[comp.edu] Teaching Math in the Late Twentieth Century

skajihar@udenva.UUCP (06/09/87)

Back when I was a lowly freshman, they told us that our university was one
of four given a grant to develop a "Twentieth Century" mathematics curriculum
(i.e., discrete mathematics) as opposed to the classical curriculum (i.e.,
continuous mathematics) of the time.  Does anyone know who the others were?

I graduated this past Saturday (June 6) with neither computer science or math
as a major.  However, I was inflicted with same experiment that the above
suffered because of my chosen field of study.  One complaint that I had about
some of the classes of the above curriculum was the emphasis that they had on
the discrete mathematics.  How useful is it to learn graph theory and
algorithms for polynomials in a linear algebra course?  Is not the usual path
one covering matrices and vector spaces?

Another complaint was the eventual phasing out of true math courses and
increasing the offering of computer science courses.  Some classes that were
two quarters long were offered only for the first quarter in alternate years.
The claim was that no one would teach these courses and that no one would
take them.  However, rumor had it that many instructors wanted to teach
computer courses over math courses because of the money involved.  As for the
number of students, I had classes of the same level that had half to a third
of the students that would take some of these other classes.

Last, but not least, is it that cruel to expect that the computer science
people have at least a basic understanding of the math that they will use?
Granted, as I have been told, this is not always necessary for the fields
that many of them take up, but who knows what these people will take up?
There are people out in the world who do scientific programming for
researchers; if the program crashes, they have no idea of how their code
relates to the oriiginal equations that they were given.  Moreover, they
teach material at junior/senior level that should have been taught in high
school.  I have been flamed by some of these instructors that I am out of the
targeted group, but I wonder if they are not aiming their expectations too low.

These are merely the opinions of a dissatisfied graduate of this fine
institution's Computer Science and pseudo-Mathematics Department.  Just
wondering what other people on the net feel about these.

     Scott Kajihara

-- 
________________________________________________________________________________

      Learn to lie effectively for if you tell people the truth, they will
      still not believe you.

      -- Scott Kajihara

      UUCP:  ...!udenva!skajihar
      BITNET: skajihar@ducair

________________________________________________________________________________

howard@cos.UUCP (06/12/87)

In article <3797@udenva.UUCP>, skajihar@udenva.UUCP ("Lord of Sith" Kajihara) writes:
> 
> I graduated this past Saturday (June 6) with neither computer science or math
> as a major. One complaint that I had about
> some of the [CS] classes of the above curriculum was the emphasis that they had on
> the discrete mathematics.  How useful is it to learn graph theory and
> algorithms for polynomials in a linear algebra course?  Is not the usual path
> one covering matrices and vector spaces?

Graph theory is intensely useful to computer science practitioners involved
with data bases and communications; it is less relevant to mathematicians.

> 
> Another complaint was the eventual phasing out of true math courses and
> increasing the offering of computer science courses. 

I hope we can learn from the physicists and others and recognize the need
for mathematical tool courses (e.g., differential equations for physics)
as distinct from mathematical theory courses.  It may be that there fewer
pure mathematics programs can be justified, if the fewer programs can be
of higher quality.

> 
> Last, but not least, is it that cruel to expect that the computer science
> people have at least a basic understanding of the math that they will use?
> Granted, as I have been told, this is not always necessary for the fields
> that many of them take up, but who knows what these people will take up?
> There are people out in the world who do scientific programming for
> researchers; if the program crashes, they have no idea of how their code
> relates to the original equations that they were given.

Yes, I think it is cruel, if the math they are taught is not the math
they will use.  "Scientific programmers," as I believe you see
them, are increasingly a minority, as better software and personal computers
are available to more computer-literate scientists.  My experience is that
the more sophisticated numerical algorithms are more apt to be written
by physical scientists and engineers than "scientific programmers."

My flame here on "the math they will use" concerns what I feel is an
emphasis on analysis and theoretical abstract algebra, as opposed to
useful discrete mathematics, statistics, and operations research.  I hae
spent about 20 years in mostly state-of-the-art operating systems,
networks, and online applications.  I have found it necessary to study
more discrete math (graph theory, groups, number theory as applied to 
coding, etc.) and statistics/OR, and have rarely needed calculus or
differential equations (even with appreciable hardware work!)

Even in communications traffic engineering, founded on queueing theory,
I find little need to, say, derive a Poisson or Erlang distribution.
For most purposes, there are adequate packages or subroutine libraries;
for special purposes, specialists are needed.  If I want a complex
queueing model developed, where special distributions are involved,
I would no more try to do it than have a "scientific programmer"
design the code for a network control center!  There are enough subtleties
involved in modern queueing theory that it is not a job for dilettantes.

> Moreover, theyteach material at junior/senior level that should have
>been taught in high
> school.  I have been flamed by some of these instructors that I am out of the
> targeted group, but I wonder if they are not aiming their expectations too low.

Without knowing your background and current status, I wonder if you may
be equating "mathematical maturity" with "software maturity?"  In a related
context, I have taken graduate CS courses where material belonging in
an undergraduate or even high school honors programs was being taught,
such as extended discussions of singly linked lists in an alleged graduate
CS course in data structures.

Howard
(howard @ cos.com  via hadron, seismo->hadron, sundc, hqda-ai)
(703) 883-2812

eugene@pioneer.arpa (Eugene Miya N.) (06/15/87)

In article <315@cos.COM> howard@COS.COM (Howard C. Berkowitz) writes:
>Graph theory is intensely useful to computer science practitioners involved
>with data bases and communications; it is less relevant to mathematicians.

I beg you pardon!  Less relevant?

>I hope we can learn from the physicists and others and recognize the need
>for mathematical tool courses (e.g., differential equations for physics)
>as distinct from mathematical theory courses.  It may be that there fewer
>pure mathematics programs can be justified, if the fewer programs can be
>of higher quality.

In a university, no one appears completely satisifed.  I have a friend
who teaches the graduate math methods for physicists class in Santa
Barbara (A great place to winter for physicists).  The physics
department teaches that class because similar math classes (and ME
classes don't have the `proper' slant).  I also counted 6 intro to
programming classes in different departments: CS, Math, Engineering,
sociology, psychology, and music.  Similarly the engineering departments
were looking for technical writing classes in English.  English dept.:
"Say what?"

>Yes, I think it is cruel, if the math they are taught is not the math
>they will use.  "Scientific programmers," as I believe you see
>them, are increasingly a minority, as better software and personal computers
>are available to more computer-literate scientists.  My experience is that
>the more sophisticated numerical algorithms are more apt to be written
>by physical scientists and engineers than "scientific programmers."

I beg to differ again.  I offer LINPACK and Jack Dongarra (a computer
scientist more than a programmer whose work is widely distributed (May
1987, CACM) as a counter example.  Many scientists (more concern with
their research) will end up reinventing principals of software
engineering (if they are smart enough, otherwise they will just create
tomorrow's dusty decks).

>My flame here on "the math they will use" concerns what I feel is an
>emphasis on analysis and theoretical abstract algebra, as opposed to
>useful discrete mathematics, statistics, and operations research.  I hae
>spent about 20 years in mostly state-of-the-art operating systems,
>networks, and online applications.  I have found it necessary to study
>more discrete math (graph theory, groups, number theory as applied to 
>coding, etc.) and statistics/OR, and have rarely needed calculus or
>differential equations (even with appreciable hardware work!)
>Howard

The problem, Howard, is that people divide the world up into their
discipline and `service' disciplines.  The physicists rely on mechnical
engineers to build things for them, but other MEs (in Universities)
do various kinds research, but the physicists don't make that
distinction.  The same goes for math and computing science.  Calculus
will come back.  Your perceptions are largely the part of they type of
computing you do, the languages, and so forth.  I thought about trying
to convince one friend to start off his students with a symbol
manipulation package like Macsyma, but so many students come to school
knowing BASIC this is a major problem (Note a recent issue of
Engineering and Science from Caltech Featured an article about using
BASIC to teach physics students at Caltech! an abomination!).

From the Rock of Ages Home for Retired Hackers:

--eugene miya
  NASA Ames Research Center
  eugene@ames-aurora.ARPA
  "You trust the `reply' command with all those different mailers out there?"
  "Send mail, avoid follow-ups.  If enough, I'll summarize."
  {hplabs,hao,ihnp4,decwrl,allegra,tektronix,menlo70}!ames!aurora!eugene