mjl@cs.rit.edu (03/11/90)
The general thread in this discussion seems to be favoring continuous
mathematics (up through differential equations) over what, for lack of
a better term, I'll call "abstract mathematics". (In this category I
include courses such as discrete mathematics and modern algebra.)
I find this disturbing because in every school I've seen (both as
student and teacher), it isn't until you get off the basic continuous
mathematical track and onto the abstract one that you learn how to
*think* mathematically. And it is *exactly* this mode of thought which
is essential to the education of those who'll be working in the
software development field. It's certainly more appropriate than the
rote, cookbook style mathematics that is the fare in introductory
calculus and differential equations.
[NOTE: the basic differential equations courses I've seen present a
potpourri of techniques, leading to exams that emphasize pattern
matching and rote transformations at the expense of depth of
understanding. I've used what I learned in differential equations
maybe 5 times in the past 20 years, but I use the abstract mathematics
I learned every time I sit down to create software of any
significance].
Of course, some computer science and software engineering graduates
will end up working on projects where knowledge of continuous
mathematics is a must; I'd advise such students to take all the
continuous mathematics they can. But *all* who choose careers in
software development need a solid foundation in abstract mathematical
reasoning, at least if we believe (as I do) that specifications,
designs, and programs are artifacts to which we can and should apply
our reasoning skills.
There are continuous mathematics courses that can help develop such
maturity, but they are generally junior/senior courses in Analysis
(notably absent from anyone's list). Furthermore, I'd argue that the
discrete and algebraic mathematics algebraic are more appropriate
because that they stress propositional and predicate calculus, sets and
relations, and proof by induction (all crucial components of the formal
systems I know).
Thus, I'd leave differential equations as an elective, and push for
more discrete mathematics or algebra (like group theory). Let's teach
mathematics appropriate to the discipline. I sometimes fear we
slavishly follow the lead of established engineering programs simply
for the cachet of being called engineers.
Mike Lutz
Mike Lutz Rochester Institute of Technology, Rochester NY
UUCP: {rutgers,cornell}!rochester!rit!mjl
INTERNET: mjl@csrit.edumquigley@kean.ucs.mun.ca (Martyn Quigley, E3044, x8656) (03/17/90)
In article <1652@cs.rit.edu>, mjl@cs.rit.edu writes: > The general thread in this discussion seems to be favoring continuous > mathematics (up through differential equations) over what, for lack of > a better term, I'll call "abstract mathematics"... > Thus, I'd leave differential equations as an elective, and push for > more discrete mathematics or algebra (like group theory). Let's teach > mathematics appropriate to the discipline. I second the motion, but why not scrap all the calculus? Presumably we've all got Macsyma or Maple or some such. I find it most interesting that so many remarks on this thread favour the retention of mathematics which is perfectly capable of being mechanised - by computer! > Mike Lutz Rochester Institute of Technology, Rochester N
gds@oahu.cs.ucla.edu (Greg Skinner) (03/18/90)
In article <70155@kean.ucs.mun.ca> mquigley@kean.ucs.mun.ca (Martyn Quigley, E3044, x8656) writes: >I second the motion, but why not scrap all the calculus? Presumably >we've all got Macsyma or Maple or some such. I find it most >interesting that so many remarks on this thread favour the retention >of mathematics which is perfectly capable of being mechanised - by >computer! Even if "we all had macsyma or maple" which we do not (at least *I* don't, and I could sure use it), it is important to learn the fundamentals of calculus because not all calculus problems are amenable to symbolic computation (or numerical, if you have those tools on hand). In addition, the concepts covered in calculus are necessary for the understanding of other types of mathematics important to computer scientists. (For example, expressing a recurrence relation in terms of a function of the derivative of another, to relate their behavior. In case you're interested, this came up in my analysis of algorithms class last fall.) --gregbo
mjl@cs.rit.edu (03/19/90)
In article <33153@shemp.CS.UCLA.EDU> gds@cs.ucla.edu (Greg Skinner) writes: > ... In addition, the concepts covered in calculus are >necessary for the understanding of other types of mathematics >important to computer scientists. (For example, expressing a >recurrence relation in terms of a function of the derivative of >another, to relate their behavior. In case you're interested, this >came up in my analysis of algorithms class last fall.) Actually, difference equations, a discrete mathematical structure, are closer models to recurrence relations than are differential equations. Still, Greg has a point, and I don't think any of us *really* want to discard all of continuous mathematics, but I would like to subordinate it to the more abstract mathematics mentioned in my earlier posting. Mike Lutz Mike Lutz Rochester Institute of Technology, Rochester NY UUCP: {rutgers,cornell}!rochester!rit!mjl INTERNET: mjl@csrit.edu