# a single text fulfilling mathematical prerequisites for SICP? [Was: Re: [plt-scheme] PLT Scheme and SICP]

On Mon, Apr 21, 2008 at 11:49 AM, Benjamin L. Russell
<dekudekuplex at yahoo.com> wrote:
>* Does anybody know of a single title that contains all
*>* of the assumed domain knowledge for SICP; in
*>* particular, the mathematical prerequisites?
*
Nope. But if you want just the prog. lang. knowledge in SICP these
exercises aren't necessary.
>* * a means of developing creativity for solving
*>* mathematical proofs, such as Exercise 1.13, where it
*>* is necessary to prove the following:
*>*
*>* Fib(n) = phi^n/sqrt(5)
*>*
*>* where phi = (1 + sqrt(5))/2, a.k.a. the Golden Ratio.
*>*
*>* (see the tinyurl http://tinyurl.com/3rbakp).
*
This one took me some time. The trick is that you need the identity
for the golden ratio given in 1.22 (phi^2 = phi + 1). I didn't show
that phi^k - psi^k is the closest integer to phi^k, and I'm not really
sure how. I guess using the binomial expansion and canceling terms
would do it.
I imagine a tool like Maple or Mathematica would be useful for
exploring these problems, and they might meet your "mathematical
scratchpad" requirement. I don't have proficiency in either, though.
N.