HDTenEightyP/NetNews huggingface dataset:
From: tdj@infonode.ingr.com (Ted Johnson)
Subject: Peculiar limit?
Organization: Intergraph Corporation, Huntsville, AL.
Date: Thu, 17 Dec 1992 20:25:31 GMT

Is the following true?

                  g        g                        g        g      
             (1/b)  - (1/a)                    (1/b)  - (1/a)       
   lim      ------------------   =   lim      ------------------    
   g->+inf.       g        g         g->-inf.       g        g      
             (1/c)  - (1/a)                    (1/c)  - (1/a)       


                          ln(1/b) - ln(1/a)
                        = -----------------
                          ln(1/c) - ln(1/a)

If necessary:
       0 < a <= b <= c <= 1;
       a < c.
Everything's real.

I'm not so concerned about the first line as with the second.   Some
numerical tests led to this conjecture.

The context is my work on response characteristics for a scanner (of
photographs).  If you're familiar with D-log(E) plots, read "gamma" for
g and you'll know what I'm referring to in the top line.  These two
equations represent the (limits of the) normalized exposure as computed
from the transmissivity T of the image, all derived from the  linear
portion of a D-log(E) plot.  The bottom expression represents the
normalized density of an image, density = 1/T,  computed from the
transmissivity of the image.
From: kumard@acsu.buffalo.edu (Deepak Kumar)
Newsgroups: sci.math
Subject: Re: History of algebra (was Re: Babri Masjid demolished)
Date: 17 Dec 92 21:26:04 GMT
Organization: State University of New York at Buffalo/Comp Sci


For whatever it is worth, and if my memory serves me right...
I remember reading in the opening paragraphs of Don Knuth's `The
Art of Computer Programming - Volume 1' that the word `algebra'
as well as `algorithm' are associated with the work(book?) and
the name of someone:

The name of the person: Abu Ja`far Mohammed Ibn Musa...Al Khowarizmi

My spellings as well as full details may be incorrect and I don't have
a Knuth#1 in front of me...but the last `Al Khowarizmi' is the name
of the town where `Abu' was from and seems to be the originator of
the word `Algorithm'

His work, supposedley documented in a book titled:

Kitab Al Jabr Wa Al Muqabla

or something like that...supposedly the puzzles and problems discussed
later evolved into Algebra (notice the `Al Jabr' in the title).

Check Knuth for exact details (the book as well as the person).

Deepak.

-- 
I'm not a teacher but I play one at school.
kumard@cs.buffalo.EDU                    Deepak Kumar, Department of Comp. Sc.
kumard%cs.buffalo.edu@ubvm.bitnet        226 Bell Hall, SUNY@Buffalo, NY 14260.
From: rags@triples.math.mcgill.ca (Robert A. G. Seely)
Newsgroups: sci.math
Subject: Re: Philosophy of Pi
Date: 18 Dec 92 20:53:35 GMT
Organization: /etc/organization

In article <1992Dec18.204929.24397@sifon.cc.mcgill.ca> rags@triples.math.mcgill.ca (Robert A. G. Seely) writes:
>In article <DREIER.92Dec18094157@durban.berkeley.edu> dreier@durban.berkeley.edu (Roland Dreier) writes:
>ove.
>>
>> ..., it is a very open question as to whether every integer
>>appears in the decimal expansion of Pi.  This is called the Goldbach
>>conjecture, and I'm not aware of any real progress toward a solution.
>>--
>>Roland Dreier                                        dreier@math.berkeley.edu
>
>Goldbach Conjecture: Every even no is the sum of (odd) primes.
                                                 ^^
                                                 two odd primes, of course
>
>How does this relate to the above?  (What am I missing here?)
Newsgroups: sci.math
From: afm@trillian (Andreas Mueller)
Subject: Re: math problem
Organization: University of Heidelberg, Germany
Date: Mon, 14 Dec 92 10:06:25 GMT

li@sce.carleton.ca (Yao Li) writes:
:                             Math Problem
:                             ------------
: 
: Getting bored? Here is a math problem.
: 
: There is a polynomial:
:        -a*y**n + y**(n-1) + y**(n-2) + ... + y + 1 = 0
: where real number a>0 and the notation "y**n" represents the nth power of y.
: 
: It's conjectured that this polynomial has a unique positive real solution y.
: 
: Can you prove it or find a counter example?
Replace y by y^(-1) (this doesn't change positivity and 0
isn't a solution to the problem anyway). Then the equation
becomes (after multiplying by y^n)

	y^n + y^(n-1) + ... + y = a

The left hand side tends to 0 as y goes to 0, and it's derivative
is
	n y^(n-1) + (n-1) y^(n-1) + ... + 1 >= 1

is strictly positive for y>0, so the left hand side is strictly
increasing. So there is a unique positive y which satisfies the
equation. Then y^(-1) is the solution You are looking for.

Hope this helps

			Andreas Mueller

-------------------------------------------------------
Dr. Andreas Mueller         afm@mathi.uni-heidelberg.de
Mathematisches Institut
Im Neuenheimer Feld 288
W - 6900 Heidelberg 1
-------------------------------------------------------
Newsgroups: sci.math,comp.edu,misc.education
From: thomasd@tps.COM (Thomas W. Day)
Subject: Re: Student attitudes
Organization: Telectronics Pacing Systems
Date: Wed, 16 Dec 1992 15:57:19 GMT

In article <1gajmaINNif2@function.mps.ohio-state.edu> edgar@function.mps.ohio-state.edu (Gerald Edgar) writes:
>>       Split the calculus sequence into three parts:
>>       a) a sequence oriented to physical scientists and engineers that
>>targets the math useful to them-- this is essentially freshman calculus
>>as we know it
>>       b) a sequence oriented to economists, business students, statisticians,
>>etc., which give them calculus without relying on "physics" problems
>>that are what calc textbooks normally have
>>        c) a sequence oriented to mathematicians, that covers the theoretical
>>aspects of calculus and offers a very early introduction to proofs and 
>>developing maturity of mathematical thought.

>A drawback to this multi-stream approach is what to do with students
>that change their minds about what to major in; or students who are
>unsure what to major in when they arrive as Freshpersons.

And a big drawback it is.  I took 12 units of math/calculus for engineers at 
the University of Nebraska in an EET program.  When I tried to transfer to 
the same kind of program at Cal State Long Beach, they offered me 3 credits 
of trig for my previous education experience and I still needed 9 units of 
calculus from Long Beach.  
Newsgroups: sci.math
From: jbaez@riesz.mit.edu (John C. Baez)
Subject: Re: Function Terminology
Organization: MIT Department of Mathematics, Cambridge, MA
Date: Sun, 13 Dec 92 19:44:53 GMT

In article <Bz48w1.G5C@mentor.cc.purdue.edu> hrubin@pop.stat.purdue.edu (Herman Rubin) writes:
>In article <1992Dec11.203802.1770@CSD-NewsHost.Stanford.EDU> pratt@Sunburn.Stanford.EDU (Vaughan R. Pratt) writes:
>>In article <1gaq3tINNg9q@uwm.edu> radcliff@csd4.csd.uwm.edu (David G Radcliffe) writes:
>>>Suppose I have a function f: A --> B, and C is a subset of B which
>>>contains the image set of f.  I define a function g: A --> C by
>>>setting g(a) = f(a) for all a in A.  Usually, f and g can be considered 
>>>as the same function, but sometimes the distinction is important.
>
>>>Is there a standard term or notation for this?

>The function is exactly the same.  A function, in whatever foundational
>system is used, is something which takes arguments in a domain and
>operates on them.  The image set depends only on f and A.  Which
>superset of the range is used does not affect the function.

I'm sure this has been pointed out (I'm behind on my sci.math!), but
while Rubin correctly expresses the viewpoint of set theory, category
theory is more comfortable treating these two functions as different;
that is, we treat them as morphisms between different objects in the
category of sets.

One could, if one wished, define a Function to be a triple consisting of
sets A and B and a function from A to B.

Newsgroups: sci.math,sci.physics,sci.bio,sci.chem,misc.education
From: brian@quake.sylmar.ca.us (Brian K. Yoder)
Subject: Re: TIME HAS INERTIA - BASS JEALOUS AND INSECURE-ABIAN VALIDATED
Organization: Quake Public Access
Date: Tue, 15 Dec 1992 00:30:13 GMT

In article <1ggssaINN9s2@gap.caltech.edu> rickert@cco.caltech.edu (Keith Warren Rickert) writes:
>In <Bz81F4.Lqt@quake.sylmar.ca.us> brian@quake.sylmar.ca.us (Brian K. Yoder) writes:

>>A similar problem exists for physicists who consider light to be a wave (or
>>a wave and something else too).  Waving is something an entity does, not a
>>thing in itself.  There can no more be a wave traveling through space than
>>there can be a room with some "jumping" going on outside of any entities which
>>are doing the jumping.

>>I think these kinds of problems both arise from physicists getting too tied up
>>with their equations to remember that they apply to things in the real world.

>The ability of light to behave as a wave, and as a particle, have
>both been able to lead to concrete predictions about real world experiments,
>and provided correct results.

I don't think you understand my point here.  I have plenty of problems with the
wave-particle duality theories (and the ludicrous conclusions people try
to draw from them), but that is not what I am complaining about here.
A wave is a property of an entity, like redness, mass, or length.  Properties
cannot exist independent of entites which posess them.  To say that there are
properties without entities which posess them undercuts some of the
necessary premises of all knowledge (ie. that it is ABOUT something).

>The ability to predict experimental behaviour correctly is the real
>test of a theory, not whether or not it can be visualized.

I am not claiming that such theories are false because they cannot be 
visualized.  I am claiming they are false because they are irrational.

--Brian
From: allenk@ugcs.caltech.edu (Allen Knutson)
Newsgroups: sci.math
Subject: The plans for a new GRE Math Subject test
Date: 12 Dec 1992 21:18:29 GMT
Organization: California Institute of Technology, Pasadena
NNTP-Posting-Host: torment.ugcs.caltech.edu
Keywords: GRE

The ETS is working on a new GRE Subject Math test. There are a bunch of
reasons why the old one is unsatisfactory - too many people get the top
score, doing mathematics isn't like multiple choice - and the ideas for
a new format include a bunch of essay-type questions with no definite
right answers. (This won't be in place for at least five years, if ever.)

I was invited to take the essay part of such a test today. The actual
questions I got were for the most part really boring. Example: define 
what it means for a function (R -> R) to be continuous at a point, and
show that x^2 + x is continuous. (Too bad they said at a point, or one
could define continous as "on any compact subset of R, a uniform limit
of polynomials" : -8 )

Much less concrete was a question about a mathematical kingdom (I quote)
in which mathematicians found triangles sufficiently much more pleasing
that they essentially define Riemann integration in terms of them. Does
this change the notion of measurable subset of the plane? 

None of the five questions took more than 5-10 minutes to have a complete
answer in one's head. But we were allotted 2.5 hours, so mostly it was
a handwriting exercise, where one would be afraid that one hadn't been
sufficiently anal about trivialities.

Just posting for general interest				Allen K.
From: tectcb@sdc.boeing.com (Tim Bodin)
Newsgroups: sci.math
Subject: Tensor question
Keywords: tensors, derivities
Date: 18 Dec 92 18:19:37 GMT
Distribution: usa
Organization: Boeing Computer Services (ESP), Seattle, WA


I have a question for you math types. I am in the process 
of reviewing tensors and in working the problems in the
book a friend of mine gave me, I encountered one problem 
that probably has a simple answer but it is giving me fits.
  
Given the tensor equation-
  
              r s 
      f = a  x x          (summation implied)
           rs
  
show that-
  
  
        r             s
   df/dx  = (a  +a  )x    (note this is a PARTIAL derivitive) 
              rs  sr
  
The part that is causing me problems is the index switch
(rs to sr) in the constant part.
  
I can solve it for a specific case (I assumed a 3 dimensional
space) but solving the general symbolic (or N dimensional)
case is causing a bad case of brain lockup.
  
Any one willing to tackle it for me?
  
Please reply by email as I will be on vacation til 1/4/93 and
net replies will probably time out before I get back.
  
Thanks in advance for your time and trouble.
From: bennett@math.ksu.edu (Andy Bennett)
Newsgroups: sci.math
Subject: Re: Would Pi repeat, were it expressed in a base other than 10?
Date: 11 Dec 92 23:03:33 GMT
Organization: Dept. of Mathematics, Kansas State University
NNTP-Posting-Host: hilbert.math.ksu.edu

werdna@cco.caltech.edu (Andrew Tong) writes:
:Intuitively (not saying much, that is), I'd say yes, but that it would re-
:quire a transcendental base....

Of course, pi to the base pi is 1.000000000....

:-)




-- 
Andrew G. Bennett         bennett@math.ksu.edu         If you count too
Dept. of Mathematics      Voice: (913) 532-6750        much you turn
Kansas State University   Fax:   (913) 532-7004        purple.  -  SARAH
Manhattan, KS 66502       STRICTLY MY OWN OPINIONS
From: bs@gauss.mitre.org (Robert D. Silverman)
Newsgroups: sci.math
Subject: Re: Philosophy of Pi
Date: 14 Dec 92 13:50:12 GMT
Organization: Research Computer Facility, MITRE Corporation, Bedford, MA

In article <1gi1bmINNsou@function.mps.ohio-state.edu> edgar@function.mps.ohio-state.edu (Gerald Edgar) writes:
:>YESSSSS!!!!!  exp(i*Pi) + 1 = 0
:>is perhaps the most beautiful identity in mathematics,
:
:I disagree.  The beautiful identity is exp(ix) = cos x + i sin x.
:Unlike the previous one, it is even useful...
 
I disagree that it is not useful.

Lindemann used it to prove the transcendence of pi, after Hermite
proved that e was transcendental. I would call that a useful result.
--
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: ak005@cleveland.Freenet.Edu (Yona Webb)
Newsgroups: sci.math
Subject: Re: TO ALL !!! -- End of Discussion, I hope
Date: 21 Dec 1992 00:11:34 GMT
Organization: Case Western Reserve University, Cleveland, Ohio (USA)
NNTP-Posting-Host: slc10.ins.cwru.edu


My posting (Dec. 18) has offended many netters.  Several people
expressed quite vocally their anger and displeasure, both publicly and in
E-Mail. There was no need for flames however, just to let me know that
I have made a mistake.
 
Why did I send the card in public posting to Sci.Math?  -- About a month
ago I posted a msg in Sci.Math seaking assistance on couple of topics.
A dozen of people replied!  They offered help, useful info and assured
me that they would be willing to help in the future, if the need arises.
A private  -Thank You Msg-  was sent to all of them.
 
There has been a lot of excitement in the air in the last week or so.
I made  *ONE*  card to reflect this excitement and to greet all my friends,
Christian and Jewish.  At one moment I thought of Sci.Math. as a single
entity because of the help I received from so many people there and ... hop,
the card was uploaded in a public msg TO ALL!!! Good intentions, wrong move!
 
Yona
-- 
Newsgroups: sci.math
From: poynor@david.wheaton.edu (George V. Poynor)
Subject: Re: Would Pi repeat, were it expressed in a base other than 10?
Organization: Wheaton College, IL
Date: Wed, 16 Dec 1992 22:47:51 GMT

In article <1gij9gINNkt8@gap.caltech.edu> allenk@ugcs.caltech.edu (Allen Knutson) writes:
>
>>>>Of course, pi to the base pi is 1.000000000....
>>>Not to nitpick, but it's 10.00000.... ;-)
>
>>Combining this with a previously-beaten-to-death result, we see that
>>pi to the base pi is 9.999... .
>
>The second statement is the only true one, if we take 9=1+1+1+1+1+1+1+1+1,
>as I tend to. (Cross-thread with "Numbers and sets", I guess! : -8 )
>In this case the number mentioned by D. Dodson is much larger than pi.
>An instructive related fact: in base 5, 5 = 10 = 4.44444.....
>								Allen K.

	Perhaps a trivial question, but what are the allowable
	values for digits in an expansion with pi as the base?
	--
	George Poynor
	poynor@david.wheaton.edu
-- 
George V. Poynor
--
poynor@david.wheaton.edu
Newsgroups: sci.math
From: edp@math.zk3.dec.com (Eric Postpischil)
Subject: Re: Pi in beatiful form --lost
Reply-To: edp@math.zk3.dec.com (Eric Postpischil)
Organization: Digital Equipment Corporation
Date: Wed, 16 Dec 1992 14:45:08 GMT

In article <1gmvieINN7al@aludra.usc.edu>, rmurphy@aludra.usc.edu (Bob
Murphy) writes:

>(pi - 3)/4 = 1/(2*3*4) + 1/(4*5*6) + 1/(6*7*8) + ...

The first term is 1/24, which is already greater than (pi-3)/4.  Should
that have been an alternating series?

A form I like is:

	pi = 2 sum from i=0 to infinity product j=1 to i j/(2j+1) .

This series has the advantage that each term is positive and less than
half the preceding term (making a maximum error easy to calculate), each
term can be computed from the preceding one by one multiplication by j
and one division by 2j+1.  Thus, tens of thousands of terms can be
computed with routines that multiply or divide an extended-precision
number by an ordinary-precision number, which are not difficult to
write.


                                -- edp (Eric Postpischil)
                                "Always mount a scratch monkey."
                                edp@rusure.enet.dec.com
Xref: sparky sci.math:17209 sci.physics:21463
From: paul@mtnmath.UUCP (Paul Budnik)
Newsgroups: sci.math,sci.physics
Subject: Re: Bayes' theorem and QM
Date: 19 Dec 92 16:30:30 GMT
Followup-To: sci.math
Organization: Mountain Math Software, P. O. Box 2124, Saratoga. CA 95070

In article <1992Dec18.134107.24536@oracorp.com>, daryl@oracorp.com (Daryl McCullough) writes:
> [...] Bell's Theorem
> shows that there is no deterministic completion of QM that uses
> classical probability theory. [...]

It only shows that there is no *local* deterministic completion of QM.
A nonlocal deterministic theory would be quite strange and I do not think
it is a likely possibility, but it is certainly a logical possibility.

Paul Budnik
Newsgroups: sci.math
From: rgep@emu.pmms.cam.ac.uk (Richard Pinch)
Subject: Re: Unsolved Integrals
Organization: Department of Pure Mathematics, University of Cambridge
Date: Sat, 12 Dec 1992 10:43:54 GMT

In article <1992Dec10.204653.29154@pellns.alleg.edu> frisinv@alleg.edu writes:
>My hobby is working on solving unsolved integrals (no successes). Lately  
>I've been wondering if I am wasting my time (aside from practice at the  
>method of integration by tricks:)) Is there any way of testing if a  
>particular integral has a closed form solution? Has anyone heard of an  
>unsolved integral being solved recently?

A good starting point might be James Davenport's book
"Om the integration of algebraic functions", Springer
Lecture Notes in Computer Science 102, 1981.

Richard Pinch
Newsgroups: sci.math,sci.philosophy.tech
From: solan@smauguio.no (Svein Olav G. Nyberg)
Subject: Re: Numbers and sets
Reply-To: solan@smauguio.no (Svein Olav G. Nyberg)
Organization: University of Oslo, Norway
Date: Mon, 14 Dec 1992 14:01:20 GMT

Just a hint to the participants of this Quote War:

Theres nothing that puts off a reader as much as 90% quotes.

Solan
From: erickson@oak.mcs.gvsu.edu (Carl Erickson)
Newsgroups: sci.math
Subject: Fourth Annual Michigan Conference on College Mathematics
Keywords: calculus technology conference
Date: 16 Dec 92 18:01:43 GMT
Reply-To: erickson@oak.mcs.gvsu.edu (Carl Erickson)
Organization: Grand Valley State University


The Fourth Annual Michigan Conference on College Mathematics
will be held at the UoM Dearborn March 19-20, 1993 and
has as its focus "Calculus in Transition".

This conference is sponsored by: 
	Michigan Calculus Network,
	MAA - Michigan section,
	MichMATYC
	University of Michigan - Dearborn

The conference consists of panel seesion, tutorials, and workshops on
Mathematica, Maple, and graphing calculators.

For more informaton, contact: Margret Hoft, hoft@um.cc.umich.edu

-- 
  Carl Erickson,  Asst Professor |  Computer Science Dept     
  Grand Valley State University  |  Allendale MI 49401
   erickson@oak.mcs.gvsu.edu     |  (616) 895-2309
Newsgroups: sci.math
Subject: Re: Need help with a constraint problem
From: a_rubin@dsg4.dse.beckman.com (Arthur Rubin)
Date: 17 Dec 92 22:19:52 GMT
Organization: Beckman Instruments, Inc.
Keywords: constraint, minimize area

In <a_rubin.724374170@dn66> a_rubin@dsg4.dse.beckman.com (Arthur Rubin) writes:

>In <1992Dec10.181800.27941@purelogic.cs.uwlax.edu> pisul_cj@glutamic.uwlax.edu (Charles Pisula S92) writes:

>>here's the problem that I'm sure will prove to be trivial although 
>>It's given me a hard time:

>>Minimize the area inside an elipse of form  x^2        y^2
>>                                            ---   +    ---   =  1
>>                                            a^2        b^2
>>such that it contains the circle x^2 + y^2 = 2y.


>>HINTS:  Area of Ellipse = (Pi)ab

>>PLEASE SEND ANY SOLUTIONS TO :
>>****************************
>>pisul_cj@cowley.uwlax.edu
>>****************************

>Looks like homework to me.

But, nonetheless, the answer can be obtained by finding the point on the
circle maximizing |x||y|, as the ellipse of minimum area containing a point
(x,y) has a = sqrt(2) x, b = sqrt(2) y, so area = 2 Pi xy.  In fact, this
does produce the correct answer.
--
Arthur L. Rubin: a_rubin@dsg4.dse.beckman.com (work) Beckman Instruments/Brea
216-5888@mcimail.com 70707.453@compuserve.com arthur@pnet01.cts.com (personal)
My opinions are my own, and do not represent those of my employer.
My interaction with our news system is unstable; please mail anything important.
Xref: sparky sci.math:17026 rec.puzzles:7968
From: columbus@strident.think.com (Michael Weiss)
Newsgroups: sci.math,rec.puzzles
Subject: Aces and Queens (P.S. to: The paradox of the second ace)
Date: 16 Dec 92 10:03:20
Organization: Thinking Machines Corporation, Cambridge MA, USA
	<1992Dec15.012404.24027@galois.mit.edu>
	<1992Dec15.055832.26324@galois.mit.edu>
	<COLUMBUS.92Dec15111255@strident.think.com>
NNTP-Posting-Host: strident.think.com
In-reply-to: columbus@strident.think.com's message of 15 Dec 92 11:12:55

Vaughn Pratt and I both posted simple combinatoric arguments that
probability (a), below, is less than probability (b):

(a) P(2nd ace | any ace), that is, the probability that a randomly chosen
    bridge hand has a second ace, given that it has at least one ace

(b) P(2nd ace | ace of spades), that is, the probability that a randomly chosen
    bridge hand has a second ace, given that it has the ace of spades

Vaughn was less lazy than I and worked out the actual probabilities.  The
difference is not small; (a) is approximately 37%, while (b) is
approximately 56%.  (I wonder, is this something any decent bridge player
would know by instinct?)  This paradox is discussed in one of Martin
Gardner's collections.

Here is a variant I haven't seen elsewhere.  Consider:

(c) P(ace | queen), that is, the probability that a randomly chosen
    bridge hand has an ace, given that it has a queen

(d) P(ace | queen of spades), that is, the probability that a randomly chosen
    bridge hand has an ace, given that it has the queen of spades

Despite what you might guess, (c) and (d) are *not the same*.  They are
close, it is true: one is about 67%, the other about 68%.  (The exact
figures are 55883/83300 and 10673305/15672338, if I haven't made any
mistakes in arithmetic.)  You may want to amuse yourselves deciding which
of these answers is (c) and which is (d).
Xref: sparky sci.math:16948 rec.puzzles:7926 alt.usage.english:9526