HDTenEightyP/NetNews huggingface dataset:
From: mantell@phage.cshl.org (Lin Mantell at Cold Spring Harbor Lab)
Newsgroups: sci.math
Subject: Graph Theory Book For Sale
Date: 28 Sep 92 20:07:11 GMT
Organization: Applied Mathematics, SUNY @ Stony Brook, New York

Hello,

I have the following book for sale:

Advances in Graph Theory, ed. by B. Bollobas, North-Holland Publishing, 1978.

It is Vol. 3 in the Annals of Discrete Mathematics.

It lists for $70.25, if you can get it...I believe it is out of print!!!

I will sell for $50  OR  Best Offer (make me an offer)!!!

Reply to:  mantell@ams.sunysb.edu

Abe
Newsgroups: sci.math
From: west@symcom.math.uiuc.edu (Douglas West)
Subject: Re: 1, 2, 4, 8, 13...where have I seen it before?
Organization: University of Illinois at Urbana
Distribution: na
Date: Wed, 30 Sep 1992 03:59:53 GMT

wjh@cbnewsl.cb.att.com (william.j.hery) writes:

>In computing something in combinatorics, a sequence that started
>with 1, 2, 4, 8, 13 (not the expected 16) came up, and I'm sure I've
>seen it before, possibly in some kind of trick problem that is set
>up to make you think the next term is 16. Does anyone recognize something
>simple that starts like this? BTW, my sequence continues with 21, 31, 45(?)


Neal Sloane's Handbook of Integer Sequences has this entry, #416 on p61:
  1,2,4,8,13,21,31,45,60,76,97,119,144,170,198,231,265,300,336,374,
  414,456,502,550,599,649,702,759,819,881,945,1010,1080,1157,1237,1318
  A SELF-GENERATING SEQUENCE.  REF AMM 75 80 68. RLG.
I believe the codes mean that Ron Graham provided the reference to the
American Mathematical Monthly, volume 75, page 80, 1968.
Newsgroups: sci.math
From: frank@Cookie.secapl.com (Frank Adams)
Subject: Re: Compactness in infinite chess ?
Date: Wed, 30 Sep 1992 15:56:28 GMT
Organization: Security APL, Inc.

In article <BvDFs5.7K8@cantua.canterbury.ac.nz> wft@math.canterbury.ac.nz (Bill Taylor) writes:
>If mate can be forced (with certain piece combinations) on an arbitrarily
>large finite board, then it can be forced (with the same pieces) on an
>infinite board.

Clearly not (as noted by others), because the finite board is not locally
identical to the infinite board.  Try it with arbitrarily large toroidal
boards, and you may get a different answer.
Xref: sparky sci.math:12665 rec.puzzles:6601
From: jpm10@cd.amdahl.com (Jim Millar)
Newsgroups: sci.math,rec.puzzles
Subject: Re: EASY NUMBER SEQUENCE PUZZLE...
Date: 2 Oct 92 17:17:59 GMT
Distribution: usa
Organization: Amdahl Corporation, Sunnyvale CA

In article <1992Oct2.151101.12899@cs.yale.edu>,
ferenbaugh-charles@CS.YALE.EDU (Charles Ferenbaugh) writes:
>In article <aet.717945133@munagin> aet@mullian.ee.mu.OZ.AU (bert
>thompson) writes:
>>25
>>1729
>>635318657
>>???
>
>You left out the first term...  There should be a 2 up at the top. 
>
>:-)
You left out the zeroth term... There should be another 2 before yours.
From: pbond@spitws100.sbil.co.uk (Philip Bond)
Newsgroups: sci.math
Subject: Re: "Solvability" in Chess
Date: 28 Sep 92 13:18:10 GMT
Reply-To: pbond@spitws100.sbil.co.uk
Organization: Salomon Brothers, Ltd.

In article 19uao4INN615@gap.caltech.edu, keith@cco.caltech.edu (Keith Allan Schneider) writes:
><RVESTERM@vma.cc.nd.edu> writes:
>
>[stuff deleted]
>B
>>it's an absolutely ridiculous problem beyond our current technology, but there
>>is no reason that the chess tree can't be found, theoretically.
>
>What about simpler games, such as checkers, or othello.  Has anyone "solved"
>these?  A while ago, I heard the a few cases of checkers had been solved,
>and that the game would be completely solved soon.  Of course, I may
>have heard wrong.  Anyone know anything about this?
>
>keith


No, checkers has not been solved.Indeed, the US genius Dr. Marion Tinsley 
just beat the best super-computer checkers program Chinook in the World
Championship. Reversi is not yet solved, but computers play at world-class
level. The games of go-moku and I believe renju as well were solved recently
 : a result announced in the Computer Olympiad in London.
	The 4 by 4 reversi game has been solved for a long time. I am sure that
the 5 by 5 case can't be hard with existing technology.
	As for chess or Go, forget it with existing computers. Furthermore,
don't forget that it is quite easy to increase the board size. The increase
in complexity will be barely noticeable on the best humans, but will reduce
the ply-search of a machine quite substantially ( depending on the particular
game in question ).

IMHO of course,

Phil B.   

Usual disclaimers of course.
From: bennett@math.ksu.edu (Andy Bennett)
Newsgroups: sci.math
Subject: Re: Most important event in the history of mat
Date: 2 Oct 1992 12:45:30 -0500
Organization: Dept. of Mathematics, Kansas State University
NNTP-Posting-Host: hilbert.math.ksu.edu

pbond@spitws100.sbil.co.uk (Philip Bond) writes:
>My vote is split : The first event was the development of the decimal 
>system. Previous cultures ( Greek, Roman etc. ) failed to develop beyond
>geometry mainly due to a lack of this system. With the invention of 
>decimal representation mankind really took a giant leap forward. Of 
>course it took time to develop but I think ( my opinion only ) that the
>Arab mathematicians should be given credit for bringing the system to 
>fruition.

One problem with this "event." Positional value systems actually evolved
earlier than the Greeks and were even known and used by greek scientists
of the hellenistic period.  

The babylonians used a positional number system on a base of 60. They 
inherited the system from the sumerians but they then developed a nice
theory of algebra using it. The system did include both integer and 
non-integer values (i.e. 1/2 was written as .(30) representing 30/60)
See "The Exact Sciences in Antiquity" by Neugebauer. Greek scientists
were aware of the system at least after Alexander's conquest of Persia
if not before and used the babylonian cuneiform for computations in their
"scientific" work, for example in Ptolemy's Almageist. The influence on
astronomy survives in our modern division of degrees into 60 minutes and
minutes into 60 seconds, along with the corresponding divisions of time.
The system was not used in "mathematical" work for philosophic reasons,
even though greek "scientists" and "mathematicians" were usually one and
the same people. This displays the two-edged nature of the Greek philosophy
of mathematics depending on proof. While it let the Greeks raise mathematics
from a set of tricks to an understood system of knowledge, it hindered them
from adopting elements outside the tradition that would be useful. You may
draw your own lessons for modern mathematics from this.

-- 
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: b102smi@utarlg.uta.edu (George M. Smiley)
Newsgroups: sci.math
Subject: Large Integers on Computers
Date: 29 Sep 92 21:14:00 GMT
Article-I.D.: utarlg.29SEP199216143099
Organization: The University of Texas at Arlington
News-Software: VAX/VMS VNEWS 1.41

When various computers spit out insanely large prime numbers, how are
these numbers represented ? 

I ask because I am currently investigating solving Linear Programming
programs using exact arithmetic. Theory shows the that the size of these
fractions are bounded from above, so I do not need the capicty to work
with arbitrarily large integers, but, I do need to work with integers
larger than what is available by programming languages. An early 
solution was to represent the integers as character strings, but, that
method has proven relatively slow for large (interesting) problems.
So, does, anyone have any suggestions to my problem ?

Thanks,

George 
b102smi@utarlg.uta.edu
Newsgroups: sci.math
From: holmes@opal.idbsu.edu (Randall Holmes)
Subject: Re: Mattel says "Math is tough."
Organization: Boise State University
Date: Tue, 6 Oct 1992 16:14:59 GMT

In article <1992Oct5.144142.2182@alchemy.chem.utoronto.ca> mroussel@alchemy.chem.utoronto.ca (Marc Roussel) writes:
>In article <1992Oct5.084002.25808@nuscc.nus.sg> matmcinn@nuscc.nus.sg
>(Mcinnes B T (Dr)) writes:
>>iltiss@owlnet.rice.edu (Steven Patrick Iltis) writes:
>>:         Mattel has just released a new product. A Barbie doll that says
>>: "Math is tough".
>>
>>What would you have her say?: 
>
>     How about "I like math" or "I want to be an engineering physicist"?
>Women get too many negative messages about their chances of succeeding in
>technical careers.  This sort of product is dangerously stupid.  It would
>have been better for the doll not to mention math than for it to say that
>math is hard.
>     Every year in my physical chemistry class, I find bright women who
>are terrified of math.  (This is far more common than male mathphobes.)
>Since their performance in this course (and indeed their past
>performance in calculus and physics) indicates that they can use
>mathematically phrased ideas if simultaneously pushed and properly
>tutored, why are they so afraid?  The only conclusion I can come to is
>that they have been brainwashed into thinking that they couldn't handle
>it.  "Math is hard" is a message that women hear far too often.  Math is
>not hard.  It is our job as educators to help them see that; it is our
>responsibility as educated persons to see to it that Mattel withdraws
>this ill-considered product from the market.  I'm sure that Mattel didn't
>do this on purpose; ignorance is potentially just as damaging as malice.
>
>				Marc R. Roussel
>                                mroussel@alchemy.chem.utoronto.ca

1.  Math is hard (not just for girls).

2.  Everyone (not just girls) is getting incorrect messages about how
much math they need to know, just how hard it is, and just how much
they need to know it anyway.

My wife (who is a chemist) recently talked to a girl starting high
school who wanted to know how much high school science she should
take.  My wife started to say the obvious (take all of it), but
realized that there was a better answer: it didn't matter all that
much whether the young woman took _any_ science, but she had to
realize that she _must_ take 4 years of _math_ and 4 years of
_English_ (or more).  With a good math background, she would do all
right in science in college.  Without the English, she'd be lost in
any field.

I find that one major problem with even good math students is that
they cannot express themselves in their native tongue (thus the
English!).

All this aside, I think that the Barbie doll saying "Math is hard" is
a revolting product, because its discouraging effect is directed at
girls specifically.  But the correct message is not "Math is easy"
(false) or "Math is fun" (it is, but it takes a while to see that),
-- 
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: jbaez@riesz.mit.edu (John C. Baez)
Newsgroups: sci.math
Subject: Re: various number systems
Date: 29 Sep 92 18:02:05 GMT
Organization: MIT Department of Mathematics, Cambridge, MA

In article <1992Sep29.110825.5382@mnemosyne.cs.du.edu> lmitchel@nyx.cs.du.edu (lloyd mitchell) writes:
>I am currently teaching a pre-calculus course at a local community college.
>We have just covered the quadratic formula, which has served as an intro-
>duction to complex numbers.  Now, I would like to expose my students to
>other numbering systems.  My goal is not to teach them the ins and outs of
>the systems, but to expose them to other ways of thinking about numbers.
>
>I'm aware of quaternions and perplex numbers.  Are there other number
>systems out there about which I should tell them?
>
>Thanks,
>Kerry Mitchell

Rather than drowning them in weird number systems, you should consider
spending a little time on what quaternions are good for, so they see
that these other number systems can be practical.  Hopefully you
have already explained how the complex numbers have a lot to do
with rotations and dilations of the plane:  multiplying by a real number
expands or contracts the complex plane, multiplying by i rotates
90 degrees, and so on.  I like to think that the point of the complex
numbers is to solve the unsolvable equation x^2 = -1 by busting out
of the real line: in the plane, rotating 90 degrees twice is equivalent
to multiplying by -1 (reflection through the origin).  This makes it
natural to wonder what one can do in 3 dimensions.  Then answer is, the
quaternions!  Of course lots has been written about this, probably
more than your students will want to learn just yet, but I highly
recommend the section "Quaternions, Cayley Numbers and the Belt Trick"
in Louis Kauffman's book Knots and Physics.  Check out p. 441 ff,
in particular.  Using a little cardboard disc with a smile painted
on one side, a frown on the other, hung from a stick by two strings:

---------------------------
          |   |
          |   |
           o o
            |
           \_/

one can easily demonstrate the relationship between the quaternions
and relations.  Let i, j, and k be rotations of the face by 180 degrees in 
the x, y, and z axes.  If you do i^2, for example, your little fellow
is smiley-face in front againg but the strings have a 360 degree tangle
in them.  This counts as -1.  Why?  Well, if you do i^4 (i.e., -1
squared) you get a 720 degree tangle in your strings but this can be
undone!  It is easy to check that all the quaternion relations hold
using this model.  Moreover, it's not just a cute trick, but has a
lot of importance in quantum mechanics, gruop theory, topology etc. -
though you needn't tell 'em that!

He also gives a friendly first intro to the Cayley numbers, aka
octonions or "octaves".

By the way, I repeat my challenge for someone to find where the
word "quaternion" appears in the bible (King James ed.)!
From: mkrogers@unix.amherst.edu (MICHAEL K ROGERS)
Newsgroups: sci.math
Subject: Re: various number systems
Date: 30 Sep 92 17:31:36 GMT
Organization: Amherst College
X-Newsreader: TIN [version 1.1 PL6]

lewis.h.mammel..jr (lew@cbnewsd.cb.att.com) wrote:
: In article <1992Sep29.180205.26078@galois.mit.edu>, jbaez@riesz.mit.edu (John C. Baez) writes:
: > By the way, I repeat my challenge for someone to find where the
: > word "quaternion" appears in the bible (King James ed.)!
: 
: I found it but I cheated. "quaternion" is in Oxford's Bible Concordance
                      = research.
: ( title approximate. )  It's interesting that the reference is to
: "four quaternion's" even though quaternion already means "a tetrad."

Perhaps they mean a total of 16 in groups of 4:
                                   xx
	x   x   x   x              xx
	x   x   x   x    or     xx    xx   or   ??
	x   x   x   x           xx    xx
	x   x   x   x              xx   
	                           xx
I looked up the original greek once, and I vaguely recall it reading
as four tetrads.
Newsgroups: sci.math
From: crb7q@kelvin.seas.Virginia.EDU (Cameron Randale Bass)
Subject: Re: Mattel says "Math is tough."
Organization: University of Virginia
Date: Tue, 6 Oct 1992 14:08:42 GMT

In article <MARTIN.92Oct6075816@lyra.cis.umassd.edu> martin@lyra.cis.umassd.edu (Gary Martin) writes:
>In article <1992Oct5.212115.3356@bnlux1.bnl.gov> kyee@bnlux1.bnl.gov (kenton yee) writes:
>
>     Why do you assume women will be turned off by math simply
>    because it is tough?   I know lots of people who like math
>     BECAUSE it is tough.  
>
>But how many of these people are women?  I keep hearing the theory that
>women aren't as likely to be attracted by the difficulty of a problem
>because (for whatever reason) they are usually less competitive than
>men.  Unfortunately, it seems that today's generation of students of
>both genders are not as turned on by the challenge of a difficult problem
>as they should be.

     Why does it 'seem' this way?  Are y'all having a difficult time
     filling mathematics faculty positions?

                               dale bass

-- 
C. R. Bass                                           crb7q@virginia.edu
Department of Mechanical and Aerospace Engineering
University of Virginia
Charlottesville, Virginia                            (804) 924-7926
From: fritz@gems.vcu.edu (J. Fritz)
Newsgroups: sci.math
Subject: Re: Topos theory for mere mortals (?)
Date: 27 Sep 92 12:11:29 -0400
Organization: Virginia Commonwealth University

In article <10698.Sep2606.43.4292@virtualnews.nyu.edu>,
  brnstnd@nyu.edu (D. J. Bernstein) writes:
> In article <1992Sep25.130656.5083@dcs.qmw.ac.uk> arodgers@dcs.qmw.ac.uk
>  (Angus H Rodgers) writes:
>> One of the faults of the standard development of mathematics in ZF,
>> to my mind, is its lack of a convincing definition of individual
>> real numbers such as pi;
> 
> Hmmm? What do you mean by ``lack''? pi is the minimum positive real
> number such that exp(i pi) = -1. Here exp(z) = \sum z^n/n!. The proofs
> behind these statements are quite straightforward. How is pi any less
> convincingly defined than, say, 7?

The point is that these statements, if translated into bare ZF, would
look quite different.  Indeed, even 7 is not particularly convincing:

{{},{{}},{{},{{}}},{{},{{}},{{},{{}}}},{{},{{}},{{},{{}}},{{},{{}},
{{},{{}}}}},{{},{{}},{{},{{}}},{{},{{}},{{},{{}}}},{{},{{}},{{},{{}}},
{{},{{}},{{},{{}}}}}},{{},{{}},{{},{{}}},{{},{{}},{{},{{}}}},{{},{{}},
{{},{{}}},{{},{{}},{{},{{}}}}},{{},{{}},{{},{{}}},{{},{{}},{{},{{}}}},
{{},{{}},{{},{{}}},{{},{{}},{{},{{}}}}}}}}

(Here {} stands for the empty set.  I _think_ the above expression
stands for 7, that is for the set {0,1,2,3,4,5,6}, but I won't swear to
it. :-)

> 
> ---Dan
Newsgroups: sci.math
From: tim@gold.iss.nus.sg (tim poston)
Subject: Crumpling bifurcations?
Originator: tim@gold
Organization: Institute of Systems Science, NUS, Singapore
Date: Tue, 6 Oct 1992 02:54:05 GMT

Buckling happens all over a beam or plate
(in sine shapes for the simplest cases),
but how does a rug crumple?

With a bit of compressibility the flat-on-the-floor state
must clearly still exist as an equilibrium when sideways compression
increases, but you get wrinkles, held local by gravity;
the rug does not form an arch.  (Relation with solitons?)
As a bifurcation problem, sneakily degenerate;
the wrinkle can form `where it likes',
so there's no one-dimensional linearization eigenspace
to which the interesting stuff lies tangent.
(Is there an eigenspace at all,
or are we meeting the continuous spectrum?)

Can anyone tell me of modelling work
(analysis or numerical)
on this kind of thing?
In any dimension?

My final concern is with the surface of the brain,
which starts smooth and crumples itself
against the inside of the skull
(with results that vary a  l o t  from brain to brain).
But any crumpling info,
or pointers to the literature,
would be very welcome.

I'll watch here for responses,
but would also appreciate e-mail.
If I get a lot, I'll summarize here.

Tim Poston




________________________________________________________________________________
"And some there were among the serpents that could not multiply as the Lord bid,
 for they were not but adders; wherefore did Noah bid Ham, Shem and Japheth to
 cut down a many trees, that they might multiply by the use of logs."
						Apocryphon of Nasrudin
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
Newsgroups: sci.math,sci.physics
From: bhv@areaplg2.corp.mot.com (Bronis Vidugiris)
Subject: Re: Another Cute Math Joke  (explanation of)
Organization: Motorola, CCR&D, CORP, Schaumburg, IL
Date: Thu, 1 Oct 1992 23:38:11 GMT

In article <marc.717947769@vieta.math.uni-sb.de> marc@vieta.math.uni-sb.de (Marc Conrad) writes:
)dms@krang.vis.citri.edu.au (David Mcgregor SQUIRE) writes:
)
)>Q: What do you get if you cross an elephant with a grape?
)
)>A: |elephant||grape|sin(theta)
)I'm stupid, but can someone explain this to me ??
)Marc

Hmm.  Well, the reason it's funny is that the joke implies you are
taking a CROSS product of an elephant and a grape, but the math shows
a DOT product of an elephant and a grape!

(if A and B are vectors, |A| * |B| * sin(theta) is one expression for the
dot product || -> absolute value, theta is the angle between the vectors).

That's pretty funny :-) :-) :-)

Newsgroups: sci.math
From: mkrogers@unix.amherst.edu (MICHAEL K ROGERS)
Subject: Re: Beauty of MATHEMATICS: A QUESTION
Organization: Amherst College
X-Newsreader: TIN [version 1.1 PL6]
Date: Mon, 28 Sep 1992 21:42:13 GMT

You might read G. H. Hardy's "A Mathematician's Apology."
Also there is an article in "Mathematics Today" (L. A. Steen, ed.)
which has interviews with three (I think) mathematicians.
Newsgroups: sci.math
From: brock@NeXTwork.Rose-Hulman.Edu (Bradley W. Brock)
Subject: Re: consequences of the Axiom of Choice
Organization: Rose-Hulman Institute of Technology
Date: Wed, 30 Sep 1992 18:31:33 GMT

Distribution: usa

In article <91012@netnews.upenn.edu> atteson@grip.cis.upenn.edu (Kevin Atteson)  
writes:
> 
> Does anyone know of any elementary results which are
> dependent upon the axiom of choice?  By elementary
> results, I mean something from elementary calculus, etc.
> 
Do these count as elementary?
1) There exists non-Lebesque measurable sets.
2) Every field has an algebraic closure.
2) Every field extension has a transcendence base.
3) (and since we have been discussing topos theory) Flasque sheaves have no  
cohomology.

--
Bradley W. Brock, Department of Mathematics
Rose-Hulman Institute of Technology  | "Honor one another above yourselves."
brock@nextwork.rose-hulman.edu       | -Paul of Tarsus to the Romans
Newsgroups: sci.math
From: holmes@opal.idbsu.edu (Randall Holmes)
Subject: Re: consequences of the Axiom of Choice
Organization: Boise State University
Date: Tue, 6 Oct 1992 21:48:24 GMT

In article <91826@netnews.upenn.edu> weemba@sagi.wistar.upenn.edu (Matthew P Wiener) writes:
>In article <1992Oct5.192243.17318@guinness.idbsu.edu>, holmes@opal (Randall Holmes) writes:
>>Solovay showed that there is a model of ZF + DC (dependent choices) in
>>which all sets of reals are Lebesgue measurable.  This requires
>>existence of an inaccessible (and I believe that this consistency
>>strength is unavoidable).  DC is enough for classical measure theory.
>
>I agree with this, although one should be careful about what "classical
>measure theory" covers.  In the sense used here, it obviously does not
>include pathological sets.  General L^p space theory sometimes invokes
>the Hahn-Banach theorem.  And general infinite products certainly need
>the Prime Ideal theorem, as does compactness of the infinite [0,1] cube.
>-- 
>-Matthew P Wiener (weemba@sagi.wistar.upenn.edu)

And, alas, the prime ideal theorem is false in Solovay's model (it
implies the existence of non-measurable sets).


-- 
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
Newsgroups: sci.math
Subject: E-mail addresses
From: <ROCHC@CUNYVM.BITNET>
Date: Tuesday, 6 Oct 1992 01:42:55 EDT
Organization: City University of New York/ University Computer Center

     Does anyone have a list of e-mail addresses for american universities
with a doctoral program in mathematics?  I would greatly appreciate it
if someone could provide me with this information.

                                               -- Ron --
Newsgroups: sci.math