HDTenEightyP/NetNews huggingface dataset:
From: cawagne@lims01.lerc.nasa.gov (PAUL WAGNER)
Newsgroups: sci.math
Subject: Books on Number Theory
Date: 7 Oct 92 21:01:00 GMT
Organization: NASA Lewis Research Center
News-Software: VAX/VMS VNEWS 1.41

Have you read any good books on Number Theory recently ?  Specifically, I
am interested in the general topics of Number Theoretic Transforms, Residue
Number Systems and Galois Fields, just to mention a few.  If you have read
such a work and could recommend it in good conscience, I would appreciate
hearing from you.  advTHANKSance from a curious electrical engineer.

Paul K. Wagner
cawagne@lims.lerc.nasa.gov 
Newsgroups: sci.math
From: leife@ii.uib.no (Leif Erik R. Hauge)
Subject: Software for Group Theory
Organization: Institutt for Informatikk, UiB, Bergen, Norge
Date: Wed, 7 Oct 92 12:11:26 GMT

What are the best/simplest to use/most powerful software packages
for `doing' group theory??

I have access to Maple, but am interested in other programs if they 
exceed Maple in convenience and/or power. 

I am primarily interested in ftp-available programs, but commercial
programs can also be of interest.

Thanks for your help.

E.


Newsgroups: sci.math
From: pratt@Sunburn.Stanford.EDU (Vaughan R. Pratt)
Subject: Re: help with recursive functions
Organization: Computer Science Department,  Stanford University.
Date: Thu, 8 Oct 1992 05:21:10 GMT

In article <1b074cINN4fu@usenet.INS.CWRU.Edu> cxm7@po.CWRU.Edu (Colin Mclarty) writes:
>
>	I'd like some help with partial recursive functions which
>do not extend to (total) recursive ones.  I can prove there is no
>effective routine for extending all partials to total recursive
>functions, but I do not see how to prove there are particular
>partial recursive functions that do not extend to recursive.  Are
>there typical methods from proving this in particular cases?
>
>Colin McLarty


Rogers, Chapter 2, Theorem II: There exists p.r. \psi with no recursive
extension.

Proof.  Take \psi(x) = \phi_x(x)+1, and let \phi_y be any recursive
extension of \psi.  Since \phi_y is recursive, \psi(y) halts, whence
\phi_y(y) = \phi_y(y)+1.

-- 
=================================================== In short, I am floundering
Vaughan Pratt   pratt@cs.Stanford.EDU  415-494-2545 around and don't take what
=================================================== I say seriously.
From: crb7q@kelvin.seas.Virginia.EDU (Cameron Randale Bass)
Subject: Re: Mattel on women
Keywords: Targetting females once again.
Organization: University of Virginia
Date: Tue, 13 Oct 1992 16:54:33 GMT

In article <1755@spam.ua.oz> mstewart@spam.ua.oz.au (Mark A Stewart) writes:
>In response to
>
>> > One thing this thread makes clear is that there are lots of folk out
>> > there who won't object to Mattel's message - even those who ought to
>> > know better (IMO)...  I had not originally planned to act on this,
>> > but now I reckon that we (ie those who share the opinion that
>> > women-in-math bashing is not to be encouraged) perhaps ought to make
>> > sure our view is recognised by Mattel - and others - and so will send
>> > a polite but firm protest as the original poster suggests.  If you
>> > agree, maybe the time spent to that end is more fruitful than another
>> > posting to this thread...
>>
>>     That's great, but there still remains a very big question
>>     if it *is* 'women-in-math bashing'.  At most, it seems to me
>>     'Barbie-in-math bashing', though I am completely sure with
>>     her positive attitude that even Barbie can make it through
>>     the required core courses.
>>
>>     I suggest you'd do more good by taking a job at a nearby middle
>>     school and teaching the children some math.  I want to warn you,
>>     it is a tough job to do successfully...
>>
>>                              dale bass
>
>   You seem to have missed the point, Barbie is a significant "Role
>Model" for many young girls, viewed as being an ideal for women to
>live up to. To present her as a bubble head incapable of understanding
>mathematics implicitly reflects upon the capacities of women.

    Inanimate objects are greatly overrated 'role models'.  Usually,
    what mommy or daddy say and do are much more important.

                           dale bass

-- 
C. R. Bass                                           crb7q@virginia.edu
Department of Mechanical and Aerospace Engineering
University of Virginia
Charlottesville, Virginia                            (804) 924-7926
Newsgroups: sci.math
From: ramsay@unixg.ubc.ca (Keith Ramsay)
Subject: Re: Infinity
Organization: University of British Columbia, Vancouver, B.C., Canada
Date: Fri, 9 Oct 1992 02:33:01 GMT

In article <1992Oct8.194415.19999@news2.cis.umn.edu> 
nichols@math.umn.edu (Preston Nichols) writes:
|An *actual* infinity, i.e. one which is "really there" all at once, is not  
|possible, and is IMO not strictly even conceivable.

There is considerable disagreement about this, of course. IMO it is
entirely possible, and conceivably true, that there are infinitely
many stars in the universe "really there" all at once. We don't know
that there are, of course; it seems likely that there are only
finitely many.

|infinities that I know about are either *potential* infinities (e.g.
|the infinity of the positive integers, especially as presented in the
|principle of induction), or are "place markers" (as when we integrate
|from zero to infinity, as shorthand for a limiting process), or
|both(?).

Current mathematical practice permits one to talk about infinite sets
implicitly as though they were completed "collections" of essentially
the same type as finite sets. An infinite set just happens to be in
1-1 correspondence with a proper subset of itself; no special fuss is
made in mainstream mathematics over the use of such sets.

Keith Ramsay
ramsay@unixg.ubc.ca
From: gjm11@cus.cam.ac.uk (G.J. McCaughan)
Newsgroups: sci.math
Subject: Re: Area of five sided polygon needed
Date: 13 Oct 92 02:20:26 GMT
Organization: U of Cambridge, England

In article <1992Oct12.200125.826@altair.selu.edu> fcs$1224@altair.selu.edu writes:

> Given a five sided polygon, is there a formula, in terms
> of its sides, for the area?

Not without further conditions, because the area isn't uniquely determined
by the side lengths. 

                      ----------------
                     / .             |
                    /   .            | 
                   /     .           | 
                  /       .          |
                  \       .          |
                   \     .           |
                    \   .            |
                     \ .             |
                      ----------------


-- 
Gareth McCaughan     Dept. of Pure Mathematics & Mathematical Statistics,
gjm11@cus.cam.ac.uk  Cambridge University, England.    [Research student]
Newsgroups: sci.math
From: rmdubash@cs.uh.edu (Rumi Dubash)
Subject: Need info. on graphs/networks, cut sets, ....
Organization: Computer Science dept.,  Univ. of Houston (Main Campus)
Date: Sat, 10 Oct 1992 15:03:12 GMT

Hi,
  I am looking for any results in graph/network theory relating minimal
cut sets and the degree of connectivity, any properties observed by the
elements in the cut set. I am not particularly familiar with this field
but need info on any such result. Yes, I could go through the books, 
papers but that would be quite time consuming, especially because I am not
even sure where to begin looking. 
  Any pointers will be greatly appreciated. 
  Thanx

Rumi Dubash
rmdubash@cs.uh.edu

P.S. I would appreciate e-mail replies since I do not really keep up with 
this newsgroup. Thanx.

Newsgroups: sci.math
From: scip1061@nuscc.nus.sg (Marc Paul Jozef)
Subject: Manifolds of constant curvature
Organization: National University of Singapore
Date: Wed, 14 Oct 1992 12:13:23 GMT

  Could anybody give me a reference for the proof
  of the following theorem (presuming that it is
  correct, of course :-)   ).

  In a manifold M of constant sectional curvature
  (p \in M), each subspace E of the tangentspace T_pM
  determines a unique totally geodesic immersed
  submanifold which has E as tangentspace at p.


  Much obliged,

  marc.

 
Newsgroups: sci.math
From: moshier@world.std.com (Stephen L Moshier)
Subject: Re: Help with Solving Frensel Integrals
Organization: The World Public Access UNIX, Brookline, MA
Date: Sat, 17 Oct 1992 00:04:48 GMT

  >Fresnel integrals
 There is a C program to compute Fresnel integrals in the book
_Methods and Programs for Mathematical Functions_ .
Newsgroups: sci.math
Subject: Re: Topological Question
From: omasaveu@cardinal.sc107.wesleyan.edu (Oscar E. Masaveu)
Date: Mon, 12 Oct 1992 18:05:50 GMT
Organization: Wesleyan University, Middletown, CT USA

In article <1992Oct12.163249.1@vmsa.technion.ac.il> chr09tk@vmsa.technion.ac.il writes:

>Hello!

>Can anyone help me with the folowing topological question:
>Is there a connected and locally connected topological space which is not path
>connected? 
>Is there such a space which is also compact?

>Thanks in advance,
>Guy 

Here is an example of a compact, connected, locally connected space which is 
not path-connected.

Let X = { (x,y) : 0 \leq x \leq 1 & 0 \leq y \leq 1 }, give X the order 
topology induced by the lexicographical ordering ( (x,y) < (u,v) iff
x < u, or x = u and y < v ). (This is the so-called lexicographical 
ordering of the unit square.)

One shows that X is a complete ordered space and hence is compact. 
Also there are no consecutive points in the order and every (bounded) 
subset of X has a l.u.b. (with regard to the order), hence X is connected,
(the former facts being equivalent to connectivity for ordered spaces).
Since all connected ordered spaces are locally connected, X has the 
properties you want because it cannot be path-connected since any path 
joining (0,0) and (1,1) must be connected and hence, as any connected 
subset of an ordered space, must be connected. But then, this interval must
be all of X. It is not hard to show that X contains uncountably many pairwise
disjoint open sets, (i.e., it is not c.c.c.), so X cannot be the continuous 
image of [0,1] since there is no uncountable collection of pairwise disjoint 
open subsets of [0,1] (because every set in such a collection must contain a 
rational). Now consider what would happen to the pre-images of the 
uncountable collection of pairwise disjoint open subsets of X.  

Oscar Masaveu
Wesleyan University
OMasaveu@Eagle.Wesleyan.Edu
Newsgroups: sci.math
From: frank@Cookie.secapl.com (Frank Adams)
Subject: Reciprocals of Fibonaccis
Date: Thu, 08 Oct 1992 19:59:19 GMT
Organization: Security APL, Inc.

This is a problem I've worked on off and on for several years, without
getting much of anywhere:

What is the sum of the reciprocals of the positive Fibonacci numbers?  (That
is, Sum(n>0, 1/F_n).)

Numerically, it is about 3.359885666243177.  The continued fraction starts:

3,2,1,3,1,1,13,2,3,3,2,1,1,6,3,2,3,1

I'm not sure about the last two numbers here; the final 3 could be 4.  The
small numbers suggest the result may be algebraic.

Closely related is the sum of the reciprocals of the Lucas numbers
L_n = F_n-1 + F_n+1.  Sum(n>=0, 1/L_n) is about 2.462858173209645; the
continued fraction starts approximately,

2,2,6,4,3,31,2,1,1,1,1,2,3,2,1,3,10

Does anybody know anything about these numbers?
Xref: sparky sci.math:13246 sci.math.num-analysis:3016
From: pjbk@cs.hw.ac.uk (Peter JB King)
Newsgroups: sci.math,sci.math.num-analysis
Subject: Optimal omega for SOR
Keywords: successive over relaxation
Date: 15 Oct 92 13:50:39 GMT
Organization: Dept of Computing & Electrical Engineering, Heriot-Watt University, Scotland

Does anyone have any good references for dynamic selection of the
optimal omega for successive over relaxation?  I am aware of the
theoretical optimum, but since this depends on the eigenvalues, the
computation of this is likely to be at least as expensive as solving the
equations with a non optimal omega.  

The problem which I'm solving involves arrays that are too large to
keep in core, so an iterative method is essential.  Also the problem
gets bigger every week, with new equations being added, and the old
solutions can be used as first estimates for the new solutions.  It may
well be that the optimum omega changes too, so an algorithm that would
adapt from any starting value for omega in range 0-2 would be best.

I have tried using Aitken acceleration on the elements of the solution
vector directly, but it seems to reduce the rate of convergence!

Literature references, code segments or good ideas welcomed.

-- 
Peter King, Computer Science Department	JANET:	pjbk@uk.ac.hw.cs
  Heriot-Watt University		ARPA:	pjbk@cs.hw.ac.uk
  Riccarton, Edinburgh EH14 4AS 	UUCP:	..!uknet!cs.hw.ac.uk!pjbk
Phone: (+44) 31 451 3433                Fax: (+44) 31 451 3431
Newsgroups: sci.math
From: hrubin@mentor.cc.purdue.edu (Herman Rubin)
Subject: Re: Mattel says "Math is tough."
Organization: Purdue University Statistics Department
Date: Wed, 7 Oct 1992 13:13:22 GMT

In article <1992Oct7.005439.193@murdoch.acc.Virginia.EDU> crb7q@kelvin.seas.Virginia.EDU (Cameron Randale Bass) writes:
>In article <1at131INNc50@roundup.crhc.uiuc.edu> hougen@vision.csl.uiuc.edu (Darrell Roy Hougen) writes:

>>In summary, I don't believe that math is hard.  Thinking is hard, but
>>who would want to discourage that?

>     Try teaching multiplication to a seven-year-old.  That way, 
>     you get to see how 'hard' it is from both sides.

The way it is usually taught, it is almost meaningless, which helps to
make it hard.  Young children can be easily taught the structure of the
number system; with this, the notion of multiplication becomes easy.

This does not make it much easier to learn how to carry out multiplication,
but it may motivate it.

Properly explained, and this is almost never done, the concepts are not
all that difficult, although practice and application are necessary to
really understand them.  The notion of variable, possibly the most important
in mathematics, is essentially the notion of pronoun.  The notions of 
theorem and proof are extremely important, and not well taught; knowing
these does not make one adept at producing them.  It does not make one
adept at using them, either, but that is of comparable difficulty to
writing sentences and paragraphs, and is even similar to that.
-- 
Herman Rubin, Dept. of Statistics, Purdue Univ., West Lafayette IN47907-1399
Phone: (317)494-6054
hrubin@snap.stat.purdue.edu (Internet, bitnet)  
{purdue,pur-ee}!snap.stat!hrubin(UUCP)
Newsgroups: sci.math
From: rjk@world.std.com (robert j kolker)
Subject: Order -> Algebraic Structure
Summary: Is there a way to get from order to algebraic structure?
Keywords: Rationals,Dense Ordering,Algebraic Structure
Organization: The World Public Access UNIX, Brookline, MA
Date: Sat, 10 Oct 1992 01:48:43 GMT

Let H be a denumerable completely ordered set, where the ordering is
dense, and there are no maximum or minumum elements. It is well known that
any two sets having these properties are order isomorphic. 

The set of rationals Q is a fortiori this set (up to an isomorphism).
Clearly the seemingly innocent densely ordered set inherits its algebraic
properties via this isomorphism or does it? 

Is there someway of showing independent of this coincidental isomorphism ,
that denumerable,densely ordered -> the algebraic structure of Q, i.e. Q
is a denumerable field or characteristic 0.

Your input would be appreciated.

Conan the Libertarian rjk@world.std.com
"If you can't love the Constitution, at least hate the Government"


Newsgroups: sci.math
From: kavuri@lips.ecn.purdue.edu (Surya N Kavuri )
Subject: Re: Probably you know the probability ;-)
Organization: Purdue University Engineering Computer Network
Date: Thu, 15 Oct 1992 04:53:08 GMT

In article <1992Oct15.025957.11871@galois.mit.edu>, jbaez@riesz.mit.edu (John C. Baez) writes:
> In article <1992Oct14.193802.25129@noose.ecn.purdue.edu> kavuri@lips1.ecn.purdue.edu (Surya N Kavuri ) writes:
> >  I am given a "rod" of fixed length l. I took a hammer and
> >  broke it into three parts.
> >
> >   (a) what is the probability that they form a triangle ?
> >   (b) what is the probability that they form an isoceles triangle ?
> 
> There is not enough information to answer unless you tell us the
> probability distribution of the lengths of the 3 parts.  In real
> life this would depend in a complicated way on how you broke the
> rod.
> 

  All the points on the rod are equally likely to be breakage points.
  

  There is a part (c) to this problem that I later added.

     (c) what is the probability that they form an acute-angled triangle ?


Surya Kavuri


Newsgroups: sci.math
From: martin@lyra.cis.umassd.edu (Gary Martin)
Subject: Re: Mattel says "Math is tough."
Organization: University of Massachusetts Dartmouth
	<1992Oct5.144142.2182@alchemy.chem.utoronto.ca>
	<9247@amsaa-cleo.brl.mil>
Date: Thu, 15 Oct 1992 05:34:29 GMT

In article <9247@amsaa-cleo.brl.mil> matt@amsaa-cleo.brl.mil (Matt Rosenblatt) writes:

   In article <1992Oct5.144142.2182@alchemy.chem.utoronto.ca> 
   mroussel@alchemy.chem.utoronto.ca (Marc Roussel) writes:
   >it is our
   >responsibility as educated persons to see to it that Mattel withdraws
   >this ill-considered product from the market.  [Marc R. Roussel]

   According to this, fair competition in the "marketplace of ideas"
   between the doll's message that "math is hard" and the educator's
   message that "math is not hard" is not good enough.  The doll's
   message must be suppressed, so that *no one* -- not even a mother
   who believes that math *really is* hard -- will be able to buy
   this particular talking doll for her daughter.

					   -- Matt Rosenblatt
					   (matt@amsaa-cleo.brl.mil)

You forgot one important point: as I understand it, you cannot tell
what a particular Barbie will say until you've already bought it.
The consumer has no choice.

--
Gary A. Martin, Assistant Professor of Mathematics, UMass Dartmouth
Martin@cis.umassd.edu
From: cxm7@po.CWRU.Edu (Colin Mclarty)
Newsgroups: sci.math
Subject: Re: Philosophical Foundations of Probability?
Date: 15 Oct 1992 17:09:03 GMT
Organization: Case Western Reserve University, Cleveland, OH (USA)
Reply-To: cxm7@po.CWRU.Edu (Colin Mclarty)
NNTP-Posting-Host: slc5.ins.cwru.edu


In a previous article, jwales@silver.ucs.indiana.edu (jimmy donal wales) says:

>MICHAEL K ROGERS writes:
>>jimmy donal wales (jwales@silver.ucs.indiana.edu) wrote:
>> for pointers to books or review articles on modern
>>: views of the philosophical foundations of probability theory.
>>: 
>>: --Jimbo
>>
>>The closest thing I know of are two books by Ian Hacking,
>>"The Emergence of Probability" and "The Taming of Chance."
>
>O.k., I've got those, that is a good beginning.
>
	I really liked Gigerenzer et al. (six coauthors) _The Empire
of Chance_.  This is a collaborative philosophical history whose 
coauthors spent years working together--yet it is quite readable.  

	It includes an entertaining review of cognitivist efforts 
to tell whether people are good Bayesian thinkers--with the 
cognitivists all evaluating their data by Neyman-Pearson methods, 
unaware that this is itelf an alternative to Bayesianism.  That
chapter actually concludes that no statistical method should
stand as the one model of rational evaluation of evidence.

Colin McLarty
Newsgroups: sci.math
From: bs@gauss.mitre.org (Robert D. Silverman)
Subject: Re: Area of five sided polygon needed
Organization: Research Computer Facility, MITRE Corporation, Bedford, MA
Date: Wed, 14 Oct 1992 12:40:37 GMT

In article <1992Oct13.030526.22048@galois.mit.edu> jbaez@riesz.mit.edu (John C. Baez) writes:
:In article <1992Oct12.200125.826@altair.selu.edu> fcs$1224@altair.selu.edu writes:
:>Given a five sided polygon, is there a formula, in terms
:>of its sides, for the area?
:
:Clearly not, because the lengths of the sides don't determine the
:area.  Pentagons are "floppy."  So are quadrilaterals, for that matter.
:
 
This is clearly correct. However, there is such a formula if the pentagon
is incribable in a circle.
 
Hint: It is an extension of Heron's formula.


--
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"
Newsgroups: sci.math
From: fengxi@prancer.eche.ualberta.ca (Fengxi Zhou)
Subject: Asymp. stability of differential inequality
Organization: University Of Alberta, Edmonton Canada
X-Newsreader: Tin 1.1 PL3
Date: Wed, 7 Oct 1992 20:38:33 GMT

Hi, netters.  I have a "simple" problem of asymptotic stability of a
differential inequality.  Suppose a differential equation
              y_dotdot+a*y_dot+b*y=0    (y_dot=dy/dt, etc)
is asym. stable, i.e., y(t)->0 as t->infinity.  Is the solution of
              y(y_dotdot+a*y_dot+b*y)<0
which is equivalent to
                y_dotdot+a*y_dot+b*y<0   if y>0
                y_dotdot+a*y_dot+b*y>0   if y<0
also asym. stable?  My hunch is that it is and the solution of the
aforementioned diff. equation actually "envelops" the solution of the
diff. inequality.  But how to prove it or is it all wrong?  Any help is greatly
appreaciated.  Please e-mail me.  Thanx.

Fengxi Zhou
From: asimov@wk223.nas.nasa.gov (Daniel A. Asimov)
Newsgroups: sci.math
Subject: Maps of Hopf Invariant 1
Date: 14 Oct 92 02:19:19 GMT
Organization: NAS, NASA Ames Research Center, Moffett Field, CA

There are continuous maps f: S^(2n-1) -> S^n, for n = 1,2,4,8
such that the inverse image of any two points are a pair of
linking (n-1)-spheres in S^(2n-1) with linking number = 1.

[These can be inferred from the construction of actual fibre 
bundles S^(2n-1) -> S^n having as fibre S^(n-1). (e.g. see 
Steenrod, Fibre Bundles)]

I vaguely recall believing that it had been proved that this
*cannot* continue for any n = 2^k, k > 3 (or any other n, for that
matter).  (Was it J. Frank Adams in the mid-fifties?)

I'm somewhat more certain that the actual fibre bundles
S^(2n-1) -> S^n with fibre = S^(n-1) can't continue the
sequence after n = 8.

In case these memories are correct, does there exist *any* nice
mappings S^31 -> S^16 (S^63 -> S^32, etc.) with pleasant properties,
which seem to be the "best you can do" in those dimensions?

Can someone clarify for me the state of knowledge about this 
situation?  Many thanks!

Dan Asimov
Mail Stop T045-1
NASA Ames Research Center
Moffett Field, CA 94035-1000

asimov@nas.nasa.gov
(415) 604-4799
From: dik@cwi.nl (Dik T. Winter)
Newsgroups: sci.math
Subject: Re: Calculating pi: help!
Date: 14 Oct 92 02:28:33 GMT
Organization: CWI, Amsterdam

In article <Bw304E.LKu@mentor.cc.purdue.edu> falatic@mentor.cc.purdue.edu (MacGyver) writes:
 > 
 > 	Just a quick query: I need a program, in either Unix C or Borland/
 > Turbo C, that will calculate Pi as far as I want... I can get it to 17 
 > digits, but I want to get it to an UNLIMITED number of digits (I know, it'd
 > be slow, but I just want to do it.
If you calculate it to 5 billion digits you will be famous.  (The current
record is 2.16 billion digits).  As far as I know there is currently no
reasonably fast algorithm that will give you any number of digits.  Current
algorithms are designed to calculate a predefined number of digits, you
can get less, but not more.  Just today I attended a lecture by Kanada
(Prof. Pi) who calculated pi to 1 billion digits, it took (if I remember
right) 7 hours on a Hitac 820; which is a Japanese supercomputer from
Hitachi; 2 nsec. cycle time.
But below you will find a short C program that will give you
pi to 800 digits:

int a=10000,b,c=2800,d,e,f[2801],g;main(){for(;b-c;)f[b++]=a/5;for(;d=0,g=c*2;c
-=14,printf("%.4d",e+d/a),e=d%a)for(b=c;d+=f[b]*a,f[b]=d%--g,d/=g--,--b;d*=b);}

It takes less than a second on a high-end work-station.
-- 
dik t. winter, cwi, kruislaan 413, 1098 sj  amsterdam, nederland
home: bovenover 215, 1025 jn  amsterdam, nederland; e-mail: dik@cwi.nl
Newsgroups: sci.math