Path: utzoo!attcan!uunet!wuarchive!rex!ames!amdcad!sun!sunfedcomm!regenmeister!chrisp
From: chrisp@regenmeister.uucp (Chris Prael)
Newsgroups: comp.software-eng
Subject: Re: CS education [engineering, mathematics, and computer science]
Message-ID: <34795@regenmeister.uucp>
Date: 20 Nov 89 19:09:13 GMT
References: <1408@cs.rit.edu>
Sender: daemon@sunfedcomm
Organization: Sun Microsystems, Inc. - Mtn View, CA
Lines: 74

From article <1408@cs.rit.edu>, by mjl@cs.rit.edu:
> Since I started this thread, let me toss out a few more thoughts.  I
> think the most important contribution of mathematics to computer
> science/software engineering is its mode of inquiry.  I'd say that it 
> is the approach to problem solving -- defining a specification or 
> reasoning about a program in the context of a rigorous axiomatic 
> system -- that most closely ties mathematics and computing.

My observation and experience is that this relationship is historical in
origin.  It traces to the fact that most computer science departments 
were spun off from mathematics departments.  I watched the process while 
I earned my BS in math.  From what I saw, it appeared that many of the
people who moved from math to computers did it not because they were 
interested in computers but they were not particularly successful at
math.  This resulted in "computer science" departments that were really
bad imitations of mathematics departments.  The repeated paragraph
implies that this is still true.

There are two other sources of the mathematical misapprehension.  The
first is that the earliest applications performed with computers were
mainly numerical analysis problems.  As a result, many thought that the
application was the field.  The other is the fact the programs are
completely abstract.  So, it is not surprising that a lay person would
assume that because computing and mathematics share the attribute of
having no concrete representation they are the same.  This confusion is
hard to excuse in a professional.

> In this respect, a good dose of discrete
> mathematics or basic modern algebra is appropriate, not so much because
> of the topics per se, but rather because the form of the proofs in
> these domains maps most closely onto the formal models of computation.

Perhaps this is another way of saying that the formal models of
computation have been copied from that of modern algebra.

> (Of course, the topics themselves contain gems of abstraction and
> generalization, for those willing to do some mining).

I found modern algebra to a little too long on recipies and a lot too
short on theoretical structure.  Far more useful would be time spent on
naive set theory, properties of the real line, logic (not the primitive
stuff!), and metatheory (theory of theories).  These are topics that you
can (and must) really chew on!

> What bothers me most is that this implies a significantly deeper
> understanding of mathematical principles than is required by other
> engineering disciplines.  

Which could be reasonably taken to imply that mathematical principals
have as much to do with software engineering as it does with the other
engineering disciplines.

> Or, to phrase it slightly differently:
> 	Formal methods of software engineering require the engineer
> 	to think like a mathematician.  This is untrue of any other
> 	engineering discipline I am aware of.  Why the discrepancy?

The discrepancy is clearly in the formal methods.  They have nothing 
functional to do with software and nothing functional to do with
engineering.  An engineer DOES NOT think like a methematician.  He/she
thinks like an engineer!  Trying to ape mathematicians will not make one
an engineer.  Not does it make one a mathematician.  It makes one an 
imitation mathematician!

> 	Can we address this by creating "boilerplate" mathematics
> 	for software engineering?

No!  This problem can only be addressed by ending the attempt to be
imitation mathematicians. 

The fact that you are questioning a quarter century of dogma is a major
step forward.  Take the next step.

Chris Prael