HDTenEightyP/NetNews huggingface dataset:
From: martin@lyra.cis.umassd.edu (Gary Martin)
Subject: Re: High Prices of Math Books. I am pissed.
Organization: University of Massachusetts Dartmouth
	<1993Jan7.170536.28221@infodev.cam.ac.uk>
	<thompson.726445179@daphne.socsci.umn.edu>
	<1993Jan8.012016.11134@infodev.cam.ac.uk>
Date: Fri, 8 Jan 1993 05:19:57 GMT

In article <1993Jan8.012016.11134@infodev.cam.ac.uk> gjm11@cus.cam.ac.uk (G.J. McCaughan) writes:

   Perhaps things are different in the USA? In my four years taking
   taught/examined courses, I don't think I've ever bought a textbook
   to match a course; I've bought books that have interested me, and
   done the course from lectures, using libraries for the occasions
   when I've needed to look up something course-related in a book I
   don't have. -- Books aren't needed so much for courses which are
   lectured, as for independent reading, surely?

As usual, things are indeed different in the USA.  Standard practice,
with numerous exceptions, but mostly at upper and graduate levels, is
to follow a selected text quite closely, assign homework problems 
from that text (often collected and weighed for a grade :-) or :-( ),
and tell students which sections of the text they need to know for
the exams.  Though it's got lots of drawbacks, there are lots of
(perhaps not very good) reasons why it is a solidly entrenched practice.
Many schools offer many sections of the same course, taught by many
instructors, some of whom are graduate students, part-timers, regular
faculty re-assigned to teach the course literally at the last minute,
etc.(?), and the department wants to impose some uniformity on the 
course so that students may transfer easily between sections if necessary,
use the sections interchangeably as a pre-requisite, etc.  Using the
same text at least gives the impression that this is acheived.  Also,
most of the students would feel lost without it.  Most of them don't
know how to take useable lecture notes and couldn't choose a reasonable
book to accompany the course on their own.  (Our students often wait 
until the first day of classes to find out what their courses are about.
I've had students express surprise at finding out during the first week
of the semester that MTH 102 Elements of College Math II is really
Calculus for Business majors and assorted others, even though it's
described in the catalog as such.  They hadn't even noticed the word
'Calculus' in big block letters on the cover of the text, and were
surprised to see me write it on the blackboard.)

Oh well.

--
Gary A. Martin, Assistant Professor of Mathematics, UMass Dartmouth
Martin@cis.umassd.edu
From: andrew@rentec.com (Andrew Mullhaupt)
Newsgroups: sci.math
Subject: Re: sum(i=1 to n, i^3) = ??   URGENT !!
Date: 9 Jan 93 16:57:35 GMT
Organization: Renaissance Technologies Corp., Setauket, NY.

In article <4820@seti.inria.fr> menissie@ausone.inria.fr (Valerie Menissier-Morain) writes:
>In article <8979@lhdsy1.lahabra.chevron.com>, jgrij@lhdsy1.lahabra.chevron.com (Joey J. Griffin) writes:
 
>[deleted]
>|> 1^3 + 2^3 + 3^3 + ... + n^3 = (1 + 2 + 3 + ... n) ^ 2
>|>        Proof by induction.
 
>In fact there is a very beautiful geometrical proof of this assertion:

[beautiful proof deleted]

I think that the legendary Rufus Bowen's first paper was on this fact, and
some generalizations. I also seem to remember that there is a bibliography
for Bowen in the memorial Publ. I.H.E.S. (v 50 or 51) for him.

Later,
Andrew Mullhaupt
From: henebry@matt.ksu.ksu.edu (Geoffrey M Henebry)
Newsgroups: sci.math
Subject: does this class of function have a particular name?
Date: 8 Jan 1993 12:33:24 -0600
Organization: Kansas State University
NNTP-Posting-Host: matt.ksu.ksu.edu

hi, i'm wondering whether the following class of functions have a particular
name:
        f(x) = [a*(x-k)^n*x^-n]^m 
thanks!
+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+ 
 Geoffrey M. Henebry                voice: (913) 532-7997   fax: (913) 532-6653 
 Division of Biology/Ackert Hall    internet:   gmh@andro.konza.ksu.edu         
 Kansas State University                        henebry@matt.ksu.ksu.edu        
 Manhattan, KS 66506 USA            Heraclitus: PANTA HREI
From: arodgers@dcs.qmw.ac.uk (Angus H Rodgers)
Newsgroups: sci.math
Subject: Re: Let's add some sci.math.* groups
Date: 11 Jan 93 19:36:56 GMT
Organization: Computer Science Dept, QMW, University of London

In <1993Jan11.142229.23554@linus.mitre.org>
bs@gauss.mitre.org (Robert D. Silverman) writes:

>I *might* vote for a split into sci.math, and sci.math.recreational,
>as well as keeping sci.math.research.

Or sci.math and sci.math.serious? (On the pattern of 
rec.humor and rec.humor.funny.) :-)
--
Gus Rodgers,  Dept. of Computer Science, | Cinema's worst romantic dialogue? --
Queen Mary & Westfield College, Mile End | "Mechagodzilla's brain is  installed
Road, London, England.   +44 71 975 5241 | in my stomach!" "I don't care if you
E-mail (JANET):   arodgers@dcs.qmw.ac.uk | are a cyborg  --  I still love you!"
Xref: sparky sci.math:17870 sci.math.num-analysis:3763
From: andrew@rentec.com (Andrew Mullhaupt)
Newsgroups: sci.math,sci.math.num-analysis
Subject: Re: Approximating decimal fractions with proper fractions
Keywords: fraction, approximation, number theory
Date: 8 Jan 93 22:40:51 GMT
Followup-To: sci.math
Distribution: na
Organization: Renaissance Technologies Corp., Setauket, NY.

In article <C0ICCG.1BJ@hsi.com> rogerh@code3 (Roger Harrison) writes:
>I am looking for an algorithm (preferably a computationally cheap one)
>to approximate a decimal fraction with a proper fraction for display 
>purposes.  The ideal algorithm would take a decimal fraction and the 
>maximum number of digits in the result's denominator to determine the 
>proper fraction (in numerator/denominator form) which best approximates 
>the original decimal fraction.


I don't know what number theory books you looked in but any decent one
should have done. What you are essentially looking for is the continued
fraction, and it is usually computed by the Gauss transformation. You
will find a discussion of this in Hardy and Wright's _Intro to Number Theory_
and most other such texts, so I'll just sketch an example.


Any real number x between 0 and 1 generates a 'continued fraction' of the
following kind:

	x_0 = x;

	x_n-1 = (a_n + x_n)^-1; a_n positive integer, 0<x_n<1, for n>0.

If you do this with the fractional part of Euler's number (e-2) you get
the sequence:

	a_1 = 1, a_2 = 2, a_3 = 1, a_4 = 1, a_5 = 4, ...

to make the pattern clear, you find that a_2 = 2, a_5 = 4, a_8 = 6, a_11 = 10,
(i.e. a_(3k-1) = 2k) and a_n = 1 for n <> 3k-1.

You will have to be careful to evaluate e to lots of digits if you want to
see the pattern clearly. The relevance of this sequence to your question is
that we have the representation for e:

	e = 2 + 1/(1 + 1/(2 + 1/(1 + 1/(1 + 1/(4 + 1/(1 + ... ))))))

called a continued fraction. In the general case we write

	x = 1/(a_1 + 1/(a_2 + 1/(a_3 + ... )))

which is often abbreviated as:

	x = [a_1, a_2, a_3, ... ]

in our particular case:

	e = 2 + [1,2,1,1,4,1,1,6,1,1,8,1,1,10,1,1,12,1,...]


Now if you start with a rational x, the continued fraction will terminate,
and it is pretty clear that a terminating continued fraction must be rational.
What isn't obvious, but the number theory books will spell out for you is
that if you truncate a continued fraction, you get a rational approximation
to x which is the best in a well defined sense. By successive truncations
you get a sequence of approximating rationals, for example:

	e_1 = 2 + [1] = 3

	e_2 = 2 + [1,2] = 8/3 ~ 2.66667

	e_3 = 2 + [1,2,1] = 11/4 = 2.75

	e_4 = 2 + [1,2,1,1] =  19/7 ~ 2.714285

	e_5 = 2 + [1,2,1,1,4] = 87/32 ~ 2.71875

and these are clearly tending to e = 2.7182818....

So in order to find a good (in some sense best) approximation to a decimal
number, work out the continued fraction and truncate it.

This is also the way to work out things like the minimum number of at bats
you need to have a .327 batting average, etc.

Later,
Andrew Mullhaupt
Newsgroups: sci.math
From: asimov@wk223.nas.nasa.gov (Daniel A. Asimov)
Subject: Re: Frankly,my dear......was: Fermat's Last Theorem
Organization: NAS, NASA Ames Research Center, Moffett Field, California
Date: Thu, 7 Jan 93 20:31:26 GMT
Distribution: usa

In article <1993Jan7.021308.10566@nuscc.nus.sg> matmcinn@nuscc.nus.sg (.) writes:
>
>I wonder if this might not be an occasion for some soul- searching on the
>part of professional mathematicians. X^n+ y^n = Z^n has no solutions....  
>frankly, who cares? It's recreational mathematics, right? The only reason
>anyone cares about it is that the proof is hard. Let me give you an
>example to show you what I mean. Theorem: 2 and 4 are the only unequal
>integers such that x^y = y^x. Why is this theorem not famous? Because [a]
>it is boring and [b] the proof is easy. But I think it is no more boring
 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

Oh, one more characteristic:  [c] it is false.  (Consider -2 and -4.)

>than FLT. Most of the [allegedly] "interesting" results of elementary
>	[...]
	
	<no signature provided with original post>
---------------------------------------------------------------------------


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

asimov@nas.nasa.gov
(415) 604-4799
From: kullmann@urz.unibas.ch (Peter Kullmann)
Newsgroups: sci.math
Subject: wanted: diff. criterium for pureness of tensors.
Date: 11 Jan 93 11:57:30 MET
Organization: University of Basel, Switzerland


Is there a differentiable criterium for the pureness *) of tensors in the 
outer tensor algebra over a real vector space? I.e. a function 
 
 f:Alt(k,V) ---> R differentiable

such that if s \in Alt(k,V): f(s) = 0 iff s is pure.

This has of course to do with Grassmanians, and what I actually want is to
have Grassmann (n,k) as a level surface in Alt(k,R^n). I doubt it very much
that this is possible, so an argument for the contrary would be welcomed as
well:-).

*) I'm not sure about the term pure = rein in German. It means: a tensor s
\in Alt(k,V) is pure iff it is the product: v1 wedge v2 wedge ... wedge vk,
where vi \in the dual of V. 

-- 
Peter

Newsgroups: sci.math
From: rgep@emu.pmms.cam.ac.uk (Richard Pinch)
Subject: Re: Looking for help
Organization: Department of Pure Mathematics, University of Cambridge
Date: Mon, 4 Jan 1993 15:31:24 GMT

In article <1993Jan4.152944.29631@infodev.cam.ac.uk> I wrote
>In article <1993Jan4.140128.20155@choate.edu> jburne@spock.uucp (John Burnette) writes:
>>[...]
>>x = .10100100010000....
>>y = .01011011101111....
>>
>>Obviously x+y=1/9 (and, please, let's not start that thread again...)
>>but I've always been at a lost about x*y.
>>
>>Over the years, I've come to *believe* that x*y is irrational, but I've 
>>been stumped by the proof.  If anyone could direct me to something which
>>would get me moving again on this problem it would be appreciated.
>>
>Just a suggestion: if x+y and xy are rational, then x and y are roots
>of the equation (Z-x)(Z-y) = Z^2 - (x+y)Z + xy = 0.  So - 9xy = 9x^2 - x
>must be rational, i.e. a recurring decimal.  But it should be fairly
>easy to prove that this has arbitrarily long sequences of 0s in its
>decimal expansion.
>
Otherwise it might be possible to use Liouville's theorem, since x and y
would have to be quadratic irrationals.
>


Newsgroups: sci.math
From: tao@fine.princeton.edu (Terry Tao)
Subject: Re: proof wanted 2
Originator: news@nimaster
Organization: Princeton University
Date: Mon, 11 Jan 1993 03:00:12 GMT

In article <1iqcp7INNoph@skeena.ucs.ubc.ca> liuli@unixg.ubc.ca (Li Liu) writes:
>In article <ARA.93Jan10172314@camelot.ai.mit.edu> ara@zurich.ai.mit.edu (Allan Adler) writes:
>>
>>
>>True or false: A metric space (X,d) is locally compact if and only if
>>for every point p of X and every closed subset Y of X, there is a
>>point q of Y such that d(p,q) = inf {d(p,r) | r in Y}.
>>
>
>False. Compactness will imply that a nearest point exists. The other
>way around is not generally true. Consider the space R^2, let a closed
>set C = { (x,y) | x=0} . Consider an outside point P= (1,0). Then
>inf{ d(P,C) } =1, with (0,0) reaching the inf.
>
>In this case C is not compact. 
>

No, what Allan is asking is that if there is a nearest point for EVERY P
and EVERY closed C not containing P, then R^2 must be locally compact.
Read the question carefully!.  In this case, R^2 is of course locally
compact.

I'd hazard that the statement is true, but I have no proof.  A way to start
would be to imply from the second property that every sequence has a
convergent subsequence or a point of least distance to a specified point x.  Why?  Let S be the set of points in the bounded
sequence, the closure of S contains a point of least distance, either this
point is in S or is a limit point of S, hence the claim.  But I have no
idea where to go from here.

Terry
Newsgroups: sci.math
From: snodgras@cs.unca.edu (Ryan Snodgrass)
Subject: Value of the US Dollar
Organization: University of North Carolina at Asheville
Date: Mon, 11 Jan 1993 18:03:18 GMT

How do I compute the value of the US dollar?  Or what is used to figure

it out?  ANY input would be helpful,



Thanks,

Ryan
From: bhahn@sw.stratus.com (Bill Hahn)
Newsgroups: sci.math
Subject: Re: Fermat's Last Theorem
Date: 8 Jan 1993 18:12:10 GMT
Organization: Stratus Computer, Inc.
Distribution: usa
NNTP-Posting-Host: oldno7.sw.stratus.com

edgar@function.mps.ohio-state.edu (Gerald Edgar) writes:
> ....
> An interesting book on the topic of this phenomenon is:
> 
> MATHEMATICAL CRANKS, by Underwood Dudley, published by the MAA.
> --
>   Gerald A. Edgar                Internet:  edgar@mps.ohio-state.edu
>   Department of Mathematics      Bitnet:    EDGAR@OHSTPY
>   The Ohio State University      telephone: 614-292-0395 (Office)
>   Columbus, OH 43210             -292-4975 (Math. Dept.) -292-1479 (Dept. Fax)

Not only interesting, but *very* entertaining.  Some cranks, while not 
having a clue about mathematics, have a powerful gift for invective....

-- 
Bill Hahn               bhahn@sw.stratus.com
Stratus Computer        "Meetings are places where minutes are kept
Marlboro, MA, USA        and hours are lost." From V. Weisskopf's memoirs.
--------- These are my opinions and not necessarily those of Stratus.------
Newsgroups: sci.math
From: ara@zurich.ai.mit.edu (Allan Adler)
Subject: resolution of singularities
Organization: M.I.T. Artificial Intelligence Lab.
Distribution: sci
Date: Wed, 6 Jan 1993 09:34:07 GMT


Let K be a germ of an analytic curve over the complex numbers. I know
one can resolve singularities in great generality (e.g. Hironaka's
resolution theorems, which would include the situation of K as a special
case). On the other hand, I know that for algebraic curves, resolution
is very straightforward: one just passes to the normalization.

I would assume there is an equally simple way to do it for K. What is it?

Allan Adler
ara@altdorf.ai.mit.edu
Newsgroups: sci.math
From: an1060@anon.penet.fi
Subject: Continuum Mechanics Book Wanted
Organization: Anonymous contact service
X-Anonymously-To: sci.math
Date: Thu, 7 Jan 1993 21:31:04 GMT

X-Anon-To: sci.math


Hello All,

Does anyone have a copy of: 

Mathematics Applied to Continuum Mechanics, by Segel & Handelman.

For those who attended RPI, this is the book used for Foundations of
Applied Mathematics II (FOAM II).

I am looking for an original copy, i.e. published by Macmillan,
the book is black hardcover with green lettering (yes, quite unattractive)...

If you have one in very good condition, please contact me.

Respond to:  mantell@ams.sunysb.edu

Thanks...

Abe Mantell


-------------------------------------------------------------------------
To find out more about the anon service, send mail to help@anon.penet.fi.
Due to the double-blind system, any replies to this message will be anonymized,
and an anonymous id will be allocated automatically. You have been warned.
Newsgroups: sci.math,rec.puzzles
From: isaak@aurora.com (Mark Isaak)
Subject: Re: Marilyn Vos Savant's error?
Reply-To: isaak@aurora.com (Mark Isaak)
Organization: The Aurora Group
Distribution: na
Date: Tue, 5 Jan 93 18:56:28 GMT

In article <1993Jan2.215958.1@stsci.edu> zellner@stsci.edu writes:
>   1.  What is the probability of two heads, when the Penny is a head?
>   2.  What is the probability of two heads, when the Nickel is a head?
>
>Obviously the probability is 1/2 in either case.  But if you ask
>
>   3.  What is the probability of two heads, when AT LEAST ONE COIN (of either
>       species) is a head?
>
>Clearly that's 1/3.  For a man to say "one of my two children is a boy" versus 
>"the elder of my two children is a boy" samples two different statistical 
>ensembles, with different results.

But now ask, What is the probability of two heads, when the coin landing
farther to the left (of whatever specie) is a head?  This probability is
1/2, and this situation is more analgous to "my child standing over there
is a boy."

If you're only examining one coin (or child), you know nothing of the side
(or sex) of the other, so the probability of it being a given side (or sex)
is 1/2.

>  "I've found one of the children, and it's a boy, but the records I've been 
>   able to peek at so far don't give its age, so I don't know whether it's
>   the older or the younger."

Even in this case, you're only looking at one child, so the probability
of the other being a boy is still 1/2.
-- 
Mark Isaak           "Every generation thinks it has the answers, and every
isaak@aurora.com      generation is humbled by nature." - Philip Lubin
Newsgroups: sci.math
From: hrubin@pop.stat.purdue.edu (Herman Rubin)
Subject: Re: High Prices of Math Books. I am pissed.
Organization: Purdue University Statistics Department
Date: Wed, 6 Jan 1993 22:26:22 GMT

In article <1idj1gINNhah@roundup.crhc.uiuc.edu> hougen@focus.csl.uiuc.edu (Darrell Roy Hougen) writes:
>goddard@NeXTwork.Rose-Hulman.Edu (Bart E. Goddard) writes:

>% In articles <> several well-meaning but misguided souls write:
>%% Have they suddenly lost the ability to use the libraries?
>% Just how many copies of a text book do you suppose a library carries?

>You said that college students didn't have the opportunity to read,
>*not* just that text books were expensive.  But if you want to devise
>a solution, why not ask professors to require less expensive books in
>their courses?  There are many very high quality books that appear as
>paper backs.

There are not too many reasonable and non-obsolete textbooks which are
in paperback.  The largest service course our department teaches has
not been able to come up with a good one in hard binding, either.  
I do not believe that there are good textbooks for most of our 
other courses, either.

The amount of effort required to produce a fairly good book when one
does not already exist for a one-semester to one-year course is two
or three person-years, and preferably involves more than one person
writing it.  An active faculty member does not have the time to do
very much writing.
-- 
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)
Xref: sparky sci.math:17679 rec.puzzles:8210
From: liuli@unixg.ubc.ca (Li Liu)
Newsgroups: sci.math
Subject: Re: proof wanted 2
Date: 10 Jan 1993 23:51:03 GMT
Organization: University of British Columbia, Vancouver, B.C., Canada
NNTP-Posting-Host: unixg.ubc.ca

In article <ARA.93Jan10172314@camelot.ai.mit.edu> ara@zurich.ai.mit.edu (Allan Adler) writes:
>
>
>True or false: A metric space (X,d) is locally compact if and only if
>for every point p of X and every closed subset Y of X, there is a
>point q of Y such that d(p,q) = inf {d(p,r) | r in Y}.
>

False. Compactness will imply that a nearest point exists. The other
way around is not generally true. Consider the space R^2, let a closed
set C = { (x,y) | x=0} . Consider an outside point P= (1,0). Then
inf{ d(P,C) } =1, with (0,0) reaching the inf.

In this case C is not compact. 

Newsgroups: sci.math
From: moore@aiag.enet.dec.com ()
Subject: Knot Invariants - computing
Reply-To: moore@aiag.enet.dec.com ()
Organization: Digital Equipment Corporation, Marlboro, MA
Date: Tue, 12 Jan 1993 23:27:35 GMT



	I'm looking for code or algorithms that can be easily coded
for computing knot invariants. 

	Any code or references would be appreciated. Thanks in advance.

		Jim Moore
From: daveb@hpgrla.gr.hp.com (Dave Boyd)
Date: Tue, 5 Jan 1993 20:51:00 GMT
Subject: Re: Pi and math in general
Organization: Hewlett-Packard, Greeley, CO
Newsgroups: sci.math

In sci.math, icdocherty@cix.compulink.co.uk (Ian Docherty) writes:

>In-Reply-To:  Clayten_Hamacher@mindlink.bc.ca (Clayten Hamacher)

> TITLE: Pi and math in general

  ... stuff deleted ...

>INITIAL VALUES

>        A = 1
>        X = 1
>        B = 1 / root(2)
>        C = 1 / 4

>LOOP:
>        Y = A
>        A = (A + B) / 2
>        B = root(B * Y)
>        C = C - X * (A - Y) * (A - Y)
>        X = 2 * X
>        print the value of (A + B) * (A + B) / (4 * C)
>        repeat from LOOP

>Where 'root' means take the square root

>Ian.

     Interesting.  A quick trial shows this appears to work.  Could
someone post (or email) a reference or a brief explanation of what's
going on here?

     Thanks,

     Dave Boyd
     Hewlett-Packard, Greeley, Colorado
     Standard Disclaimers Apply
Newsgroups: sci.math
From: tbmorris@acs.ucalgary.ca (Thomas B. Morrison)
Subject: Scheduling Algorithms for shift workers
Date: Wed, 06 Jan 93 21:20:49 GMT
Distribution: na
Organization: The University of Calgary, Alberta

Hi there,

An associate of mine was asked about the availability of software to
determine shift work schedules.

If you know of public domain or store-bought software, or papers with
algorithms, please e-mail me.

Thank you for your help.  
-- 
Tom Morrison 
Morrison Scientific Problem Solving
Suite 400, 604-1st Street S.W., Calgary, Alberta, T2P 1M7, CANADA
Internet: tbmorris@acs.ucalgary.ca
From: hougen@focus.csl.uiuc.edu (Darrell Roy Hougen)
Newsgroups: sci.math
Subject: Re: proof wanted 2
Date: 8 Jan 1993 21:04:46 GMT
Organization: Center for Reliable and High-Performance Computing, University of Illinois at Urbana-Champaign
NNTP-Posting-Host: focus.csl.uiuc.edu

cazelaig@ERE.UMontreal.CA (Cazelais Gilles) writes:


%                                                        n
% Is it true that if  C  is a nonempty closed subset of R  and x is a point
% not in  C  that there exists a point c in C that is closest in C to x.
%  
% i.e. such that:   |x-c'| % = |x-c| for all c' in C.

I'm a little rusty on analysis, but ..., intuitively, the closest
point to x in C must be on the boundary of C which is no problem if C
is closed.

More precisely, if there were no closest point to x in C, that would
imply that given any point c in C, one could find a point c'' in C
that was closer to x.  Therefore, one could construct a sequence of
points in C such that each point was closer to x than its predecessor
but whose limit point was not in C.  But, if C is closed, then it
contains all of its limit points, so there exists c' as defined above.

Note that c' need not be unique.  For c' to be unique, you need
convexity of C.

Darrell R. Hougen
From: goddard@NeXTwork.Rose-Hulman.Edu (Bart E. Goddard)
Newsgroups: sci.math
Subject: test
Date: 4 Jan 1993 19:08:16 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

that is, more t than anything else...
Newsgroups: sci.math