As of May 4 2007 the scripts will autodetect your timezone settings. Nothing here has to be changed, but there are a few things

## Monday, October 15, 2007

### Difference sequences

Rather early in our math education we learn about functions and derivative functions.
                f(x+h)-f(x)f'(x) = lim   -----------         h-> 0    h For example: f(x) = x^nf'(x) = n*x^(n-1)

Something similar can be defined for sequences, in that case the 'derative' is called the difference sequence.
a_n = {1, 16, 81, 256, ... }f(n) = n^4f'(n) = 1 + 4n + 6n^2 + 4n^3f''(n) = 14 + 24n + 12n^2f(3)(n) = 36 + 24nf(4)(n) = 24For an arbitrary sequence f:f(m)(n) = Sum[(-1)^(k)*Binomial[m,k]*f[n-k+m],{k,0,m}]

Here also we see that Pascal's Triangle has a crucial meaning.

## Welcome to The Bridge

Mathematics: is it the fabric of MEST?
This is my voyage
My continuous mission
To uncover hidden structures
To create new theorems and proofs
To boldly go where no man has gone before

(Raumpatrouille – Die phantastischen Abenteuer des Raumschiffes Orion, colloquially aka Raumpatrouille Orion was the first German science fiction television series. Its seven episodes were broadcast by ARD beginning September 17, 1966. The series has since acquired cult status in Germany. Broadcast six years before Star Trek first aired in West Germany (in 1972), it became a huge success.)