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seen Jun 24 '13 at 0:06

No, his mind is not for rent
to any god or government.
Always hopeful, yet discontent.
He knows changes aren't permanent,
but change is.

— Rush, Tom Sawyer


Taking an externally-imposed and much-needed break from SE activities.

E-mail (flipped ROT13): zqd˙ʎʌuzʇ@ʇɐʌǝɥʇʌssqɹǝɥɟuɹʎɔ
Any code I've posted here I place under the WTFPL.


Aug
18
comment Fitting a curve to a decreasing data set undefined at zero
Could you elaborate "scale is too small" and "curve is too pronounced"? Again, where did these points come from? As an aside, reciprocal powers $cx^{-n}$ satisfy "becomes closer to infinity as x grows closer to 0, and closer to 0 the closer x gets to infinity."
Aug
18
comment Fitting a curve to a decreasing data set undefined at zero
A succinct way to summarize Tom's comment: there are far too many ways to connect dots, some wigglier and some stiffer than others.
Aug
18
comment Fitting a curve to a decreasing data set undefined at zero
Even with that restriction, there are far too many functions that are singular at the origin, the reciprocal and logarithm functions being two examples. Again, without a plot or knowledge of where said points came from, there is no useful answer we can give.
Aug
18
comment Fitting a curve to a decreasing data set undefined at zero
(0,inf)? Is that even a valid point? Without insight into where the points came from, or even a plot of the points, any attempt to model those points with an arbitrary equation might as well be voodoo.
Aug
18
comment An elementary way of simplifying a trigonometric triple integral?
Probably the galling thing about it is that the hypergeometric function keeps on cropping up even after the use of Assuming[] to tell Mathematica that I have integer variables; on the other hand, I also noticed during my preliminary analysis that the binomial sum from 0 to 2k can be converted into a sum ranging from 0 to k due to odd powers of cosine vanishing when integrated from 0 to $2\pi$. I'll look into your approach and report back. Thanks!
Aug
17
comment A nicer proof of Lagrange's 'best approximations' law?
Nice pic Grigory, did you scan it or redraw the whole thing? :)
Aug
17
comment What are some uses for Monte Carlo simulations in mathematics?
Indeed, all different variations of sampling n-space as sparsely as one can get while still getting usable answers.
Aug
17
comment Is it possible to find the position of a prime number online?
Sieving is more or less what Mathematica does, using the logarithmic integral as an (over)estimate.
Aug
17
comment Is it possible to find the position of a prime number online?
Mathematica has a built-in ceiling for both Prime[] and PrimePi[]; see the documentation for the error message PrimePi::largp. This is probably both version and machine dependent.
Aug
17
comment An elementary way of simplifying a trigonometric triple integral?
Somehow, doing that replacement after performing the binomial expansion resulted in an even more hellish-looking integrand. I'll try to slug it out and see what develops though.
Aug
16
asked An elementary way of simplifying a trigonometric triple integral?
Aug
16
answered What are some uses for Monte Carlo simulations in mathematics?
Aug
16
comment What are some uses for Monte Carlo simulations in mathematics?
One should, BTW, distinguish between Monte Carlo algorithms, which can only compute approximations, and Las Vegas algorithms which, even with the "random" component of the algorithm, gives an exact answer.
Aug
16
comment What are some uses for Monte Carlo simulations in mathematics?
Probably a bit inaccurate to say "only practical choice"; "quasi-Monte Carlo" methods (i.e. using more "deterministic" sequences like the Niederreiter or Sobol sequences instead of a PRNG) can sometimes give better results than Monte Carlo proper.
Aug
16
comment Common English language mistakes in mathematical writing
I tend to see those grammatical wrinkles in European work (e.g. German, French). At this point, may I refer people to this nice book: maths.manchester.ac.uk/~higham/hwms
Aug
16
comment Common English language mistakes in mathematical writing
For wiki-ing I suppose.
Aug
16
comment On applying the quadratic formula to a first-degree equation
A further note: if you take the projective geometry view that parallel lines "intersect at infinity", that corresponds to setting a and b equal to 0 in ax²+bx+c.
Aug
16
comment On applying the quadratic formula to a first-degree equation
For those who didn't understand "solving a+b/x+c/x² for 1/x", observe that treating 1/x as an atom and performing completing the square gives you $\frac1{x}=\frac{-b\pm\sqrt{b^2-4ac}}{2c}$. Now try working out the degenerate case of $a=0$ using this formula.
Aug
16
comment On applying the quadratic formula to a first-degree equation
Qiaochu essentially did the equivalent of moving b to the RHS as is usual when isolating variables.
Aug
16
answered On applying the quadratic formula to a first-degree equation