HDTenEightyP/NetNews huggingface dataset:
From: pete@bignode.equinox.gen.nz (Pete Moore)
Subject: Re: Finding best mate
Newsgroups: sci.math
Organization: Equinox Networks
Reply-To: pete@bignode.equinox.gen.nz
X-Newsreader: TIN [version 1.1 PL8]
Date: 5 Jan 93 20:05:52 +1200
Organization: Equinox Networks

Jesse Goldman (your-email-addr@a1.mscf.upenn.edu) wrote:
>Dear Mathematicians;

>     This weekend I saw an interview on T.V. with a mathematician who
>stated that if a woman assumes she is to have 100 suitors in her life then
>her best chances of finding an ideal mate would be to reject the first 37
>and then choose the next one better than the preceeding 37.

I've seen this referred to as the `secretary problem' - you interview 100
candidates for a job as your secretary, and must decide at the end of each
interview whether or not to hire the current candidate. If you decide no,
the candidate leaves and can't be recalled, if yes, the interviews stop
and any remaining candidates are sent away. The best strategy is to
interview 37% (or 1/e more precisely) and send them away, then continue
with the remaining candidates and select the first one who is better than
all his/her predecessors. Of course, if the best candidate was actually in
that first 37%, you are stuck with the last candidate!

A couple of years ago I attended a lecture in which Paul Halmos presented
a version of this problem as follows:

  I have a box containing 100 slips of paper. On each slip is a positive
  number (not necessarily an integer or even a rational). You may draw
  slips of paper one at a time and read the numbers thereon. At any point,
  you can stop and bet that you have just drawn the largest number in the
  box. I will give you 4 to 1 odds. Will you play?

The lecture room (containing about a dozen professional mathematicians and
an equal number of students) was completely silent - no-one was willing to
accept Prof Halmos' offer!
In fact, the simple stategy of examining & discarding the first 50, then
betting on the first number thereafter which is bigger than all its
predecessors, gives you a chance better than 1 in 4, since you will win if
the 2nd-biggest number is in the first 50 (50% chance) and the biggest is
in the 2nd 50 (50% chance) & there are other ways you can win also (e.g. if
the 2 biggest numbers are both in the 2nd 50, provided that the biggest
appears before the 2nd-biggest).

The best strategy is again to examine and discard 1/e of the numbers and
then bet on the first number (if any) which exceeds all its predecessors.
You should play if you are offered any odds better than e to 1. Proving
this is left as an exercise for the reader  8-)
--
 +-------------------  pete@bignode.equinox.gen.nz  -------------------+
 | The effort to understand the universe is one of the very few things |
 | that lifts human life above the level of farce, and gives it some   |  
 | of the grace of tragedy   -  Steven Weinberg                        |
 +---------------------------------------------------------------------+
Newsgroups: sci.math
From: mcherm@msc.cornell.edu (Michael Chermside)
Subject: Re: Let's add some sci.math.* groups
Organization: Cornell-Materials-Science-Center
Date: Tue, 12 Jan 1993 17:03:31 GMT

Newsgroups: sci.math
Subject: Re: Let's add some sci.math.* groups
Summary: 
Expires: 
Followup-To: 
Distribution: 
Organization: Cornell-Materials-Science-Center
Keywords: 


I'd just like to add that, although I would really enjoy reading
sci.math, I don't normally, because there the volume is too great and
I don't have time.  So a split that decreased the traffic would gain
you at least this ONE reader.  (BTW: this is the first time I've
actually looked in sci.math in 3-5 weeks, and that's about average.
Unfortunately, that's not enough to allow an estimate of the number of
other non-readers like me who would read it if there were lower
traffic.)  Oh, and I have my own fields of preference, but I like the
eclecticness -- if split, I would read the other sci.math.* groups
(besides my favorites) on an infrequent basis just to keep in touch
with a wider world.
-- 
                                            --- Michael
Newsgroups: sci.math
From: shibin@uxmail.ust.hk (Mr. Xiao Shi Bin)
Subject: Looking for Wen Guoqing
Organization: Hong Kong University of Science and Technology
Date: Tue, 5 Jan 1993 08:26:24 GMT

Hi everyone,

I intend to look for a friend of mine. 

His name is Wen Guoqing, coming from Beijing Information Technology
Institute, PRC. I only know that He is studying in a Univ. of USA.
 
If you know he, please ask he to contact me.
Thanks.

My name is Xiao Shibin, also coming from Beijing Information Technology
Institute, PRC. I am working at Hong Kong University of Science and
Technology as Visiting Scholar.

My e_mail address: shibin@uxmail.ust.hk
From: goddard@NeXTwork.Rose-Hulman.Edu (Bart E. Goddard)
Newsgroups: sci.math
Subject: Re: Frankly,my dear......was: Fermat's Last Theorem
Date: 7 Jan 1993 18:33:33 GMT
Organization: Computer Science Department at Rose-Hulman
Distribution: usa
Reply-To: goddard@NeXTwork.Rose-Hulman.Edu (Bart E. Goddard)
NNTP-Posting-Host: g214-1.nextwork.rose-hulman.edu

In article <1993Jan7.021308.10566@nuscc.nus.sg> matmcinn@nuscc.nus.sg (.)  
writes:
> I wonder if this might not be an occasion for some soul- searching on the
> part of professional mathematicians. X^n+ y^n = Z^n has no solutions....  
> frankly, who cares? 

Actually, you have it backwards.  Fermat and friends were usually thinking of a  
broader field (proto-algebraic geometry or some such) and posed key examples of  
the difficulty of theory in order to drum up interest.  They didn't just go  
around trying random problems to see which ones were hard or easy.

--
Bart Goddard   
Math. Dept. Rose-Hulman Inst. of Tech.
goddard@nextwork.rose-hulman.edu
Newsgroups: sci.math
Subject: Re: Rounding Rules
From: a_rubin@dsg4.dse.beckman.com (Arthur Rubin)
Date: 4 Jan 93 22:11:57 GMT
Organization: Beckman Instruments, Inc.

In <1993Jan4.142226.9639@iscsvax.uni.edu> kraai4712@iscsvax.uni.edu writes:

>In article <1992Dec23.140148.21009@hubcap.clemson.edu>, steve@hubcap.clemson.edu ("Steve" Stevenson) writes:
>> In article <1992Dec20.003018.14325@sol.ctr.columbia.edu> shaw@toadflax.UCDavis.EDU (Rob Shaw) writes:
>>>What is the rationale behind the following rounding rule?
>>>
>>>when dealing with 5's followed by all zero's, check the
>>>next digit to the left. If it's even, round down; odd,
>>>round up.
>>>
>>>For example both 1.13500 and 1.14500 are 1.14 to 3 places.
>>>What is the advantage of having the interval closed at both
>>>ends around even digits, and open at both ends around odds?
>>>
>> 
>> The problem with many of the "rounding rules" is that they are biased.
>> In the IEEE round of rules, an attempt is made to make rounding as unbiased
>> as possible. Round to even is specified as the rule of choice, since it
>> avoids many of the problems of "round to infinity" or "round towards zero".

>My personal favorite rounding rule is to round anything that has {0,1,2,3,4} in
>the "rounding place" "down" and anything that has {5,6,7,8,9} "up".  So as in
>the previous example, 1.13500 would be rounded to 1.14 and 1.14500 would be
>rounded to 1.15.

>To this my teachers always gasped that this method was biased, and no amount of
>pursuasion using the above-mentioned sets could pursuade them.

Well, it IS biased.  Rounding n places is biased by +1/2 10^-n.

--
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.
Newsgroups: sci.math
From: roth@3d.enet.dec.com (Jim Roth)
Subject: Re: math dictionary
Organization: Digital Equipment Corporation
Date:  8 JAN 93 18:53:02    


In article <C0JMw6.6G9@dcs.glasgow.ac.uk>, jack@dcs.glasgow.ac.uk (Jack Campin) writes...
>glenne@csd4.csd.uwm.edu (Neuromancer ) wrote:

>Not quite "for idiots", but at only a slightly higher level than the Penguin,
>about the same size, and vastly better in its explanations: the French
>"Dictionnaire des mathematiques modernes" (published by Larousse, I think).
>There's no English translation that I know of, but the French is not overly
>complicated.

Is this still in print?  I ask since many years ago I read some French
research papers and wanted to find a French language math dictionary
to help with that.  The title you mention sounds like exactly the
one that Ned Anderson recommended to me, though I think the publisher
was Hermann.  At the time, I was told it was out of print...

- Jim
From: hoey@zogwarg.etl.army.mil (Dan Hoey)
Newsgroups: sci.math
Subject: Re: Lunde's problem (least number with n divisors)
Keywords: unique factors
Date: 4 Jan 93 16:49:23 GMT
Organization: Naval Research Laboratory, Washington, DC

shallit@graceland.uwaterloo.ca (Jeffrey Shallit) writes:

>Basically, you're looking for the smallest integer M with n positive
>*divisors* (although most mathematicians would include 1 and M in the
>enumeration).

>Beiler also sketches an algorithm that will find such numbers.  To
>the best of my knowledge, it is not known how to produce the prime
>factorization of the solution in polynomial time (in log n, of
>course).

If it were, we would have a polynomial-time factoring algorithm, since
one plus the exponent of 2 is a factor of n, and a proper factor if n
is composite.

If the prime factorization of n were given as input, would there then
be a polynomial-time algorithm for this function?

Dan
Newsgroups: sci.math
From: jbaez@riesz.mit.edu (John C. Baez)
Subject: Re: spell this?
Organization: MIT Department of Mathematics, Cambridge, MA
Date: Tue, 12 Jan 93 21:43:45 GMT

In article <1993Jan12.070026.18380@CSD-NewsHost.Stanford.EDU> pratt@Sunburn.Stanford.EDU (Vaughan R. Pratt) writes:

>On the other hand both F&W and Webster gave "impotence" as the primary
>usage and "impotency" as a secondary equivalent.  But so as to be truly
>democratic in such matters they both reversed this for "potence" vs.
>"potency", preferring the latter.

>As for me I'm going to stick to "idempotence" and "nilpotence," which
>somehow sound nicer to my ear.

I suppose that an "impotent" operator is one equal to the identity,
since the identity doesn't do anything.  It'd be nice if there was some
wider class of operators that deserved to be called impotent.


Newsgroups: sci.math
From: muelleru@Mathematik.TU-Chemnitz.DE (Ulrich Mueller)
Subject: Re: proof wanted 2
Organization: University of Technology Chemnitz, FRG
Date: Mon, 11 Jan 1993 14:23:28 GMT

In article <1iorntINNoal@skeena.ucs.ubc.ca> liuli@unixg.ubc.ca (Li Liu) writes:

>The claim that there is a closest point in C (a close set) to a point
>x (a point outside C) is not true for general metric spaces.

>A simple example is to take the metric space to be { 1/n | n is positive
>integers }, under the usual metric d(a,b)= |a-b|. Let C be the space 
>itself. C is closed. Let x be 0. There is no point in C that is closet to
>zero.

No, I think that example isn't true.
Because 0 isn't a point of your metric space. If it was one, so {1/n} 
was not closed.

I think, in every closed non-empty subset C of a metric space M there is a 
point with the minimal distance to a point x from M-C.
Prove I just sent.
From: hdev@dutiai.tudelft.nl (Hans de Vreught)
Newsgroups: sci.math
Subject: Re: High Prices of Math Books. I am pissed.
Date: 6 Jan 93 09:42:16 GMT
Organization: Delft University of Technology

goddard@NeXTwork.Rose-Hulman.Edu (Bart E. Goddard) writes:

>In articles <> several well-meaning but misguided souls write:

>>Have they suddenly lost the ability to use the libraries?

>Just how many copies of a text book do you suppose a library carries?

None, all the interesting books are in my room. I'm not intending to bring
them back before my contract ends. The other interesting books are in the
rooms of my colleagues. But more serious, most of the interesting books are
never there, because they are lent out.

>> The idea that some are going without food is ridiculous.

>No it isn't.  I can't imagine a time in my future when I will cease to be 
>bitter about the ignorant comments made by middle-class frat boys who've
>had everything handed to them on a silver-plated platter.

I've worked before I went to the university so I had money during my studies.
I've spent almost every nickle during my studies (on my graduation day my
total possessions were less than $5). I knew at forehand, if the money ran out
I had to stop. Going out of food is a bit ridiculous, but having to stop your
studies because you're out of money isn't. Being critical on where to spent
your money on isn't a bad attitude.
--
Hans de Vreught                          | John von Neumann:
hdev@dutiba.twi.tudelft.nl               | Young man, in mathematics
Delft University of Technology (TWI-ThI) | you don't understand things,
The Netherlands                          | you just get used to them.
Newsgroups: sci.math,alt.flame
From: matmcinn@nuscc.nus.sg (brett mcinnes)
Subject: Re: Frankly,my dear......was: Fermat's Last Theorem
Organization: National University of Singapore
X-Newsreader: Tin 1.1 PL4
Distribution: usa
Date: Fri, 8 Jan 1993 02:32:02 GMT

gjm11@cus.cam.ac.uk (G.J. McCaughan) writes:
: In article <1993Jan7.021308.10566@nuscc.nus.sg> matmcinn@nuscc.nus.sg (.)
: complains that Fermat's Last Theorem is boring, on the grounds that it's
: recreational mathematics, and claims that people are only interested in it
: because it's hard.
: 
: A few comments: 
: 
:  * It's pretty. If the only reason for being interested in any mathematical
:    result is because it helps you prove other mathematical results, there's
:    a bit of an infinite regress there. In my opinion, one of the main reasons
:    for doing mathematics at all is its aesthetic appeal; and FLT *does* have
:    aesthetic appeal.
I disagree. :)  My point is that if the proof were easy, nobody would have
heard of this result or care about it.: 
:  * It does connect with the rest of mathematics, anyway. Not just the algebraic
:    geometry you say you've heard all the propaganda for, but other areas of
:    number theory, to do with modular forms and the like.
: I did not say that I had heard propaganda for algebraic geometry, only
for FLT. Algebraic geometry does not need propaganda; it really is
significant.
:  * "frankly, who cares? It's recreational mathematics, right?" Does the fact
:    that something is "recreational" -- that people other than professional
:    mathematicians are interested in it, in other words -- make it boring?
: Usually. Look at this newsgroup. 
:  * Work on FLT was one of the big motivators for the theory of ideals. I don't
:    call that trivial, boring, or even "recreational".
: Neither did I. Only FLT itself.
: --
From: goddard@NeXTwork.Rose-Hulman.Edu (Bart E. Goddard)
Newsgroups: sci.math
Subject: Re: Let's add some sci.math.* groups
Date: 8 Jan 1993 16:31:14 GMT
Organization: Computer Science Department at Rose-Hulman
Reply-To: goddard@NeXTwork.Rose-Hulman.Edu (Bart E. Goddard)
NNTP-Posting-Host: g214-1.nextwork.rose-hulman.edu

Well, most of the worthless posts we have to wade through are ones like this,  
that is, completely mathless.  I would recommend the following split:
sci.math.math
sci.math.chat

(A program could be written to automatically post inflammatory remarks and
stupid questions to sci.math.chat, to help keep it going :-)
--
Bart Goddard   
Math. Dept. Rose-Hulman Inst. of Tech.
goddard@nextwork.rose-hulman.edu
Newsgroups: sci.math
From: regeorge@magnus.acs.ohio-state.edu (Robert E George)
Subject: Re: High Prices of Math Books. I am pissed.
Organization: The Ohio State University
Date: Thu, 7 Jan 1993 00:21:09 GMT

In article <1993Jan6.221352.18657@infodev.cam.ac.uk> gjm11@cus.cam.ac.uk (G.J.
McCaughan) writes:
[deletions to save space]
[discussion of "electronic publishing" bypassing publishers]
>
>All very well, except that no book publisher is going to be happy about
>an author entering into such an agreement, and they'll probably refuse
>to publish books on which the author retains that right. And the scheme
>you describe probably won't make so much money for the author as the
>"usual" way of selling books, what with copying being so much easier;
>writing a book is a heck of a lot of effort, and most authors will want
>more in return than just the satisfaction of a job well done.
>
[deletions to save space]
     Can somebody give me some idea of what amounts of money we
are discussing?

     I have been told by the author of a couple widely-used statistics
texts ("widely-used" at the graduate level, which means something much
different than a "widely-used" freshman calc book) that the amount of
royalties an author receives is very small: so *very few* people buy
such  a book, his royalties ran only about $300 per year.  He said
that one wrote a book mainly because one felt the discipline needed it;
and that writing a textbook was not particularly helpful toward tenure.
Both his books seem to have begun as class notes.

     A lot of work, yes. A big cash reward -- No.

Robert George
(speaking only for myself)
Xref: sparky sci.math:17934 sci.logic:2562
From: ara@zurich.ai.mit.edu (Allan Adler)
Newsgroups: sci.math,sci.logic
Subject: Product of sites
Date: 10 Jan 93 17:55:54 GMT
Distribution: sci
Organization: M.I.T. Artificial Intelligence Lab.


Does the category of sites have products and if so how does one construct them?

It follows from material I found in Johnstone's book Topos Theory
that the category of Grothendieck toposes has products but I don't know
if the same is true for sites in general.

Allan Adler
ara@altdorf.ai.mit.edu
Newsgroups: sci.math
From: kellmeye@ux1.cso.uiuc.edu (kellmeyer steven l)
Subject: Re: Lifestyle Choices and Secular Reasoning 
Organization: University of Illinois at Urbana
Date: Tue, 5 Jan 1993 05:36:45 GMT

shallit@graceland.uwaterloo.ca (Jeffrey Shallit) writes:

>In article <C0Az1r.CGu@ux1.cso.uiuc.edu> kellmeye@ux1.cso.uiuc.edu (kellmeyer steven l) writes:
>>
>>Pardon.  Perhaps you are unaware of Godel's work.  He demonstrates that
>>there can be *NO*, nada, zero, zilch, empirical evidence and/or line of
>>theoretical reasoning which can show _a_priori_ that a logical system is
>>valid.

>A little knowledge is a dangerous thing.  This is not what Goedel proved.

>Goedel's incompleteness theorem proved that any *sufficiently powerful*
>formal system cannot be proved consistent *within that system*.

>There are many results that have proved the consistency of various
>formal systems.  For example, Gentzen's proof of the consistency of 
>"pure number theory", and its generalizations by Takeuti.  Presburger
>proved the consistency of a theory involving only addition of numbers.
>Reference:  Encyclopedic Dictionary of Mathematics, 2nd edition.

>There must be more popular misapplications of Goedel's theorem than almost
>any other theorem in mathematics.

p. 611, Carl Boyer's "A History of Mathematics" - 
 "Godel showed that within a rigidly logical system _such_as_ Russell
and Whitehead had developed for arithemtic, propositions can be formulated
that are undecidable or undemonstrable within the axioms of the system.
That is, within the system there exist certain clear-cut statements that
can be neither proved nor disproved.... it appears to foredoom hope of
mathematical certitude ... Perhaps doomed als, as a result, is the ideal
of science - to devise a set of axioms from which all phenomena of 
the natural world can be deduced."   Emphasis mine.

And if rigidly logical systems such as math, cannot be proved valid,
where does that leave everything else?  I assume that the natural world
is at least as complex as arithematic.  

>Follow-ups to sci.math.

>Jeff Shallit

>"The trouble with people is not that they don't know but that they know so
>much that ain't so."
>	Josh Billings' Encyclopedia of Wit and Wisdom (1874) 

Truly.

Steve Kellmeyer
-- 

Steve Kellmeyer 
kellmeye@ux1.cso.uiuc.edu
Xref: sparky sci.math:18066 sci.logic:2592 sci.philosophy.tech:4770
From: zeleny@husc10.harvard.edu (Mikhail Zeleny)
Newsgroups: sci.math,sci.logic,sci.philosophy.tech
Subject: The Phallogocentric Cabal
Summary: announcing a new term
Keywords: forcing categories topoi
Date: 13 Jan 93 01:44:31 GMT
Article-I.D.: husc3.1993Jan12.204432.19258
Expires: December 31, 1999
Organization: The Phallogocentric Cabal

Announcing a new term of the Phallogocentric Cabal, dedicated to the
study of categories and topoi, with a special emphasis on applications
to logic and set theory.  Semi-official texts are:

Colin McLarty, _Elementary Categories, Elementary Toposes_, Oxford,
1992 (now on sale from the OUP; MacLane's _CftWM_ may be substituted,
but is not nearly as readable);

Saunders MacLane and Ieke Moerdijk, _Sheaves in Geometry and Logic_,
Springer, 1992 (accept no substitutes).

All participants are expected to know algebra on the level of
Herstein's _Topics in Algebra_, and topology, to the extent of the
Chapters 0--5 of Kelley's _General Topology_; failing that, they will
be requested to fake a modicum of mathematical maturity.  Some
familiarity with lattices and Boolean algebras will be very helpful;
however, no special exposure to logic or set theory is required, and
all facts about forcing will be presented _ab ovo_.

As always, we accept participants from all walks of life, without
regard to kingdom, species, race, nationality, religion, gender, age,
sexual orientation, marital status, or political affiliation; if you
are metabolically active, and can understand, and express yourself in
variegatedly accented English, you are welcome to join.  No fees will
be charged; no compromising pictures will be taken; no mailing lists
will be maintained; no salesmen will visit your home.

We meet weekly, generally from 6 to 8 p.m.; participants alternate
presentations on the week's reading and problem solutions.  Auditors
are welcome.  Email access is a must.  Write for more information.

cordially,
mikhail zeleny@husc.harvard.edu
"Les beaulx bastisseurs nouveaulx de pierres mortes ne sont escriptz
en mon livre de vie.  Je ne bastis que pierres vives: ce sont hommes."
Newsgroups: sci.math
From: matmcinn@nuscc.nus.sg (.)
Subject: Einstein Manifolds
Organization: National University of Singapore
X-Newsreader: Tin 1.1 PL4
Date: Tue, 5 Jan 1993 09:08:06 GMT


Can anyone tell me a good way to construct examples of compact
*non-orientable* Einstein manifolds with positive Ricci curvature and odd
dimensions? Dimensions 4n-1 [ n>1 of course] are the ones giving me trouble.
Thanks.
Newsgroups: sci.math
From: yeomans@austin.onu.edu (Charles Yeomans)
Subject: Re: Postscript cmd to turn ON the startup page
Date: Fri, 8 Jan 1993 18:07:26 GMT
Organization: Ohio Northern University


> 
> Bailey Szeto (bszeto@netcom.com) wrote:
> : Hello all.
> :    Does anybody know the postscript command to turn on the startup page for
> : a laserwriter? I need to know the exact command because the printer is not
> : connected to a mac, and therefore, I cannot run the Laserwriter font utility.
> : 
> :    I believe that there are two ways to accomplish this. One is to connect
> : a terminal straight to the serial port, and the other is to put a postscript
> : header around the postscript command. I need to know what the command is.
> : 
> :   Any help/info/suggestions/comments would be greatly appreciated! Thanks
> : in advance.
> 

Use the LaserWriter Font Utility that comes with system 7 to turn off the
startup page.

Charles Yeomans

Xref: sparky sci.math:17977 sci.physics:22495