J. M.
Reputation
424/400 score
 Oct 9 comment How can I read this mathematical sentence aloud in English? @yatima: nope, the Greek alphabet has only twenty-four; the Latin alphabet has twenty-six. Oct 9 comment How can I read this mathematical sentence aloud in English? "Communicating any significant amount of math in a purely oral manner is incredibly hard because mathematical notation is much denser than ordinary spoken language" - indeed. +1 for this. Oct 9 comment How can I read this mathematical sentence aloud in English? What book is this from? Otherwise, I verbalize $\nu_X$ as "nu sub x" Oct 9 revised Convergence of $\sum_{n=1}^{\infty} \frac{\sin (n x)}{2^n}$ edited tags; edited title Oct 9 revised Are there addition formulas for the Riemann Zeta function? edited tags Oct 8 comment Are all polynomials solvable? As a commenter mentioned in the blog post Qiaochu linked to, for the cubic case, whether a solution to the cubic can be expressed as radicals of real quantities depends on the discriminant of the cubic equation; for the so-called casus irreduciblis, you are essentially forced to use trigonometric functions (alternatively, hyperbolic functions) if you do not want to stray into the realm of $\mathbb{C}$, even if all the solutions are real. Oct 8 revised Bell numbers and moments of the Poisson distribution because Bell and Poisson are proper nouns Oct 8 revised Good Resources for Understanding Finite Field Arithemtic edited tags Oct 8 revised Are there integer solutions to $9^x - 8^y = 1$? edited tags Oct 7 comment Weird distance estimate? More importantly... what book is this? Oct 7 comment Weird distance estimate? What are the $\sigma$'s supposed to be? If those other variables are indeed polar coordinates, you have the wrong formula. Oct 7 revised What does E mean in 9.0122222900391E-5? edited tags Oct 7 comment What's the value of this Viète-style product involving the golden ratio? After a cursory look at this article, I suspect that this may come out in terms of an (Jacobi or Weierstrass) elliptic function, but I'm still trying to digest the formulae given. Maybe somebody with better analytical powers than me may be able to quickly figure out a closed form from the stuff in that paper. Oct 7 answered Can this sum be simplified: $\sum_{k=0}^{n-1} { n -1 \choose k } (-2)^{k} (2n - k)!$? Oct 7 comment What's the value of this Viète-style product involving the golden ratio? As to how I got that number in Mathematica: SequenceLimit[FoldList[Times, 1, NestList[Sqrt[1 + #] &, N[1, 50], 50]/GoldenRatio]]. Oct 7 comment What's the value of this Viète-style product involving the golden ratio? FWIW, attempts to find 0.509490972847535755... in the Plouffe inverter yielded nothing. Oct 7 comment Teaching mathematics in intuitive and thought provoking way From my experience, it is a sad fact that there exist students that for some reason are unable to imagine; that is to say, they are unable to see with their mind's eye. For me that proved a tough barrier to overcome since I see things geometrically, but I still have no clue on how to teach imagination to students. Oct 6 comment FitzHugh- Nagumo caricature of the Hodgkin-Huxley equations Why not try substituting $U(x+ct)$ and $V(x+ct)$ into the PDE and see what you get? Oct 6 revised FitzHugh- Nagumo caricature of the Hodgkin-Huxley equations edited tags Oct 6 comment The pseudoness of pseudorandom number generators As for the sort of PRNGs that are easy to break with current standard tests, linear congruential generators have so short a period that they are caught quickly, unless one augments them with thing like L'Ecuyer's tricks.