HDTenEightyP/NetNews huggingface dataset:
From: goddard@NeXTwork.Rose-Hulman.Edu (Bart E. Goddard)
Newsgroups: sci.math
Subject: Spelling nilpotency
Date: 12 Jan 1993 15:12:28 GMT
Organization: Computer Science Department at Rose-Hulman
Reply-To: goddard@NeXTwork.Rose-Hulman.Edu (Bart E. Goddard)
NNTP-Posting-Host: g214-1.nextwork.rose-hulman.edu


The score is:

nilpotency   57
nilpotentcy   0
other         5

I think this is a large enough sample.... thanks.

--
Bart Goddard   
Math. Dept. Rose-Hulman Inst. of Tech.
goddard@nextwork.rose-hulman.edu
Xref: sparky sci.math:17774 sci.math.symbolic:3392 sci.math.num-analysis:3740
From: kingshu@ccwf.cc.utexas.edu (King Cheung SHU)
Newsgroups: sci.math,sci.math.symbolic,sci.math.num-analysis
Subject: .articleask
Date: 7 Jan 93 01:46:00 GMT
Reply-To: kingshu@ccwf.cc.utexas.edu (King Cheung SHU)
Followup-To: sci.math
Organization: The University of Texas at Austin, Austin TX
Originator: kingshu@happy.cc.utexas.edu

From: kingshu@ccwf.cc.utexas.edu (King Cheung SHU)
Newsgroups: sci.math.symbolic,sci.math.num-analysis,sci.math
Subject: help on programming !
Reply-To: kingshu@ccwf.cc.utexas.edu (King Cheung SHU)
Distribution: world
Organization: The University of Texas at Austin, Austin TX

Hello,
I will have a programming project next semester. The program is solving
integral using different method. I looked for books about computation
of integral on computer but I found nothing.  I believe there are some
people can help me on the usernet.

My questions are:

1. How many methods can be employed to find the solution of a integral
function on computer ?

2. What are the methods about ?

3. Are there any books that summarized all the methods ( at least some of
them ) ?

I will prefer email. However any help is appreciated. 

Thanks in advance.

-- 
## King Cheung SHU                  |  \                                /  ##
## G232, Roberts, 303 East 21st St. |   `__________()_____()___________'   ##
## Austin, TX 78705                 |             (  _   _  )              ##
##----------------------------------|              \ 0   0 /               ##
## E-mail: kingshu@ccwf.cc.utesas.edu\_             \     /                ##
## University of Texas at Austin      \_             \   /                 ##
From: rogerh@code3 (Roger Harrison)
Subject: Approximating decimal fractions with proper fractions
Keywords: fraction, approximation, number theory
Organization: 3M Health Information Systems
Distribution: na
Date: Thu, 7 Jan 1993 23:38:39 GMT

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.

I have spent a fair amount of time perusing books on number theory, but 
these seem to deal with calculating decimal equivalents of fractions 
rather than finding best-fit fractions for decimal equivalents.  I 
would greatly appreciate any help either with an algorithm itself or 
pointers toward published sources on the subject.

--
Roger G. Harrison
3M Health Information Systems
rogerh@code3.com
From: goddard@NeXTwork.Rose-Hulman.Edu (Bart E. Goddard)
Newsgroups: sci.math
Subject: Re: Lifestyle Choices and Secular Reasoning
Date: 5 Jan 1993 15:55:07 GMT
Organization: Computer Science Department at Rose-Hulman
Reply-To: goddard@NeXTwork.Rose-Hulman.Edu (Bart E. Goddard)
NNTP-Posting-Host: g214-1.nextwork.rose-hulman.edu

In article <C0D8xo.7or@ux1.cso.uiuc.edu> kellmeye@ux1.cso.uiuc.edu (kellmeyer  
steven l) writes:
> And if rigidly logical systems such as math, cannot be proved valid,
> where does that leave everything else?  I assume that the natural world
> is at least as complex as arithematic.  
> Steve Kellmeyer 
> kellmeye@ux1.cso.uiuc.edu

If a system has the property that some statements are undecidable, it
hardly makes that system "invalid".

bart
Newsgroups: sci.math
From: brumleve@iboga (Dan Brumleve)
Subject: Re: Of Pascal's triangle and limits
Organization: University of Illinois at Urbana
Date: Tue, 12 Jan 1993 22:33:37 GMT

llk@kepler.unh.edu (Local Genius) writes:

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

>Is there a limit to this thing, where the rule is to start at the top of the
>triangle and form triangles by joining odd entries (I have skipped the bases
>of the triangles to simplify the picture)?

Pascal's Triangle contains an infinite number of odd integers (1, 1, 1..., and
1, 2, 3, ...), so there can't possibly be a finite number of triangles joined
by them

-Dan
From: lry1219@cfdd40.boeing.com (Larry Yeagley)
Newsgroups: sci.math
Subject: Re: John Kemeny,66,Computer Pioneer and Educator is dead
Summary: A precis of the NYT's obituary of John Kemeny
Date: 5 Jan 93 15:52:09 GMT
Organization: Boeing Computer Services, Seattle - CFD lab


What follows is a summary of the obituary of John Kemeny appearing in the
12/27/92 issue of the New York Times.

 . born in Hungary on May 31, 1926.

 . immigrated to US in 1940.

 . attended George Washington High school beginning in 1940. Graduated in 3
   years at top of class.

 . became American citizen in 1945.

 . served in Army as assistant in theoretical division @ Los Alamos (1945-46).

 . doctorate in math from Princeton at 23 years old.

 . research assistant to Albert Einstein - after graduation from Princeton.

 . full professor of math at Dartmouth at 27.

 . chairman of Dartmouth math department at 29.

 . president of Dartmouth at 43.

 . creator of widely used computer language - BASIC.

 . head of Federal commission investigating Three Mile Island accident (1979).

 . resigned as president of Dartmouth in 1981 and returned to math department
   where he remained active until 1990.


Larry Yeagley
lry1219@cfdd42.boeing.com

P.S. The advice, opinions and mistakes expressed here are my own and certainly
     not Boeing's.
                                 +--------------------------------------------+
                            ||   |                                            |
                            ||   |                I am NOT,                   |
                 _)---+___  ||   |                                            |
                /o--+||+-+||xx|  |                therefore                   |
               /||  |||| |||xx|  |                                            |
  L___________/ ||__|||+-+||xx|  |              I don't think !               |
  |  Yeagley    |" +|||   ||xx|  |                                            |
  |   ___       |   |||   ||xx|  +--------------------------------------------+
 _| )/   \    +-+---+++---+-||-----------H-------+            |--------------|
|_|_/ x x  \__|_|___||----|_||______x x_____x x__|            |_x x_____x x__|
 )   x o x      |___||____|        x o x   x o x               x o x   x o x
      x x                           x x     x x                 x x     x x
From: ara@zurich.ai.mit.edu (Allan Adler)
Newsgroups: sci.math
Subject: graded commutative rings
Date: 13 Jan 93 01:39:28 GMT
Distribution: sci
Organization: M.I.T. Artificial Intelligence Lab.


Can a graded commutative ring be regarded as a commutative ring object
in some category? Graded commutative means that if x has degree m
and y has degree n then yx=(-1)^{mn}xy.

Allan Adler
ara@altdorf.ai.mit.edu
Newsgroups: sci.math,alt.flame
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: Fri, 8 Jan 1993 04:22:11 GMT

In article <1993Jan8.023202.9012@nuscc.nus.sg> matmcinn@nuscc.nus.sg (brett mcinnes) writes:
>gjm11@cus.cam.ac.uk (G.J. McCaughan) writes:
...
>: 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.
>I disagree. :)  My point is that if the proof were easy, nobody would have
>heard of this result or care about it.: 

On what grounds do you say this? Just saying that you don't happen to find it
exciting isn't enough, of course.

>:  * 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.
>: I did not say that I had heard propaganda for algebraic geometry, only
>for FLT. Algebraic geometry does not need propaganda; it really is
>significant.

I beg your pardon; I should have said "about" rather than "for".

>:  * "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?
>: Usually. Look at this newsgroup. 

Oh, rubbish. You're arguing backwards. Yes, most problems about which ignorant
people produce crap are simple to state, like FLT; that's because the really
complicated things are beyond them. It doesn't follow that most simple-to-state
problems are bad ones.

>:  * Work on FLT was one of the big motivators for the theory of ideals. I don't
>:    call that trivial, boring, or even "recreational".
>: Neither did I. Only FLT itself.

You haven't answered either of my main points: namely, that FLT is interesting
on its own account, and that it is connected quite intimately with other areas
of mathematics, and has given rise to work which is clearly important.

Actually, you have sort of answered my first point, simply by disagreeing with
me. So -- do you agree that the aesthetic element is a very important one in
mathematics? If so, what sort of thing do you consider aesthetically pleasing
enough? Is incomprehensibility to all who don't have at least a good degree in
mathematics a necessary condition?

Perhaps I'll understand better if you tell me what you think of some other
famous conjectures. What do you think of:
 * the twin prime conjecture?
 * the Goldbach conjecture?
 * the four-colour problem?
 * the Poincare conjecture?
 * the Riemann hypothesis?

-- 
Gareth McCaughan     Dept. of Pure Mathematics & Mathematical Statistics,
gjm11@cus.cam.ac.uk  Cambridge University, England.    [Research student]
From: goddard@NeXTwork.Rose-Hulman.Edu (Bart E. Goddard)
Newsgroups: sci.math
Subject: Re: Frankly,my dear......was: Fermat's Last Theorem
Date: 9 Jan 1993 17:23:16 GMT
Organization: Computer Science Department at Rose-Hulman
Distribution: usa
Reply-To: goddard@NeXTwork.Rose-Hulman.Edu (Bart E. Goddard)
NNTP-Posting-Host: g214-1.nextwork.rose-hulman.edu

In some articles some folks write:

> >:  * the Riemann hypothesis? :  : -- 
> >Utterly boring in itself, like FLT; but unlike FLT, it is important
> >because you need it to prove things that are interesting. Just imagine the
> >sensation if it turns out to be wrong.                                    

I think a problem is interesting if it points to a fundamental gap (or chasm)  
in our understanding.  One of the problems with math is that addition and  
exponentiation don't work well with each other. (Except in the 'Freshman's
Dream'.)  FLT exemplifies the hostility of these two operations have for each  
other, and work on this problem is actually study of their relationship.  FLT  
is, in some sense, the acid test of any, uh, "theory of hostility resolution."

Similarly, Number Theory wouldn't be hard if an integer's prime factorization  
had something to with its decimal expansion (i.e. if we understood what they  
had to do with each other.)  In our attempts to uncover the key idea, the zeta
function keeps popping up in generating functions of arithmetic functions.   
Study of the zeta function IS study of the how two (seemingly) hostile ideas
(decimal expansion and prime factorization) are related.  

Sooooo....I disagree with the previous post.  The Riemann Hypothesis is not  
just a lemma we need in order to prove a bunch of other stuff, but is at the  
core of what all the other stuff has in common and why the other stuff is so  
hard to understand.
--
Bart Goddard   
Math. Dept. Rose-Hulman Inst. of Tech.
goddard@nextwork.rose-hulman.edu
From: rlward1@afterlife.ncsc.mil (Robert Ward)
Newsgroups: sci.math
Subject: Re: analytic geometry
Keywords: polynomial curve, locus of mobile point
Date: 7 Jan 93 13:13:24 GMT
Followup-To: sci.math
Organization: National Computer Security Center

One approach that works is to compute the resultant of the two polynomials 
as functions of one of the variables, yielding a polynomial in the other 
variable.  The roots of this polynomial give you one coordinate of the 
intersection points of the two polynomial curves.  

For example, if one curve is f(x,y) = a(x) y^2 + b(x) y + c(x) = 0, and the 
other curve is F(x,y) = A(x) y^2 + B(x) y + C(x) = 0, then the resultant is 

         | a(x) b(x) c(x)  0   |
         |                     |
         |  0   a(x) b(x) c(x) |
R(f,F) = |                     |
         | A(x) B(x) C(x)  0   |
         |                     |
         |  0   A(x) B(x) C(x) |

and the roots of R(f,F) = 0 as a polynomial in x will give you the x-coord-
inates of the points of intersection.  The y-coordinates may be found by 
substituting the x-coordinates back into f(x_i,y) = 0 and solving for y_i.  

This all reduces the problem to one of finding roots of polynomials in one 
variable.

Robert L. Ward
From: nps1@ukc.ac.uk (N.P.Smart)
Newsgroups: sci.math
Subject: Elliptic Logs
Keywords: Elliptic Curves, Linear Forms in Logs
Date: 11 Jan 93 16:00:07 GMT
Organization: Computing Lab, University of Kent at Canterbury, UK.

Does any body know of any published papers on linear forms in
elliptic logarithms, for elliptic curves which do not 
necassarily have complex multiplication.

I would like an explicit (and easily calculated) lower bound
on such a linear form (in terms of heights of generators of MW ?)

Thanks for any help.

Nigel
From: gjm11@cus.cam.ac.uk (G.J. McCaughan)
Newsgroups: sci.math
Subject: Re: Two (I think) interesting Problems
Date: 8 Jan 93 09:48:41 GMT
Organization: U of Cambridge, England

In article <Haavard.Johnsbraaten.4@tmlh.no> Haavard.Johnsbraaten@tmlh.no (Haavard Johnsbraaten) writes:
>
>To Gareth McCaughan.
>
>If I have misunderstood "your" folding procedure, I apologize.
>I regard point 3 of your construction as a "doubling".
>Then one of the angles of the regular pentagon is already 
>established in point 2 of the construction.
>But this angle is 109.5 degrees and not 108 (the exact value).
>I get this both by calculations and by measuring the angle.
>Am I right?

Aargh, yes you are. The angle is 2.atn(root(2)), which is indeed about 109.5
degrees. I hereby apologise, with much grovelling, to anyone who believed me
when I said this was an exact construction.

I'm sure I checked *something* to do with it was right. Perhaps I worked out
one of the other angles, and got it to be something with root(5) in, and
decided it must be right. I can't be bothered to work out now what the other
angles are...

Oh dear. Sorry.

-- 
Gareth McCaughan     Dept. of Pure Mathematics & Mathematical Statistics,
gjm11@cus.cam.ac.uk  Cambridge University, England.    [Research student]
Newsgroups: sci.math,sci.logic
From: yeomans@austin.onu.edu (Charles Yeomans)
Subject: Re: Frankly,my dear......was: Fermat's Last Theorem
Date: Tue, 12 Jan 1993 20:58:27 GMT
Distribution: usa
Organization: Ohio Northern University

In article <1993Jan11.180310.11037@galois.mit.edu>, jbaez@riesz.mit.edu (John C. Baez) writes:
> 
> In article <1ilihlINN6ke@shelley.u.washington.edu> petry@zermelo.math.washington.edu (David Petry) writes:
> Ilan Vardi writes:
> >While it is true that no one can explain why Fermat's Last theorem has to 
> >be true, there are very convincing heuristics arguments that it really 
> >ought to be true.  Briefly, for a given large exponent p, the set of
> >numbers which are perfect p'th powers is a very sparse set of numbers,
> >and the probability that some number from such a set is the sum of two
> >others from the set is very small.
> >
> >> This is a natural phenomenon that should be explained. 
> >
> >Actually, it's questionable whether it should be called a phenomenon
> >at all.  Usually we think of a "phenomenon" as something that occurs
> >which is improbable (don't we?).  Fermat's Last theorem is far from 
> >being improbable.
> 
> Of course the notion of "probability" here is even more murky than
> usual.  One is approximating a deterministic system by a stochastic one
> and hoping that one is not neglecting any important patterns.  
> 
> But I tend to agree with Petry.  My friend Bruce Smith has proposed that
> there should be large classes of conjectures which are "probably true"
> by simple heuristic arguments, but are not provable.  

Here is something which is not what you are asking for, but it has a similar
flavor.

Let K be a perfect field.  We say that K is pseudo-algebraically closed (PAC)
if every geometrically irreducible variety defined over K has a K-rational
point.

Let E be an algebraic closure of Q.  Let s1,..., sn be automorphisms of E and let
E(s1,...sn) be the subfield of E fixed by these automorphisms.  It is a theorem
of Moshe Jarden that, if one picks s1,..., sn at random, then the probability
that E(s1,...sn) is PAC is 1.

But, to the best of my knowledge, there is not a single concrete example
of such a field known to be PAC.  It is known that the fixed field of an
automorphism of order 2 (the real algebraic numbers, for instance) is not PAC.

Charles Yeomans
From: kraai4712@iscsvax.uni.edu
Newsgroups: sci.math
Subject: Re: Rounding Rules
Date: 4 Jan 93 14:22:26 -0600
Organization: University of Northern Iowa

In article <1992Dec23.140148.21009@hubcap.clemson.edu>, steve@hubcap.clemson.edu ("Steve" Stevenson) writes:
> In article <1992Dec20.003018.14325@sol.ctr.columbia.edu> shaw@toadflax.UCDavis.EDU (Rob Shaw) writes:
>>What is the rationale behind the following rounding rule?
>>
>>when dealing with 5's followed by all zero's, check the
>>next digit to the left. If it's even, round down; odd,
>>round up.
>>
>>For example both 1.13500 and 1.14500 are 1.14 to 3 places.
>>What is the advantage of having the interval closed at both
>>ends around even digits, and open at both ends around odds?
>>
> 
> The problem with many of the "rounding rules" is that they are biased.
> In the IEEE round of rules, an attempt is made to make rounding as unbiased
> as possible. Round to even is specified as the rule of choice, since it
> avoids many of the problems of "round to infinity" or "round towards zero".

My personal favorite rounding rule is to round anything that has {0,1,2,3,4} in
the "rounding place" "down" and anything that has {5,6,7,8,9} "up".  So as in
the previous example, 1.13500 would be rounded to 1.14 and 1.14500 would be
rounded to 1.15.

To this my teachers always gasped that this method was biased, and no amount of
pursuasion using the above-mentioned sets could pursuade them.

I have come to believe that the people who thought this was biased believed
that anything that had a zero digit in the place to be rounded couldn't be
rounded or didn't need to be rounded or some other mental block.

Isn't it be less computationally intensive to round this way instead of looking
at the _previous_ digit?

--jim
Newsgroups: sci.math
From: mcherm@msc.cornell.edu (Michael Chermside)
Subject: Re: Let's add some sci.math.* groups
Organization: Cornell-Materials-Science-Center
Date: Tue, 12 Jan 1993 17:01:43 GMT


I'd just like to add that, although I would really enjoy reading
sci.math, I don't normally, because there the volume is too great and
I don't have time.  So a split that decreased the traffic would gain
you at least this ONE reader.  (BTW: this is the first time I've
actually looked in sci.math in 3-5 weeks, and that's about average.
Unfortunately, that's not enough to allow an estimate of the number of
other non-readers like me who would read it if there were lower
traffic.)  Oh, and I have my own fields of preference, but I like the
eclecticness -- if split, I would read the other sci.math.* groups
(besides my favorites) on an infrequent basis just to keep in touch
with a wider world.
-- 
                                            --- Michael
Newsgroups: sci.math.num-analysis
From: gmmiller@mcs.drexel.edu (Michael R. Miller)
Newsgroups: sci.math.num-analysis
Subject: Applied math - what do YOU do?
Summary: survey of applied mathematicians
Keywords: tools, applied math, visualization, modeling
Date: 8 Jan 93 18:54:05 GMT
Distribution: sci.math.num-analysis
Organization: Drexel University

I would like to gather information regarding some of the more 
interesting work done by applied mathematicians in industry and 
in academia.

I am especially interested in users of tools such as Mathematica, 
Maple, Matlab, et. al. in visualization, modeling, and data analysis work.

I welcome all responses, but am curious about the following areas:
     medical research
     image processing (esp. fractals)
     space, aeronautics
     weather forecasting
     physics (esp. lasers)
     signal processing
     information theory

Please e-mail your responses (short or long!) directly to me 
(gmmiller@mcs.drexel.edu).  The survey is for my own use (academic and 
career guidance).  If the responses warrant it, I will summarize and 
post the results.

If you love your job, here's a chance to brag about it!    :)

Thanks very much -- and happy 1993!

Mike Miller
(gmmiller@mcs.drexel.edu)
Newsgroups: sci.math.num-analysis
From: maxim@uwovax.uwo.ca
Subject: F-distribution
Organization: University of Western Ont, London
Date: Fri, 8 Jan 1993 02:44:58 GMT

F-distribution

I am looking for either a reference or some fortran source code
that will allow me to calculate an f-value (percentile) given
that the area (probability) and degrees of freedom DF1 and DF2
are known.  There are numerous references that suggest how the
area might be calculated given that the percentile is known, but
I have yet to come across the opposite.

The algorithm must be accurate to at least the fifth decimal place.
Any suggestions would be greatly appreciated.


-- 


Paul Maxim                         | Internet:  Maxim@uwovax.uwo.ca
Department of Sociology            |  
University of Western Ontario      |
London, Ontario                    |    Phone:  519-679-2111 Ext. 5121
CANADA    N6A 5C2                  |      Fax:  519-661-3200