HDTenEightyP/NetNews huggingface dataset:
From: fateman@peoplesparc.Berkeley.EDU (Richard Fateman)
Newsgroups: sci.math,sci.math.symbolic
Subject: Re: Honest Plotting (was: Integral Tables)
Date: 29 Sep 1992 21:29:20 GMT
Organization: University of California at Berkeley
NNTP-Posting-Host: peoplesparc.berkeley.edu

A "correct" plotting function can be constructed by using correctly
implemented interval arithmetic.  See, for example,

R. Fateman,  Honest Plotting, Global Extrema, and Interval Arithmetic.
in Proc. ISSAC '92, (Assoc. for Comp. Mach., ISBN 0-89791-489-9)
pp. 216-223.  

Programs for doing this in Mathematica are illustrated, modulo
Mathematica's (incorrect) interval arithmetic.

See files available on this machine: ~ftp/pub/plotinterval.m  and
realinterval.m

Better programs for computing correctly with intervals in Lisp,
as well as "native" plotting  are under development;  perhaps some other
systems that support intervals, like Pascal SC could do a better job.



-- 
Richard J. Fateman
fateman@cs.berkeley.edu   510 642-1879
From: holmes@opal.idbsu.edu (Randall Holmes)
Newsgroups: sci.math
Subject: Re: Most important event in the history of mathematics
Date: 29 Sep 92 16:05:47 GMT
Organization: Boise State University

In article <BvC6rs.HFy@cantua.canterbury.ac.nz> wft@math.canterbury.ac.nz (Bill Taylor) writes:
>Got to be the discovery of irrationals by a Pythagorean (whose name escapes me).
>
>Its supreme significance is affirmed by its unique (apocryphal?) status as 
>the only time a mathematician has been killed for making a shattering mathematical discovery ! 

This was my immediate reaction, too, although I'm not certain.


-- 
The opinions expressed		|     --Sincerely,
above are not the "official"	|     M. Randall Holmes
opinions of any person		|     Math. Dept., Boise State Univ.
or institution.			|     holmes@opal.idbsu.edu
From: dchatterjee@kuhub.cc.ukans.edu
Newsgroups: sci.math
Subject: Hawking's portrayal of Newton and Einstien
Date: 4 Oct 92 18:49:09 CDT
Organization: University of Kansas Academic Computing Services


 Hi !

 I was reading Stephen W.Hawking's " A Brief History of Time ". Hawking
 comments that Isaac Newton was an unpleasant character and had always
 (or most of the time) engaged in personal quarrels or brawls with his
 fellow scientists. This seems very amusing, because, why people of the
 stature of Newton be so mundane, while on a comparative scale, Einstien
 was more pleasant and very unassuming in appearance and of humble habits ?

 Seems to me that Hawking could be biased ! 

 Comments ? 

 - DC
Newsgroups: sci.math
From: cs202144@umbc8.umbc.edu (cs202144)
Subject: Re: Roman Numerals
Organization: University of Maryland, Baltimore County Campus
Date: Mon, 5 Oct 1992 14:41:04 GMT

> This may be a dumb question, but I am curious...How are roman numerals larger
> than 3999 expressed? Is there an extended symbology or are the existing
> symbols altered in some way to express larger values?

Ok...Some people pointed out the bar trick to multiply by 1000 and I actually
knew this, but was wondering if there are any rules for this. For example would
4000 be:
            __     _
            IV or MV

or would both be acceptable and equally correct?

Like should an existing, non-modified value be used over a value that has been
altered with the bar or would both be prefered?
From: arodgers@dcs.qmw.ac.uk (Angus H Rodgers)
Newsgroups: sci.math
Subject: Re: Rename the Calculus sequence?
Date: 28 Sep 92 14:55:16 GMT
Organization: Computer Science Dept, QMW, University of London

In R1STORY@VM1.CC.UAKRON.EDU writes:

>When talking to my computer science colleagues, I have always been impressed
>with the titles they have given their courses

>I thought that I would make change of title for some of our tradional courses
>such as Calculus I, II, and III.

>Any other suggested titles?
>--------------------------

Happy to oblige:

 Set Theory                  Formal Methods I
 Algebra I                   Formal Methods II
 Real Analysis               Theory of Numerical Methods
 Logic I                     Formal Semantics of Declarative Languages 
 Number Theory               Digital Systems Theory
 Differential Equations      Abstract Dynamic Systems Theory
 Catastrophe Theory          Software Engineering
 Graph Theory                Network Topology
 Dynamics                    Continuous Automata Theory
 Computer Programming        Lambda Calculus and its Applications
 Category Theory             Object-Oriented Set Theory

(And I didn't even say "structured" or "user-friendly" once!)

--
Angus H. Rodgers  (PhD student), | arodgers@dcs.qmw.ac.uk  
Dept. of Computer Science, Queen | [ +44 | 0 ] 71 975 5241   
Mary & Westfield College,  Mile  | This space has not been left blank,
End Rd., London E1 4NS, England  | intentionally or otherwise.
Newsgroups: sci.math
From: blanc@caroli.csis.dit.csiro.au (Jacques Blanc-Talon)
Subject: Re: Graph isomorphism problem
Reply-To: blanc@caroli.csis.dit.csiro.au
Organization: CSIRO Division of Information Technology
Date: Wed, 30 Sep 1992 00:42:46 GMT

In article <guan.717776162@bruce.cs.monash.edu.au>, guan@cs.monash.edu.au (NAME) writes:
>    Hello.  I am working on an algorithm for a problem very similar to
> the Graph Isomorphism Problem.  I have heard that it might not be possible
> to solve the Graph Isomorphism Problem in Deterministic polynomial time.
> Is this true?   Does anyone know of any (relevant) known lower (or upper)
> time bounds (e.g. NP-completeness)?
> 
> Please direct responses to me rather than to the newsgroup.
> 
> Regards
> 
> Guan Xiaoxiang

  According to:

  Christoff M. Hoffmann's book "Group-theoretic algorithms and
  Graph isomorphism", Springer Verlag, LNCS 136, 1979:

  The following problems are polynomial-time equivalent:

  - decide if 2 graphs are isomorphic
  - decide if 2 labelled graphs are isomorphic
  - construct the isomorphism between 2 graphs
  - given a graph, determine a generating set of the group of automorphims
  - determine the order of the group of automorphisms of a given graph
  - determine the number of automorphisms between 2 graphs

  page 6, one can find the following paragraph:

  If P is not equal to NP, then one can show the existence of many problems
  of intermediate difficulty (...) Furthermore, despite the large numbers of
  known natural NP-complete problems and of natural problems in P, there seems
  to be a paucity of candidates for natural problems of intermediate difficulty.
  The only 2 commonly proposed  candidates are testing "graph isomorphism" and
  testing "primality".

  Hope it helps.

Jacques Blanc-Talon
*
From: radcliff@csd4.csd.uwm.edu (David G Radcliffe)
Newsgroups: sci.math
Subject: Re: A Problem to Amuse You
Date: 3 Oct 1992 16:32:26 GMT
Organization: UW-Milwaukee Math Department
NNTP-Posting-Host: 129.89.7.4

tao@ginger.princeton.edu (Terry Tao) writes:
:In article <1992Sep30.193552.34183@Cookie.secapl.com>, frank@Cookie.secapl.com (Frank Adams) writes:
:|> In article <BvEBA5.KyH@world.std.com> rjk@world.std.com (robert j kolker) writes:
:|> >Let D be an enumerable subset of the Euclidean plane. Show that D can be
:|> >written as D_x U D_y where D_x intersects all the lines parelell to the x
:|> >axis in a finte number of points, and D_y intersects all the lines
:|> >parallel to the y axis in a finite number of points.
:|> 
:|> (This should really say "each line", not "all the lines".)
:|> 
:|> This is easy.  You don't even need the axiom of choice.  And it doesn't have
:|> to be RxR; SxS for *any* set S will work just as well.
:
:Forgive me if I'm stupid.  If D is QxQ, what are D_x and D_y?
: 
: 
: Terry

Solution:


First, solve the problem for the special case NxN.  (N is the positive integers)
One solution is D_x = { (m,n) : m < n } and D_y = { (m,n) : m >= n } .

For the general case, let A,B be denumerable subsets of R such that D is a
subset of AxB.  Let f:A-->N and g:B-->N be finite-to-one functions.  Then
 
  D_x = { (x,y) \in D : f(x) <  g(x) }
  D_y = { (x,y) \in D : f(x) >= g(x) }

For example, a partition for QxQ can be found as follows: 

  D_x = { (p/q, r/s) : |p| + |q| <  |r| + |s| }
  D_y = { (p/q, r/s) : |p| + |q| >= |r| + |s| }

Of course p/q and r/s are assumed to be in lowest terms.

--
David Radcliffe                                
radcliff@csd4.csd.uwm.edu
From: RVESTERM@vma.cc.nd.edu
Newsgroups: sci.math
Subject: and can you guess which answer i want to hear?
Date: 4 Oct 92 18:57:41 GMT

let's assume, for a moment, that you are writing a basic topology text.
in it, you decide to print the following exercise:

    a. show that Rw (read R omega) is not connected in the box topology
       by showing that the set of all bounded sequences is both open
       and closed.

    b. what happens if Rw is given in the uniform topology?

now my question is this: by part b, do you mean, "is it possible to show that
Rw is not connected in the uniform topology by considering the set of all
bounded sequences", or do you mean, "is Rw connected or not in the uniform
topology"?
Newsgroups: sci.math,rec.puzzles
Newsgroups: sci.math
Subject: Re: Another Cute Math Joke (explanation of)
From: a_rubin@dsg4.dse.beckman.com (Arthur Rubin)
Date: 6 Oct 92 15:58:39 GMT
 <1992Oct2.123755.22685@ulrik.uio.no> <1992Oct2.185445.3484@sfu.ca> <1992Oct4.205137.29695@clark.edu>
Organization: Beckman Instruments, Inc.

In <1992Oct4.205137.29695@clark.edu> watson@clark.edu (Dennis Watson) writes:

>Sometime back someone posted the following  joke?   

>\epsilon < 0   

There's a \delta for every \epsilon,
That's a fact the can be relied upon,
There's a \delta for every \epsilon,
...and now and again, there's also an \n.

But one condition I musta give,
The \epsilon must be positive,
A lonely life all the others live,
.
.
.

-- Tom Lehrer

(I can't remember the rest of the song.)


--
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:12574 rec.puzzles:6561
From: clong@remus.rutgers.edu (Chris Long)
Newsgroups: sci.math,rec.puzzles
Subject: Re: EASY NUMBER SEQUENCE PUZZLE... (SPOILER)
Date: 1 Oct 92 14:53:11 GMT
Followup-To: sci.math
Organization: Rutgers Univ., New Brunswick, N.J.

In article <aet.717945133@munagin>, Bert Thompson writes:

> 25
> 1729
> 635318657

The next is the smallest positive integer that can be written as
a sum of fifth powers in two distinct ways, but I have no idea what
it is.
-- 
Chris Long, 265 Old York Rd., Bridgewater, NJ  08807-2618
Newsgroups: sci.math
From: pratt@Sunburn.Stanford.EDU (Vaughan R. Pratt)
Subject: Re: consequences of the Axiom of Choice
Keywords: Axiom of choice; Cartesian product
Organization: Computer Science Department,  Stanford University.
Date: Thu, 1 Oct 1992 15:27:04 GMT

In article <1992Oct1.084836.14057@infodev.cam.ac.uk> rgep@emu.pmms.cam.ac.uk (Richard Pinch) writes:
>As an elementary equivalent of the Axiom of Choice, how about
>  " The product of non-empty sets is non-empty "

Yep, that's my favorite too.  But I'm biased, I see the whole world as
built up using products (and sums, pushouts, etc.)

Bertrand Russell used to explain choice this way.  Imagine you are
blessed with infinitely many pairs of shoes and socks.  You wish to
choose one of each pair.  With the shoes it is easy:  you could take
all the left ones, or all the right ones.  But can you choose one sock
from each pair?  To claim that you can is to assert the axiom of
choice.

-- 
=================================================== In short, I am floundering
Vaughan Pratt   pratt@cs.Stanford.EDU  415-494-2545 around and don't take what
=================================================== I say seriously.
Newsgroups: sci.math
From: guckes@math.fu-berlin.de (Sven Guckes)
Subject: Re: Mattel says "Math is tough."
Originator: guckes@medusa
Organization: Free University of Berlin, Germany
Date: Mon, 5 Oct 1992 02:16:30 GMT

iltiss@owlnet.rice.edu (Steven Patrick Iltis) writes:

>Mattel has just released a new product. A Barbie doll that says
>"Math is tough".
>
>        This thoughtless attack on mathematics education in general and
>women in particular should not be allowed to happen without a significant
>protest from the mathematics and scientific community.

Let's hear it for math prof puppets who say "Women suck." !

--
Sven@revenge.r.us | Mattel dolls - the end of science is nigh!
Xref: sparky sci.math:12376 sci.math.symbolic:2575
From: huang@deakin.OZ.AU (Weiguang Huang)
Newsgroups: sci.math,sci.math.symbolic
Subject: RE: trouble with symbmath
Date: 29 Sep 1992 11:55:29 +1000
Organization: Deakin University, Victoria, Australia
Distribution: world
NNTP-Posting-Host: sol.deakin.oz.au

From: BF04000 <BF04@UTMARTN.bitnet>
Subject: troubles with symbmath 2.1.1a

I just got a copy of this program for a student to use (I was hoping it
would go well for him and I could use it in teaching calculus) but when
we get in the run window (particularly after a syntax error) the program
seems to lock up and not let us back to the menu bar.  I tried
everything I could think of (F10, alt-f4, ctrl-c, esc,...) nothing
seemed to work.  I could not even find how to leave run even mentioned
in the documentation.  Can you help us?

Chris Caldwell
Math/CS UT Martin
Martin, Tennessee


Subject: Re:  troubles with symbmath 2.1.1a

Did you read the document file SymbMath.DOC and README before running ?
Did you put the end statement at the end of your program ? One of often mistakes
is to omit the end statement.

If you want to
back MSDOS system during running, try the <Break> key or <ctrl><Break> keys.

Please try it again, and let me know if it works.


**********************************************************************
*   Dr. Weiguang HUANG                                               *
*   5/6 Cara Road, Geelong, Vic. 3216, Australia                     *
*   Email: huang@deakin.oz.au,      Phone: 61-52-443282              *
* ------------------------------------------------------------------ *
*   SymbMath - a symbolic calculator with learning                   *
*   PlotData - a plotter with analysing data                         *
**********************************************************************
From: bumby@no.rutgers.edu (Richard Bumby)
Newsgroups: sci.math
Subject: Re: Lebesgue measure in Fractal Dimension
Date: 6 Oct 92 16:39:29 GMT
Distribution: usa
Organization: Rutgers Univ., New Brunswick, N.J.

thompson@atlas.socsci.umn.edu (T. Scott Thompson) writes:

>sassoj@rs6412.ecs.rpi.edu (John J. Sasso Jr.) writes:

>>   In Real Analysis, I learned that the set {x : 0 < x < 1} has Lebesgue 
>>measure 1 for the Lebesgue measure defined in R^1, but is 0 for the Lebesgue
>>measure defined in R^2 ...

> . . .

>>   Now, the Cantor set has Lebesgue measure 0 for the Lebesgue
>>measure defined in spaces R^1, R^2, etc...  However, the Cantor does
>>have a fractal dimension (or Hausdorff dimension) between 0 and 1 (I
>>cannot recall the value), ...

The dimension is (log 2)/(log 3), which expresses the fact that the
classical Cantor set is a union of 2 copies of scalings of itself by a
factor of 1/3.

>Sounds like you are looking for Hausdorff measure.  Look in Patrick
>Billingsley, "Probability and Measure, 2nd Edition," (John Wiley
>Press, 1986).  The idea is as follows (working from rather vague
>memories here):...

>What I don't recall is what sigma-algebra is needed to make this a
>proper measure. ...

See C. A. Rogers, "Hausdorff Measures", Cambridge, 1970 for some of
the measure theoretic details of construction of Hausdorff measures.

On the original question of finding the actual measure of certain sets
in the critical dimension, there is some work by H. Wegmann in Math.
Ann. 193 (1971) that deals with the sets defined by forbidding a digit
in the base-g expansion (generalizing the idea that the classical
Cantor set is obtained by forbidding the digit 1 in the base-3
expansion).  He obtained some results which I found incredibly precise
when I first saw them.  The thing that makes this work so impressive
is that the results are obtained for the measure based on coverings by
all intervals.  The best coverings may not be the "cylinders" of your
favorite Cantor set construction, but there will be come construction
for which the coverings by intervals occurring in the construction
suffice for computing the Hausdorff measure.
-- 
R. T. Bumby **  Rutgers Math ||   Amer. Math. Monthly Problems Editor
bumby@math.rutgers.edu       || P.O. Box 10971 New Brunswick, NJ08906-0971
bumby@dimacs.rutgers.edu     || Phone: [USA] 908 932 0277 * FAX 908 932 5530
From: edgar@function.mps.ohio-state.edu (Gerald Edgar)
Newsgroups: sci.math
Subject: Re: Most important event in the history of mathematics
Date: 29 Sep 1992 10:44:16 -0400
Organization: The Ohio State University, Dept. of Math.
NNTP-Posting-Host: function.mps.ohio-state.edu


The discovery by the Greeks that: (1) simple (obvious) geometric facts
require proof; and (2) it is possible to provide proofs for them.
-- 
  Gerald A. Edgar                Internet:  edgar@mps.ohio-state.edu
  Department of Mathematics      Bitnet:    EDGAR@OHSTPY
  The Ohio State University      telephone: 614-292-0395 (Office)
  Columbus, OH 43210             -292-4975 (Math. Dept.) -292-1479 (Dept. Fax)
Newsgroups: sci.math
From: rjk@world.std.com (robert j kolker)
Subject: A Problem to Amuse You
Summary: A Problem to Aumuse you
Keywords: Mathematics,Problem
Organization: The World Public Access UNIX, Brookline, MA
Date: Wed, 30 Sep 1992 14:37:16 GMT

Let D be an enumerable subset of the Euclidean plane. Show that D can be
written as D_x U D_y where D_x intersects all the lines parelell to the x
axis in a finte number of points, and D_y intersects all the lines
parallel to the y axis in a finite number of points.

Enjoy

Conan the Libertarian  rjk@world.std.com
"If you can't love the Constitution, then at least hate the Government"
From: mkrogers@unix.amherst.edu (MICHAEL K ROGERS)
Newsgroups: sci.math
Subject: Re: Trisect an angle???
Date: 5 Oct 92 19:16:19 GMT
Organization: Amherst College
X-Newsreader: TIN [version 1.1 PL6]

Christopher J. Henrich (cjh@tinton.ccur.com) wrote:
: It cannot be done using straightedge and compass, which are the tools
: generally assumed for "geometrical construction."
: 
: _What Is Mathematics_, by Courant & Robbins, explains why. (This is
: a very good book for any high-school teacher of math to have.)
: The bare bones of the story are:
: 1. Use of straightedge and compass allows you to add, subtract,
:    multiply, divide, and take square roots.  Conversely, every
:    ruler & compass construction can be described with these
:    algebraic tools.  Thus ruler and compass amount to being able
:    to solve linear and quadratic equations.
: 
: 2. Trisecting an angle would amount to solving a cubic equation.
: 
: 3. There is just no way to get an exact solution of a cubic
:    equation from asny amount of solving quadratic equations.

An excellent precis.  Note that if we could solve systems of
quadratic equations (via ruler and compass), we could solve
	 y = x^2,
	2x = y^2,
and duplicate the cube.  We could also trisect an angle.  Of
course we can't do this sort of thing with a ruler and compass.
From: pbond@spitws100.sbil.co.uk (Philip Bond)
Newsgroups: sci.math
Subject: Re: "Solvability" in Chess
Date: 30 Sep 92 09:30:56 GMT
Reply-To: pbond@spitws100.sbil.co.uk
Organization: Salomon Brothers, Ltd.

In article 24956@cbnewsl.cb.att.com, ed@cbnewsl.cb.att.com (edward.m.hummel) writes:
>In article <xeno.717471510@pv34ad.vincent.iastate.edu> xeno@iastate.edu (Gary L Snethen) writes:
>>It is not possible for both players to have better than a draw and
>>less than a win....  What one player has, the other does not.  One's
>>loss is the other's win... zero sum game.
>>
>>How do I prove this?  The rules of chess state it quite plainly...
>>If white wins, black loses.  If black loses, white wins.  A draw is
>>considered a perfect 50%/50% game for each (a half-loss, half-win situation).
>
>There is a loop hole:  the rules do not give a value to games that do
>not end.


Ah, but games always end. You must capture a piece within 50 moves ( well 
it used to be fifty, the FIDE rule is now 100 or some such ). Since there 
are a finite number of pieces, the maximal number of moves possible is
finite and a game terminated due to the 100 move rule is declared drawn.


My own opinion as usual ,

PB


Usual disclaimers apply.
From: weemba@sagi.wistar.upenn.edu (Matthew P Wiener)
Newsgroups: sci.math
Subject: Re: consequences of the Axiom of Choice
Date: 2 Oct 92 14:46:33 GMT
Article-I.D.: netnews.91423
Reply-To: weemba@sagi.wistar.upenn.edu (Matthew P Wiener)
Organization: The Wistar Institute of Anatomy and Biology
In-reply-to: brnstnd@nyu.edu (D. J. Bernstein)

In article <26913.Oct200.15.5792@virtualnews.nyu.edu>, brnstnd@nyu (D. J. Bernstein) writes:
>> And I for one, never cared again much
>> about AC assumptions except when it actually matters. 

>All metamathematical issues aside, there is a sound _pedagogical_ reason
>to explicitly identify each use of the axiom of choice.

I certainly don't think you should _not_ mention AC when it's used.  I
just think, a la Gunning's comment, the decision on _whether_ to use AC
or some other assumption is pretty much a stylistic matter.
-- 
-Matthew P Wiener (weemba@sagi.wistar.upenn.edu)
From: jake@skatter.usask.ca
Newsgroups: sci.math
Subject: Bifurcation theory, nuts and bolts.
Date: 1 Oct 92 23:56:43 GMT
Distribution: usa
Organization: University of Saskatchewan

Hello everyone,

I have encountered a differential equation which seems to exhibit a bifurcation
in the solution as a parameter is increased from zero.
What I would like to do is 1) show that this is or is not the case and
2) if so characterize the bifurcation.

The difficulty is that I don't really know how.  I would be grateful if
some kind soul could point me to a "nuts and bolts" reference on how this is
done.  

Thank you very much in advance.

jason breckenridge

jake@skatter.usask.ca

--
Jason C. Breckenridge 				jake@skatter.usask.ca
Newsgroups: sci.math
From: cyeomans@ms.uky.edu (Charles Yeomans)
Subject: Re: Most important event in the history of mathematics
    <1992Sep28.174237.26784@Cookie.secapl.com> 
    <1992Sep28.231245.10867@infodev.cam.ac.uk>
Date: Tue, 29 Sep 1992 16:41:23 GMT
Organization: University Of Kentucky, Dept. of Math Sciences

In article <1992Sep28.231245.10867@infodev.cam.ac.uk> gjm11@cus.cam.ac.uk (G.J. McCaughan) writes:
>In article <1992Sep28.174237.26784@Cookie.secapl.com> frank@Cookie.secapl.com (Frank Adams) writes:
>
>>All right; what was the most important event in the history of mathematics?
>>My vote is in; what do the rest of you think?
>
>I don't have a single event I'd vote for. High contenders:
>
> * Discovery of irrational numbers
> * Discovery of coordinate geometry
> * [not an event as such] Realisation that issues of convergence etc. are
>   harder than they look, leading to rigorisation of analysis
> * Riemann's paper on prime numbers and the zeta-function
> * Discovery of the calculus
> * Cantor's proof that 2^x>x
> * Discovery of the Lebesgue integral and measure
> * Discovery of generating functions
> * Birth of the idea of proof from axioms ("Elements" or soon before)
> * Birth of Gauss (OK, not the sort of event you meant)
>

I pick the appearance of Springer-Verlag in mathematics publishing, based on 
the preponderance of the color yellow on my bookshelves.

Charles Yeomans
cyeomans@ms.uky.edu
yeomans@austin.onu.edu