HDTenEightyP/NetNews huggingface dataset:
From: pratt@Sunburn.Stanford.EDU (Vaughan R. Pratt)
Subject: Re: Job Application Skills
Organization: Computer Science Department,  Stanford University.
Distribution: sci
Date: Sat, 9 Jan 1993 19:45:57 GMT

In article <ARA.93Jan9133843@camelot.ai.mit.edu> ara@zurich.ai.mit.edu (Allan Adler) writes:
>
>Here is another point of some concern to me:
>Many places say that they encourage people with disabilities to apply.
>However, who has the right to define what is a disability? I would say
>that any condition that makes it more difficult to perform or obtain a
>job is a disability, but this definition does not have the force of law.
>Accordingly, I would be inclined to list among my disabilities:
>(1) inability to write an appropriate resume, cover letter, research proposal,
>    and here the emphasis is on "appropriate behavior", understood by one and
>    all except myself to be appropriate.
>(2) inability to find suitable housing on my own, which has left me living
>    in the most incredible dumps at times and at other times homeless
>(3) idealistic attitudes about education and employment
>(4) inability to confine my creative tendencies to areas where I am 
>    specifically paid to be creative
>(5) unconventional lifestyle and career history
>
>
>I am however dimly aware that I am not supposed to list these on my resume.
>May I interpret this as follows: any disability that does not have the
>force of law is severely punished?

While these can all be somewhat crippling disabilities, since you
didn't mention the inability to get an adequate letter of
recommendation you are in a lot better shape than a couple of billion
others.  That's the most crippling disability of all.

One can look forward to the day when all disabilities will be
recognized and accorded their due.  Meanwhile there is a long line
ahead of you, for example victims of chronic fatigue syndrome, for whom
some of us have more sympathy, whether or not justly.

I only hope my employers will be lenient with my inability to resist
posting to Usenet, which I have found quite incapacitating.  If that
disability ever finds its way onto one of my letters of recommendation
I'm a dead duck.  In the letters I write I reserve that criticism for
those I would simply have shot were California still part of the Wild
West.
-- 
Vaughan Pratt				There's safety in certain numbers.
Newsgroups: sci.math,sci.philosophy.tech
From: swann@divsun.unige.ch (SWANN philip)
Subject: Re: Numbers and sets
Organization: University of Geneva, Switzerland
Date: Mon, 11 Jan 1993 14:24:58 GMT

In article <1ioee8INN9sc@bang.hal.COM>, landman@hal.COM (Howard Landman) writes:

> 
> Or is MZ using "analytically true" to mean something which might not be
> "true" in the normal sense?

No, he's just trying to motivate or justify technical choices by appeal to
an unspecified version of an irrelevant and worn-out philosophical doctrine...
Xref: sparky sci.math:17818 sci.math.num-analysis:3750
From: petry@zermelo.math.washington.edu (David Petry)
Newsgroups: sci.math,sci.math.num-analysis
Subject: Re: Approximating decimal fractions with proper fractions
Date: 8 Jan 1993 04:07:18 GMT
Organization: University of Washington, Mathematics, Seattle
Distribution: na
NNTP-Posting-Host: zermelo.math.washington.edu
Keywords: fraction, approximation, number theory

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.
>
>Stated more precisely:
>
>Given the decimal fraction F, ( F = x/y where x < y, y = 10^n, n >= 1 ),
>what is the proper fraction, a/b, that best approximates F if b < 10^m, 
>m >= 1, m <= n.


The following short C program will do the trick.  It works by 
converting a real number into a contiunued fraction.   I'm not sure
if all C math libraries have the function modf, so there might be
some problems on some systems.


David Petry



#include <stdio.h>
#include <math.h>


#define rational struct rat_
rational {
	int a,b;
};



#define rational_to_real(r)       ((double) (r).a / (double) (r).b)

rational
real_to_rational(r, err) double r, err;			
{
	int  k=1, A;
	rational rat1, rat2, rat3;
	double r1, rA;
	r1 = modf(r, &rA);
	A = (int) rA;
	rat1.a = 1; 
	rat1.b = 0;
	rat2.a = A; 
	rat2.b = 1;
	while ( (k++<40) && (fabs(rational_to_real(rat2) - r) > err) ) {
		r1 = modf(1./r1, &rA);
		A = (int) rA;
		rat3.a = A*rat2.a + rat1.a;
		rat3.b = A*rat2.b + rat1.b;
		rat1 = rat2;
		rat2 = rat3;						
	}
	return rat2;						
}



void
print_rat(rat) rational rat;			
{
	printf("%d/%d", rat.a, rat.b);		
}

main ()						{
	double r;
	rational rat;
	while (1)				{
		printf("Enter real >> ");
		scanf("%lf", &r);
		rat = real_to_rational(r, .00000001);
		printf("%d/%d\n", rat.a, rat.b);	
	}	
}
From: gjm11@cus.cam.ac.uk (G.J. McCaughan)
Subject: Re: Frankly,my dear......was: Fermat's Last Theorem
Organization: U of Cambridge, England
Distribution: usa
Date: Thu, 7 Jan 1993 17:17:19 GMT

In article <1993Jan7.021308.10566@nuscc.nus.sg> matmcinn@nuscc.nus.sg (.)
complains that Fermat's Last Theorem is boring, on the grounds that it's
recreational mathematics, and claims that people are only interested in it
because it's hard.

A few comments: 

 * It's pretty. If the only reason for being interested in any mathematical
   result is because it helps you prove other mathematical results, there's
   a bit of an infinite regress there. In my opinion, one of the main reasons
   for doing mathematics at all is its aesthetic appeal; and FLT *does* have
   aesthetic appeal.

 * It does connect with the rest of mathematics, anyway. Not just the algebraic
   geometry you say you've heard all the propaganda for, but other areas of
   number theory, to do with modular forms and the like.

 * "frankly, who cares? It's recreational mathematics, right?" Does the fact
   that something is "recreational" -- that people other than professional
   mathematicians are interested in it, in other words -- make it boring?

 * Work on FLT was one of the big motivators for the theory of ideals. I don't
   call that trivial, boring, or even "recreational".

-- 
Gareth McCaughan     Dept. of Pure Mathematics & Mathematical Statistics,
gjm11@cus.cam.ac.uk  Cambridge University, England.    [Research student]
Organization: City University of New York/ University Computer Center
Date: Friday, 8 Jan 1993 05:31:13 EST
From: Dimitri Vulis <DLVGC@CUNYVM.BITNET>
Newsgroups: sci.math
Subject: Re: High Prices of Math Books. I am pissed.
 <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>

A few remarks...

1. A few years ago I xlated a book for one well-known publisher.  I was
supposed to be paid.  When I turned over the book (this included typing
in the whole translation, including formulas, in TeX), I was paid about
1/3 of the sum, and was told that they went over the budget and can't
pay me.   It took me three years of reminders to get (most of) the
balance.  These particular guys are a bunch of crooks.

The book, by the way, sells for $169 (gasp).

2. I too am p.o. at the rising book prices.  When I was an undergraduate,
$40 was a lot for a book; these days, $70 is common, and I'm talking
about the same books that were kept in warehouses for several years,
not new editions.

3. 'Most' publishers of math books pay the author either no royalty
or a symbolic royalty.  At the same time, they insist now that the
authors turn over either a camera-ready MS or a diskette with TeX
source.  In the pas, typesetting a math book by hand was a major cost;
now that the cost has shifted to the authors, the prices continue to
rise.

4. A friend of mine, who runs a publishing business, claims that the
cost of printing 1,000 hard-bound 200-page books on good paper would
be about $4--6 a piece. The prohits the publishers rake in
are enormous.

So, yes, there's a niche for an enterpreneur: collect TeX mss
from authors, have them printed and bound, pay reasonable royalties,
and and half the margin of the big publishers you can make a lot
of $$$ (and do a great service to the mathematical community).
Any takers? :)


Dimitri
Department of Mathematics
CUNY GC

Disclaimer: Represent CUNY, me???
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 15:29:44 GMT

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.

Richard Pinch
From: blom@husc15.harvard.edu
Newsgroups: sci.math
Subject: Re: probability = 0
Date: 5 Jan 93 18:46:31 GMT
Article-I.D.: husc15.1993Jan5.134631.19024
Organization: Harvard University Science Center

In article <9301051655.AA22441@aplpy.jhuapl.edu>, louis@aplpy.jhuapl.edu (Louis Vasquez) writes:
> Hello,
> 	My friend and I got in a debate about the probability of 
> something happening.  The event was that another friend of ours
> could win the superbowl.  Not that he would play on a winning team
> in the superbowl but that he would win it.
> 	My thinking is that anything at all is possible and there are
> ways that this could happen however unlikely they are.  For example
> the rules of the superbowl could change to allow a single person to 
> be a team and this friend of ours would by some incredible luck, win it.
> I also say that there are many many other ways that it is possible.  
> Therefore I say there is a probability of greater than zero of this
> happening.
> 	His arguments (although I must admit I probably don't fully 
> understand them) are that by definition a single person cannot win
> the superbowl.  And the case that I gave is a finite case in an 
> infinite number of possible cases and therefore the probability is
> n devided by infinity, a limit which approaches zero.  Therefore he
> says there is a probability of exactly zero that this will happen.
> 	Anyone care to comment?
> 	Lou,
> 	louis@aplpy.jhuapl.edu

You're both right.  The probability is indeed infinitesmal, and approaches
zero, as your friend says.  But it is not exactly zero, and weird things can
happen.  Now, consider another case: that some very, very weak team will win
the Superbowl.  Even if the chance in any particular year that the team will
win the Superbowl, it's bound to happen eventually, if the team competes every
year forever.  Your problem is that this friend will not live forever, and
would have to win the superbowl in his lifetime.  Thus the odds remain small,
and almost zero (though never quite zero).

Eric Blom
Harvard U

P.S.  I could walk through a wall, but the odds that all the particles in my
      body and in the wall were correctly aligned are vanishingly small.
From: rvanhorn@nrtc.nrtc.northrop.com (Bob Van Horn <rvanhorn>)
Newsgroups: sci.math
Subject: Need Help With Advanced Algebra Problems (10 each)
Date: 4 Jan 93 03:48:47 GMT
Reply-To: rvanhorn@nrtc.nrtc.northrop.com (Bob Van Horn <rvanhorn>)
Distribution: usa
Organization: Northrop Research & Technology Center, Palos Verdes, CA

Have four friends who are trying to solve 10 Advanced Algebra
problems and asked me for help.  I looked at them and they
are beyond me so I am looking for a guru in Advanced Algebra
who would be willing to help them out.  Please e-mail me at the
address, below, or call (number has voice-mail) if you can spare
the time.  Not sure of the circumstances but would like to help
them.

bob van horn
rvanhorn@nrtc.northrop.com
(213)600-3991

PS  Not sure original post went out,,,,this is a second shot.
Newsgroups: sci.math
From: steele@isis.cgd.ucar.edu (Alfred Steele)
Subject: Euclidean domains
Organization: Climate and Global Dynamics Division/NCAR, Boulder, CO
Date: Mon, 11 Jan 1993 00:53:20 GMT


In article <23741@sbsvax.cs.uni-sb.de> you write:
|>>> |>Why there are not other candidates for the Euclidean function?
|>
|>I'm not sure what the original question was, but hopefully the following
|>is not altogether irrelevant!
|>
|>A Euclidean domain is a ring equipped with a special kind of a valuation -- an
|>euclidean valuation, essentially one that makes it amenable to carry out the
|>Euclidean algorithm. As usual, one can get a norm out of this by taking a nega
tive
|>exponential. Ostrowski's classic theorem asserts that the only possible norms 
on
|>the rationals are the absolute value and the p-adic norms obtained from p-adic
|>valuations. I am unaware of of similar general normal form results about 
|>euclidean valuations on various classes of rings. Perhaps a book on Valuation
|>Theory (such as Endler's, which unfortunately is inaccessible to me at present
)
|>might shed some light on this.


Functions for Euclidean rings satisfy an inequality.  The multiplicative
property of norms is essential for something like Ostrowski.  The post
by R. T. Bumby shows us that we are on the wrong track.  I will repeat it.
The problem in Hungerford would be easy if one restricted oneself to 
absolute value norm but if you take it at face value and allow the function
to be arbitary (except for the conditions) it might be very difficult.
Hay - everything is Hungerford is not correct - he has other errors.

If I wanted to really find out about the answer I would get off my butt an
go check out the references in the following post:

|>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.
|>The derived set of {0} consists only of units.  If all proper ideals
|>have index greater than the number of units (only 2 except for some
|>rings that are already Euclidean for the norm), the process stops
|>there.
|>
|>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

Alfred T. Steele (steele@isis.cgd.ucar.edu)
From: singerm@cpva.saic.com
Newsgroups: sci.math
Subject: More Fermat - sort of
Date: 11 Jan 93 01:41:46 PST
Organization: Science Applications Int'l Corp./San Diego


Here are some results of some work I have done on something I call the 
min function.  It is an attempt to evaluate min(n) = the minimum number 
of 'perfect' nth powers required to sum to another perfect nth power:


      min(n)
     -------
      \
       \       n       n
       /      A    =  A             for any positive, integral value of n.
      /        i       min(n)+1
     -------
      i = 1


Theorem:       min(n) is an increasing function.
 
Discussion:    Certain discrete values for min(n) are known:

                                               1    1    1
                   min(1)  =  2    example:   2  + 3  = 5

                                               2     2     2
                   min(2)  =  2    example:   3  +  4  =  5

                                               3     3     3     3
                   min(3)  =  3    example:   3  +  4  +  5  =  6

                                        4         4         4         4
                   min(4)  =  3    95800  + 217519  + 414560  = 422481

                                     5    5     5     5     5
                   min(5) <=  4    27 + 84 + 110 + 133 = 144

I also have results for some fractional and negative exponents.  It is my
hope that by extending the domain of min(n) in this way I can get a better
feel for the behavior of the function.  This has proven correct, but it
still hasn't led me to a general approach - YET.

I believe this is enough information to give you the idea of what I've
been working on.  Any thoughts/recommendations/help will be welcomed!

And, of course, Fermat's Last Theorem will be nothing more than a simple
corollary of this theorem.

Mark Singer
singerm@cpva.saic.com
Newsgroups: sci.math
From: baseggio@deshaw.com (Franco Baseggio)
Subject: How do you use an abacus?
Organization: D. E. Shaw & Co.
Date: Mon, 4 Jan 1993 20:23:04 GMT

Can anyone instruct me in the use of an abacus or point me to
appropriate references?  I'd like to know how to do things at least as
hard as square roots.

Thanks,
 Franco
From: G.Joly@cs.ucl.ac.uk (Gordon Joly)
Newsgroups: sci.math
Subject: Hypergraphs in (Software) Engineering and other areas.
Date: 4 Jan 93 18:11:31 GMT


I am trying to survey the application of hypergraphs to science and
engineering, in particular software engineering. Hypergraphs as
defined in Berge's book.

I am aware of

%A S. L. Lauritzen
%A D. J. Spiegelhalter
%T Local Computations with Probabilities on Graphical Structures and
their Application to Expert Systems
%J Journal of the Royal Statistical Society, Series B
%V 50
%N 2
%D 1988
%P 157-224

which uses some (hyper-)graph theory (cliques), but is mainly
concerned with the probability theory.

Please reply directly to me, if possible.

____

Gordon Joly      Phone  +44 71 387 7050 ext 3703      FAX  +44 71 387 1397
Internet: G.Joly@cs.ucl.ac.uk        UUCP: ...!{uunet,uknet}!ucl-cs!G.Joly
Computer Science, University College London, Gower Street, LONDON WC1E 6BT
Newsgroups: sci.math
From: yeomans@austin.onu.edu (Charles Yeomans)
Subject: Re: High Prices of Math Books. I am pissed.
Date: Thu, 7 Jan 1993 21:43:12 GMT
Organization: Ohio Northern University

In article <ARA.93Jan7012128@camelot.ai.mit.edu>, ara@zurich.ai.mit.edu (Allan Adler) writes:
> 
> In article <C0GEBz.98t@mentor.cc.purdue.edu> hrubin@pop.stat.purdue.edu (Herman Rubin) writes:
> 
>    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.
> 
> Why is this so? I heard a rumor that Serge Lang can knock off a book in
> a weekend.
> 
I heard it was a month.

Lang's books tend to be of somewhat uneven quality; also, given his 
writing technique, the quality is actually quite high, I suppose.
And Lang's mathematical insight is an order of magnitude above that of 
most mathematicians.

Charles Yeomans
From: bevan@cs.man.ac.uk (Stephen J Bevan)
Newsgroups: sci.math
Subject: Re: High Prices of Math Books. I am pissed.
Date: 8 Jan 93 01:18:36 GMT
	<BEVAN.93Jan6215256@panda.cs.man.ac.uk>
	<1993Jan7.170536.28221@infodev.cam.ac.uk>
Organization: Department of Computer Science, University of Manchester
In-reply-to: gjm11@cus.cam.ac.uk's message of 7 Jan 93 17:05:36 GMT

In article <1993Jan7.170536.28221@infodev.cam.ac.uk> gjm11@cus.cam.ac.uk (G.J. McCaughan) writes:

   I don't think the fact that all students complain about book prices
   proves that they are wrong.

Nor does it prove they were right.  My point is only that each intake
moans about the cost but without any hard data on the relative prices
I find it difficult to take the moaning seriously.

   Yes, I know, I'm moaning. But even if there is no solution to the problem,
   it should at least be admitted that the problem of text-book prices is a
   real one.

See above.

bevan
Newsgroups: sci.math
From: thf@cbnewsm.cb.att.com (thomas.h.foregger)
Subject: combinatorial? problem
Organization: AT&T
Date: Sun, 10 Jan 1993 03:16:04 GMT


In article <Dec.23.18.15.49.1992.22657@pepper.rutgers.edu>, gore@pepper.rutgers.edu (Bittu) writes:
> 
> Someone please help me with the following problem. I have pretty much
> given up on it after a lot of thinking. We want to show the following:
> 
> given m,n nonnegative integers, the quantity
> 
>      (2m)! (2n)!
>     -------------      is an integer.
>      m! n! (m+n)!
> 
> 
> Note that this is very easy to show by the standard argument where for
> every prime p, you find the highest power of p (say p^k) that divides
> the denominator and then show that p^k divides the numerator as well.
> 
> I want a combinatorial proof of this. I have tried rewriting the above
> as C(2m,m)*C(2n,n)/C(m+n,m) where C(a,b) is "a choose b" and also in
> other ways, but I still haven't come up with a combinatorial proof.
> 
> --Bittu


This problem is harder than I thought. I have now run 
across a generalization of the problem in the American Math. Monthly,
for Dec.  1976, p. 817, Problem 6121, which is solved in
AMM for Aug-Sept, 1978, p. 602. 
The method is to look at the number of times a prime p divides
the numerator and denominator. 
It is stated: "It would be interesting to have a combinatorial proof." 

tom foregger
Newsgroups: sci.math
From: kimball@stsci.edu (Timothy Kimball)
Subject: Re: Let's add some sci.math.* groups
Organization: Space Telescope Science Institute
X-Newsreader: TIN [version 1.1 PL6]
Date: Mon, 11 Jan 1993 19:48:22 GMT

Robert D. Silverman (bs@gauss.mitre.org) wrote:
: 
: Mathematics is getting too specialized as it is. Let's not make it 
: worse.
: 
: I *might* vote for a split into sci.math, and sci.math.recreational,
: as well as keeping sci.math.research.
:

This sounds like a good idea.
Not everyone who reads this group is a mathematician by trade,
and over-dividing sci.math will ruin its eclectic nature.

-- tdk
Organization: University of Illinois at Chicago
Date: Tue, 5 Jan 1993 09:02:24 CST
From: Manuel M. Flores <U15803@uicvm.uic.edu>
Newsgroups: sci.math
Subject: Simpson's Paradox

Does anybody know where I might find a text file explaining Simpson's
Paradox as it applies to statistics? Or any other text files explaining
other such theories?

Thanks,

MMF
Xref: sparky sci.math:17656 sci.math.num-analysis:3711