HDTenEightyP/NetNews huggingface dataset:
From: somos@ces.cwru.edu (Michael Somos)
Newsgroups: sci.math
Subject: Allan Adler
Date: 13 Jan 1993 00:30:30 GMT
Organization: Computer Engineering and Science, Case Western Reserve University
Distribution: world
NNTP-Posting-Host: george.ces.cwru.edu

Allan Adler continues to assault the newsgroup sci.math with his
personal problems based on a complete fantasy that some people may
be even interested in them to warrant posting about it.

I am only too familiar with his postings to be astonished any more.

Shalom, Michael Somos <somos@ces.cwru.edu>
From: gjm11@cus.cam.ac.uk (G.J. McCaughan)
Newsgroups: sci.math
Subject: Re: proof wanted 2
Date: 10 Jan 93 17:23:53 GMT
Organization: U of Cambridge, England

In article <1iorntINNoal@skeena.ucs.ubc.ca> liuli@unixg.ubc.ca (Li Liu) writes:

>The claim that there is a closest point in C (a close set) to a point
>x (a point outside C) is not true for general metric spaces.

Correct.

>A simple example is to take the metric space to be { 1/n | n is positive
>integers }, under the usual metric d(a,b)= |a-b|. Let C be the space 
>itself. C is closed. Let x be 0. There is no point in C that is closet to
>zero.

Incorrect. 0 is not in the space you consider; if you put 0 into the space,
C is no longer closed.

To get a correct counterexample, we need a space in which closed&bounded
does not imply compact. One of the most famous such spaces is called l^2,
and consists of all square-summable sequences of real numbers; it's a
vector space in the obvious way, it's got a norm (sqrt of sum of squares),
and this induces a distance (d(x,y) = norm(x-y)); but (e.g.) the unit
sphere is closed and bounded, but not compact.

Take x=0; C = { (1+1,0,0,0,0,0,0,...),
                (0,1+1/2,0,0,0,0,0,...),
                (0,0,1+1/3,0,0,0,0,...),
                (0,0,0,1+1/4,0,0,0,...), ... }
and notice: the points of C get successively closer to x; C is closed
despite appearences (because no subsequence of points of C converges.
Note, for instance, that the distance between any two members of C is
at least root(2).) We're done.

-- 
Gareth McCaughan     Dept. of Pure Mathematics & Mathematical Statistics,
gjm11@cus.cam.ac.uk  Cambridge University, England.    [Research student]
Newsgroups: sci.math,alt.books.technical
From: rivin@SAIL.Stanford.EDU (Igor Rivin)
Subject: Re: High Prices of Math Books. I am pissed.
Organization: Computer Science Department,  Stanford University.
Date: Tue, 5 Jan 1993 18:00:25 GMT

In article <1993Jan5.173010.19718@Princeton.EDU> bathurst@phoenix.Princeton.EDU (Bruce Bathurst) writes:
>There is an illusion in American society that those who are educated
>are (or can be) financially secure.  Accordingly, there is a lack of
>concern for the inability of those in the process of educating
>themselves to buy the books they need.
>
>Because of this (I suspect) there is no mechanism, as there is in
>medicine, for the cost of expensive necessities to be shared by the
>rest of society.  Many students can't buy even basic texts, others
>sell them back.  Students, as a consequence, are not only less
>educated, but have not learned how to teach themselves, through
>reading.  Those who choose to devote their lives to advancing
>knowledge in basic fields face the choice of purchasing books or food.
>

There IS another way -- go to the library. I gather that there are a
couple in Princeton, NJ, courtesy of the rest of society.
From: crb11@cus.cam.ac.uk (Colin Bell)
Newsgroups: sci.math
Subject: Re: Fields Medal Winners
Date: 10 Jan 93 00:30:51 GMT
Organization: U of Cambridge, England

In article <1452@kepler1.rentec.com>, andrew@rentec.com (Andrew Mullhaupt) writes:
|> In article <erwin.726504145@trwacs> erwin@trwacs.fp.trw.com (Harry Erwin) writes:
|> >This impression is associated with one of those stories. I understand
|> >Artin, Atiyah, and Bott were the first three at the math tripos one year
|> >at Oxford (1950?). Apparently it made quite an impression.
|> 
|> I'm a bit surprised at the idea that the tripos still existed in 1950,
|> since Hardy successfully abolished them but did not see 1950. Can
|> anyone clear this up?
|> 
|> Later,
|> Andrew Mullhaupt

To clear a couple of things up:

Atiyah was at Cambridge at the time. I _think_ he graduated in 1950, it's
certainly within a year or so of then.

The Tripos is an exclusively Cambridge object: it's alive and reasonably well.
Hardy didn't get it abolished, merely reformed (this was in 1910). Since then,
it's spread to other subjects apart from mathematics (in fact all other
undergraduate exams are now Tripos).   

-- 
-
Colin Bell, CRB11@CUS.CAM.AC.UK
Department of Pure Mathematics, University of Cambridge.
Newsgroups: sci.math
From: swann@divsun.unige.ch (SWANN philip)
Subject: Re: Let's add some sci.math.* groups
Organization: University of Geneva, Switzerland
Date: Mon, 11 Jan 1993 13:29:22 GMT

I support this idea!
Newsgroups: sci.math
From: rbk5287@usl.edu (Kearfott Ralph B)
Subject: Math. Modeling and Sci. Computing  -- Conference
Organization: University of Southwestern Louisiana
Date: Tue, 12 Jan 1993 16:00:20 GMT

Date: September 14--17, 1993
Place: Sozopol, Bulgaria
Conference Title: Mathematical Modeling and Scientific Computation
                  (MMSC-93)

Official Language: English

The purpose of the conference is to make new methodologies for
scientific computation and new software tools widely available, to
promote contacts between software companies and diverse groups of
specialists, and to train and encourage beginning researchers.  Topics
include advanced numerical methods (involving interval and parallel
techniques) and applications, mathematical models with interval-valued
input data, enclosure methods with automatic result verification,
interval methods in automatic theorem proving, program packages, and
applied modeling.

Papers, nominally four pages long, should be submitted via e-mail and in
printed form to one of the contact persons by April 1, 1993.
Notification of acceptance will be by June 15, 1993.  Preregistration
($100 U.S.) is before July 15, 1993, and on-site registration is $130.

Contact persons: S. Markov (chairman), N. Dimitrova (secretary)
                 Institute of Biophysic,s BAS
                 Acad. G. Bonchev str. bl. 21
                 BG-1113 Sofia, Bulgaria
                 email: neli@bgearn.bitnet

                 D. V. Shiriaev, Karlsruhe
                 email: dima@iamk4058.mathematik.uni-karlsruhe.de

                 I. Dimov, Sofia
                 email: ivdimov@bgearn.bitnet

                 R. B. Kearfott
                 Department of Mathematics
                 University of Southwestern Louisiana
                 U.S.L. Box 4-1010
                 Lafayette, LA 70504-1010
                 USA
                 Work phone: (318) 231-5270
                 Home phone: )318) 981-9744
                 email: rbk@usl.edu (Internet)

                 Ch. Ullrich, Basel
                 email: ullrich@urz.unibas.ch

                 A. P. Voshinin, Moscow
                 email: apv@mei.msk.su

                 K. Madsen, Lyngby
                 email: numikm@vm.uni-c.dk

                 J. Wolff von Gudenberg, Wuerzburg
                 email: wolff@informatik.uni-wuerzburg.de
From: carsten@pizza.fb10.tu-berlin.de (Carsten Schultz)
Newsgroups: sci.math
Subject: Re: probability = 0
Date: 5 Jan 1993 22:03:30 GMT
Organization: ZRZ/TU-Berlin
Distribution: world
Reply-To: carsten@pizza.fb10.tu-berlin.de (Carsten Schultz)
NNTP-Posting-Host: pizza.fb10.tu-berlin.de

In article <1993Jan5.134631.19024@husc15.harvard.edu>  
blom@husc15.harvard.edu writes:
..
> You're both right.  The probability is indeed infinitesmal, and  
approaches
> zero, as your friend says.  But it is not exactly zero, 
..

What kind of probability theory are you talking about? I always thought,  
probabilities had to be real numbers.

Carsten
From: torb@stud.cs.uit.no (Tor Berger)
Newsgroups: sci.math
Subject: Re: What is the 'sinc' function?
Keywords: sinc
Date: 12 Jan 93 14:40:29 GMT
Organization: University of Tromsoe, Norway

In article <1993Jan12.093439.27666@cv.ruu.nl>, ger@cv.ruu.nl (Ger Timmens) writes:
|> In <1itehhINN8v1@roundup.crhc.uiuc.edu> hougen@focus.csl.uiuc.edu (Darrell Roy Hougen) writes:
|> 
|> >I came accross it in a paper about the scattering of electromagnetic
|> >radiation. 
|> 
|>           sin(Pi * x)
|> sinc(x) = -----------,
|>            (Pi * x)
|> 
|> So it's 0 at {...,-2,-1,0,1,2,...}. It's the Fourier transform of an ideal
|> lowpass filter.         ^

sinc(0) = 1   (not 0)

---

Tor
From: petry@zermelo.math.washington.edu (David Petry)
Newsgroups: sci.math
Subject: Re: Frankly,my dear......was: Fermat's Last Theorem
Date: 9 Jan 93 03:58:45 GMT
Article-I.D.: shelley.1ilihlINN6ke
Distribution: usa
Organization: University of Washington, Mathematics, Seattle
NNTP-Posting-Host: zermelo.math.washington.edu

In article <1993Jan7.054017.25511@leland.Stanford.EDU> ilan@leland.Stanford.EDU (ilan vardi) writes:
>
>  One of the reasons people are interested [Fermat's Last Theorem] is that
>a certain phenomenon is taking place (i.e., *no* solutions exist) and
>no one can explain why this happens. 

While it is true that no one can explain why Fermat's Last theorem has to 
be true, there are very convincing heuristics arguments that it really 
ought to be true.  Briefly, for a given large exponent p, the set of
numbers which are perfect p'th powers is a very sparse set of numbers,
and the probability that some number from such a set is the sum of two
others from the set is very small.


> This is a natural phenomenon that should be explained. 

Actually, it's questionable whether it should be called a phenomenon
at all.  Usually we think of a "phenomenon" as something that occurs
which is improbable (don't we?).  Fermat's Last theorem is far from 
being improbable.


Anyways, if the probabilities behind Fermat's Last theorem were more widely
known, maybe fewer amateurs would choose to seek glory through finding
a proof of the theorem.



David Petry
Newsgroups: sci.math
From: nickh@CS.CMU.EDU (Nick Haines)
Subject: Re: High Prices of Math Books. I am pissed.
Originator: nickh@SNOW.FOX.CS.CMU.EDU
Organization: School of Computer Science, Carnegie Mellon University
	<1993Jan7.170536.28221@infodev.cam.ac.uk>
	<thompson.726445179@daphne.socsci.umn.edu>
	<1993Jan8.012016.11134@infodev.cam.ac.uk>
	<MARTIN.93Jan8001957@lyra.cis.umassd.edu>
Date: Fri, 8 Jan 1993 17:57:25 GMT

In article <MARTIN.93Jan8001957@lyra.cis.umassd.edu> martin@lyra.cis.umassd.edu (Gary Martin) writes:

   [about set texts]

   [...]

   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.

   [...]

Maybe American universities should concentrate on teaching their
intake how to be students, before trying to teach them mathematics?

:-)/2

Nick Haines nickh@cmu.edu
Newsgroups: sci.math
From: orourke@sophia.smith.edu (Joseph O'Rourke)
Subject: Re: Help find optimum display of directed graphs
Organization: Smith College, Northampton, MA, US
Date: Thu, 7 Jan 1993 17:57:46 GMT

In article <103943@netnews.upenn.edu> bill@amy.med.upenn.edu (Bill Tozier) writes:
>I need some help with a problem in visualizing mathematical graphs. [...]
>I'd appreciateanyone's hints re: Mathematica, or just a theoretical
>optimization in 2-space or 3-space.

Since you mentioned Mathematica, you should look at the function ShowGraph
in the Combinatorica package (discussed in the Guide to Standard Mathematica
Packages), and look at Steve Skiena's book on the theory behind the functions
in that package.
From: llk@kepler.unh.edu (Local Genius)
Newsgroups: sci.math
Subject: Of Pascal's triangle and limits
Date: 10 Jan 1993 23:51:47 GMT
Organization: Department of Mathematics
NNTP-Posting-Host: kepler.unh.edu

                                  1
                                 / \
                                 1 1
                                1 2 1
                               / \  /\
                               1 3 3 1
                              1 4 6 4 1
                             /\       /\
                            1 5 10 10 5 1
                           1 6 15 20 15 6 1
                          /\   /\    /\   /\
                         1 7 21 35 35 21 7  1
                                 .
                                 .
                                 .

Is there a limit to this thing, where the rule is to start at the top of the
triangle and form triangles by joining odd entries (I have skipped the bases
of the triangles to simplify the picture)? This may be a totally stupid 
question to ask but I couldn't resist asking! :-)






-- 
lk(with the man in the yellow hat)              /\   /\
       llk@unh.edu                             /  \_/  \ 
%__________________________%                  /         \
% Math Dept, UNH, Durham,  %                 /           \
% NH 03824, USA            %             \__              __/ 
%  FAX : (603) 862 - 4096  %             Charu ndimazgora. Chika- 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%          zgora ba Gamphani pa Nkhamanga 

Newsgroups: sci.math,comp.edu,misc.education
From: osan@cbnewsb.cb.att.com (Mr. X)
Subject: Re: Education crisis (was RE: how much math...)
Organization: Twilight Zone
Date: Sat, 9 Jan 1993 00:39:28 GMT

In article <1hr5fjINN972@mirror.digex.com> kfl@access.digex.com (Keith F. Lynch) writes:
>In article <PRENER.92Dec12015805@prener.watson.ibm.com> prener@watson.ibm.com (Dan Prener) writes:
>> Little kids learn much faster. ...
>> But the fact that little kids' learning capacity is so much greater
>> than that of older people ...
>
>Is there any evidence for this?  It goes against my experience.

	I think there may be some truth to the statement, however I also
	feel it may be exagerrated quite a bit.  

	I don't think that a child is inherently more able to learn than an
	adult, from the point of cognition.  Indeed, it may well be the other
	way around.  However, children may have less internal interference
	to distract them, i.e. less in the way of noise... like paying the
	mortgage, finding your wife in bed with your best friend and a life
	time of things like these that tend to preoccupy the minds adults to
	the effective detriment of their ability to learn, in some cases.
	Compound this with years of too much booze, smoking, LSD, marginal
	sex, etc. and you may have some physical basis for reduced learning
	ability.

	In support of this theory I invite you to check out children that
	have been severely abused.  Their levels of internal noise are
	higher than normally found in kids and sure enough you see lots of
	problems in such children with learning.

	What thinks y`all?

	-Andy V.
Newsgroups: sci.math
From: hdev@dutiai.tudelft.nl (Hans de Vreught)
Subject: Re: High Prices of Math Books. I am pissed.
Organization: Delft University of Technology
Date: Thu, 7 Jan 1993 09:36:26 GMT

bevan@cs.man.ac.uk (Stephen J Bevan) writes:
>As to the subject line: each new intake of students
>complains about the price of books (I'm sure I did).

When I was studying at my polytechnic I had to spend about $700 a year on
textbooks, when I was studying at my university this was less than $200 (there
are many *cheap* readers). I found it strange that other students complaint
about the high prices for text books at the university: being used to the
higher prices, I found it a bargain.
--
Hans de Vreught                          | John von Neumann:
hdev@dutiba.twi.tudelft.nl               | Young man, in mathematics
Delft University of Technology (TWI-ThI) | you don't understand things,
The Netherlands                          | you just get used to them.
From: ara@zurich.ai.mit.edu (Allan Adler)
Newsgroups: sci.math
Subject: Re: proof wanted 2
Date: 10 Jan 93 22:23:14 GMT
	<1iorntINNoal@skeena.ucs.ubc.ca>
	<1993Jan10.172353.13507@infodev.cam.ac.uk>
Organization: M.I.T. Artificial Intelligence Lab.



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}.

One direction has been discussed abundantly.

I know that a metric space is compact if and only if every continuous
function on the space assumes a minimum. This seems to be in a similar
spirit.

Allan Adler
ara@altdorf.ai.mit.edu
Newsgroups: sci.math
From: rusin@mp.cs.niu.edu (David Rusin)
Subject: Re: spell this?
Organization: Northern Illinois University
Date: Tue, 12 Jan 1993 18:07:39 GMT

In article <1isvrsINNe11@master.cs.rose-hulman.edu> goddard@NeXTwork.Rose-Hulman.Edu (Bart E. Goddard) writes:
>
>The raging debate here is the correct spelling of (choose one and 
>supply a reference):
>
>a) nilpotentcy
>b) nilpotency
>c) other
grep -i tcy /usr/dict/words
bankruptcy

So I would say that the -tcy ending is not at all common in English.
From: tallynnk@NeXTwork.Rose-Hulman.Edu (Nicholas K Tallyn)
Newsgroups: sci.math
Subject: Feb 1993 Points and Angles
Date: 9 Jan 1993 05:19:49 GMT
Organization: Computer Science Department at Rose-Hulman
Reply-To: tallynnk@NeXTwork.Rose-Hulman.Edu (Nicholas K Tallyn)
NNTP-Posting-Host: o231-26.nextwork.rose-hulman.edu

If anybody who reads this group gets the journal "Points and Angles", could  
they email me the results of the mathematical modeling contest?

Thanks

Nick
Newsgroups: sci.math
From: tao@fine.princeton.edu (Terry Tao)
Subject: Re: proof wanted 2
Originator: news@nimaster
Organization: Princeton University
Date: Sat, 9 Jan 1993 19:37:59 GMT

In article <1ikq9eINNmue@roundup.crhc.uiuc.edu> hougen@focus.csl.uiuc.edu (Darrell Roy Hougen) writes:
>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

I think this proof needs a bit of tightening up - after all, I can think of
some sort of "spiral" sequence of points which get closer and closer to x
though perhaps staying always a given distance away from x at least, but
have more than one limit point.

also Darrel's sequence of c's have to satisfy |x - c_i| --> inf_{c \in C}
|x - c| for the argument to work.

However, the sequence Darrell mentioned is contained inside a closed ball,
which is a compact set, so there must be at least one accumulation point,
and this point is in C, as C is closed.  Taking limits you should get the
result.

Is the result true for any metric space?  I don't think the space of
l^2 sequences will work, if you take the set composed of elements which are
0 everywhere except at one place where they are 1...

Terry
From: cohen@alioth.greco-prog.fr (Henri Cohen)
Newsgroups: sci.math
Subject: Re: Euclidean Domain
Date: 12 Jan 93 09:53:11 GMT
Reply-To: cohen@alioth.greco-prog.fr (Henri Cohen)
Organization: ceremab

In article <Jan.10.09.44.57.1993.15296@dimacs.rutgers.edu>,
bumby@dimacs.rutgers.edu (Richard Bumby) writes:
|> steele@isis.cgd.ucar.edu (Alfred Steele) writes:
|> 
|> 
|> >In article <HAMMOND.93Jan3134111@annemarie.albany.edu>,
hammond@csc.albany.edu (
|> >William F. Hammond) writes:
|> >|> In article <Jan.3.02.05.44.1993.24643@spade.rutgers.edu>
|> >|>    cadet@spade.rutgers.edu (Uniquely TiJean) writes:
|> >[....]
|> 
|> >|>If someone can answer the question:
|> >|>Why there are not other candidates for the Euclidean function?
|> 
|> >I have asked the very same question and do not know the answer....
|> >Any information netters know about this, I would be interested in hearing
|> >about.  What is the "folklore" on the subject?
|> 
|> This should be a FAQ.  T. S. Motzkin, "The Euclidean Algorithm", Bull.
|> Amer. Math. Soc. 55(1949), 1142-1146, gave a simple analysis of the
|> properties of any Euclidean Algorithm in an integral domain.  The idea
|> is to work backwards, starting with the set consisting only of zero,
|> and applying the following construction.  The derived set of a set, S,
|> consists of all elements of the domain which have a complete set of
|> residues in S.  This construction may be extended transfinitely if
|> necessary by taking unions at limit ordinals.  In order to have a
|> Euclidean Algorithm, you must be able to exhaust the domain in this
|> way.  For quadratic number rings, there are only finitely many units.

Of course this is only for IMAGINARY quadratic number rings.
 
|> Another major article on Euclidean Algorithms is P. Samuel, "About
|> Euclidean Rings", J. Algebra 19 (1971), 282-301.  It would appear that
|> the next major exposition is due this year.
|> -- 
|> R. T. Bumby **  Rutgers Math ||   Amer. Math. Monthly Problems Editor
|> bumby@math.rutgers.edu       || P.O. Box 10971 New Brunswick, NJ08906-0971
|> bumby@dimacs.rutgers.edu     || Phone: [USA] 908 932 0277 * FAX 908 932 5530

A result which I believe is due to H. W. Lenstra is that under the Generalized
Riemann Hypothesis, ALL number fields with class number 1 (i.e. with unique
factorization) are Euclidean for SOME Euclidean algorithm (of course usually
not the one given by the norm), EXCEPT those which have finitely many units,
in other words imaginary quadratic fields.

	Henri Cohen
Newsgroups: sci.math