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 Dec24 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))? Sep19 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? Mar30 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. Mar24 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. Mar12 comment Chernoff bounds - basic results One question: did you check the Wikipedia article on Chernoff Bound? Mar1 comment Statistics resources with examples for a C.S. student He wants statistics resources not probability. Jan28 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. Jan28 comment Conditional expectation of $E[X|Z]$ where $Z= \max(X,Y)$ @Didier Piau, I don't understand why the numerator isn't $zf_X(z)F_Y(z) + \mathbb{E}(X|X \le z)f_Y(z)F_X(z)$. Jan22 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? Jan20 comment find the distribution of $Z = Y\sqrt X$ Is it truly $V_1/V_2$ and $V_2$? If so then yes. Sep13 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. Jul21 comment Help with a derivative Just do it the normal way; or take the log of your expression and calculate its derivative. Jul20 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. Jun18 comment Good textbooks on combinatorics for self-study I would not classify this book as introductory at all. Apr14 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. Mar16 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 $16 new. Mar5 comment Explain$-\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\$. Mar2 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. Feb28 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. Feb27 comment Help calculating a series I like this more than the choosen answer because it is easily seen to be true.