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

From: Benjamin L. Russell (dekudekuplex at yahoo.com)
Date: Mon Apr 21 06:49:33 EDT 2008

Does anybody know of a single title that contains all
of the assumed domain knowledge for SICP; in
particular, the  mathematical prerequisites?  Most
courses that use that book just list "a course in
discrete mathematics," which I've already taken, but
that was about 15 years ago.

Most important requirement:

* 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).

<only-half-facetious joke>
I.e., at some point in this proof, there is an "aha!"
moment--a moment in which insight strikes.  The
problem is how to arrive at this "aha! moment"
deterministically, for other problems in SICP
involving creative mathematical proofs as well.

Another useful tool would be a means and apparatus for
performing mathematical scratchpad work on a computer,
without using a pencil or paper, perhaps by using a
graphical input tablet.  (This is very useful for
people living in extremely cramped apartments, where
there is no room for an extra table.)

The need for these two tools is one requirement that
distinguishes SICP from most other programming texts,
which usually only require a computer with an
interpreter/compiler and editor.
</only-half-facetious joke>

Benjamin L. Russell

--- "Benjamin L. Russell" <dekudekuplex at yahoo.com>

> [snip]
> I was surprised to read that Eli Bendersky skipped
> some of the SICP exercises.  I had always tried to
> do
> every single exercise, with the unfortunate result
> of
> getting stuck and not easily being able to proceed
> further on some.  Since it is apparently possible to
> skip some of the exercises and still essentially
> complete the book, I am now tempted to resume this
> quest.
> Eli's story is very motivating....
> Benjamin L. Russell
> --- Shriram Krishnamurthi <sk at cs.brown.edu> wrote:
> > That's really cool.  It's even more neat that he
> > could avail of a
> > world-class computer science education from the
> > comfort of home!
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