HDTenEightyP/NetNews huggingface dataset:
From: holmes@opal.idbsu.edu (Randall Holmes)
Subject: Re: consequences of the Axiom of Choice
Organization: Boise State University
Date: Fri, 2 Oct 1992 20:55:26 GMT

In article <91423@netnews.upenn.edu> weemba@sagi.wistar.upenn.edu (Matthew P Wiener) writes:
>In article <26913.Oct200.15.5792@virtualnews.nyu.edu>, brnstnd@nyu (D. J. Bernstein) writes:
>>> And I for one, never cared again much
>>> about AC assumptions except when it actually matters. 
>
>>All metamathematical issues aside, there is a sound _pedagogical_ reason
>>to explicitly identify each use of the axiom of choice.
>
>I certainly don't think you should _not_ mention AC when it's used.  I
>just think, a la Gunning's comment, the decision on _whether_ to use AC
>or some other assumption is pretty much a stylistic matter.
>-- 
>-Matthew P Wiener (weemba@sagi.wistar.upenn.edu)

It's not entirely a matter of style.  It is legitimate, for instance
(although not usually done) to assume that all sets of real numbers
are Lebesgue measurable.  But then one _cannot_ assume AC in
unrestricted form...


-- 
The opinions expressed		|     --Sincerely,
above are not the "official"	|     M. Randall Holmes
opinions of any person		|     Math. Dept., Boise State Univ.
or institution.			|     holmes@opal.idbsu.edu
Newsgroups: sci.math
From: hporopudas@tnclus.tele.nokia.fi
Subject: Re: Pt 1/6: STRUCTURE OF TIME (at numerous requests)
Organization: Nokia Telecommunications.
Date: Fri, 2 Oct 1992 07:04:52 GMT


In article <717984321.F00001@monly.wlink.nl.monly.wlink.nl>,
hporopudas@f1.n100.z60.wlink.nl (hporopudas) writes:

>
> Hi !

  This falsification was done by some malicious writer who possible
 can change usernames in his/her own computer.

  ---Hannu.

Xref: sparky sci.math:12485 comp.theory:2088 comp.graphics:10124 comp.sys.mac.apps:15157 comp.sys.mac.misc:17208
From: fife@calvin.edu (Earl D. Fife)
Newsgroups: sci.math,comp.theory,comp.graphics,comp.sys.mac.apps,comp.sys.mac.misc
Subject: Re: XYZ GeoBench V4.4.0 available via anonymous ftp
Date: 30 Sep 92 05:58:23 GMT
Organization: Calvin College
X-Xxdate: Wed, 30 Sep 92 06:50:10 GMT
X-Useragent: Nuntius v1.1.1d11

In article <1992Sep29.191804.23310@neptune.inf.ethz.ch> Peter Schorn,
schorn@inf.ethz.ch writes:
>The XYZ GeoBench software for geometric computation has been upgraded to
>version 4.4.0. A summary of changes is at the end of this article. 
>
>  (passage deleted)
>
>Availability: Object code and documentation via anonymous ftp from
>neptune.inf.ethz.ch (129.132.101.33) in directory XYZ:

This is also posted at a US site.  I have posted them in the Mathematics
Archives located at wuarchive.wustl.edu in the directory edu/math/mac.
These particular files are in the geometry subdirectory.

The Mathematics Archive is a new archive dedicated to shareware and public
domain software suitable for mathematics education at the college and 
university level.  If you have or know of appropriate software (currently
only
DOS and Macintosh platforms are included), please notify me at the address
below for Macintosh software, or Larry Husch at husch@WUARCHIVE.WUSTL.EDU 
for DOS software.

The current newsletter for the Mathematics Archive is also posted in
several
news forums.

-------------------------------------------------------------------------

Earl D. Fife          |          Department of Mathematics
fife@calvin.edu       |          Calvin College
(616)957-6403         |          Grand Rapids, MI 49546

"Make up your mind, Margaret. First you tell me 3 plus 3 is 6, 
and now you tell me 4 plus 2 is six!"     --Dennis the Menace

=========================================================================
From: m1dxm00@fed.frb.gov (Douglas X. McManus)
Newsgroups: sci.math
Subject: large deviations of sums of correlated variables
Keywords: large deviations, correlation
Date: 2 Oct 92 21:12:11 GMT
Reply-To: m1dxm00@fed.frb.gov (Douglas X. McManus)
Organization: Federal Reserve Board, Wash, DC

Can anyone direct me to some results on large deviations of correlated random variables.  I have a rather specific application that has the following form:

let X be multivariate normally distributed with (1) the correlation between any two elements a fixed constant, and (2) the means and variances each element of X are also constants.

Define Yi = min[0, Xi - Mi]  where the Mi are known constants.

Let Sn = (Y1 + Y2 + ... + Yn)/n

What is the limiting behavior of PR{ Sn < C } as n gets large?

I expect that 

 (1/n) ln ( PR{ Sn < C } ) = - I("the constants")

with I being refered to as the "rate function" (sometimes).

There is also a related and less formal approximation of the probability that is sometimes used in statistics,

 PR{ Sn < C } == K("the constants") exp ( -nI("the constants")

any advise is welcome.
Newsgroups: sci.math
From: mroussel@alchemy.chem.utoronto.ca (Marc Roussel)
Subject: Re: Mattel says "Math is tough."
Organization: Department of Chemistry, University of Toronto
Date: Mon, 5 Oct 1992 14:41:42 GMT

In article <1992Oct5.084002.25808@nuscc.nus.sg> matmcinn@nuscc.nus.sg
(Mcinnes B T (Dr)) writes:
>iltiss@owlnet.rice.edu (Steven Patrick Iltis) writes:
>:         Mattel has just released a new product. A Barbie doll that says
>: "Math is tough".
>
>What would you have her say?: 

     How about "I like math" or "I want to be an engineering physicist"?
Women get too many negative messages about their chances of succeeding in
technical careers.  This sort of product is dangerously stupid.  It would
have been better for the doll not to mention math than for it to say that
math is hard.
     Every year in my physical chemistry class, I find bright women who
are terrified of math.  (This is far more common than male mathphobes.)
Since their performance in this course (and indeed their past
performance in calculus and physics) indicates that they can use
mathematically phrased ideas if simultaneously pushed and properly
tutored, why are they so afraid?  The only conclusion I can come to is
that they have been brainwashed into thinking that they couldn't handle
it.  "Math is hard" is a message that women hear far too often.  Math is
not hard.  It is our job as educators to help them see that; it is our
responsibility as educated persons to see to it that Mattel withdraws
this ill-considered product from the market.  I'm sure that Mattel didn't
do this on purpose; ignorance is potentially just as damaging as malice.

				Marc R. Roussel
                                mroussel@alchemy.chem.utoronto.ca
Newsgroups: sci.math
From: bs@mendel.mitre.org (Robert D. Silverman)
Subject: Re: Closed form solution for Sum[ 1/x , {x,1,n} ] ?
Organization: Research Computer Facility, MITRE Corporation, Bedford, MA
Date: Fri, 2 Oct 1992 19:16:05 GMT

In article <5357@balrog.ctron.com> wilson@ctron.com (David Wilson) writes:
:
:>	This is kind of cheesy, but Sum(1/x,{x,1,n}) does equal ln n -
:> Euler's Gamma Constant, which is approx. 0.577+
:
:	ln n - gamma is an asymptotic expression for the required sum
:	(never precisely equal, but arbitrarily close for sufficient n).
:	If there is a closed form not involving a sum, I would be very
:	surprised.
:
Surprise!

sum(1/x, {x,1,n}) = integral from 0 to 1 of  (1- (1-t)^n)/t  dt.

Is an expression as an integral from zero to 1 sufficiently 'closed form'?

--
Bob Silverman
These are my opinions and not MITRE's.
Mitre Corporation, Bedford, MA 01730
"You can lead a horse's ass to knowledge, but you can't make him think"
From: hunt@shy.umd.edu (Brian Hunt)
Newsgroups: sci.math
Subject: Re: Looking for a slick proof
Date: 7 Oct 92 02:07:35 GMT

bubai@matt.ksu.ksu.edu (P.Chatterjee) writes:
>How does one prove that 2^n divides n*(n+1)*(n+2)*......*(2n) without     
>having to resort to the 'odd' and 'even' induction? Any ideas?

In fact 2^n divides (n+1)(n+2)...(2n), and it's the largest power of 2
to do so.  Let [x] be the greatest integer less than or equal to x.
Then the largest power of 2 which divides n! is

[n/2] + [n/4] + [n/8] + ...

(above is {# of multiples of 2 <= n} + {# of multiples of 4 <= n} + ...)
while the largest power of 2 which divides (2n)! is

[n] + [n/2] + [n/4] + ...

so the largest power of 2 which divides (2n)!/n! is [n] = n.

Brian Hunt
hunt@ipst.umd.edu
From: wilson@web.ctron.com (David Wilson)
Newsgroups: sci.math
Subject: Function Problem
Date: 5 Oct 92 16:08:09 GMT
Reply-To: wilson@web.ctron.com (David Wilson)
Organization: Cabletron Systems INc.



    For positive integer x, define f(x) recursively as follows:

	f(x) =  1			x = 1

                  x
		 sum  f(floor(x/n))	x > 1
		n = 2

    where floor(x) is the greatest integer <= x.  It is not difficult to
    show that f(x) takes on integer values, and is an increasing function
    of x.

    Show that

	         x
	f(x) =  sum  g(x)
	       n = 1

    where g(x) depends only on the parity and prime factor exponent
    multiset of x.


-- 
David W. Wilson (wilson@web.ctron.com)

Disclaimer: "Truth is just truth...You can't have opinions about truth."
- Peter Schikele, introduction to P.D.Q. Bach's oratorio "The Seasonings."
From: brnstnd@nyu.edu (D. J. Bernstein)
Newsgroups: sci.math
Subject: Re: Topos theory for mere mortals (?)
Date: 26 Sep 92 06:43:42 GMT
Organization: IR

In article <1992Sep25.130656.5083@dcs.qmw.ac.uk> arodgers@dcs.qmw.ac.uk (Angus H Rodgers) writes:
> One of the faults of the standard development of mathematics in ZF,
> to my mind, is its lack of a convincing definition of individual
> real numbers such as pi;

Hmmm? What do you mean by ``lack''? pi is the minimum positive real
number such that exp(i pi) = -1. Here exp(z) = \sum z^n/n!. The proofs
behind these statements are quite straightforward. How is pi any less
convincingly defined than, say, 7?

---Dan
Xref: sparky sci.math:12350 sci.math.num-analysis:2858
From: baliga@ecs.umass.edu
Newsgroups: sci.math,sci.math.num-analysis
Subject: Need algorithm for generalized e-val problem
Date: 28 Sep 92 14:08:24 GMT
Summary: eigenvalue solver for unsymmetric band matrices
Keywords: unsymmetric band matrices, eigenvalues

I need an efficient algorithm that solves a generalized eigenvalue 
problem A*x= eval*B*x where A,B are unsymmetric band matrices. A 
routine that would yield only the extreme eigenvalues and eigenvectors 
would be particularly useful. The algorithm must take advantage of 
the sparseness of the coefficient matrices.

Any advice or references to literature is welcome. Email responses will
be appreciated.

thanks
arvind baliga
email - baliga@risky.ecs.umass.edu
        baliga@ecs.umass.edu


Newsgroups: sci.math
From: rairan@ecf.toronto.edu (RAI Ranjan)
Subject: Matrix Problem !
Organization: University of Toronto, Engineering Computing Facility
                               A     kBB'
  Hi.  I have a matrix H(k) =              where ' means transpose
                              -kC'C  -A'
  and k is a constant.  
  A, B , and C are nxn matrices.  So H(k) is a 2nx2n matrix.  
Date: Wed, 30 Sep 1992 01:35:06 GMT

  I have to compute the eigenvalues of H(k) for various values of 
  k that differ by a factor of 2.  ie H(k) then H(2k) then H(4k) ...

  The question is:  Is there an elegant way of doing this.  A method
  that makes use of the symmytries of the original matrix, or uses
  previous results to make each H(k) computation more efficient would
  be appreciated.

-- 
Ranjan Rai                             <rairan@ecf.toronto.edu> 
Engineering Science 9T3                <rairan@eecg.toronto.edu>
University of Toronto                      
Newsgroups: sci.math
From: kai@IASTATE.EDU (Kai Sun)
Subject: OPtimization subroutines
Reply-To: kai@IASTATE.EDU (Kai Sun)
Organization: Iowa State University
Date: Mon, 28 Sep 1992 19:07:23 GMT

Hi fellow netters:

I am looking for some contrained optimization subroutines.  I would appreciate
it very much if somebody could guide me to the right ftp sites.

Thanks in advance.

kai

--
*******************************************************************
* In business, customers gain;      |   kai@iastate.edu           *
* in war, all sides lose.           |   N1.Kai@isumvs.iastate.edu *
*******************************************************************
From: lamouche@ERE.UMontreal.CA (Lamouche Guy)
Newsgroups: sci.math
Subject: Integral of Airy function squared
Date: 28 Sep 92 20:08:25 GMT
Organization: Universite de Montreal

Hi,
I have to evaluate

        / Infinity
        |
        |  (Ai(z))^2  dz
        |
        |
        /-Infinity

where Ai(z) is the standard Airy function (Abramowitz and Stegun 10.4.1).
Being lazy by nature, I tried to feed Mathematica with it. The integrand
is to oscillatory, so it was useless.
Could someone be kind enough to tell me where I could find this integral
evaluated. I need it to normalize a wavefunction.

Thanks in advance.                              Guy.
Newsgroups: sci.math,sci.physics
From: bschlesinger@nssdc.gsfc.nasa.gov (Barry Schlesinger)
Subject: Re: Another Cute Math Joke  (explanation of)
News-Software: VAX/VMS VNEWS 1.41    
Organization: NASA - Goddard Space Flight Center
Date: Tue, 6 Oct 1992 18:59:00 GMT

In article <1992Oct1.193334.531@ulrik.uio.no>, jarleb@athena.uio.no (Jarle Brinchmann) writes...
> 
>In article <marc.717947769@vieta.math.uni-sb.de>, marc@vieta.math.uni-sb.de (Marc Conrad) writes:
>--
>Well, sorry if this disturbs you, but there isn't really an explanation. 
>The original versions are :
> 
>Q: What do you get if you cross an elephant with a zebra.
>A: Elephant zebra sin theta.
> 
>Q: What do you get if you cross an elephant with a mountain climber.
>A: You can't do that.  A mountain climber is a scalar.
> 
>or 
>"What do you get when you cross an elephant with a banana?
> 
>Elephant banana sine theta in a direction mutually perpendicular to the two
>as determined by the right hand rule."
>---------
> 
>Quite surrealistic really.
> 
> 
>				Jarle.
> 
> 
>      ---------------------------------------
>       Internet: jarleb@medusa.uio.no         
>       or        Jarle.Brinchmann@astro.uio.no
>      ---------------------------------------
> 
> 
The version I first heard (Chicago, 1963) was

What do you get when you cross a rabbit with an elephant?
From: cxm7@po.CWRU.Edu (Colin Mclarty)
Newsgroups: sci.math
Subject: Re: Mattel says "Math is tough."
Date: 6 Oct 1992 14:32:27 GMT
Organization: Case Western Reserve University, Cleveland, OH (USA)
Reply-To: cxm7@po.CWRU.Edu (Colin Mclarty)
NNTP-Posting-Host: slc12.ins.cwru.edu


In a previous article, martin@lyra.cis.umassd.edu (Gary Martin) says:

>In article <1992Oct5.212115.3356@bnlux1.bnl.gov> kyee@bnlux1.bnl.gov (kenton yee) writes:
>
>     Why do you assume women will be turned off by math simply
>    because it is tough?   I know lots of people who like math
>     BECAUSE it is tough.  
>
>But how many of these people are women?  I keep hearing the theory that
>women aren't as likely to be attracted by the difficulty of a problem
>because (for whatever reason) they are usually less competitive than
>men.  Unfortunately, it seems that today's generation of students of
>both genders are not as turned on by the challenge of a difficult problem
>as they should be.
>--
>Gary A. Martin, Assistant Professor of Mathematics, UMass Dartmouth

	Yes, this is what it comes down to.  If we know that only
boys can aspire to something challenging, and girls need to be 
shielded (even from the obvious truth when something IS hard), then 
this Barbie is definitely a bad thing.

Colin
Newsgroups: sci.math,sci.physics
From: erick@fraser.sfu.ca (Erick Bryce Wong)
Subject: Re: Another Cute Math Joke  (explanation of)
Organization: Simon Fraser University, Burnaby, B.C., Canada
Date: Fri, 2 Oct 1992 18:54:45 GMT

jarleb@athena.uio.no (Jarle Brinchmann) writes:
>        TOP TEN EXCUSES FOR NOT DOING THE MATH HOMEWORK
>
>2.      Isaac Newton's birthday.

I thought Newton was born on December 25, 1642?  :-)

-- 
 -- Erick, the perfect square  :-)
From: sichase@csa3.lbl.gov (SCOTT I CHASE)
Newsgroups: sci.math
Subject: Re: Infinity
Date: 30 Sep 1992 15:38 PST
Organization: Lawrence Berkeley Laboratory - Berkeley, CA, USA
Distribution: na
NNTP-Posting-Host: 128.3.254.198
News-Software: VAX/VMS VNEWS 1.41    

In article <1367.2ac9ae4e@atlas.nafb.trw.com>, dsimon@atlas.nafb.trw.com writes...
>Does infinity actually exist, or is it simply a mathematical tool?  
>Does an infinity of something actually exist?  Is it *possible*
>for there to be an infinity of something?

There is an infinity of integers.  They don't take up very much room.

The serious answer to your question is that it depends on whether the 
Universe is open or closed.  If it is closed, then there is only a large,
but finite, amount of room to fill up with stuff.  If it is open,
then you could hide an infinite number of anything in a little corner 
somewhere.  We just don't know the answer to your question.

-Scott
--------------------
Scott I. Chase			"The question seems to be of such a character
SICHASE@CSA2.LBL.GOV		that if I should come to life after my death
				and some mathematician were to tell me that it
				had been definitely settled, I think I would
				immediately drop dead again."      - Vandiver
From: clong@remus.rutgers.edu (Chris Long)
Newsgroups: sci.math
Subject: Re: Barbie
Date: 30 Sep 92 21:27:45 GMT
Organization: Rutgers Univ., New Brunswick, N.J.

In article <1992Sep28.214018.5190@henson.cc.wwu.edu>, Jenny Bridge writes:

> Mattelle has come out with a new talking teen Barbie.
> One of the four things it says is, "Math class is hard."
> If you would like to comment to Mattelle, the phone number
> is 1-800-421-2887

Questions of political correctness aside, I'd suggest telling
them to change it to "Math class is trivial" or "Your notation
sucks!".  The possibilities boggle the mind.  How about a nerd
Barbie?  "Use the binomial theorem" "Calculus is fun" "I enjoy
problem sets" "Number theory is cool" "Take the derivative".
-- 
Chris Long, 265 Old York Rd., Bridgewater, NJ  08807-2618
From: mapsj@gdr.bath.ac.uk (Simon Juden)
Newsgroups: sci.math
Subject: Re: Hyperbolic space?
Date: 29 Sep 92 14:03:52 GMT
Organization: School of Mathematics, University of Bath, UK

In the referenced article, jane@mathematik.uni-Bremen.de (wayne tvedt) writes:
>Allan Adler (ara@zurich.ai.mit.edu) wrote:
>>Maybe it is time someone wrote for hyperbolic space the book analogous to
>>Flatland.
>
>A French guy, Jean-Pierre Petit, has written some nice cartoon books about
>curved spaces, relativity, and like topics.  I have some German editions
>from Physik-Verlag.
[stuff deleted]
  Unfortunately, 
>Petit's _The Black Hole_ will never be used in American primary schools, 
>because it starts off with Anselm and his friend Herr Albert toking on 
>a hookah. 

...you never know: if Dan Qauylee gets back in such practices could become a
compulsory part of the curriculum next to sppeling and sums. Still compared to
some of the Secretaries of State for Education and Science we've had over here
Quaylee is a dangerous intellectual...

Simon
Newsgroups: sci.math
From: matmcinn@nuscc.nus.sg (Mcinnes B T (Dr))
Subject: Re: Warm and Fuzzy?  Koalas vs. Math
Organization: National University of Singapore
Date: Thu, 1 Oct 1992 04:28:13 GMT

zlsiida@fs1.mcc.ac.uk (dave budd) writes:
: In article <1992Sep14.012850.17387@nuscc.nus.sg> matmcinn@nuscc.nus.sg (Mcinnes B T (Dr)) writes:
: 
: >By the way, John, what IS the best flavour of ice cream?
: 
: Ice cream has only one flavor: cream.
: All else is additives.
: 
Including the ice.


: 
:               Have another day    [Armageddon, the musical] 
:   Dave Budd, MCC, Oxford Rd, Manchester, England   (44|0)61-275-6033
From: holmes@opal.idbsu.edu (Randall Holmes)
Newsgroups: sci.math
Subject: Re: consequences of the Axiom of Choice
Date: 5 Oct 92 19:22:43 GMT
Organization: Boise State University

In article <1akbpqINN8hk@usenet.INS.CWRU.Edu> cxm7@po.CWRU.Edu (Colin Mclarty) writes:
>
>In a previous article, holmes@opal.idbsu.edu (Randall Holmes) says:
>
>
>>>
>>>I certainly don't think you should _not_ mention AC when it's used.  I
>>>just think, a la Gunning's comment, the decision on _whether_ to use AC
>>>or some other assumption is pretty much a stylistic matter.
>>>-- 
>>>-Matthew P Wiener (weemba@sagi.wistar.upenn.edu)
>>
>>It's not entirely a matter of style.  It is legitimate, for instance
>>(although not usually done) to assume that all sets of real numbers
>>are Lebesgue measurable.  But then one _cannot_ assume AC in
>>unrestricted form...
>>
>>
>>-- 
>>The opinions expressed		|     --Sincerely,
>>above are not the "official"	|     M. Randall Holmes
>>opinions of any person		|     Math. Dept., Boise State Univ.
>>or institution.			|     holmes@opal.idbsu.edu
>>
>
>	This is something I have asked around about but never got
>much of an answer.  Is there any use doing measure theory this way?
>Or is the theory so cut up by the loss of unrestricted choice that
>it is harder than the classical theory?
>
>Colin McLarty
>
>Nous savons lire les guillemets, et nous savons lire a travers eux.

I am opening Jech...  (p. 537)

Solovay showed that there is a model of ZF + DC (dependent choices) in
which all sets of reals are Lebesgue measurable.  This requires
existence of an inaccessible (and I believe that this consistency
strength is unavoidable).  DC is enough for classical measure theory.

-- 
The opinions expressed		|     --Sincerely,
above are not the "official"	|     M. Randall Holmes
opinions of any person		|     Math. Dept., Boise State Univ.
or institution.			|     holmes@opal.idbsu.edu