HDTenEightyP/NetNews huggingface dataset:
From: brnstnd@nyu.edu (Dan Bernstein)
Newsgroups: sci.math
Subject: Re: You know, the integers (was: Re: Stupid question about FLT)
Date: 21 Jul 92 12:44:36 GMT
Organization: IR

In article <1992Jul21.034140.10920@galois.mit.edu> tycchow@riesz.mit.edu (Timothy Y. Chow) writes:
> But wait a second, someone will say.  Why can't we just take the syntactic
> entities of ZFC to BE our sets?  We just DEFINE a set to be a syntactic
> entity of ZFC.  Won't this solve our problems?  We don't have to worry about
> MODELS of ZFC, which we don't even know exist.  We DO have the syntactic
> entities, so why not just take those to be our sets.  Then math will be
> reduced to syntax as per plan.

Since that is exactly what mathematicians have always done and will
always continue to do, what are you worried about?

> The problem is this: just what IS ZFC?

Who cares? It's defined well enough for people to be able to prove
things using it (syntactically), and that's what's interesting. (Hell,
for many centuries people found Euclid's axioms interesting enough to
spend lots of time on; and of course you can work with his axioms within
ZFC.) Besides, for whatever unknown reasons, the things we can do in ZFC
seem to be highly effective at modelling the real world (even if they
are ``inconsistent'' in some sense!), so mathematics will always be
funded. There you have it: intellectual challenge and a steady job. What
more could you ask for? (``Pretty pictures,'' say the fractals folks...
oh, never mind.)

> We must at the very least distinguish between the sets involved in
> constructing ZFC and the sets that ZFC talks about,

Yes, of course. Tarski wrote some very clear things about this. When
you're working in mathematical logic, you're studying various syntactic
constructs (like proofs), and it really doesn't matter if you
consistently replace one syntactic symbol (like the word ``set'') with
another one (``frobozz'') when you're writing out those constructs. The
objects of study don't have anything to do with the words you use in
talking about them.

---Dan
Newsgroups: sci.math
Subject: Matrix lib. request
From: Ivan.Murray@comp.vuw.ac.nz (Ivan Andrew Murray)
Date: Mon, 27 Jul 1992 04:25:12 GMT
Organization: Dept. of Comp. Sci., Victoria Uni. of Wellington, New Zealand.
Keywords: matrix


If anybody has a library of general matrix handling algorithms e.g. inversion,
eigen-problems, Gauss-Jordan reduction etc., could you please email them to me
( C++ source preferably ).

thanks in advance.



-- 

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
 Ivan A. Murray,                       |    email: imurray@comp.vuw.ac.nz
 BSc Student (Computer Science)        |
From: edgar@function.mps.ohio-state.edu (Gerald Edgar)
Newsgroups: sci.math
Subject: Re: Ellipsoid formula wanted
Date: 29 Jul 1992 08:25:12 -0400
Organization: The Ohio State University, Dept. of Math.
NNTP-Posting-Host: function.mps.ohio-state.edu

In article <148960001@hpcvra.cv.hp.com> jimd@hpcvra.cv.hp.com (Jim Donnelly) writes:
>
>Apologies if this is absurdly simple, but:
>
>Does anyone have a formula for the surface area of an ellipsoid
>given unequal length semi-axes a,b, and c?
>

The related (simpler?) problem of finding the perimeter of an ellipse
gives rise to an elliptic integral.  So the answer is not an elementary
function of the semi-axes a, b.


-- 
  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)
Newsgroups: sci.math
From: cmenzel@tamsun.tamu.edu (Christopher P Menzel         )
Subject: Re: Stupid question about FLT
Organization: Texas A&M University, College Station
Date: Fri, 24 Jul 1992 17:47:52 GMT

In article <1992Jul19.231456.21018@mailer.cc.fsu.edu> rose@fsu1.cc.fsu.edu writes:
>I suggest that if FLT is undecidable in one model of the integers, it is 
>undecidable is ALL models. It is no paradox that if it is undecidable, then 
>it is true. This is because undecidable simply means unable to prove true or 
>false. If we cannot (in principle) prove FLT false, this means that it IS 
>NOT FALSE.  

You seem to be saying that inability to prove the negation of a
sentence implies that the sentence isn't false.  But, for example, we
cannot prove (in PA) the negation of the G\"{o}del sentence for PA,
but (reasoning in the usual way in our metatheory) it is false (in the
natural numbers) all the same.


>Whereas, it might be possible that no method exist to prove FLT
>is true.  Since we say that FLT is true if it is not false, we say that if 
>FLT is undecidable, then it is true.

Correct me if I'm wrong, but I *think* the reason that the
undecidability of FLT implies its truth is simply that any
counterexample to FLT (i.e., a formula of the form a^n + b^n = c^n)
would be provable in PA.  Hence, FLT can't be both undecidable and
false.

Chris Menzel
From: benzvi@riemann.geom.umn.edu (David Ben-zvi)
Newsgroups: sci.math
Subject: Re: Please help name this book.
Date: 27 Jul 92 18:08:30 GMT
Organization: Geometry Center, University of Minnesota

In article 7966, Bill Taylor writes:

   I would dearly love it if anyone can help me with this math text.
   

   I don't know EITHER the author OR the title, (what a great start!).
   Yes, I *do* remember the subject. It was the topology of manifolds, written
   in a fairly non-technical style, for the general mathematical reader. The 
   topic was the Thurston work on 3-dimensional manifolds, and the problem of
   their classification, (which I gathered from the book was approaching 
   completion). 
   
   The book was written in a rather chatty way (which I found rather engaging),
   with plenty of diagrams and pleasantly down-to-earth explanations. There
   was a lot of talk about the (abstract) glueing together of spaces. There
   was a lot of attention given to spaces made from regular solids, with faces
   glued together after the corners had either been inflated or deflated so as
   to fit them together correctly, providing the final manifold with positive
   or negative curvature respectively.
   
   I think the book was published in the mid-80's; certainly sometime in the
   80's.  If anyone thinks they recognize it from my garbled description, I
   would greatly appreciate it if they could let me know the details. 
   
   Thanks,    Bill Taylor         wft@math.canterbury.ac.nz




The book you are referring to is "The Shape of Space : How
to Visualize Surfaces and Three-Dimensional Manifolds" by Jeff R. Weeks,
published by Marcel Dekker Inc, Pure and Applied Mathematics series #96, 1985.
This is the only fairly elementary introduction to Thurston's ideas
and is very well written. The classification problem for 3-manifolds is still
quite far from completion. The essential missing step is the
Thurston Geometrization Conjecture (which implies the Poincare Conjecture)
asserting that any 3-manifold can be broken up into pieces which
carry geometric structures. There is a bunch of people
working on this problem and quite significant progress- I believe the
most recent is David Gabai's announcement of his proof of the
Seifert Fiber Space conjecture in the October 1991 Bull. AMS. (See
also references in the back of the book and Thurston's
survey article "Three Dimensional Manifolds, Kleinian Groups and Hyperbolic
Geometry", Bull. AMS May 1982)

David Ben-Zvi
From: jimd@hpcvra.cv.hp.com (Jim Donnelly)
Date: Tue, 28 Jul 1992 21:14:00 GMT
Subject: Ellipsoid formula wanted
Organization: Hewlett-Packard Co., Corvallis, OR, USA
Newsgroups: sci.math


Apologies if this is absurdly simple, but:

Does anyone have a formula for the surface area of an ellipsoid
given unequal length semi-axes a,b, and c?

Thanks in advance!

Jim Donnelly
jimd@cv.hp.com
From: carabalo@phoenix.Princeton.EDU (David G. Caraballo)
Newsgroups: sci.math
Subject: Re: Homeomorphism
Keywords: glitch, bicontinuous, hmmm?
Date: 24 Jul 92 14:10:35 GMT
Organization: Princeton University
Originator: news@ernie.Princeton.EDU

In article <_1gmcfj@lynx.unm.edu> weishaup@vesta.unm.edu () writes:
>I was looking at Gelbaum's book of problems in Analysis (Springer, ~1990),
>and i found a problem that I don't understand:
>
>1.)Show that the set [0,1) is homeomorphic to the Real Line...

As others have pointed out, this is impossible.  Fortunately, the error has
been corrected in Gelbaum's newer book _Problems in Real and Complex Analysis_,
(Springer, 1992).  

Here, the problem (2.10) is stated as follows:

2.10 True or false:  R is the continuous image of [0,1)?

In the solution, the map f(x) = [1/(1-x)] sin [1/(1-x)] is used.

David Caraballo
Newsgroups: sci.math
From: djvelleman@amherst.edu
Subject: Re: You know, the integers (was: Re: Stupid question about FLT)
Organization: Amherst College, Amherst Mass.
Date: Wed, 22 Jul 1992 13:46:40 GMT

In article <9601.Jul2112.44.3692@virtualnews.nyu.edu>, brnstnd@nyu.edu (Dan Bernstein) writes:
> In article <1992Jul21.034140.10920@galois.mit.edu> tycchow@riesz.mit.edu (Timothy Y. Chow) writes:
>> But wait a second, someone will say.  Why can't we just take the syntactic
>> entities of ZFC to BE our sets?  We just DEFINE a set to be a syntactic
>> entity of ZFC.  Won't this solve our problems?  We don't have to worry about
>> MODELS of ZFC, which we don't even know exist.  We DO have the syntactic
>> entities, so why not just take those to be our sets.  Then math will be
>> reduced to syntax as per plan.
> 
> Since that is exactly what mathematicians have always done and will
> always continue to do, what are you worried about?

  This is not *at all* what mathematicians have always done.  If you took the
syntactic objects to be the sets, then since there are only countably many
syntactic objects, there would only be countably many sets.

  Mathematical *reasoning* can be accurately represented syntactically--that's
basically what the completeness theorem says.  But that's quite different
from saying that the *objects* of mathematics are syntactic.

  You could argue that mathematicians should take their objects to be
syntactic.  But that would be quite a change from the way mathematicians
ordinarily do things.

  Dan Velleman
  Dept. of Mathematics & Computer Science
  Amherst College

Newsgroups: sci.math
From: thomasc@lobachevskii.geom.umn.edu (Thomas Colthurst)
Subject: Re: Partition number question
Organization: Geometry Center, University of Minnesota
Date: Fri, 24 Jul 1992 14:20:36 GMT

In article <4574@balrog.ctron.com> wilson@web.ctron.com () writes:
>
>    For n >= 0, let p(n) be the unrestricted partition number of n.
>
>    1.  For all k >= 0, is it true that
>
>	a.  5  | p(5k+4)
>	b.  7  | p(7k+5)
>	c.  11 | p(11k+6)
>

Yes.  These congruences were first discovered by Ramanujan.  See
Hardy & Wright's _Number Theory_, pages 287-290 for details.

>    2.  Given (1) is true, are there other triples (a > 0, b > 0, c >= 0)
>	such that a | p(bk+c) for all k >= 0?
>

There are congruences for the various powers of 5, 7, and 11, such as
p(25k+24) = 0 (mod 25).

>    3.  Why does 11 divide so many small partition numbers?

Beats me.  

>David W. Wilson (wilson@ctron.com)

-Thomas C
Newsgroups: sci.math,wsu.math.news,sci.math,analysis,sci.math.stat
From: uds@surya.cs.wayne.edu (Seetamraju)
Subject: Book surveying new optimization tech.....?
Followup-To: poster
Organization: Wayne State University, Detroit, MI
Date: Thu, 30 Jul 1992 22:00:56 GMT


Could someone please  post replies about some good
books on optimization techniques, preferably those
on latest topics.

I have a computer science and computer engg background.
So I am not an ingnorant person, as far as math topics
are concerned.

My thesis advisor, seems to have a bunch of ideas to
pursue for my thesis. one of them is Hardware for
optimization, and a technique that we just thought up
to be implemented might have been already published upon.

So could you help me in referring to a couple of books
that are comprehensive in their review of literature..

Even highly concise journal referneces will be suitable.

thanx a lot for your help...


Seetamraju Udaya Bhaskar Sarma
(email : seetam @ ece7 . eng . wayne . edu)
Xref: sparky sci.math:9578 sci.chem:2806 sci.engr.chem:382 sci.engr.mech:139 sci.physics:11748 sci.bio:2758 bionet.journals.contents:183
From: bashford@scripps.edu (Don &)
Newsgroups: sci.math,sci.chem,sci.engr.chem,sci.engr.mech,sci.physics,sci.bio,bionet.journals.contents
Subject: Re: Survey on the Future of Electronic Information Distribution
Date: 27 Jul 92 19:46:07 GMT
Distribution: usa
Organization: The Scripps Research Institute, La Jolla, CA, USA

>>>>> In article <1992Jul25.044321.18144@news.acns.nwu.edu>, jlemay@nwu.edu (John LeMay) writes:

jlemay>            ELECTRONIC SURVEY ON THE FUTURE OF
jlemay>             DIGITAL INFORMATION DISTRIBUTION 

jlemay> The Boston Consulting Group is conducting a study on the 
jlemay> future of electronic publishing and distribution, and would 
jlemay> like to get your input....

This looks to me like a blatant commercial use of the net.

Boston Consulting Group is asking us to spend our time to
give them information, yet there is nothing in their post to
indicate that the results of the survey will be made available to
the net community.  Evidently they intend to sell the information
as part of their consulting business.  In other words, we are being
asked to make a collective effort for the sake of their profit
rather than our own collective benefit.

I urge members of the net community NOT to cooperate with this
survey unless the Boston Consulting Group agrees to the following:

1)  The raw email input of the survey, names and addresses deleted,
should be put on an anonymous ftp server so that any member of the
net community can access them.  This accumulation simply reflects
our own collective effort with little or no value added.

2) The Boston Consulting Group should not use or allow the use of the
survey as a means of electronic marketeering (e.g. electronic
junk-mail lists of survey respondents for sale).  To this end, B.C.G
must delete from their systems the names or addresses of the
respondents or anything allowing them to identify a particular survey
response with a particular respondent, or allowing them to compile a
list of respondents.  This means that the raw data available to B.C.G.
should be identical to the raw data available to all of us on the
anonymous ftp server mentioned in (1), above.

3)  A summary of the results including the percentage response of
all questions and the address of the anonymous ftp server mentioned
in (1) should be posted at least as widely as the appeals for data.

4) If B.C.G. wants to add value by analyzing the data further and
using it in its consulting business, fine.  But anyone else in
the net community should be able to get equal access to the raw
data, do their own further analysis and use it as they wish, for profit
or whatever.  B.C.G. should promise to take no action, legal or
otherwise, to block people from doing this.

Please do NOT participate in this survey until Boston Consulting Group
agrees to these conditions.

These are my opinions, not those of The Scripps Research Institute.

Donald Bashford
Assistant Member
Department of Molecular Biology
The Scripps Research Institute

bashford@scripps.edu
Newsgroups: sci.math
From: magdi@uxh.cso.uiuc.edu (Magdi N Azer)
Subject: Marquardt Algorithm for Chi-Square Non-Linear Functions
Organization: University of Illinois at Urbana
Date: Wed, 29 Jul 1992 14:07:18 GMT
Keywords: Nonlinear Fitting

I am working on doing a non-linear fit and I have heard that the Marquardt
algorithm in Bevington's book "Data Reduction and Error Analysis in the 
Physical Sciences" is a good one to use.  Is this true?  If not, can you
suggest other non-linear fitting routines.  I would prefer not to use the
IMSL libraries, simply because I want to do this on a P.C.  Thank you

Magdi N. Azer
magdi@uxh.cso.uiuc
*****************************************************************************
*****************************************************************************
|
|      o        	Magdi N. Azer
|---    \       	Laser-Aided Materials Processing Laboratory
|\|/   O/       	Department of Mechanical and Industrial Engineering
|    \/|        	University of Illinois at Urbana-Champaign
|     / \       	1206 W. Green Street
|     \  \      	Urbana, IL 61801
|               	Ph: (217) 333-5989
|               	email: magdi@uxh.cso.uiuc.edu
*****************************************************************************'
*****************************************************************************'
Newsgroups: sci.math
Newsgroups: sci.math
Subject: Re: ALGEBRAIC NUMBER ARITHMETIC
From: a_rubin@dsg4.dse.beckman.com (Arthur Rubin)
Date: 30 Jul 92 16:39:47 GMT
Keywords: algebraic numbers arithmetic

In <a_rubin.712513261@dn66> a_rubin@dsg4.dse.beckman.com (Arthur Rubin) writes:

Yep, talking to myself again.

>If you want to perform arithmetic on algebraic reals, the result from
>mathematical logical the Th(R) is decidable should allow you to compute
>using representations as you suggest.

Th(R) (as an ordered field) is decidable and admits elimination of
quantifiers, so there is a way a to do computations on a similar algebraic
structure, but it might have:

x^4 -2 = 0
x^2+x-1 >= 0

rather than:

x^4 - 2 = 0
x >= 0

--
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.
Our news system is unstable; if you want to be sure I see a post, mail it.
Newsgroups: sci.math
From: pruss@unixg.ubc.ca (Alexander Pruss)
Subject: Topos not over SET with natural number system?
Organization: University of British Columbia, Vancouver, B.C., Canada
Date: Thu, 23 Jul 1992 21:31:12 GMT

Can there exist a topos not defined over SET with a natural number
system?  If so, what would be an example?

A topos E is defined over SET iff there is a geometric morphism
gamma:E->SET iff there are arbitrary set-indexed coproducts of 1 in
the topos.  (SET here is the topos of sets, i.e. the category of sets.)
A topos E has a natural number system iff there is an infinite object A
of E.  (And object A is infinite iff A+1 is isomorphic to A, + being
coproduct, 1 being a terminal object.)

Alex.
Xref: sparky sci.math:9686 sci.math.symbolic:2125 sci.math.num-analysis:2334 k12.ed.math:1067
From: nickh@CS.CMU.EDU (Nick Haines)
Newsgroups: sci.math,soc.culture.british
Subject: Re: American mathematical hegemony
Date: 23 Jul 92 13:44:57 GMT
Article-I.D.: VOILA.NICKH.92Jul23084457
	<BrtL4D.Mnq@news.cso.uiuc.edu>
Organization: School of Computer Science, Carnegie Mellon University
Originator: nickh@VOILA.VENARI.CS.CMU.EDU

In article <BrtL4D.Mnq@news.cso.uiuc.edu> sbrown@symcom.math.uiuc.edu (Scott Brown) writes:

      Oh...Of course...food served with sauces that have _flavor_.
     No wonder you brits don't get it.

Certainly not. In fact, we've never even heard of this "flavor". What
is it, some kind of herb? What flavour does it have?

Nick
From: U53644@uicvm.uic.edu
Newsgroups: sci.math
Subject: Re: library cutbacks
Date: 28 Jul 92 06:02:38 GMT
 <Jul.14.03.38.05.1992.27933@remus.rutgers.edu>
 <1992Jul17.212740.16594@ariel.ec.usf.edu>
Distribution: sci
Organization: University of Illinois at Chicago

I know that it's rude to repeat oneself in a newsgroup, but..........

      What's wrong with desktop publishing ? Instead of having a professional
printer do the work (in effect, that's where the expense is coming in),
all that is necessary for such publication is a PC, a printer (maybe a few
universities can pool a little "petty cash" and buy a top quality model for
this purpose), and some commonly marketed software. One loses a little
elegance (the journals might end up stapled from front to back rather than
along the side), but if the other option is to have too few journals, it
would seem to be an acceptable loss. One could cut down on the expense of
typing by having article submitted electronically, where practical. The main
limitation on this, of course, would be the need to replace symbols that
can't be transmitted over the internet, but it would cut down on a lot of
redundant typing. Now, if 1000 copies of a journal are to be sent out, and a
student can seal and stamp 5/minute (say, you pay him $7/hr.), it will take
200 / 60 man - hours = 3 1/3 man - hours to seal them all (costing $23.33 in
all, or .2333 cents per issue, next to nothing). By the way, you will get
plenty of volunteers at that price, and 12 seconds to seal a magazine into
a protective envelope (a little more expensive at 33 cents each, but still...)
is much slower than most can work with even a little practice.

So, why not ? The issue is what's in the journals, not how they look, right ?
$15,000 bought a top quality printer in 1983 (computer, not printing press).
The price probably hasn't gone up that much, print quality has improved greatly
(some small local magazines publish that way, and the print quality is
 indistinguishable from regular type - though the usual cheap laser printer
 won't do that for you), and given the large amount of copy it can put out,
could probably be shared by the printers of a large number of small journals
(and would pay for itself rather quickly - set up a time sharing scheme, and
divide purchasing and maintenence costs proportionally by the amount of time
allocated per unit period.

Any thoughts ?


                                               Joseph B. Dunphy
From: u7023595@ucsvc.ucs.unimelb.edu.au
Newsgroups: sci.math
Subject: Re: Roots Of Integer Poly's
Date: 23 Jul 92 01:38:37 GMT
Organization: The University of Melbourne

>In article <1992Jul21.172356.3167@ucsvc.ucs.unimelb.edu.au>, 
>u7023595@ucsvc.ucs.unimelb.edu.au writes:
>>In article <4547@balrog.ctron.com>, wilson@ctron.com (David Wilson) writes:
>> 
>>>I wonder if any one out there knows anything on the following.
>>>
>>>Let F(x) be a monic polynomial with integer coeff's of degree n.
>>>Let F(x) have roots   \alpha_{1}, ... , \alpha_{n}  is there a
>>>constant C depending only on n such that
>>>
>>>       | \alpha_{j} - \alpha_{i} | >= C
>>>
>>>For all i,j. Ie the roots cannot be too close together.
>>>This is trivially true for n=1 or n=2 but what about general n ?
>> 
>> [Stuff deleted]
>> 
>> 
> WLOG assume the monic polynomial is irreducible over the rationals as 
> this is the interesting case.
I meant the maximum of the absolute values of 
  |\alpha_j - \alpha_i|  for all i,j.
Then one has C=\sqrt(3), etc. as in my previous posting. If one is interested
in the minimum of these absolute values then no such C exists but that is
another question. 
Sorry about the confusion.

Bill Lloyd-Smith
Xref: sparky sci.math:9579 sci.chem:2808 sci.engr.chem:385 sci.engr.mech:140 sci.physics:11755 sci.bio:2759 bionet.journals.contents:184