HDTenEightyP/NetNews huggingface dataset:
From: hrubin@pop.stat.purdue.edu (Herman Rubin)
Subject: Re: who should teach mathematics?
Organization: Purdue University Statistics Department
Date: Sun, 15 Nov 1992 15:42:32 GMT

In article <hdev.721610039@dutiag> hdev@dutiag.tudelft.nl (Hans de Vreught) writes:
>hrubin@pop.stat.purdue.edu (Herman Rubin) writes:

>>In article <1992Nov10.223300.19016@murdoch.acc.Virginia.EDU> tep2j@amsun.apma.Virginia.EDU (Todd E. Peterson) writes:

>>>Is it a good or bad practice to use non-mathematicians to teach mathematics
>>>courses?  In particular, what about the use of engineering faculty to teach
>>>engineering calculus courses, and other applied mathematics courses?

>>If they can teach it mathematically, it would be appropriate to have
>>them do so in the mathematics department. 

>Actually over here at my university every department is an enginering
>department, including the mathematics department. So, almost al math is given
>by engineers. When you study math here, you study it mathematically: starting
>with the axioms. So what's the big difference? Well, the topics that are
>covered during a math study over here are more focussed on problems you
>encounter as an engineer. The specific topics in math that are taught here are
>at the same level as the level you will encounter at a non-enginering math
>department of other universities.

>In principle a subject must be taught by a fully qualified person (i.e. a
>person with a degree on the subject he / she teaches). If he has an Arts /
>Science / Engineering background isn't that important, as long he presents his
>stuff the right way.

With that requirement, Knuth could not teach computer science, and I could
not teach statistics.  However, there are many with degrees in statistics
who do not understand it, and plenty with degrees in computer science likewise.

It used to be possible to get a PhD in mathematics and not know what a group
is, and it is almost possible now.  Most mathematicians have not even had a
course in partial differential equations or numerical analysis or logic.  
Some of these know enough of the subjects not only to be able to teach them,
but to be scholars in them.  Others do not.
-- 
Herman Rubin, Dept. of Statistics, Purdue Univ., West Lafayette IN47907-1399
Phone: (317)494-6054
hrubin@snap.stat.purdue.edu (Internet, bitnet)  
{purdue,pur-ee}!snap.stat!hrubin(UUCP)
From: andrew@rentec.com (Andrew Mullhaupt)
Newsgroups: sci.math
Subject: Re: closed forms
Date: 23 Nov 92 19:02:37 GMT
Organization: Renaissance Technologies Corp., Setauket, NY.

In article <1992Nov22.225043.12618@galois.mit.edu> jbaez@riesz.mit.edu (John C. Baez) writes:
>In article <1992Nov22.100111.42575@urz.unibas.ch> kullmann@urz.unibas.ch writes:
>
>>Another question that could belong here: How does one proof that there is
>>no closed form expression of \int(exp(-x**2))? 
>
>In practice, here's how: "If there was such a closed form, I would have
>heard about it.  But I haven't.  So there isn't.  QED."    

The requisite facts form what is sometimes called Liouville theory. See for
example the section of that name on pp. 79ff of Zwillinger's _Handbook of
Integration_, Jones and Bartlett, Boston (1992).

Later,
Andrew Mullhaupt
From: franz@ccrl.nj.nec.com (test user for max)
Newsgroups: sci.math
Subject: compactness ?
Date: 20 Nov 92 21:16:48 GMT
Organization: C&C Research Labs, NEC USA, Princeton, N.J.

I am trying to teach myself analysis; i'm stuck on the notion of compactness.
One book's definition:
  A subset S of a metric space E is compact if whenever S is
  contained in the union of a collection of open subsets of E,
  then S is contained in the union of a finite number of these
  open subsets.

The book (M.Rosenlicht,Intro.to Analysis) then gives an example of
a non-compact set- the open interval (0,1), which is contained in the 
union of sets (1/n,1) but not contained in any finite number of these.

? It seems to me that (0,1) is contained in the collection of
open sets { (0,0.6) (0.5,1) (0,1) } and this has finite subsets that 
contain (0,1), so (0,1) should be compact.  Does the definition mean that
S must be contained in any possible collection, as opposed
to just one possible collection being sufficient?  If so, then 
I would intuitively think that a (1/n,..) type construction
would prevent any open set from being compact.  
Is a 'collection of sets' a stricter notion than I'm assuming?
(Is 'contained in' the same as 'covered by'?)

Any insight on understanding the definition (and its relevance)
would be appreciated.  
Xref: sparky sci.math:15354 sci.physics:19373 sci.astro:12294 sci.bio:4198 sci.chem:4770 misc.education:4447
Newsgroups: sci.math,sci.physics,sci.astro,sci.bio,sci.chem,misc.education
Subject: Re: What can we have for an educational system?
From: kmushal@eis.calstate.edu (KAYE MUSHALIK)
Date: Sun, 22 Nov 1992 00:09:28 GMT
Organization: Calif State Univ/Electronic Information Services

bs@gauss.mitre.org (Robert D. Silverman) writes:
> In article <BxrGCs.4tp@mentor.cc.purdue.edu> hrubin@pop.stat.purdue.edu (Herman Rubin) writes:
> :In article <1992Nov15.122659.129397@zeus.calpoly.edu> mhorning@zeus.calpoly.edu (Mark E. Horning (Captain Neutrino)) writes:
> :>clin@eng.umd.edu (Charles Lin) states
> :
> :>>In article <ARA.92Nov11034458@camelot.ai.mit.edu>, ara@zurich.ai.mit.edu (Allan Adler) writes:
> :
> :
> :>>>As I have pointed out on other occasions, if they would improve the
> :>>>working conditions, they could have PhD's teaching in the public schools.
> :>>>I don't mean improve them a little. I mean offer working conditions that
> :>>>would make a PhD happy and the glut of unemployed and underemployed
> :>>>PhD's will beat down the doors of the schools trying to get in.
>  
> Actually, at least in my experience, the conditions that would make 
> most PhD's happy are essentially impossible to obtain. Nothing the
> schools or school systems could do would provide what they want.
> 
> What they want of course is motivated students and students who
> are *interested* in learning. This is the responsibility of parents.
> Currently, cultural conditions in the U.S. are such that most people
> do not place a high value on education. The result? Students who
> don't give a shit.
> --
> Bob Silverman
> These are my opinions and not MITRE's.
> Mitre Corporation, Bedford, MA 01730
> "You can lead a horse's ass to knowledge, but you can't make him think"

I had a teacher in high school who had a PhD but couldn't teach worth
"beans". It was obvious that he knew his subject well but he couldn't 
convey any excitement to us. I don't claim to be brilliant, but there
were kids in my class who were and they even had trouble with the subject.
Yes, it's important to know the subject matter, but it is more important to
know how to make that subject EXCITING and RELEVANT to the students' lives.

**Kaye**
Newsgroups: sci.math
From: gardnerm@griffin (Mack GardnerMorse)
Subject: "Fair" Votes
Keywords: Voting, Mathematics
Organization: University of Vermont -- Division of EMBA Computer Facility
Distribution: na
Date: Mon, 16 Nov 1992 14:07:09 GMT

I have lost the reference to the mathematical analysis which shows why "one
person one vote" is not always "fair" that was posted last week.  If anyone
could E-Mail the reference or repost it, I would greatly appreciate it.

Sincerely yours,

Mack Gardner-Morse
E-Mail: gardnerm@uvm-gen.emba.edu
University of Vermont
Dept. of Orthopaedics & Rehab.
Burlington, VT 05405
From: RVESTERM@vma.cc.nd.edu
Newsgroups: sci.math
Subject: no, this is not homework
Date: 19 Nov 92 11:07:36 GMT

given an n-chromatic graph on m vertices, what is the maximum number
of edges possible?

bob vesterman.
From: geversti@oasys.dt.navy.mil (Gordon Everstine)
Newsgroups: sci.math
Subject: Re: Magic Squares (was: Re: Sum of Numbers)
Date: 17 Nov 92 18:35:50 GMT
Reply-To: geversti@oasys.dt.navy.mil (Gordon Everstine)
Organization: David Taylor Model Basin, Bethesda, Md.

In addition to the brute force approaches to generating magic squares,
there are various algorithms available for square generation.  Of
course, each algorithm will generate only one of the many possible
squares of a given order.

Odd and even order squares must be constructed by different approaches.
For odd orders, the most common algorithm is a recursive scheme
devised by de la Loubere about 300 years ago.  For even orders, one
procedure is the Devedec algorithm, which treats even orders not
divisible by 4 slightly differently from those which are divisible by
4 (doubly even).
  
These algorithms and others are described in, for example, "Magic
Squares and Cubes" by W.S. Andrews (The Open Court Publishing Co.,
Chicago, 1908; may also be available from Dover) and "Mathematical
Recreations" by M. Kraitchik (Dover, 1953).
From: perkins@tallis.enet.dec.com (Eric Perkins)
Newsgroups: sci.math
Subject: Gnu Multi-precision Package (GMP):
Date: 23 Nov 92 18:07:30 GMT
Reply-To: perkins@tallis.enet.dec.com
Organization: Digital Equipment Corporation, Littleton MA


Has anyone used the Gnu Multi-precious Package (GMP)?
I have been trying to use it and have had not end of trouble
trying to get simple things to work.

If anyone else has tried it I would be curious to know if they
find it is working or not.

Are there any other multi-precision packages out there in the public
domain?

-- Eric
===============================================================================
-- Note: All views questions, and thoughts are my own and in no way represent
--       those of my employer or anyone else.
--
-- I can be reached by the following means:
-- Eric Perkins			E-Mail : perkins@tallis.enet.dec.com
-- Digital Equipment Corp	Phone  : (508) 952-3144
-- 153 Taylor Street		FAX    : (508) 952-3023
-- Littleton, MA 01460-1407
===============================================================================
Newsgroups: sci.math
Subject: Re: no, this is not homework
From: a_rubin@dsg4.dse.beckman.com (Arthur Rubin)
Date: 21 Nov 92 00:00:59 GMT
Organization: Beckman Instruments, Inc.

In <92324.060736RVESTERM@vma.cc.nd.edu> <RVESTERM@vma.cc.nd.edu> writes:

>given an n-chromatic graph on m vertices, what is the maximum number
>of edges possible?

m = k n + r, 0<=r<n

E = m(m-1)/2 - r (k+1)(k+2)/2 - (n-r) k (k+1)/2


--
Arthur L. Rubin: a_rubin@dsg4.dse.beckman.com (work) Beckman Instruments/Brea
216-5888@mcimail.com 70707.453@compuserve.com arthur@pnet01.cts.com (personal)
My opinions are my own, and do not represent those of my employer.
My interaction with our news system is unstable; please mail anything important.
From: thornton@carson.u.washington.edu (Kenneth Thornton)
Newsgroups: sci.math
Subject: Smooth functions on the sphere
Date: 16 Nov 92 20:25:06 GMT
Article-I.D.: u.1992Nov16.202506.22162
Distribution: usa
Organization: University of Washington, Seattle




Let's say I have a smooth C^2 function f: S->R defined
on the 2-sphere S.

Let's also assume that the local maxima of this function
trace out a set of connected closed curves (there are
no isolated maxima) on S.

Is there a name for functions of this type? 

Ken Thornton
From: israel@unixg.ubc.ca (Robert B. Israel)
Newsgroups: sci.math
Subject: Re: ODE problem...
Date: 18 Nov 92 23:43:57 GMT
Organization: The University of British Columbia
NNTP-Posting-Host: unixg.ubc.ca

In <1992Nov17.205237.21447@athena.mit.edu> frisch1@athena.mit.edu (Jonathan Katz) writes:

>The following ODE problem came up recently.
>I know how to solve it by the power series method, but was wondering
>if anyone could figure out an easier way of solving it (maybe a nice
>substitution?).
>(x and y are functions of t, a is a constant)
>x'=(a)(x)cost+(a)(y)sint
>y'=(a)(x)sint-(a)(y)cost.
>It may be worth noting that, viewing this as a matrix problem:
>x'=Ax,
>A^2=I.

>I don't know if that helps.


Quite a neat problem!  I hope nobody was sadistic enough to
assign it as homework.

First go to polar coordinates: x = r cos(s), y = r sin(s)
(I'm too lazy to type "theta").
(1)   r' = (x x' + y y')/r = r cos(t-2s)
(2)   s' = (x y' - y x')/r^2 = a sin(t-2s)

Substitute u = t-2s in (2) to get 

(3)   u' = 1 - 2 a sin(u).

This can be solved, but it's a mess.  However, since the
problem is linear, it's enough to get two particular solutions.
The easy ones are where u = constant.  Let c = arcsin(1/(2a)).
(This assumes |a| > 1/2, if you want real solutions)
Then two solutions of (3) are u = c and u = pi - c.  
Correspondingly, we get, with k = cos(c) = sqrt(1 - (1/2a)^2),
and taking r(0) = 1, 
(for u = c) s = (t-c)/2
            r' = r cos(c) = k r
            r =  exp(k t)
            x =  exp(k t) cos((t-c)/2)
            y =  exp(k t) sin((t-c)/2)
(for u = pi - c)
            x =  exp(-k t) cos((t - pi + c)/2)
              =  exp(-k t) sin((t+c)/2)
            y = -  exp(-k t) cos((t+c)/2)
and the general solution is a linear combination of these.

-- 
Robert Israel                            israel@math.ubc.ca
Department of Mathematics             or israel@unixg.ubc.ca
University of British Columbia
Vancouver, BC, Canada V6T 1Y4
Xref: sparky sci.math:15394 comp.edu:1927
From: rsc@altair.csustan.edu (Steve Cunningham)
Newsgroups: sci.math,comp.edu
Subject: Re: Minimum standards for math "competency"
Keywords: math competency education university college standards
Date: 23 Nov 92 05:55:27 GMT
Organization: CSU Stanislaus

crawford@boole.mitre.org (Randy Crawford) casts some doubts on the claims of
the original posting by rjfrey@rentec.com (Robert J Frey) speaking of the
critical shortage of mathematically literate people (as well as mathematical
specialists) and doubting the low standing of American students in mathematics.

Without going to my references (I'm in my office late to staunch a roof-leak
flood and can't dig them out from the piles of materials under plastic) let
me assure Mr. Crawford that Mr. Frey's general points are entirely valid.  For
references, consult the large literature on the subject from the Mathematical
Association of America and the National Research Council, who have documented
this situation well.  It's real, and it's frightening -- if you can make time
to work with your local schools in bringing a sense of the reality and fun of
mathematics (oh, dear -- I said mathematics is fun, didn't I?  It is, and it's
one of the most rewarding of human endeavors, IMHO...) to the students, you'll
do yourself, the students, the nation, and perhaps even humanity a favor...
From: cyeomans@ms.uky.edu (Charles Yeomans)
Newsgroups: sci.math
Subject: Re: Square root
Date: 21 Nov 92 16:06:07 GMT
    <By1A7t.3o@undergrad.math.waterloo.edu>
Organization: University Of Kentucky, Dept. of Math Sciences

In article <By1A7t.3o@undergrad.math.waterloo.edu> kekamins@zeno26.math.UWaterloo.ca (kekaminsky) writes:
>In article <n9146070.722056383@waldorf> n9146070@waldorf.cc.wwu.edu (Jacob C Kesinger) writes:
>>There was a previous post about ways to find the square root of a number...
>>
The following technique is, I imagine, well-known. I like it because I 
found it for myself in 9th grade or so.

Define two sequences a(k) and b(k) as follows:  Set a(1) = a, b(1) = 1.
Then define a(k) = [a(k-1) + b(k-1)])/2, b(k) = a/a(k).  Then one checks
that the two sequences a(k) and b(k) converge to sqrt(a).

Charles Yeomans
cyeomans@ms.uky.edu
yeomans@austin.onu.edu
From: goddard@NeXTwork.Rose-Hulman.Edu (Bart E. Goddard)
Newsgroups: sci.math
Subject: Phase Plane and Mathematica
Date: 18 Nov 1992 21:34:06 GMT
Organization: Computer Science Department at Rose-Hulman
Reply-To: goddard@NeXTwork.Rose-Hulman.Edu (Bart E. Goddard)
NNTP-Posting-Host: g214-1.nextwork.rose-hulman.edu


I am about to start teaching a DE course in which we cover
the stability of linear systems (sophomore level).  We have
not usually included any discussion of non-linearizable systems.
However, we have just switched to using Boyce and DiPrima, and
they have a section about chaos and strange attractors.  Also,
this is my first attempt at using Mathematica in the course.

Sooooooooo, I'm asking for packages, notebooks, exercises, modules,  
ideas, etc, that I might like to use in the stability/phase plane
stuff, and in particular, in the chaos and strange attractors
sections (which is essentially the analysis of one problem.)

Many thanks. Please use email.

Bart Goddard
goddard@nextwork.rose-hulman.edu

Newsgroups: sci.math
From: asimov@wk223.nas.nasa.gov (Daniel A. Asimov)
Subject: Decomposing the sphere into (pointwise) congruent pieces
Organization: NAS, NASA Ames Research Center, Moffett Field, California
Date: Mon, 23 Nov 92 19:42:12 GMT

For which n can the 2-sphere S^2 = {(x,y,z) | x^2 + y^2 + z^2 = 1}
be decomposed into n disjoint pieces any two of which are isometric?

To make this question precise, I want to specify a few definitions:

Each "piece" must consist of the interior of a spherical polygon
(its edges are arcs of great circles) and some specified part of 
its boundary.  Assume further that each piece is "spherically convex":
any two points in the interior of a piece can be connected by a 
great circle arc lying entirely inside the piece.

The decomposition is down to the last point:  each point of S^2
must lie in one and only one of the pieces.

And for pieces P1 and P2 to be "isometric" here will mean that 
there is a bijection between P1 and P2 that preserves spherical
distance.

As an example: n = 2 works.  One piece could be the northern hemisphere,
plus a semicircle of the equator which includes just one of its endpoints.
The other piece is what remains.  The antipodal map is an isometry between 
the pieces.

Dan Asimov
Mail Stop T045-1
NASA Ames Research Center
Moffett Field, CA 94035-1000

asimov@nas.nasa.gov
(415) 604-4799
From: mroussel@alchemy.chem.utoronto.ca (Marc Roussel)
Newsgroups: sci.math.symbolic
Subject: Re: Serious Programming
Date: 20 Nov 92 02:29:10 GMT
Organization: Department of Chemistry, University of Toronto

In article <BxwrMF.Ctw@news.cso.uiuc.edu> Richard J. Gaylord
<gaylord@ux1.cso.uiuc.edu> writes:
>i  am comparing  cas languages ONLY in terms of their ability to do 
>functional programming .
[...]
>i maintain that mathematica does the best job of bringing the functional
>style of programming into scientific computing.

     Perhaps, but most physical scientists don't care whether they are using a
functional programming paradigm as opposed to something else.  In fact,
I doubt that the average physical scientist would even know what
functional programming is.  Certainly none of the people with whom I
have daily contact do, save perhaps one chap.  To be honest, even though I know
what functional programming is, I've never understood why I should care
about this sort of (to me at least) superficial style issue.

>(1)  mathematica's use of fully spelled out english names for its
>built-in functions and its use ofa  mathematical equational style  is
>superior to the syntax of other  languages  (with the exception of APL
>whose runic symbols and one way evaluation  scheme are especially
>appealing ). 

     Examples, please?  How many ways can you write "factor" or
"simplify"?  These two are typical of Maple functions in that they are
fully spelled out English names.  So what's so special about
Mathematica's naming scheme?  What other aspects of Mathematica's
notation are closer to written math than Maple's?  Allowing whitespace
to stand for multiplication?  Personally, I don't like that one because
it's a source of insidious bugs.

				Marc R. Roussel
                                mroussel@alchemy.chem.utoronto.ca
Newsgroups: sci.math.symbolic
From: siegman@EE.Stanford.EDU (Anthony E. Siegman)
Subject: Re: The Real Meaning of Efficiency?  (Re: Serious Programming, etc.)
Organization: Stanford University
Date: Fri, 20 Nov 92 19:46:01 GMT

This is not to argue with any of the other points made in this
discussion so far, just to add a factual observation, for whatever
it's worth:

At least in my observation, in the past few years working engineers in
industry have been taking to Mathematica as an everyday working tool
in very much the same way that business/financial types took to
VisiCalc and its Lotus/Excel successors when they first came out.

I'm a university professor type myself, but I deal with working level
engineers in classes and consulting relations; and these days, when
they have a numerical calculation to do or some simple (or not so
simple) analysis to work out, they just slap the equations into mma,
see what comes out, and pass along the printout, or paste it into
their notebook or monthly report.

They may do this intelligently, or efficiently, or with some
sophistication, or they may not; but it's what they do; the dramatic
increase in their routine reliance on this approach is very evident.
From: t68@nikhefh.nikhef.nl (Jos Vermaseren)
Newsgroups: sci.math.symbolic
Subject: Re: an example of comparative CAS programming
Date: 23 Nov 92 09:59:42 GMT
Organization: Nikhef-H, Amsterdam (the Netherlands).

In article <dzpqj3g@lynx.unm.edu>, jpg@spectre.unm.edu (Jeffrey P. Golden) writes:
> Reply-To: jpg@macsyma.com
> 
> Given all the recent messages about comparative programming in 
> the various CAS, I thought the following might be elucidating.
> 
> Barry Simon, "Symbolic Math: Problems and Solutions", 
> Notices of the AMS, Vol. 39, No. 7, pp. 700-710, Sept. 1992 
> has the following problem:
> 
>   9.  Rule based algebra
>   Consider the Clifford algebra in 10 variables, that is the 
>   complex algebra with ten generators, s0,...,s9 obeying
>           si sj + sj si = 0 if i is different from j
>           si si = 1
>   That is multiplication is NOT commutative (but is assumed
>   associative).  Compute (s0+s1+....+s9)^5

The FORM solution seems easiest to me.
1: Brute force:
F   sa,sb,s0,s1,s2,s3,s4,s5,s6,s7,s8,s9;
Local F = (s0+s1+s2+s3+s4+s5+s6+s7+s8+s9)^5;
repeat;
    id sa?*sa? = 1;
    id,disorder,sb?*sa? = -sa*sb;
endrepeat;
print;
.end
This takes of the order of 3 minutes on a SPARC 2.
Slightly better:
2: Build up the powers:
#define MAXPOW "5"
F   sa,sb,s0,s1,s2,s3,s4,s5,s6,s7,s8,s9;
Local F = s0+s1+s2+s3+s4+s5+s6+s7+s8+s9;
#do i = 2,'MAXPOW'
multiply,right,(s0+s1+s2+s3+s4+s5+s6+s7+s8+s9);
repeat;
    id sa?*sa? = 1;
    id,disorder,sb?*sa? = -sa*sb;
endrepeat;
.sort
#enddo
print;
.end
This takes of the order of 0.1 sec on a SPARC 2
Note that programming the anticommutation relation is rather natural.
Note 2:  The disorder option does not exist in FORM 1. You need FORM 2 for it.

Jos Vermaseren
Newsgroups: sci.math.symbolic