z_{1}}{z_{2}}\right)\left(1+\frac{z_{2}}{z_{3}}\right)…\left(1+\frac{z_{n}}{z_{1}}\right)\in\mathbb R$
should be 2\cos(t_i-t_j)e^(i(t_i-t_j))?
Sep
19
comment Limit of an integral containing a product
Are the integral limits 1 to infinity and do you mean N approaches infinity instead of of x?
Mar
30
comment If a rational number has a finite decimal representation, then it has a finite representation in base $b$ for any $b>1?$
Not true. 0.1 base 10 = 0.00011001100110011.... in base 2.
Mar
24
comment How can I use Cauchy integral formula for this integral $g(z)=\int_{C}\frac{s^2+s+1}{s-z}ds$?
Also you should remember if f(z)/(z-z_0) is analytic within and on C, then the integral is 0.
Mar
12
comment Chernoff bounds - basic results
One question: did you check the Wikipedia article on Chernoff Bound?
Mar
1
comment Statistics resources with examples for a C.S. student
He wants statistics resources not probability.
Jan
28
comment Conditional expectation of $E[X|Z]$ where $Z= \max(X,Y)$
@Didier Piau, thanks for the clarification! For some reason I had always thought $;$ or $|$ meant the same thing; similar to $:$ and $|$ for describing sets.
Jan
28
comment Conditional expectation of $E[X|Z]$ where $Z= \max(X,Y)$
@Didier Piau, I don't understand why the numerator isn't $zf_X(z)F_Y(z) + \mathbb{E}(X|X \le z)f_Y(z)F_X(z)$.
Jan
22
comment Real life applications of Topology
Knowledge of topology is often crucial for passing your PhD qualifying exams in math. You do want your PhD, don't you?
Jan
20
comment find the distribution of $Z = Y\sqrt X$
Is it truly $V_1/V_2$ and $V_2$? If so then yes.
Sep
13
comment Is there any math operation defined to obtain vector $[4,3,2,1]$ from $[1,2,3,4]$?
It's the called the reverse identity matrix J. J[1 2 3 4]^T = [4 3 2 1]^T.
Jul
21
comment Help with a derivative
Just do it the normal way; or take the log of your expression and calculate its derivative.
Jul
20
comment What are the Axiom of Choice and Axiom of Determinacy?
This answer is at the wrong level and self-indulgent. And honestly probably doesn't help the original poster.
Jun
18
comment Good textbooks on combinatorics for self-study
I would not classify this book as introductory at all.
Apr
14
comment Algorithmic Complexity of Iterated Sums
I don't think so. Let f(a,n) := {if (n>1) n*f(a,n-1) else 1} = n!. Then f(a,n) is a polynomial-time algorithm using simple operations but F(n) is not a polynomial-time algorithm.
Mar
16
comment Recommend a statistics fundamentals book
If you just want a review, just read Schaum's Outline of Probability and Statistics. It's less than $16 new.
Mar
5
comment Explain $-\int^{a}_{b}\frac{Q}{4 \pi \epsilon \bar{r}^{2}} \cdot d \bar{r}= \left[\frac{Q}{4\pi \epsilon \bar{r}}\right]^{a}_{b}$
In American textbooks, curl is usually written $\nabla \times$.
Mar
2
comment Line simplification algorithm
Is the shape important or is only the frequency of the teeth important? If only the frequency of the teeth, you can use a color gradient instead. You have 5000 points but only 450 pixels, then split the line into fixed number intervals (each with 30 points for example) and calculate how many teeth there are in each interval. Then color code with red for very few teeth and blue for very many teeth.
Feb
28
comment Mathematical difference between white and black notes in a piano
"harpsichords had to be retuned each time one wanted to play in a different key, right?" No they did not because only some keys would sound disagreable but not all. It is far easier to avoid certain keys than to retune an instrument; a harpsichord can be retuned but not a pipe organ. Sorry, I'm off topic.
Feb
27
comment Help calculating a series
I like this more than the choosen answer because it is easily seen to be true.