HDTenEightyP/NetNews huggingface dataset:
Organization: University of Illinois at Chicago
Date: Wednesday, 8 Apr 1992 17:45:09 CDT
From: <U53415@uicvm.uic.edu>
Newsgroups: sci.math
Subject: Re: Erdos Interview circa 1987
 <STROMME.92Apr6130830@jeeves.math.utah.edu>
 <sundquis.702591357@s6.math.umn.edu> <1992Apr7.051902.4889@rata.vuw.ac.nz>
 <1992Apr7.235418.12640@newshost.anu.edu.au>

In article <1992Apr7.235418.12640@newshost.anu.edu.au>,
gerry@macadam.mpce.mq.edu.au (Gerry Myerson) says:
>
>In article <1992Apr7.051902.4889@rata.vuw.ac.nz>, harper@kauri.vuw.ac.nz (John
>Harper) writes:
>>
>>
>>  >Pardon my ignorance. Who is this Erdos dude?
>> Several people have been abusing one another instead of answering the
>> question. Paul Erdos is a very famous Hungarian mathematician (aged around
>> 80 I'd guess)
>
>79; he'll be 80 next March. Does everyone know his story about being three
>billion years old? It seems that when he was a young man, the geologists
>said the world was a billion years old; now, they say it's four billion years
>old; ergo....
>
      If you're interested, there was an interview with Erdos published in the
      Atlantic a few years back.  I forget the exact issue, but it would have
      been sometime between fall 1987 and spring 1988.


Mitch Pollack, Dept. of Mathematics, University of Illinois at Chicago

>> John Harper Mathematics Dept. Victoria University Wellington New Zealand
>
>Gerry Myerson
From: cet1@cl.cam.ac.uk (C.E. Thompson)
Newsgroups: sci.math
Subject: Re: Oh, those primes sure are popular
Date: 7 Apr 92 00:13:09 GMT
Reply-To: cet1@cl.cam.ac.uk (C.E. Thompson)
Organization: U of Cambridge Computer Lab, UK

In article <3631@tuegate.tue.nl>, angelo@gem.stack.urc.tue.nl 
 (Angelo Wentzler) writes:
|>
|> So, what is the first sequence after 10010111 that satisfies 2,3,4,5
and 6-ary?
|> 

No-one seems to have posted the answer to that particular question. 
It is 111110100001 which is prime in bases 2,3,4,5,6 AND 7; but not 8
(of course, as the sum of the digits is 7).

Chris Thompson
JANET:    cet1@uk.ac.cam.phx
Internet: cet1@phx.cam.ac.uk
From: gdcarson@icaen.uiowa.edu (Gregory Donald Carson)
Newsgroups: sci.math
Subject: Need a subroutine to.....
Date: 10 Apr 92 01:24:00 GMT
Distribution: usa
Organization: Iowa Computer Aided Engineering Network, University of Iowa
Originator: gdcarson@temp2

Hello Computer and Math Guru's

	I have a problem which I hope someone can help with.  I am transporting
a very large program from VMS to Unix, one of the calls the program makes is to
a VMS FORTRAN math extension named SNLS1 or SNLS1E.  
	This routine calculates and yields the two means from a bimodal 
gaussian distribution.  What is sent to the subroutine is an array of data
points, the length of that array, and several other items of little 
importance.  What the main program expects the subroutine to do is to calculate
the two means from the assumption that the data fits a bimodal gaussian 
distribution.  The program SNLS1 uses the Levenberg-Marquardt method to find
the two means of the data, these are then returned to the program.
	What I am looking for is a program that will accomplish this task.  I
do need to be able to get the code for the program.  Does anyone have any
suggestions on a program to use.  
	Please send responses to me in mail.  Thanks in advance for your help
and for reading my post.

Greg
Newsgroups: sci.math
From: cxm7@po.CWRU.Edu (Colin Mclarty)
Subject: Re: nonexistance of counterexample -> existance of proof?
Reply-To: cxm7@po.CWRU.Edu (Colin Mclarty)
Organization: Case Western Reserve University, Cleveland, OH (USA)
Date: Fri, 10 Apr 92 13:20:34 GMT


In a previous article, ec120wee@sdcc4.ucsd.edu (Anthony Minkoff) says:

>Forgive a little question from a poor, ignorant undergraduate who's
>not even a math major:
>
>An acquaintance and I were recently discussing Goldbach's conjecture
>(that every even number greater than 2 is the sum of two primes).
>He made the statement "If no counterexample exists, then a proof
>exists."  Of course, I can't prove him wrong (I accused him of
>making a "safe" statement, since clearly he could not be proven
>wrong in the case of the Goldback conjecture), but I want to know,
>in general, is his statement correct?  (I was hesistant to apply
>Godel's theorem, since neither of us really understands it).
>
>Anyway, the story continues, but it gets kinda silly from here.  I'm
>mostly interested in an answer to this first part, but I'll share
>the rest with you, and you may have some interesting insights...
>
>
>Tony Minkoff
>
	Other posters have replied to the second part, which is the
more interesting as it stands.  But I think your acquaintance may have
made his claim based on a misunderstanding of another point, which has
been discussed here recently.  It is widely held (though it depends
somewhat on your philosophy of math) that for *some kinds* of claims, if
there is no disproof in formal Peano Arithmetic then the claim is true.

	But this is held only for claims of the form "there are no
numbers satisfying the following (multivariable) equation".  For
example, the Fermat conjecture "there are no numbers x,y,z and n
satisfying (x+1)^(n+2) + (y+1)^(n+2) = Z^(n+2)".  

	Notice that the usual form of the conjecture says "there are no
non-zero numbers x, y, z, and number n greater than 2, such that
  x^n+y^n=z^n "  but that is not just an equation on x,y,z and n, it poses
other conditions.  But we can restate it as an unrestricted equation
byt using x+1 instead of x, and n+2 instead of n.

	The reasoning is that if there really were such numbers then they 
would be represented in the formal arithmetic, they would make the equation
true, and so the claim would be disprovable, and so not undecidable.  So
if it is undecidable--the *formal* theory can not prove there are such
numbers or that there are not--then we know there actually are not.  This
would not make sense for more complcated claims such as that  "for every
even number greater than 2 THERE EXIST two primes such that...."  Of
course we could replace "even even number grater than 2" by an unrestricted
"for every number n, the number 2n+2 has the following..."  But we can not
get rid of the "THERE EXIST" that way.

	Why aren't you a math major?

Colin McLarty
Xref: sparky sci.math:6071 comp.sys.sun.wanted:661
From: et11ltab@sbusol.rz.uni-sb.de (Alexander Bachmann)
Newsgroups: sci.math,comp.sys.sun.wanted
Subject: Address of LINDO and CPLEX
Date: 15 Apr 92 07:15:36 GMT
Followup-To: poster

Hello,
I'm looking for the address of LINDO and CPLEX, which are Linear
Programming Tools (Mail, Phone, Fax and/or Email). Please e-mail 
your response.
Thanx in advance
+----------------------------------------------------------------------+
|                       Alexander Bachmann                             |
| Universitaet des Saarlandes    | Tel.    ++49/681/3023576            |
| Lehrstuhl fuer Mikroelektronik | Fax                 2678            |
| D-6600 Saarbruecken            | E-mail  bachmann@ee.uni-sb.de       |
+----------------------------------------------------------------------+
Newsgroups: sci.math
From: luzeaux@campanile.berkeley.edu (Dominique Luzeaux)
Subject: Re: An elementary, "naturally occurring" problem
Reply-To: luzeaux@campanile.berkeley.edu (Dominique Luzeaux)
Organization: University of California
Date: Fri, 10 Apr 1992 17:25:51 GMT


In article <1992Apr10.000446.24127@math.ucla.edu>,
oliver@oak.math.ucla.edu (Mike Oliver) writes:
|> (...) One might ask:  is
|> there such a partition such that the intersection of each set
|> with any open interval is uncountable?
|>  (...)
|> I don't know whether it can be done without AC.  It seems like
|> the kind of thing that might be inconsistent with the Axiom of
|> Determinacy but I don't immediately see why.
|> 

You can even ask: is there a partition of [0,1] into A and B such that 
A is dense in B, B dense in A and A and B have non null Lebesgue measure;
and for any open interval C, the intersection of A and C, and B and C have
both non null measure.

This is done by constructing a Cantor-like set with positive measure:
instead of always taking the third of any interval, take the \mu_i th
of the interval at each step i with:
 \mu_i \in ]0,1[ and \prod(1-\mu_i) = m_j \in ]0,1[
This leaves you with holes and intervals; on each interval, you construct 
another Cantor-like set, which leaves you with more holes and less intervals,
and you do this ad infinitum (choosing a family m_j with similar conditions to
the \mu_i); the set of holes is A and its complement is B
(which is the limit of the remaining intervals and converges to dust).

And of course, A and B intersect any open interval and the intersection has
non null measure.
The proof uses picking of the \mu_i and the m_j is no big deal and taking
countable limits.

	Dominique Luzeaux
From: israel@unixg.ubc.ca (Robert B. Israel)
Newsgroups: sci.math
Subject: Re: nonexistance of counterexample -> existance of proof?
Date: 10 Apr 92 09:01:57 GMT
Article-I.D.: unixg.1992Apr10.090157.6590
Organization: University of British Columbia, Vancouver, B.C., Canada

In article <31475@sdcc12.ucsd.edu> ec120wee@sdcc4.ucsd.edu (Anthony Minkoff) writes:
>  [stuff deleted]
>Anyway, the story continues...  I then tried to present an example
>of a theorem with no proof, and no counterexamples.  First, I made
>the claim that there must be real numbers with no finite expression.
>(A finite expression does not necessarily imply a finite expansion.
>For example, sqrt(2) is a finite expression.)  I offered the
>following proof:
>
>Any finite expression can be encoded as a finite sequence of bits,
>according to the following scheme:  Begin the sequence with an ASCII
>text description of how to decode the part of the sequence following
>the description.  (Of course, the entire description may be the
>ASCII text.)
>
>Since a one-to-one correspondence can be established between finite
>sequences of bits and integers, but not between reals and integers,
>there are reals with no finite expressions.
>
>Then I proposed the theorem, "All reals *do* have some finite
>expression."  Clearly, no proof exists, since the statement is not
>true.  Then we got into an argument over whether counterexamples
>exist.  Certainly he could not give me one, and nobody ever could.
>So it became a question of what is really meant by the statement, "a
>counterexample exists."
>
>Tony Minkoff

    Actually, there IS a counterexample to your "theorem".  I assume that
you have a precise definition of what it means for a "finite expression"
to "represent" a real number (otherwise the "theorem" is ambiguous).
Those "finite expressions" that represent real numbers can then be 
enumerated (e.g. in order of the positive integers that we get when 
representing ASCII strings as hexadecimal digits). 
Let r(n) be the number represented by the n'th "finite expression"
that represents a real number.  Let d(n) be the n'th decimal digit 
(after the decimal point) of r(n) (with whatever convention you want
for numbers with nonunique decimal expansion).  Let c(n) = 1 if d(n) = 2
and c(n) = 2 otherwise.  My counterexample is 0.c(1)c(2)c(3)... .

    Have I specified a unique real number?  Yes, if you have defined
"finite expression" and  "representing" (unless you are a constructivist). 
And it's certainly not represented by any of your finite expressions: it
has a unique decimal expansion, and differs in at least one place from
each number "represented by a finite expression".  My 
definition does _look_ like a finite expression representing a real number, 
but of course it can't be one according to whatever definition you used.  
It's certainly not a _computable_ expression, if your definitions are 
sufficiently powerful, because there won't be an algorithm that can decide
whether or not an expression represents a number.  
 
Robert B. Israel
Department of Mathematics
University of British Columbia
Vancouver, BC, Canada
Xref: sparky sci.math:5910 alt.security:2742
From: murphy@symcom.math.uiuc.edu (Michael L. Murphy)
Newsgroups: sci.math,alt.security
Subject: Mathematics "dictionary" file?
Summary: Is there, somewhere on the net, a list of mathematical terms/persons?
Date: 10 Apr 92 17:35:48 GMT
Article-I.D.: ux1.1992Apr10.173548.24770
Followup-To: poster
Organization: Math Dept., University of Illinois at Urbana/Champaign

Does anyone have a list (preferably in the format of /usr/dict/words,
one words per line, but if it's not, I'm sure I can get it in that
format) of mathematical terms and famous names in mathematics?  I'd
like to have it for a proactive password checker that is used on our
Symcom computer network, since most of the users are mathematics
professors and graduate students.

Also, does anyone know where additional dictionaries for use in
password cracking and proactive password checking programs can be
found?  (/usr/dict/words in SunOS only has 25000 words, which
isn't really comprehensive by any means....)  Thanks for any help,
especially in locating the mathematics dictionary.
-- 
+=And=the=Master=said=unto=the=silence,="In=the=path=of=our=happiness=shall=+
\ we find the learning for which we have chosen this lifetime." - R. Bach   /
/ Michael Murphy, senior (Math/C.S.), U of Ill.  |   Address: URH 10 Carr   \
+=send=e-mail=to=<murphy@symcom.math.uiuc.edu>==/^\==Urbana,=IL=61801=======+
From: paris@cma.cma.fr (Jean-Pierre Paris)
Newsgroups: sci.math
Subject: ftp site for prime numbers
Keywords: ftp primes
Date: 6 Apr 92 14:01:09 GMT
Reply-To: paris@cma.cma.fr
Organization: CMA ENSMP Sophia Antipolis


 I am looking for large prime numbers and I want to know if there is an
anonymous ftp site where I can find these?

 If this question has been already posted, please respond via mail.

 Thanks

-- 
==========================================================================
Jean-Pierre PARIS,                                        paris@cma.cma.fr  
C.M.A. Ecole des Mines, B.P. 207,     06904 Sophia-Antipolis Cedex, FRANCE
Phone: (33) 93 95 74 92.  FAX: (33) 93 95 74 88
   Or
CISI Ingenierie, Les Cardoulines, Sophia Antipolis, 06565 VALBONNE, FRANCE
Phone: (33) 93 65 31 31.  FAX: (33) 93 65 21 21
From: afarrell@unix1.tcd.ie (Andrew Farrell)
Newsgroups: sci.math
Subject: Re: Fermat's Last Theorem
Date: 10 Apr 92 10:13:45 GMT
Organization: Trinity College, Dublin

In <1992Apr9.133316.24615@linus.mitre.org> bs@gauss.mitre.org (Robert D. Silverman) writes:

>In article <sundquis.702591357@s6.math.umn.edu> sundquis@s6.math.umn.edu (Thomas Sundquist) writes:
>:>   >>No, Erdos only offers money for his own problems.
>:>   >Pardon my ignorance. Who is this Erdos dude?
>:
>:>   You're joking right???  April 1 is tomorrow, not today, right???
>:>   This must be a joke. How can anyone who reads or posts to this newsgroup
>:>   not know who Paul Erdos is???
>:>   I can understand Joe Blow off the street not knowing, but how can anyone
>:>   with an interest in math [evidenced by the fact that he reads this group]
>:>   Bob Silverman
>:>   These are my opinions and not MITRE's.
>:>   Mitre Corporation, Bedford, MA 01730
>:
>:>Come on, Bob, as a reader of this group you must have noticed that its
>:>contributors range from the professional to the not-so-professional.
>:>Why not just answer the question? After all, the poster says "Pardon
>:>my ignorance", and then he does not deserve to be run over like that.
>:>Stein 
>:
>:My thoughts exactly.	Tom


>Huh?  I was simply expressing my surprise that someone who claims an
>interest in math did not know who one of the greatest mathematicians of
>the 20th century is!!! How is that "running over someone"???

>The relevent phrase is "interest in mathematics". One need not be a
>professional to still recognize who the outstanding contibutors are!

>You are probably not a professional sports player, yet I'm sure you
>know who the greatest pros are. Why do you know? Because you are
>interested in sports and follow them! Why should not the same thing
>apply in mathematics??? 

Because Maths isn't a televised competitive sport. It's a quiet science. Hell,
I don't know who Paul Erdos is, and I've beenn studying (Irish) College Maths
for 4 years

Andrew
Newsgroups: sci.math,sci.math.symbolic
From: Victoria Bush <vbush@copper.ucs.indiana.edu>
Subject: Dynamic programming packages?
Followup-To: sci.math.symbolic
Summary: Request for info on packages/programs for dynamic programming
Keywords: maple, mathematica, dynamic programming, optimization
Organization: Office of Statistical and Mathematical Computer Applications
Date: Mon, 6 Apr 1992 11:27:31 -0500

I have had a barrage of requests for programs which will do dynamic 
programming (usually time variant). Most of the people would be interested 
in packages for Maple or Mathematica, but I would also like to include 
any and all programs which will handle this. 

Post if you like; otherwise send replies to vbush@copper.ucs.indiana.edu.
If enough interest exists, I'll summarize to the net. 

-Vic
-- 
Victoria Bush, a lowly graduate student| For by your words you will be   
Indiana University                     | acquitted, and by your words you
vbush@iubacs (Bitnet)                  | will be condemned.
vbush@copper.ucs.indiana.edu (Internet)|      -Matthew 12:37
Xref: sparky sci.math:5975 sci.math.stat:995
From: hrubin@pop.stat.purdue.edu (Herman Rubin)
Newsgroups: sci.math,sci.math.stat
Subject: Re: "Half or plus".
Date: 12 Apr 92 13:05:18 GMT
Followup-To: sci.math
Organization: Purdue University Statistics Department

In article <1992Apr10.180746.4628@csc.canterbury.ac.nz> wft@math.canterbury.ac.nz (Bill Taylor) writes:
>This one has bothered me for a long time.


>"HALF-OR-PLUS" is a simple discrete-time stochastic process. 
> ~~~~~~~~~~~~
>Start with value 1; and at each time step, either halve or add one to the current
>value, with probability 1/2 each, independently of what's happened before.


>Formally....    Y   = 1
>                 0

>                        /   Y  + 1  .....   if  X = 0
>                       /     n                   n
>              Y     = <
>               (n+1)   \    Y  / 2  .....   if  X = 1
>                        \    n                   n

>where { X  } is a Bernoulli sequence with parameter 1/2 .
>         n

			.......................

>It seems reasonably easy to calculate (numerically), coarse approximations to 
>the limiting distribution; i.e. the limiting discrete distribution on the set 
>of disjoint intervals of unit width; or of half-unit width; and so on. 
>But it's frustrating trying to extend the results to a continuous distribution.

The limiting distribution is continuous, as is the case for just about any
situation of this kind.  It clearly does not depend on the initial value.

One way to get at it is to use the moment generating function.  If we call
this function m, we get

	m(t) = .5*m(t)*e^t + .5*m(t/2),

from which m(t) is the infinite product of the reciprocals of the
quantities 2 - exp(t/2^j), j = 0, 1, ... .  The characteristic function
computed for u = 2^j * pi is a non-zero constant, so there cannot be a
density.

As for computing the distribution numerically, I would suggest intelligent
use of contour integration, using the formula for the cdf.
-- 
Herman Rubin, Dept. of Statistics, Purdue Univ., West Lafayette IN47907-1399
Phone: (317)494-6054
hrubin@pop.stat.purdue.edu (Internet, bitnet)  
{purdue,pur-ee}!pop.stat!hrubin(UUCP)
From: watson@clark.edu (Dennis Watson)
Newsgroups: sci.math
Subject: Mathematics Position
Date: 7 Apr 92 22:54:00 GMT
Article-I.D.: clark.1992Apr7.225400.16412
Organization: Clark College, Vancouver, Wa.  USA

Full-time, tenure track teaching position. Requires MA or MS in Mathematics.
Teaching basic math through first two years of college math.  Salary
$25,900 - 32,900.

Application materials may be obtained from Clark College Personnel Services,
1800 E McLoughlin Blvd., Vancovuer WA 98663; (206) 699-0105. Closing 
date:  May 14, 1992, 5 p.m.

Clark College is an equal opportunity employer and places particular emphasis
on achieving affirmative action hiring goals.  Protected group members are
strongly encouraged to apply.
From: esm@che.utexas.edu (Edward Scott Meadows)
Newsgroups: sci.math
Subject: Question on Positive Definite Matrices
Date: 15 Apr 92 18:53:19 GMT
Reply-To: esm@che.utexas.edu (Edward Scott Meadows)
Organization: UT Department of Chemical Engineering
Originator: esm@june.che.utexas.edu


I have seen the following as a hypothesis in a technical paper recently:

Given positive definite matrix Q, there exist a, b both greater than zero such that

       0 < a I <= Q <= b I

What exactly does this mean?  Doesn't _every_ positive definite matrix
Q meet this condition for some a,b?  If not, what is a counterexample?

Scott M.



-- 
Edward S. Meadows               esm@che.utexas.edu
Department of Chemical Engineering   
University of Texas at Austin
Newsgroups: sci.math
From: algebra@leland.Stanford.EDU (Leong Weng Ng)
Subject: On expected convergence 
Organization: DSG, Stanford University, CA 94305, USA
Date: Fri, 10 Apr 92 09:50:30 GMT

Hi,
	I'm a freshman at Stanford (undeclared but will be majoring in math),
and a newcomer to this newsgroup. As an opening line, I would like to
solicit opinions regarding a simple idea which I have been toying with lately.
Please correct me on any errors I make in my line of reasoning.
	Conventionally speaking, when a series converges, it does so towards
one and only one limit. Any case other than that is termed divergent. In
particular, a series which has a finite but variable limit

e.g. 1-1+1-1+... = 1 or 0 depending on where the series stops

is divergent. My query is: need convergence be defined with such strictness
that series such as the above, which are relatively well-behaved excepting the
fact that they do not have definite limits, are ostracized.
	The great mathematician Leonhard Euler obtained the following identity
by non-rigorous reasoning:

                             1-1+1-1+... = 1/2

	Most of you would know that the identity comes about from "illegally"
substituting x = 1 into the binomial expansion for 1/(1+x). My idea is that
this identity can be obtained by probabilistic reasoning. Grant me that
infinity can be treated as a random variable integer R. To evaluate the infinite
series, take the Rth term as the last term (dangerous I know). Since R is
random, it has equal probabilties of being odd or even. If R lands on a odd
term, the sum is 1; if even, the sum is 0. So the expected sum of the series is 
1/2(1)+1/2(0) = 1/2, thus agreeing with the binomial method. My aim in giving
this example is to suggest that there may exist a deep principle regarding 
indeterminacy. It is my opinion that wherever math encounters a
problem whereby numerical determinacy is not possible, it offers the mean of
all possible numerical answers as an answer. If such a principle does exist,
then it is perhaps not unnatural for us to extend our current understanding of
convergence to a more open notion of "expected convergence", whereby a series
is called "convergent" as long as it has a finite sum, regardless of
non-uniqueness of limits.
	Comments and criticisms are much appreciated.

                                                                          Al
 
Newsgroups: sci.math
From: cxm7@po.CWRU.Edu (Colin Mclarty)
Subject: Re: Probability puzzle 
Reply-To: cxm7@po.CWRU.Edu (Colin Mclarty)
Organization: Case Western Reserve University, Cleveland, OH (USA)
Date: Sat, 11 Apr 92 20:31:29 GMT


In a previous article, algebra@leland.Stanford.EDU (Leong Weng Ng) says:

>Puzzle:
>
>	Choose any straight line in a plane. The plane is then divided into two
>half-planes by the line. Select any two points on the plane not lying on the
>chosen line. What is the probability that both points lie on different half-
>planes? Is it 1/2 or something else?
>
>Cheers                                                                 Al
>
>
	No, the probability of their being in different half planes is 0,
since it happens that I am arbitrarily energetic about how far I'll go for a 
first choice and terribly lazy about how far I'll move for the second.

	More soberly, it depends on how the points are to be selected.

Colin McLarty
Newsgroups: sci.math