HDTenEightyP/NetNews huggingface dataset:
Newsgroups: sci.math
Subject: Re: 1992 Putnam problems and unofficial solutions
From: elkies@ramanujan.harvard.edu (Noam Elkies)
Date: 18 Dec 92 14:24:22 EST
Organization: Harvard Math Department
Summary: yes, the n^2 bound in B-6 is sharp

In article <a_rubin.723836042@dn66>
a_rubin@dsg4.dse.beckman.com (Arthur Rubin) writes:
">Problem B6
"
">Let M be a set of real n by n matrices such that
">(i) I \in M, where I is the n by n identity matrix;
">(ii) if A \in M and B \in M, then either AB \in M or -AB \in M, but not both;
">(iii) if A \in M and B \in M, then either AB = BA or AB = -BA;
">(iv) if A \in M and A \noteq I, there is at least one B \in M such that
">     AB = -BA.
"
">Prove that M contains at most n^2 matrices.
"
"But can it actually contain n^2 matrices?
"
"I KNOW this is NOT part of the problem as stated, but I am a little curious.


Yes it can: let n be a power of 2; let G be the extraspecial group of
order 2n^2 which has a *real* (even rational) n-dimensional representation
with nontrivial central character; and let M consist of half of the images
of G under that representation, using one of each pair of opposite matrices
and of course choosing the identity out of the pair {I,-I}.  Indeed it
readily follows from the posted solution that G ( = M union -M ) is an
extraspecial 2-group, and thence that the above construction is the only
way to attain equality.

--Noam D. Elkies (elkies@zariski.harvard.edu)
  Dept. of Mathematics, Harvard University
From: pluto@cs.ucsd.edu (Mark Plutowksi)
Newsgroups: sci.math
Subject: Re: nonstandard analysis
Date: 12 Dec 92 23:10:40 GMT

solan@smauguio.no (Svein Olav G. Nyberg) writes:

>In article <24210@galaxy.ucr.edu>, baez@guitar.ucr.edu (john baez) writes:
>|> In article <1992Dec6.025006.16915@athena.mit.edu>
>jelliott@athena.mit.edu (Jesse C Elliott) writes:
>|> >Does anyone know of any colleges or universities which hold a course in
>|> >nonstandard analysis?



I believe Prof Max Stinchcombe (Dept Economics, UCSD) has taught
a course in nonstandard analysis.  That's all I know,
so follow this pointer on your own..

= Mark

Newsgroups: sci.math
From: slory@onyx.cuc.ab.ca (stuart lory)
Subject: Re: Please help with INTEGRATION for final exam!
Organization: Wanna be
Date: Sun, 13 Dec 1992 22:49:12 GMT
X-Newsreader: Tin 1.1 PL5

Thanks to all who replied to my posting.  I was obviously off-track trying 
to use substitution when I should have plugged in the values and integrated
right away.

+---------------------------------------------------------------+
| Stuart Lory		Internet:	slory@onyx.cuc.ab.ca    |
| Calgary, Alberta	  -or-  :	slory@onyx.cuug.ab.ca   |
| Canada				FAX: (403) 289-1893     |
+---------------------------------------------------------------+
Organization: Penn State University
Date: Wed, 16 Dec 1992 13:40:07 EST
From: <B7D@psuvm.psu.edu>
Newsgroups: sci.math
Subject: Re: '-' operation
 <1992Dec16.160754.6893@black.ox.ac.uk>

I like to thank all you gentlemen who have responded to my question
 by either posting here or e-mailing to my account. I realized we may not be
 able to 'define' operations such as '+', '-', '*', and '/', but we may give
 sufficient conditions for them, just as we may not say what math is but say
 what math does. Following the same reasoning for '-', I give sufficient
 conditions for other operations of Real numbers so that this kind of questions
 won't bother students of talent anymore in the future:-):
               '*':    x@1 = x, x@(y@z) = x*y*z;
               '/':    x@1 = x, x@(y@z) = x/y/z, y and z nozero;
               '+':    x@0 = x, x@(y@z) = x+y+z.
I believe these conditions are sufficient but not sure whether they are
 necessary.

  Duane
Xref: sparky sci.math:16964 sci.physics:21214 sci.bio:4593 sci.chem:5424 misc.education:5294
From: corleyj@helium.gas.uug.arizona.edu (Jason D Corley )
Newsgroups: sci.math,sci.physics,sci.bio,sci.chem,misc.education
Subject: Re: TIME HAS INERTIA - NewScientist Article
Date: 15 Dec 92 18:01:17 GMT
Organization: University of Arizona, Tucson

In article <1992Dec15.032030.7459@dmp.csiro.au> lachlan@dmp.csiro.au (Lachlan Cranswick) writes:
>crb7q@kelvin.seas.Virginia.EDU (Cameron Randale Bass) writes:
>
>As I got on to this thread late, I still have trouble
>differentiating the attempted theory with the
>slagging match that is going on.  Re:-
>
>"STATUS QUO" "RESISTANCE TO CHANGE" "RAVING LOONY" etc etc.
>
>How do you differentiate the abuse from the
>theory?

Can't be done.  Abian continually states that those who oppose his
theory, by virtue of opposing it, prove it to be true.  When asked:
"Well, if we had accepted it, would it then be proved false?" he
of course said "No!  It would still be proved true."

The problem with Abian's theory is not that it does not prove
anything-- it is that it can be made to prove ANYTHING, even
false and self-contradictory things.

And I'm sorry about the cross-posting to groups who do not really
need TIME HAS INERTIA in them.  I think I speak for most of
sci.physics in that we will abide by anyone setting the followups
to only include us.  Usually it is Abian himself who expands the
"debate" (I use the word in the loosest possible sense) to other
groups.

	Jason
	Where Are The Jasons At Oxford Of Yesteryear?
Newsgroups: sci.math
From: ross@tarski.tmc.edu (David Ross)
Subject: Re: nonstandard analysis
Organization: University of Hawaii Mathematics Department
Date: Mon, 14 Dec 1992 21:26:18 GMT

In article <Bz5F04.5p3@mentor.cc.purdue.edu> hrubin@mentor.cc.purdue.edu (Herman Rubin) writes:
>In article <1992Dec11.234035.1668@news.Hawaii.Edu> ross@tarski.tmc.edu (David Ross) writes:
>
>>There are many results in analysis, especially probability theory, for which
>>the only known proofs use nonstandard analysis.  
>
>This is at best illusory.  Nonstandard analysis is useful in finding theorems
>and simplifying arguments, but with caveats involved in interpretation.
>
>However, since any nonstandard proof of a standard theorem can be mechanically
>translated into a standard proof

This is only true in a very weak sense.  Nonstandard arguments which just
use Los Transfer can indeed be translated mechanically into standard
arguments; since the first 15 years of n.s.a. arguments relied solely
on transfer, the argument made sense through, say, 1975 (and still
applies to arguments which use IST).

However, 'nonstandard hull' arguments, which have become common in
measure theory and functional analysis, are not solely transfer-based, so
are not amenable to easy translation, except perhaps by a 'local
recreation' of the nonstandard model (i.e., taking a sufficiently 
saturated ultraproduct of a Banach space or of a measure space).  I
know of several results - for example, Keisler's strong existence
theorems for stochastic differential equations, Arkeryd's work on the
Boltzmann equation, some of my own results on stochastic couplings -
for which, while there are possibly standard proofs without the
aforementioned local re-creation, such proofs are not obtainable by
mechanical translation and are not easy to see.  (Even arguments where
the nonstandard hull is used primarily to simplify a weak limit argument
- for example, in the superprocess constructions of Doug Perkins - it
conversion is not automatic.)


- David


--
David Ross, Dept. of Math., Univ. of Hawaii at Manoa, Honolulu HI  96822
Internet: ross@math.hawaii.edu  -or- ross@tarski.math.hawaii.edu
Phone: 808-956-9949
Newsgroups: sci.math,sci.physics
From: daryl@oracorp.com (Daryl McCullough)
Subject: Re: Bayes' theorem and QM
Organization: ORA Corporation
Date: Fri, 18 Dec 1992 13:41:07 GMT

jbaez@riesz.mit.edu (John C. Baez) writes:

>Classical mechanics and quantum mechanics are fundamentally different in
>that the latter is fundamentally probabilistic. The former is only
>probabilistic in the sense that computational limitations may prevent us
>from computing the precise future state that is in principle determined by a
>given present state.

When you say that quantum mechanics is fundamentally probabilistic, do
you mean (A) QM is a probabilistic theory with no known deterministic
completion, or (B) QM is a probabilistic theory that is known *not* to
have a deterministic completion?

The second statement is unwarranted, in my opinion. Bell's Theorem
shows that there is no deterministic completion of QM that uses
classical probability theory. However, Bell's Theorem does *not* say
that there are no deterministic completions of quantum mechanics, if
one is willing to give up classical probability theory.

As I have mentioned several times before, there *is* a
hidden-variables theory for quantum mechanics developed by Pitowsky
and Gudder. However, the probabilities associated with the hidden
variables are non-classical; in particular, the measurable sets do not
form a sigma algebra.

Daryl McCullough
ORA Corp.
Ithaca, NY
From: dak@kaa.informatik.rwth-aachen.de (David Kastrup)
Newsgroups: sci.math
Subject: The truth/lie puzzle at some gate
Date: 14 Dec 92 23:22:10 GMT
Organization: Rechnerbetrieb Informatik - RWTH Aachen
NNTP-Posting-Host: kaa.informatik.rwth-aachen.de

I have some times read a riddle where there are two brothers (or
such) positioned at two gates, one to pleasure (heaven, whatever),
one to hell. You want to find out which is which, and may ask only
one of them one question. The usual solution is
<here comes the spoiler>

What would your brother say if i asked him whether the left door was
the right one (I mean rather, the pleasurable one :]). If he says
yes, it is not, and if he say no, it is. (think about it)

The solution I propose is more subtle and in my opinion more appealing:
<next spoiler>

What would you say if I asked you whether the left door leads to pleasure?

And for yes, enter left, for no right.

What version do you prefer?
From: clong@romulus.rutgers.edu (Chris Long)
Newsgroups: sci.math
Subject: Re: Philosophy of Pi
Date: 15 Dec 92 08:52:21 GMT
Organization: Rutgers Univ., New Brunswick, N.J.

In article <1992Dec11.200538.928@CSD-NewsHost.Stanford.EDU>,
  Vaughan Pratt writes:

>>3.  Would Pi have a different value in a different universe? [...]

> I think the last formulation does the most justice to the spirit of
> this question.  So let's imagine a universe where circles are square.

For a concrete example, consider "taxicab geometry", i.e. where the
distance between (a,b) and (c,d) is |a-c|+|b-d|.
-- 
Chris Long, 265 Old York Rd., Bridgewater, NJ  08807-2618

"S.B., with an I.Q. of 161, failed to complete his course of study,
running away instead with his professor's wife."
H. J. Eysenck, _Know Your Own I.Q._
Newsgroups: sci.math
From: sasbmt@jjoyce.unx.sas.com (Bruce Tindall)
Subject: Re: Not-a-Number
Originator: sasbmt@jjoyce.unx.sas.com
Date: Fri, 18 Dec 1992 18:23:00 GMT
Organization: SAS Institute Inc.


In article <7ZJ0uB1w165w@west.darkside.com>, susskind@west.darkside.com (Mark Susskind) writes:
>On to the main purpose.  I believe that it would be pointless to assign
>Not-a-Number to a variable because one cannot really do any algebra with
>it.  For a quick example, let x=NaN.  What would be x+1?  What about 2x?
>And 0x would be every real (or complex) number, would it not?

Certain software systems, such as the SAS system, recognize several
different "not a number" values (which SAS calls "missing values").  
Usually, any arithmetic operation on a missing value yields a missing 
value.  There are some circumstances in which missing values are 
treated as zero instead.  In sorting and comparisons, missing values 
sort as less than the "most negative" number (i.e., less than the 
negative number with the greatest absolute value).

These properties, and the ability to select between them, are useful 
in applications such as survey research (in which you may want to
distinguish among different kinds of missing data, such as "respondent
not home," "refused to answer," "didn't know," "not applicable," etc.)
and statistical analysis.  

-- 
Bruce Tindall, Core Testing Mgr., SAS Institute Inc., Cary, N.C. 27513
From: weemba@sagi.wistar.upenn.edu (Matthew P Wiener)
Newsgroups: sci.math
Subject: Re: Haughty quote
Date: 13 Dec 92 16:56:59 GMT
Reply-To: weemba@sagi.wistar.upenn.edu (Matthew P Wiener)
Organization: The Wistar Institute of Anatomy and Biology
In-reply-to: bruck@mathj.usc.edu (Ronald Bruck)

In article <1gb49eINN3ra@mathj.usc.edu>, bruck@mathj (Ronald Bruck) writes:
>I very much doubt that Euler made a similar statement.  This is probably a
>case of faulty memory on the part of the high-school teacher.

There is, however, an almost certainly false story told about Euler that
is vaguely similar.  Diderot was espousing atheism at the tzarina's court,
and Euler was to provide a proof of God's existence, which went something
like "(a+1/b)^n=x, therefore God exists, reply" and Diderot left in great
embarrassment.

This story, I've read, first appeared in de Morgan's BUDGET OF PARADOXES
about a century after the alleged incident.  Diderot certainly knew enough
mathematics to not be bamboozled by the above.
-- 
-Matthew P Wiener (weemba@sagi.wistar.upenn.edu)
Newsgroups: sci.math
From: banana@panix.com (Walter Polkosnik)
Subject: Measures, and Measurability
Date: Fri, 18 Dec 1992 19:14:46 GMT
Organization: PANIX Public Access Unix, NYC

I am reading a few papers, and they mention the concept of measures
(particularily Lebesque measures) and the concept of measurability and the
non-measurability of a set. Can anyone provide me with references, or are the
concepts simple enough to explain in e-mail or a post?

Thanks. I'm just a Physicist, so be gentle



-- 
Walter Polkosnik                 
Physics Department         banana@panix.com        
Queens College, CUNY       {cmcl2,apple}!panix!banana
From: riddle@mathcs.emory.edu (Larry Riddle)
Newsgroups: sci.math
Subject: Any Math REU announcements yet?
Keywords: REU
Date: 11 Dec 92 09:14:28 GMT
Article-I.D.: emory.1gapakINNdav
Organization: Emory University, Dept of Math and CS
NNTP-Posting-Host: emory.mathcs.emory.edu

Has anyone seen announcements for any Research Experiences for
Undergraduates in mathematics for summer 1993? We have several
students who are interested in participating in one this summer.
Thanks.

-- 
Larry Riddle        | riddle@mathcs.emory.edu         PREFERRED
Agnes Scott College | {rutgers,gatech}!emory!riddle   UUCP 
Dept of Math        | riddle@emory.bitnet             NON-DOMAIN BITNET
Decatur, GA 30030   | Phone: Voice 404-371-6222, FAX 404-371-6177
Newsgroups: sci.math
From: martel@marvin.mr.sintef.no (Paulo Martel)
Newsgroups: sci.math,rec.games.abstract
Subject: Game of pentominos
Date: 14 Dec 92 14:11:32 GMT
Organization: University of Trondheim, Norway

After several tries I gave up a combinatorial analysis of the game of
pentominos. Would someone point me to a reference, or briefly explain
how one could compute the total number of solutions for a grid of a
given size (6x10, 5x12, 4x15, 3x20). 

Thanks in advance

Paulo

--
|)      /\/\             | e-mail: martel@marvin.mr.sintef.no |               
|aulo  /    \artel       | phone: +47-7-997700                | This sentence
MR-Center, SINTEF        | FAX:   +47-7-997708                |   is false.
N-7034 Trondheim, NORWAY |                                    |               
Newsgroups: sci.math
From: kaila@ii.uib.no (Kailasanathan Chandrapal (Nunmerisk/Databehandling))
Subject: unsolveble problem
Organization: Dept. of Informatics, University of Bergen
Date: Sat, 12 Dec 92 17:35:45 GMT


Hi,
     Can any one respond me to the following problem.

      A , B ,C ,D belong to { ....,-2,-1,0,1,2,... } 

      and A is always greater than 1.

      a , b , c belong to { -1, 0 , 1}.

      (A + B + C - a - b -c) ( a + b + c)  greater than or equal to 0 and

      (A - B + D - a + b) ( a - b )        greater than or equal to 0 and

      (A - C - D - a + c) ( a - c )        greater than or equal to 0 and
 
      (-C + B + D - b + c) ( b - c )       greater than or equal to 0 

       Can you show that B, C, D cover the whole integer space while A>1
 
       and a, b, c in {-1, 0 ,1}.

I thank you in anticipation.

       
Newsgroups: sci.math,sci.philosophy.tech
From: sillke@math25.mathematik.uni-bielefeld.de (Torsten Sillke)
Subject: discrete optimization (fixpoints of polynomials)
Date: Wed, 16 Dec 1992 20:47:12 GMT
Organization: Math MadHouse Bielefeld, Germany
Keywords: discrete optimization, polynomial fixpoints

Discrete Optimization:

  Find Polynomials

             n
            ---
            \           i       n-i
   P  (x) =  >     a   x   (1-x)      
    n       /       i 
            ---
            i=0

   with integer coefficients 0 <= a  <= Binomial[n,i]
                                   i

   such that P_n(x) is not the identity and has as many as
   possible fixpoints in closed interval [0,1].


   For n = 1..5 you can get n different fixpoints in the interval [0,1].
      p_1 :  [1,0] = [a0, a1]
      p_2 :  [0,0,1] = [a0, a1, a2]
      p_3 :  [0,3,0,1]
      p_4 :  [0,0,6,2,1]
      p_5 :  [0,2,0,10,3,1]

   The case n=6 is the first time, where you can get only n-1 different
   fixpoints in [0,1].

   For n=20 I managed to get 17 fixpoints. Can you beat this? 
   What are optimalization procedures in this case?
   (Simulated Annealing with the neightbourhood 'change one coefficient
   a little bit' is no good idea, as almost all fixpoints will be
   complex typically.)

   You can construct polynomials with 0.2*n fixpoints. Can you find
   a better lower bound?

This was a exercise in a 2nd year math course. We recieved one 
solution. Three students constructed (4 pages) a polynomial with
fix points at k/(n-1). Then they showed that the coefficients
are integers and in the allowed range. So they constructed
at least n different fixpoints. But they missed that they had
found the identity. They started their induction for n=3. 

Torsten Sillke
From: corbier@edmund.cs.andrews.edu (Daniel Corbier)
Subject: Ucalc v1.2
Followup-To: sci.math
Organization: Andrews University
Date: Thu, 17 Dec 1992 00:01:00 GMT

I have released a shareware scientific calculator which supports
many built-in functions, operators, numerical notations, and modes.
It is a numerical expression evaluator with the following features:

o High precision: 18 significant digits. Range: 3.4E-4932 to 1.2E+4932
o Arithmetic, bitwise, and relational operators
o Trig, hyperbolic, and many other common functions
o Summations, numerical integration, equation solving
o Radian, Degree, and Gradient modes for trig functions
o User defined functions and variables
o Decimal, Hexadecimal, Binary and Octal notations
o Flexible notations:  ** or ^, SQR or SQRT, MOD or % etc...
o Line editor with expression recall
o Expressions can also be entered at the DOS command line
o Online help

Ucalc can be used for anything from quick arithmetic, to
advanced financial & scientific calculations alike.

** Finger corbier@andrews.edu for a free registration offer **

File Description
----------------

It runs on IBM PC compatibles & the shareware version is fully
functional.

Name:     UCALC12.ZIP
Size:     53K bytes
Where:    FTP  garbo.uwasa.fi, under pc/math
       or Exec-PC, 414-789-4210

-- 
--------------------------------------------------------------------
Daniel Corbier            |   Can you rub your tummy and press
corbier@andrews.edu       |   <ctrl> <alt> <F6> at the same time?
--------------------------------------------------------------------
From: brock@NeXTwork.Rose-Hulman.Edu (Bradley W. Brock)
Newsgroups: sci.math
Subject: '-' operation
Date: 15 Dec 1992 23:39:17 GMT
Organization: Computer Science Department at Rose-Hulman
Reply-To: brock@NeXTwork.Rose-Hulman.Edu (Bradley W. Brock)
NNTP-Posting-Host: g210b-1.nextwork.rose-hulman.edu

In article <92350.145501B7D@psuvm.psu.edu> <B7D@psuvm.psu.edu> writes:
> Recently my daughter brought back Problem Set II of Wisconsin Mathematics
> Science and Engineering Talent Search, and Question 4 in it is as following:
>          Operation @ satisfies the conditions that
>                 X @ (Y @ Z) = X @ Y + Z and X @ X = 0 for any real numbers
>           X, Y, Z. Show that @ must be subtraction.
>For the above question, is only
>thing I have to prove is X @ 0 = X?, which is not very difficult because
>X @ 0 = X @ (X @ X) = X @ X + X = 0 + X = X.
>I just like to know what you
>  have to do to say some operation MUST be one of the basic operations.

You would need to show that X @ Y = X - Y for all X and Y.  Given what you  
already have, simply let Z=Y in the first equation to discover
X=X@0=X@(Y@Y)=X@Y+Y which implies X-Y=X@Y.
--
Bradley W. Brock, Department of Mathematics
Rose-Hulman Institute of Technology  | "Resist not evil.... Love your
brock@nextwork.rose-hulman.edu       |  enemies."--Jesus of Nazareth
Newsgroups: sci.math
From: mcfarlan@corona.math.washington.edu (Thomas J. McFarlane)
Subject: Re: Difference between "show" and "prove"
Keywords: proof  demonstration
Organization: University of Washington, Mathematics, Seattle
Date: Wed, 16 Dec 1992 19:54:52 GMT

In article <1992Dec16.191442.12895@news.Hawaii.Edu> lady@uhunix.uhcc.Hawaii.Edu (Lee Lady) writes:
>
>Many years ago when I was a computer programmer, one of my fellow workers
>was complaining about a former professor and said, very emphatically,
>"He didn't even know the difference between a proof and a demonstration."
>Not wanting to reveal that I was equally ignorant, I never asked my
>fellow worker exactly what the distinction was.  
>
>Later on, after I became a graduate student in mathematics, I did ask
>several mathematicians and none of them thought there was a difference
>between the two terms.  But obviously somewhere, maybe in mathematical
>logic, some people have attached different meanings to these two words
>and I'm still curious about it.  
>
A distinction between demonstration and proof can be made as follows.
When one is working within an axiomatic system and derives formal
consequences of the axioms, this is called a demonstration.  It's
something a computer could verify (in principle).  On the other hand,
when we prove something we appeal to insight.  You might say proofs
are informal, while demonstrations are formal.  Of course, one may
add axioms and definitions to formalize an informal argument, in which
case the proof becomes a demonstration.

I first learned of this distinction from the logician G. Spencer-Brown
in his book _Laws of Form_.

Tom McFarlane
Newsgroups: sci.math
From: ydavid@dxds04.cern.ch (David Yann)
Subject: Riemann Hypothesis (wanted)
Organization: CERN European Lab for Particle Physics
Date: Fri, 18 Dec 1992 10:25:00 GMT
Newsgroups: sci.math
Distribution: world
Reply-To: ydavid@dxds04.cern.ch (David Yann)
Organization: CERN - European Laboratory for Particle Physics

Could someone explain in a few words what the "extended Riemann Hypothesis" states?  Please email your answer, for I don't read this newsgroup too often.

Thanks in advance!


Yann David
student at CERN
Xref: sparky sci.math:16832 sci.physics:21077 sci.bio:4556 sci.chem:5384 misc.education:5228 talk.bizarre:41495
From: bhoughto@sedona.intel.com (Blair P. Houghton)
Newsgroups: sci.math,sci.physics,sci.bio,sci.chem,misc.education,talk.bizarre
Subject: Re: TIME HAS INERTIA - BASS JEALOUS AND INSECURE-ABIAN VALIDATED
Date: 14 Dec 1992 04:51:15 GMT
Organization: Intel Corp., Chandler, Arizona
NNTP-Posting-Host: alfalfa.intel.com

In article <abian.724200923@pv343f.vincent.iastate.edu> abian@iastate.edu (Alexander Abian) writes:
>FLAGRANT MANIFESTATION OF JEALOUSY AND INSECURITY BY C.R. BASS 
>PATHETIC METHODS FOR GAINING A FEELING OF SECURITY. BASS  PROVES (A3) 

I want this in a fortune-cookie.
Then I'll believe "(A3)".

The fortune will probably have
a printers'-union bug and the
X-Industries logo[*] on it.

				--Blair
				  "Crossposting to the group in which
				   this entire net.epoch should
				   have began in the first place."

[*]  Crossed dendrites above a
suspiciously familiar blue marble.
Newsgroups: sci.math