HDTenEightyP/NetNews huggingface dataset:
From: mroussel@alchemy.chem.utoronto.ca (Marc Roussel)
Subject: Re: jump in price of journals
Organization: Department of Chemistry, University of Toronto
Date: Thu, 19 Nov 1992 21:05:12 GMT

In article <1992Nov19.193647.24279@CSD-NewsHost.Stanford.EDU>
rivin@SAIL.Stanford.EDU (Igor Rivin) writes:
>Again, with the current state of
>funding, I find it hard to believe that many libraries will find the
>$200 to pay for North Holland/Elsevier books (easily triple Springer
>prices for comparable titles).

     We shouldn't unfairly single out Elsevier.  First of all, some
North Holland paperbacks are quite affordable.  Secondly, most of the
major publishers have a few overpriced titles.  I would love to own a
copy of d'Ari and Thomas' book "Biological Control Systems" (a CRC Press title)
but I can't afford it.  I'm sure that CRC Press priced it thinking that
few individuals would want to own it, but then that just becomes a
self-fulfilling prophecy.

				Marc R. Roussel
                                mroussel@alchemy.chem.utoronto.ca
Xref: sparky sci.math:15278 sci.physics:19283
From: bhoughto@sedona.intel.com (Blair P. Houghton)
Newsgroups: sci.math,sci.physics
Subject: Re: Three-sided coin
Date: 20 Nov 1992 06:20:49 GMT
Organization: Intel Corp., Chandler, Arizona
NNTP-Posting-Host: alfalfa.intel.com

In article <1992Nov17.130147.26746@oracorp.com> daryl@oracorp.com (Daryl McCullough) writes:
>bhoughto@sedona.intel.com (Blair P. Houghton) writes:
>>Summary: probability is distributed according to entropy, not energy
>
>If we are talking about a flipped coin, I don't think it is
>distributed according to either. The probability distribution on coins
>depends on the way the coin is flipped and the initial orientation.
>For example, if my coin is a cylinder (three sides), and flipping
>consists of rolling it, then it has essentially zero probability of
>landing on either of its two ends.

Don't do that.

You are further constraining the system, and thus
altering its entropy at the outset.

You are correct that, given the new initial conditions, the
probability is almost unity that the coin will remain
"on-edge."  This is because you have made the change of
state from on-edge to on-face an entropy *decreasing*
event.

You can't constrain the system with anything other than
"what is the probability that the coin will end up on its
edge?"  Even if you say the coin is flipped, you have
constrained the form of motion and therefore altered the
entropy.

In order for the entropic analysis to work, the method of
reorienting the coin, and indeed whether the coin is
reoriented or left alone, must remain unknown, and be
allowed to assume all possible values; otherwise, you end
up with a morass of conditions and trajectories and phase
spaces and the need to define *everything* [*] rather than
*nothing*.

				--Blair
				  "It's sort of how it
				   all works, really..."

[*] This is okay if you *can* define everything.  You
simply partition the entropy further according to the
number of similar states and the gross probability of the
dichotomies, but in this example you can't even define the
probabilities of the type of floor covering...
From: blom@husc15.harvard.edu
Newsgroups: sci.math
Subject: exp(pi*sqrt(x))
Date: 22 Nov 92 17:41:31 GMT
Article-I.D.: husc15.1992Nov22.124131.17689
Organization: Harvard University Science Center

Aitken once remarked that exp(pi*sqrt(163)) differs from an integer by
less than 10^-12.  Why and when does exp(pi*sqrt(x)) approximate an integer?

--Eric Blom
  Harvard U
From: dima@maths.uwa.oz.au (Dima Pasechnik)
Newsgroups: sci.math
Subject: Re: Counting Families of Subsets
Date: 16 Nov 1992 09:02:04 GMT
Organization: The University of Western Australia
NNTP-Posting-Host: madvax.maths.uwa.oz.au

kinnersley@kuhub.cc.ukans.edu (Bill Kinnersley) writes:

>Take a base set S with N elements.  There are 2^N subsets of S.
>I want to consider families of these subsets.  All together there
>are 2^{2^N} such families, but I want to impose a condition.

>Let F be a family such that all elements of F are distinct subsets,
>and no element of F is a subset of another.

>How many families like this are there, for given N?

>If you call the number K(N), then the first few values are:

>N        K

>0        1
>1        2
>2        5
>3       19
>4      167

>Can you tell me even the order of magnitude for K(N)?  It appears to be
>much less than 2^{2^N}.

Such families are called clutters, or antichains. The question on |K(N)|
seems to be open. Few more values of K are known:
N	K
4	7580
6	7828354

There is a result of computer search due to M.Deza, I.Faradjev and
K.Fukuda.

See, say, Europ. J. Comb. for the last 5-6 years. (say, 7(1986), 271-82)



Dmitri Pasechnik.

Newsgroups: sci.math
From: frank@Cookie.secapl.com (Frank Adams)
Subject: Re: Minimum standards for math "competency"
Date: Mon, 23 Nov 1992 20:04:03 GMT
Organization: Security APL, Inc.
Keywords: math competency education university college standards

In article <1339@kepler1.rentec.com> rjfrey@rentec.com (Robert J Frey) writes:
>       o       The Jobs Almanac's top 5 jobs are all mathematically based:
>		actuary, computer programmer, systems analyst, mathematician
>		and statistician.

It appears that a number of people are doubting this, based on the
assumption that these are the jobs which [will] have the most jobs opening
up.  On that basis, it is very dubious.  A more plausible assumption is that
these are the jobs with the greatest *shortfall* of qualified applicants
compared to positions to be filled.  (Although I would still wonder about
including "mathematician".  Maybe it's the *ratio* of jobs to applicants.)

Then again, the Almanac may be using some other criteria entirely.
From: sichase@csa3.lbl.gov (SCOTT I CHASE)
Newsgroups: sci.math
Subject: Re: Solutions to a cubic equation
Date: 17 Nov 1992 11:49 PST
Organization: Lawrence Berkeley Laboratory - Berkeley, CA, USA
Distribution: usa
NNTP-Posting-Host: 128.3.254.198
News-Software: VAX/VMS VNEWS 1.41    

In article <1992Nov16.221527.0313263@locus.com>, markd@locus.com (Mark Dubinsky) writes...
>OK, this bugged me back in high school, and then I was sick last week
>with nothing better to do, and I tried to figure it out, and it's 
>bugging me again.  What is the formula for the solutions of a cubic
>equation
> 
>x3 + ax2 + bx + c = 0    ?

It is actually quite simple once you know how:

Step 1:

	Y^3 + A*Y^2 + B*Y + C = 0		(*)

Eliminate the Y^2 term by suitable substitution.  Since

	(Y+K)^3 = Y^3 + 3*K*Y^2 + ...

the correct substitution is clearly X = Y - A/3.  I'll skip the trivial
algebra and simply conclude that the original equation (*) reduces to

	X^3 + D*X + E = 0			(**)

	where 	D = 1/3  * (3*A - B^2) 	and
		E = 1/27 * (2*A^3 - 9*A*B + 27*C).

Step 2:

	Solve (**).  This is the part I had to look up.  The idea is to 
use the trignometric identity:

	4*cos^3(x) - 3*cos(x) - cos(3*x) = 0.	(***)

This equation has the same form as (**).  Let X = M*COS(x).  Then (**) becomes

	M^3*cos^3(x) + D*M*cos(x) + E = 0.

Thus, the sum on the left hand side is identically zero (see (***)) if:

	M^3   - D*M	E
	--- = ------ = ----------, or if
	 4 	 3	-COS(3*x)


	M 	 = 2*SQRT(-D/3)

	COS(3*x) = 3*E/(D*M).

There you have it.  Any equation with a solution with theta = x will
have two others at theta = x + 2*PI/3 and x + 4*PI/3.  QED.

Of course, it is possible by appropriate choice of the original constants to
have ABS( COS(3*x) ) > 1.  This simply requires allowing imaginary x.  The COS
then becomes a COSH and you continue in the same way.

-Scott
--------------------
Scott I. Chase			"It is not a simple life to be a single cell,
SICHASE@CSA2.LBL.GOV		 although I have no right to say so, having
				 been a single cell so long ago myself that I 
				 have no memory at all of that stage of my 
				 life." - Lewis Thomas
Newsgroups: sci.math
Subject: MATHEMATICAL MORPHOLOGY (anyone involved in it?)
From: broggi@verdi.eng.unipr.it (Alberto Broggi)
Date: 16 Nov 92 18:14:43 +0100
Distribution: world



	Hi everybody.

	I'm just working on digital images with mathematical morphology.
	Is there anyone who would like to exchange some opinions, answer 
        a few qustions, or anything else... ?

	Please, if you are interested, e-mail directly to me, since I usually
        do no have enought time to read the NEWS.

		Thanks, Alberto Broggi


				(broggi@aida.eng.unipr.it)

-- 
  Alberto Broggi    
  Dipartimento di Ingegneria dell'Informazione   phone: +39 (521) 905707
  Universita` degli Studi di Parma                 fax: +39 (521) 905723
  43100 Parma - Italy                    E-Mail broggi@aida.eng.unipr.it
From: gjm11@cus.cam.ac.uk (G.J. McCaughan)
Newsgroups: sci.math
Subject: Re: Arch algorithm
Date: 16 Nov 92 04:53:32 GMT
Organization: U of Cambridge, England

In article <1992Nov15.023738.29429@osuunx.ucc.okstate.edu>, gcouger@olesun.okstate.edu (Gordon Couger) writes:

> I doing some design work of hyper parabolic (saddle shaped) structures 
> it occurred to me that cantary (absolutely unsure of the spelling) arch, .
> if a chain is hung by its ends it forms the arch I am interested in, would
> give much better use of the floor space near the walls. 
> 
> If anyone is aware of an algorithm  or formula for this arch I would very
> much like to have it.

You mean "catenary", and probably "hyperbolic" rather than "hyper parabolic",
but that's just boring quibbling. The equation for a catenary is y=a.cosh(x),
where 'a' can be any constant, and cosh(x) is the hyperbolic cosine function
defined by cosh(x) = (e^x+e^(-x))/2. It looks rather like a parabola for
small values of x. Errm, probably this is only really true if the ends of the
chain have x=-1 and x=+1, or something.

-- 
Gareth McCaughan     Dept. of Pure Mathematics & Mathematical Statistics,
gjm11@cus.cam.ac.uk  Cambridge University, England.    [Research student]
Newsgroups: sci.math
From: buxamusaa@woods.ulowell.edu
Subject: Square root of a number
Organization: University of Lowell
Date: Mon, 16 Nov 1992 00:40:49 GMT


Please could someone help me with an assignment that I have to do.
It is a very general question, though the answer could be quite lengthy.
"Discuss methods for finding the square root of a number."

What I am looking for are all possible methods/alogrithms for this.

Please respond to either directly to me (preferably) or via the net.

Thanks a million!

Anees Buxamusa
Email:  buxamusaa@woods.ulowell.edu
From: tenny@euclid.uucp (Nathan Tenny)
Newsgroups: sci.math
Subject: Topology and CS?
Date: 17 Nov 92 00:21:25 GMT
Organization: Department of Mathematics, University of Oregon


A question...

I'm given to understand that both point-set and low-dimensional topology are of
some interest in computer science.  (At a vague level, I can see where this
would be true; if you want to know about optimal ways to connect your
processors, why, that's graph theory.)  Now, I'll be getting a degree and
looking for a job in a couple of years (if all goes well), and it seems like
this would be a nice thing to know about, because of the job market if for no
other reason---a topologist who can work usefully with CS people might look
more interesting than a topologist who can't.

The problem: I have a nodding acquaintance with CS, but not enough to read
papers in it.  The literature I've found on topology and CS seems to be written
from the CS end.

Could anyone give me a couple of suggestions about where to start reading, or
possibly even a quick braindump on the subject?

For reference: I'm a third-year graduate student, working in topology;
3-manifolds and 2-complexes are my native tongues.  I've done a lot of
programming, but I know computers operationally rather than theoretically.

Thanks.

	NT
From: bs@gauss.mitre.org (Robert D. Silverman)
Newsgroups: sci.math
Subject: Re: Prime test algorithm
Date: 18 Nov 92 20:43:34 GMT
Organization: Research Computer Facility, MITRE Corporation, Bedford, MA

In article <1992Nov14.154528.17440@husc15.harvard.edu> blom@husc15.harvard.edu writes:
>Does anyone have C source code for an algorithm to determine whether an
>enormous number (over 1000 decimal digits) is prime or composite?  I have
>Derive and Mathematica for my 486, but they run slowly on some of my large
>prime-test problems (546!-1) and I would like to be able to use my VAXstation
>4000-90.  I think I may also be able to compile Fortran, and maybe Pascal.  I
>have the best luck with C programs because they are so portable.
>
>Thanks in advance.
>--Eric Blom
>  Harvard

You are not going to be able to prove 1000+ digit *general* numbers prime on a
single workstation in a reasonable time, regardless of whether you
use the Goldwass-Killian-Atkin-Morain elliptic curve method, or the
Cohen-Lenstra-Bosma cyclotomic ring method. 

Do you really need prime proofs? Are you willing to settle for probable
primes? If you are testing n!+1  or n!-1, once you know it is a prp,
proving it prime is trivial, because N-1 or N+1 factors readily. In the
first case you can find a primitive root. In the second, a Lucas-Lehmer
test will suffice.

Others have already looked at when n!-1,  n!+1,  n#+1, n#-1 are prime.
[n# = product of distinct primes up to n]  Have you checked the
literature?

See, for example, 

Buhler, Crandall, & Penk
Primes of the form n!+/- 1  and 2*3*5...p +/- 1

Mathematics of Computation vol. 38, 1982 pp 639-645

Be aware that the computations have been carried much further
than given in that article by H. Dubner (and others).

--
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: awpaeth@watpix.uwaterloo.ca (Alan Wm Paeth)
Subject: Re: dodecahedron in S3
Organization: University of Waterloo
Date: Wed, 18 Nov 1992 23:17:51 GMT

In <1992Nov17.204258.5994@samba.oit.unc.edu> Jim.Buddenhagen@launchpad.unc.edu:

>Given a (regular pentagonal faced) dodecahedron of edge  e  living in
>a 3-sphere of radius  r  , how does one compute the dihedral angle in
>terms of s = e/r ?

The face dihedral of any regular pentagonal dodecahedron has a tangent of -2.
Evaluating Pi + arctan(-2) gives -2.03444 or about 116.5 degrees. (Pi is added
assuming an arctan returning a principle angle in the range (-pi/2 .. Pi/2)).

I've published a table of symbolic dihedrals sin(theta) and tan(theta) for the
Platonic and quasi-regular Archemidean solids in _Graphics Gems II_ (Academic
Press 1992, Ed: J. Arvo). A very compact table taking advantage of the
versatile halfed-tangent (explored in a companion gem) gives:

   	Regular solid	Dihedral tan(theta/2)
	-------------	---------------------
	tetrahedron	sqrt(2)/2
	hexahedron	1
	octahedron	sqrt(2)                 ________
	dodecahedron	phi  (or -1/phi)	| Note: the golden ratio
	icosahedron	phi^2 = phi+1		| phi = 1/2 (sqrt(5) + 1)
                                                --------
Space packing (possible when all dihedrals about a common edge sum to 2 Pi)
is also touched upon, as are Kepler's ``snub'' solids.

    /Alan Paeth
    Computer Graphics Laboratory
    University of Waterloo
From: molrchon@mehta.anu.edu.au (Rory Molinari )
Newsgroups: sci.math
Subject: Help with Algebraic Number Theory
Date: 23 Nov 1992 03:35:28 GMT
Organization: Australian National University
Distribution: world
Reply-To: molrchon@mehta.anu.edu.au
NNTP-Posting-Host: 150.203.43.50
Keywords: hilbert algebraic number

Hi,
	I'm a maths undergraduate, nearing the end of my 4th (and last) year.
As a result, the due-date on my Honours thesis is looming, and I am still stuck
with a couple of problems that neither I nor my project supervisor have
been able to crack.  I am hoping someone on the net might be able to give
me a few hints.

My thesis topic is "Hilbert's 10th Problem and a Generalization to
Algebraic Integers".  In the course of the year, one of the papers I read
was:

    Denef & Lipshitz, "Diophantine Sets Over Some Rings of Algebraic Integers",
	J. London Math. Soc., v18, 1978, pp385-391.

and I am covering the contents of that paper in my thesis.  One of the theorems
proved in that paper is the following:

Notation:  For a number field L (ie. a field of algebraic numbers, of finite
  degree over the rationals) the ring of algebraic integers in L will be
  denoted O(L).  The multiplicative group of units in O(L) will be denoted U_L.
  The torsion free rank of a group G will be denoted rk G.

THEOREM:
  Let L be any number field and d \in O(L) such that sqrt(d) \not\in L.
  Write L' = L(sqrt(d)).  Define

       V_L = {x + y.sqrt(d) : x,y \in O(L) and x^2 - dy^2 = 1}

  Then V_L is a subgroup of U_{L'} and

       rk V_L = rk U_{L'} - rk U_L
ENDTHEOREM

The proof suggested by Denef & Lipshitz starts as follows:

  Let N:U_{L'} -> U_L be the restriction of the norm from L' to L.  In this case
  we have N(u + v.sqrt(d)) = u^2 - dv^2, so that V_L is a subgroup of
  kernel(N).  The claim is that V_L in fact has finite index in kernel(N).
  Denef & Lipshitz do not explicitly prove this, but say it follows easily from
  the following lemma:

    Suppose K is a number field, e \in U_K and 0 != t \in O(K).  Then there is
    m > 0 such that t | e^m - e^{-m}.

  My supervisor and I have been unable to see quite how this implies what we need.



The second problem I have is much more minor, but I can't for the life of me
see how it.  Suppose J is some number field, and x \in O(J).  Then the claim
is that:

      x != 0  <==>  (\exist v, y \in O(J))[xy = (2v-1)(3v-1)]

It apparently follows from the Chinese Remainder Theorem, but I can't see the
trick.  No doubt it is embarassingly easy.




   If anybody has any ideas I would be very grateful.  Full credit will be given
in my thesis (though I don't suppose this is  much of a reward :).
I don't think this has much global appeal, so replies by email are probably
best.


Cheers,
Rory Molinari
molrchon@mehta.anu.edu.au
Newsgroups: sci.math
From: steve@hubcap.clemson.edu ("Steve" Stevenson)
Subject: Re: 1+1/2+1/3+1/4+...+1/n
Organization: Clemson University
Date: Thu, 19 Nov 1992 13:34:51 GMT

Mutter Christoph Johannes <K3032E2@ALIJKU11.BITNET> writes:

>I've a problem. I have to calculate the sum 1+1/2+1/3+1/4+...+1/n.
>The result should be 100.


This problem is fraught with difficulties. This is the harmonic series so
it does not converge.  One can expect (and you won't be disappointed)
difficulties. A first crack is to sum the series from smallest number to
highest (1/n ->1). That should help.







-- 
===============================================================================
Steve (really "D. E.") Stevenson           steve@hubcap.clemson.edu
Department of Computer Science,            (803)656-5880.mabell
Clemson University, Clemson, SC 29634-1906
From: jmount+@CS.CMU.EDU (John Mount)
Newsgroups: sci.math
Subject: Re: compactness ?
Date: 21 Nov 92 18:08:14 GMT
Article-I.D.: cs.By2vpr.EpJ.2
Organization: Carnegie Mellon University

In article <1992Nov20.211648.3583@research.nj.nec.com>, franz@ccrl.nj.nec.com (test user for max) writes:
|> I am trying to teach myself analysis; i'm stuck on the notion of compactness.
|> One book's definition:
|>   A subset S of a metric space E is compact if whenever S is
|>   contained in the union of a collection of open subsets of E,
|>   then S is contained in the union of a finite number of these
|>   open subsets.

You should read the above definition as:

  A subset S of a metric space E is compact if for EVERY collection of
  open subsets of E such that the union of the members of E contains S
  there is a finite collection E' contained in E such that S is contained
  the union of the members of E'.
   
|> The book (M.Rosenlicht,Intro.to Analysis) then gives an example of
|> a non-compact set- the open interval (0,1), which is contained in the 
|> union of sets (1/n,1) but not contained in any finite number of these.
|> 
|> ? It seems to me that (0,1) is contained in the collection of
|> open sets { (0,0.6) (0.5,1) (0,1) } and this has finite subsets that 
|> contain (0,1), so (0,1) should be compact.  Does the definition mean that
|> S must be contained in any possible collection, as opposed
|> to just one possible collection being sufficient?  If so, then 
|> I would intuitively think that a (1/n,..) type construction
|> would prevent any open set from being compact.  
|> Is a 'collection of sets' a stricter notion than I'm assuming?
|> (Is 'contained in' the same as 'covered by'?)

The closed interval [0,1] in R with the usual topology is compact.  I
won't prove it here- but you will notice that this fact isn't
contradicted by the collection E = {(1/n,2),n=1,2....} example because
while no finite subcollection of E covers [0,1] you will notice that E
doesn't cover [0,1] either (0 isn't a member of any member of E- so
fails to be covered).

-- 
--- It is kind of strange being in CS theory, given computers really do exist.
John Mount: jmount+@cs.cmu.edu               (412)268-6247
School of Computer Science, Carnegie Mellon University, 
5000 Forbes Ave., Pittsburgh PA 15213-3891
From: hdev@dutiag.tudelft.nl (Hans de Vreught)
Newsgroups: sci.math
Subject: Re: who should teach mathematics?
Date: 15 Nov 92 23:33:19 GMT

hrubin@pop.stat.purdue.edu (Herman Rubin) writes:

>In article <hdev.721610039@dutiag> hdev@dutiag.tudelft.nl (Hans de Vreught) writes:

>>In principle a subject must be taught by a fully qualified person (i.e. a
>>person with a degree on the subject he / she teaches). If he has an Arts /
>>Science / Engineering background isn't that important, as long he presents his
>>stuff the right way.

>With that requirement, Knuth could not teach computer science, and I could
>not teach statistics.  However, there are many with degrees in statistics
>who do not understand it, and plenty with degrees in computer science likewise.

Quite right. That was why I said "In principle". I regard Knuth as a good
computer scientist at what he is doing (it's as a matter of fact quite
annoying if you use the citation index to look for people that refer to him).
Because of his numerous scientific papers Knuth is a fully qualified person to
teach computer science. BTW, in the time that Knuth graduated (I believe mid
60s), did a CS program exist at his university?

Although I know several people that succesfully has shifted their carreer from
the subject to a new subject, I'm cautious to give everybody the benefit of
the doubt. If you write scientific papers on a certain topic, that you are
qualified for that topic (if the scientific community finds your papers good
enough, who am I to question your qualifications on that topic). But being
qualified for one specific topic of an entire subject, doesn't immediately
qualify you for the rest. Somebody who graduated in the entire subject has
always a head start of someone of a different subject.

But there is one other point which I like to stress that it makes a difference
in what subject you graduted. If you have a sociology background, you probably
will never teach algebra. On the other hand if you have studied computer
science, algebra will probably be not a difficult topic to master. So if you
have graduated in a "neigbouring" subject, it will take probably not much
effort to get qualified in the other subject as well.
--
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.
Newsgroups: sci.math
From: ara@zurich.ai.mit.edu (Allan Adler)
Subject: Re: Bozos Synonymous
Organization: M.I.T. Artificial Intelligence Lab.
	<burt.722061313@aupair.cs.athabascau.ca>
Date: Mon, 23 Nov 1992 18:54:37 GMT


I read an excellent article recently in the American Scholar criticizing
the approaches that some feminist theorists take to discussing science and its
relation to gender questions. I think it was in the 1989 issues, I forget
now. The author was a woman mathematician, I think named Levin.

Allan Adler
ara@altdorf.ai.mit.edu
Newsgroups: sci.math