HDTenEightyP/NetNews huggingface dataset:
From: brock@NeXTwork.Rose-Hulman.Edu (Bradley W. Brock)
Newsgroups: sci.math,alt.politics.elections
Subject: Re: Electoral college (was Re: Bill Clinton and Complex Analysis)
Date: 13 Nov 1992 16:14:00 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 <israel.721610297@unixg.ubc.ca> israel@unixg.ubc.ca (Robert B.  
Israel) writes:
> (A) How many electoral votes could Perot have taken, given the number of
> votes he received?  Here I'm allowing votes to be moved around, subject to
> keeping fixed the total national votes for each candidate, and the total
> number of votes cast in each state. 
> 
> (B) How many votes must a candidate in a 3-way race receive in order to
> get a majority in the electoral college?  Again I'm assuming the total
> number of votes cast in each state is fixed.

> I used data from the New York Times (not-quite-complete returns, but at least
> 99% in almost all states), and solved the problem using LINDO.  Note that
> P = 19,237,247, or 19.02% of the votes cast.
> 
> Results: 
> (A) Perot takes 338 electoral votes (62.8% of the total), winning all 
> states except Fla, Ill, La, Md, Mass, Mich, Minn, Mo, NJ, Ohio, Pa, Va and  
Wis.
> (B) 14,802,010 votes (14.64% of the total), winning all states except 
> Colo, Conn, Fla, Ill, Kans, Mass, Mich, Minn, Mo, NJ, NY, Ohio, Pa, Texas,  
Va, 
> and Wis.

Aside from its slight knapsack nature, I think the problem is simple enough so  
that Lindo is not necessary.  The best strategy would be to select the states  
that have the best ratios of electoral votes to popular votes.  These would  
tend to be the smallest states because all states start with at least 3  
electoral votes, but this could vary depending on voter turnout.  If the state  
that makes the running total go over 270 electoral votes makes it go over by  
too much, then do some knapsack jugglings to find the optimum.  The states that  
are excluded either have high voter turnout, e.g. Colo, Conn, Kans, Minn, Mo,  
and Wis, large populations, e.g.  NY, Texas, Fla, Pa, Ill, NJ, and Va, or a  
little of both, e.g. Ohio, Mich and Mass.  Apparently California is included  
because voter turnout was abysmal.
--
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: frank@Cookie.secapl.com (Frank Adams)
Subject: Re: An Interesting Function
Date: Thu, 12 Nov 1992 19:58:39 GMT
Organization: Security APL, Inc.

In article <BxKEDt.sL@unx.sas.com> sasrdt@shewhart.unx.sas.com (Randall D. Tobias) writes:
>In article <1992Oct29.001255.35683@Cookie.secapl.com>, frank@Cookie.secapl.com (Frank Adams) writes:
>|> Consider the function W(n) = sum(0<i<n,mod(n,i)).  The problem is to find an
>|> asymptotic expression for W(n).
>|>
>|> It is pretty clear that W(n) = O(n^2).  In fact, we can write
>|> W(n)=c n^2 + o(n^2).  The question is, what is c?  I know the answer, and
>|> will post it later if no one gets it.
>|>
>|> I think in fact W(n) = c n^2 + O(n), but I can't prove it.  It seems that
>|> W(n) /= c n^2 + d n + o(n); the O(n) stuff "wanders around".
>
>Well?

The key is to look at the summation from the "back end".  Between n/2 and
n, the values go in arithmetic sequence from just under n/2 to 0.  Between
n/3 and n/2, they go from n/3 to 0.  This works well enough back to
sqrt(n); and the terms up to sqrt(n) sum to at most O(n).  So

  W(n) ~ SUM((k,1,sqrt(n)),(n/k - n/(k+1))*n/(2(k+1)))
       ~ n^2 * (SUM(k,1/(k*(k+1)))-SUM(k>0,1/(k+1)^2))/2
       = n^2 * (1 - (pi^2/6 - 1))/2
       = (1 - pi^2/12) * n^2

So c = pi^2/12.

(A more precise analysis is required to get an error estimate.)
From: hrubin@pop.stat.purdue.edu (Herman Rubin)
Newsgroups: sci.math
Subject: Re: who should teach mathematics?
Date: 12 Nov 92 15:35:29 GMT
Organization: Purdue University Statistics Department

In article <1992Nov10.223300.19016@murdoch.acc.Virginia.EDU> tep2j@amsun.apma.Virginia.EDU (Todd E. Peterson) writes:
>I am interested in hearing net.opinions on the following:

>Is it a good or bad practice to use non-mathematicians to
>teach mathematics courses?  In particular, what about the
>use of engineering faculty to teach engineering calculus
>courses, and other applied mathematics courses?

If they can teach it mathematically, it would be appropriate to have
them do so in the mathematics department. 

This problem is especially bad in statistics, where it is often the
case that most statistics is taught by psychologists and social scientists
who know nothing about the problems, but only methodology.
-- 
Herman Rubin, Dept. of Statistics, Purdue Univ., West Lafayette IN47907-1399
Phone: (317)494-6054
hrubin@snap.stat.purdue.edu (Internet, bitnet)  
{purdue,pur-ee}!snap.stat!hrubin(UUCP)
Newsgroups: sci.math
From: mroussel@alchemy.chem.utoronto.ca (Marc Roussel)
Subject: Re: What can we have for an educational system?
Organization: Department of Chemistry, University of Toronto
Date: Mon, 9 Nov 1992 02:10:24 GMT

In article <BALDWIN.92Nov8172729@csservera.scs.usna.navy.mil>
baldwin@csservera.scs.usna.navy.mil (J.D. Baldwin) writes:
>       (Also, note the high quality, in general, of teaching as
>    practiced at the University level in the U.S.  Ask yourself how
>    much "education" training the typical college professor has.)

     I don't agree that most university professors are terribly good
teachers.  My personal observations suggest that a typical university
department has, roughly, the following makeup:

	  1.  At most half-a-dozen individuals who really know how to
	      teach.
          2.  20-40 individuals who are good at reaching the fraction of
	      the class whose learning styles ressembles the
	      instructor's.
          3.  Another half-a-dozen or so who should never be allowed
	      near a classroom.

     Note too that members of both groups 1 and 2 often fail to reach
their potentials due to time pressures and so may be unrecognized as
belonging in one of these categories.  The large size of class 2
suggests that there is something to what J.D. has written, but that some
work, perhaps even some training is required for most of us to become
good teachers.  Personally, I wouldn't mind knowing a little more
developmental and cognitive psychology; I especially would like to learn
something about these subjects if I were to teach younger children.  I
have developed a set of rules of thumb which seem to get me through
undergraduate teaching assignments, but there is no science to my
approach.  While I reserve the right to disagree with someone else's
theories, I would at least like to know what the evidence is and what
other people's thinking has produced before I claim that I know anything
about how children and adults learn anything.

				Marc R. Roussel
                                mroussel@alchemy.chem.utoronto.ca
Newsgroups: sci.math,comp.theory
From: pratt@Sunburn.Stanford.EDU (Vaughan R. Pratt)
Subject: Re: NP Completeness Question
Organization: Computer Science Department,  Stanford University.
Date: Fri, 13 Nov 1992 15:44:06 GMT

In article <BxMu2J.2JD@watserv1.uwaterloo.ca> nrswart@phonon.uwaterloo.ca (Nicholas R. Swart) writes:
>Professor E.R. Swart of the Computer Science Department at the University
>of Guelph, has recently developed a polynomial-sized linear programing
>formulation of the graph isomorphism problem and he has been able to show
>that with minor modifications, this same formulation can be used to solve
>the Hamilton tour, clique and other subgraph isomorphism problems.

Papadimitriou showed in 1975 an exponential lower bound on
simplex-based solutions of the travelling salesman problem.  Since
linear programming solves simplex problems (and indeed has polynomial
time solutions), the above account renders the claim very unconvincing
by making no mention of an additional trick.
-- 
Vaughan Pratt	  		A fallacy is worth a thousand steps.
Newsgroups: sci.math
From: sasrdt@shewhart.unx.sas.com (Randall D. Tobias)
Subject: Re: An Interesting Function
Originator: sasrdt@shewhart.unx.sas.com
Date: Wed, 11 Nov 1992 18:37:05 GMT
Organization: (none)


In article <1992Oct29.001255.35683@Cookie.secapl.com>, frank@Cookie.secapl.com (Frank Adams) writes:
|> Consider the function W(n) = sum(0<i<n,mod(n,i)).  The problem is to find an
|> asymptotic expression for W(n).
|>
|> It is pretty clear that W(n) = O(n^2).  In fact, we can write
|> W(n)=c n^2 + o(n^2).  The question is, what is c?  I know the answer, and
|> will post it later if no one gets it.
|>
|> I think in fact W(n) = c n^2 + O(n), but I can't prove it.  It seems that
|> W(n) /= c n^2 + d n + o(n); the O(n) stuff "wanders around".

Well?  I got as far as empirically verifying the

   W(n) /= c n^2 + d n + o(n)

for n up to 100000 or so.  But i haven't got the number theory know-how
to go much further.  Pretty function, though.

-- 

Randy Tobias          SAS Institute Inc.     sasrdt@unx.sas.com
(919) 677-8000 x7933  SAS Campus Dr.         72450.2545@compuserve.com
(919) 677-8123 (Fax)  Cary, NC   27512-8000  norat@aol.com

 ... just my $(-exp(2*sqrt(-1)*arcos(0))/(((2**(2 + 1)) - 1)**2 + 1)).

Newsgroups: sci.math
From: pratt@Sunburn.Stanford.EDU (Vaughan R. Pratt)
Subject: Re: Mercator Projection
Organization: Computer Science Department,  Stanford University.
Date: Sun, 8 Nov 1992 21:43:29 GMT

In article <israel.721212129@unixg.ubc.ca> israel@unixg.ubc.ca (Robert B. Israel) writes:
>In <a34uTB4w165w@netlink.cts.com> kfree@netlink.cts.com (Kenneth Freeman) writes:
>
>>My Mercator projection goes 'up' to only 84 degrees, ~the northern
>>tip of the classically huge Greenland. I'd like to know three things.
>>1) For a given area, what is its apparent increase in size for a 
>>given latitude? I.e., what is the rate of increase the closer you
>>get a pole (and infinity)?
>
>At latitude t, linear dimensions are multiplied by sec(t), so areas are
>multiplied by sec^2(t).

Turns out if you try to calculate this using the 1986 Encyclopedia
Britannica you get sec^3(t).  The reason is that EB defines the
Mercator Projection to be the result of projecting the globe from its
center onto the cylinder tangent to the equator.  If this were true the
vertical direction would scale not by sec(t) but by the derivative of
tan(t), namely sec^2(t).

Since the Rand McNally Mercator projection of the world hanging in our
kids' playroom fits your formula exactly, and since the EB definition
would make Greenland (.84M sq.mi) look at least five times bigger than
South America (6.8M sq.mi) (it looks roughly the same size), I'd say
you were right.

So how is the Mercator projection defined?  One way I've seen is that
it maps rhumb lines (lines of constant bearing, not sailors waiting for
their daily ration) to straight lines of the corresponding slope, which
would seem to determine it uniquely up to dilatation (translation or
scaling).

An immediate consequence of this definition is that the Mercator
projection is conformal (locally shape-preserving).  However
conformality in the plane is weaker than dilatation (e.g. z^2 as a
transformation of the complex plane, which sends z+e to z^2+2ze for
small e, rotating and scaling e by 2z).  So conformality alone isn't
enough to define the Mercator projection.  One might ask for the
projection to be linear, but what does linearity mean when projecting
from a globe?  The EB definition gives a notion of linear projection
from a globe, but unfortunately it's wrong.

So with the goal being to patch the EB definition:

1.  What is the weakest condition required in addition to conformality
to uniquely determine the Mercator projection up to dilatation?

2.  What other natural definitions exist for the Mercator projection?

The EB should use the best definition.
-- 
Vaughan Pratt
Xref: sparky sci.math:14834 sci.physics:18756 sci.astro:11910 sci.bio:4107 sci.chem:4530 misc.education:4260
From: don@ohm.york.ac.uk (Don Goodeve)
Newsgroups: sci.math
Subject: Graph theory questions
Date: 9 Nov 92 09:59:53 GMT
Organization: Electronics Department, University of York, UK

I am interested in the problem of graph isomorphism
and graph embedding in general. Are there any good
(textbook) references that anyone could reccomend?

My background is electronic engineering and so I have
a fair grounding in mathematics and more recently in
computer science. I feel capable therefore of attacking
this area of maths as long as I am given a good
run-up.

Thanks in anticipation

Don

don@ohm.york.ac.uk

-- 
 ---------------------------------------------
| Don --- Well why not? Someone has got to be!|
 ---------------------------------------------
Newsgroups: sci.math
From: jchen@sct.gu.edu.au (Jinghong CHEN)
Subject: To express Q(x)/P(x) into continued fraction
Originator: jchen@tomahawk.me.gu.edu.au
Organization: Griffith University, Brisbane, Australia
Date: Thu, 5 Nov 92 06:44:14 GMT


Suppose there are two n-th order polynomials Q(x) and P(x), how can we
express Q(x)/P(x) into a continued fraction, i.e.

      Q(x)             a0
     ------ = ----------------------
      P(x)                a1
               x + -----------------
                                an
                    x + ... + ------
                               x + a

I am not sure if it is possible. Thank you in advance.

---------------------------------------------------------------------------
J.CHEN                               |E-MAIL: jchen@tomahawk.me.gu.edu.au
School of Microelectronic Engineering| Phone: +61-7-8755050
Faculty of Science and Technology    |   Fax: +61-7-8755198
Griffith University                  |   Fax: +61-7-8755050
Nathan, QLD 4111, Australia          |
---------------------------------------------------------------------------

-- 
ehunjfnlkdf dfdfjnlkdfl
Newsgroups: sci.math,misc.education
From: clin@eng.umd.edu (Charles Lin)
Subject: Re: Is Math Hard?
Date: Wed, 11 Nov 92 21:27:10 GMT
Organization: College of Engineering, Maryversity von Uniland, College Park
Originator: clin@delta.eng.umd.edu


   I had read somewhere (Scientific American, I think) that one problem that
poorer youths had was the inability to accurately tell time or estimate
how much time something would take.   So, early on, I think it's fairly
important -- if not at home, then at school -- to teach children
to estimate time, to try to do some marginal planning of tasks.

   In addition, there are a lot of these mental puzzles that are often
used, which in and of itself, are not terribly useful, but those
who can solve them seem to do better on in math.  An example is
where you have ten boxes of coins.  Each box has coins that all weigh
the same.  9 of the 10 boxes have the same wieght coins.  The tenth
box has slightly heavier coins, but you don't know which box.
Given a scale that accurately measures weight, and given that each
box is numbered 1 to 10, find a way, in one weighing, to find which
is the box with the heavier coins.   The problem itself is perhaps
not useful in everyday life, but solving it makes one sharper mentally.

   Another more controversial idea I have is for teaching a kind
of "standard English".  One problem that may cause discrimination
is not learning "standard English".  I think it should be taught as
if it were a foreign language rather than as if it were the "correct"
way to speak.  As pervasive as TV is in the US, it seems that parents
and friends are more likely to influence speaking patterns (notice that
almost all TV shows have people speaking "standard English", and yet
many people don't) than TV programs.  A radical solution would be to
teach classes in French.  That way, everyone starts in the same boat.

   The biggest change will have to be culturally however, and I have
touched upon that in a previous post.

   In any case, education problems have a number of different causes
and only some are being addressed.

--
Charles Lin
clin@eng.umd.edu
Xref: sparky sci.math:14645 comp.ai:4208 comp.lang.lisp:2834
From: tao@potato.princeton.edu (Terry Tao)
Subject: Re: Assorted questions and problems
Originator: news@nimaster
Organization: Princeton University
Date: Mon, 9 Nov 1992 19:10:22 GMT

Alright, I've got my answers to my questions.  Many thanks to the dozen people who responded.  I'll now summarize in an attempt to forestall another dozen.

|> >(1) what is the current status of the Bieberbach conjecture, that any
|> >univalent holomorphic function f on the unit disk such that f(0) = 0 and
|> >f'(0) = 1 satisfies the fact that the taylor expansion f(x) = \sum a_n x^n
|> >has the property |a_n|  \leq n? The last I heard, it was proved for n up to
|> >7 only, and also for all n sufficiently large |a_n| \leq 1.08 n.

The general consensus seems to be it was proven in controversial circumstances by Louis de Branges somwhere between 1975 and 1984.  If someone has the exact date, the reason behind the controversy, and/or a reference, could you please email me.  By the way, the book I was using as a reference was printed in 1983, so if it was proven in 1975, there's something wrong with the math grapevine...

|> 
|> >(2) Suppose X and Y are Banach spaces.  Can one construct a linear mapping
|> >from X to Y which is NOT continous?e.g. a map from L^2 to L^2 which is not
|> >bounded.  Is it possible to construct one without AC?
|> 

The answer is a resounding YES if axiom of choice is true, though someone pointed out to me that L^2 was a bad choice for an example (yes, I know it's a Hilbert space, but what's the point of this?), and apparently there is a "Soloway model" under which the answer is always NO.

|> >(3) Assume the axiom of choice and the axiom of the continuum.  Is it
|> >true that two chains (totally ordered sets) which both have the
|> >cardinality of the continuum have a one-to-one and onto order
|> >preserving mapping betweem them?
|> 

OK, so I screwed up this question.  I have a dozen different counterexamples now of the original question.  I'll rephrase this question into two different ones

(3a) if you assume that the chains are unbounded above and below, and are dense, i.e. between any two elements there is a third, is the above now true?

(3b) is (3) true if you remove the "onto" criterion, i.e. is there an order imbedding from the first chain to the other?

I'm fairly sure that both of these are true.

As soon as my news reader tells me how, I'm going to cancel the original article.  Thank you again for the large number of responses.

Terry
From: myrberger@elmer.e.kth.se (Johan Myrberger)
Newsgroups: sci.math
Subject: Error correction code question
Date: 5 Nov 92 17:59:04 GMT
Reply-To: myrberger@elmer.e.kth.se (Johan Myrberger)
Organization: School of EE, Royal Institute of Technolgy

Hello,

has someone got any hints or references on repeated root codes?

I'm interested in a binary code which is derived from a BCH(31,21) code
by shorten it and adding
a double root (x+1)^2.

What properties does a code get when adding repeated roots?
Can you use the algorithms for BCH-codes to decode and correct a code as above?
Is there a NEWSgroup which deals with this kind of things?

Hope someone can help me...

Johan Myrberger   MAIL: myrberger@elmer.e.kth.se
Xref: sparky sci.math:14718 sci.physics:18607
From: aephraim@physics.Berkeley.EDU (Aephraim M. Steinberg)
Newsgroups: sci.math,sci.physics
Subject: Re: Three-sided coin
Date: 10 Nov 1992 18:57:13 GMT
Organization: University of California, Berkeley
NNTP-Posting-Host: physics.berkeley.edu

In article <1992Nov10.032643.10467@galois.mit.edu> jbaez@riesz.mit.edu (John C. Baez) writes:
>In article <5413@daily-planet.concordia.ca> mckay@alcor.concordia.ca (John McKay) writes:
>>
>> von Neumann was asked, when about to enter a taxi,
>>
>>"How thick should a coin be to have equal (=1/3) probability
>> of landing on its head,tail,or edge?"
>My best shot at answer invoked an idea from stat mech, namely,
>equipartition.  This says that the solution occurs when the *energy* of
>standing upright equals the energy of lying on edge.  Guess this means
>the radius should equal half the thickness of the coin, or if you
>prefer, the diameter should equal the thickness.

Isn't this only true if one assumes that the number of microstates 
corresponding to each situation is the same?  For example, a molecule
in thermal equilibrium is not likely to be in the rotational ground state,
simply because the degeneracy goes as 2J+1 (or I guess 2\nu +1 or some
such is the standard notation), making higher J's somewhat more likely.

I would have said that if you can somehow ignore all dynamics (or perform
the coin toss in a viscous fluid, say, though I in no way claim this is
_necessary_) the important thing is for the solid angle pointing along
the edge to be the same as the solid angle along each side.

Thus each side must subtend 4\pi/3 steradians, meaning that the angle from
the axis of cylindrical symmetry to the ``diagonal'' must be
arccos (1/3), and the radius divided by half the thickness must be
the tangent of that angle (by the way, I drew a picture in front of me
and did some trig-- von Neumann I'm not) or 3\sqrt{1-1/9} or 2\sqrt{2}.

The radius should be \sqrt{2} times the thickness, goes my guess.

Note that this would make the surface area of the edge \sqrt{2} times the
surface area of each face, contradicting my original guess that the area
determined the likelihood... I stick with the solid angle approach, though.

Any experimentalists out there?


-- 
Aephraim M. Steinberg                    | "WHY must I treat the measuring
UCB Physics                              | device classically??  What will
aephraim@physics.berkeley.edu            | happen to me if I don't??"
                                         |       -- Eugene Wigner
Newsgroups: sci.math
From: jbaez@riesz.mit.edu (John C. Baez)
Subject: Re: Assorted questions and problems
Organization: MIT Department of Mathematics, Cambridge, MA
Date: Tue, 10 Nov 92 02:57:19 GMT

In article <1992Nov8.181631.13298@Princeton.EDU> tao@fine.princeton.edu (Terry Tao) writes:
>I have three questions that I can't do.  I hope you can see from the
>diversity of them that they are not homework.
>
>(1) what is the current status of the Bieberbach conjecture, that any
>univalent holomorphic function f on the unit disk such that f(0) = 0 and
>f'(0) = 1 satisfies the fact that the taylor expansion f(x) = \sum a_n x^n
>has the property |a_n|  \leq n? The last I heard, it was proved for n up to
>7 only, and also for all n sufficiently large |a_n| \leq 1.08 n.

This sounds like a homework problem.  (Just kidding.)  This conjecture
was proved by deBranges a few years ago.  It's a famous story because he
had earlier claimed to have proved it, but had made a mistake; this made
people not take his second attempt seriously at first.  (Perhaps someone
who knows the whole story may have fun telling it.)

>(2) Suppose X and Y are Banach spaces.  Can one construct a linear mapping
>from X to Y which is NOT continous?e.g. a map from L^2 to L^2 which is not
>bounded.  Is it possible to construct one without AC?

Yes, let D be a dense subspace of X that's not all of X.  Define f:X ->
Y to be zero on D but then extend f to a nonzero linear function on all
of X, which can be done by linear algebra nonsense.  In general this may
use the axiom of choice, but there might be hope for a constructive
example --- one needs an example of X with dense D such that there is an
*explicit* basis for a complementary subspace E (i.e., X = D + E as
vector spaces (not as Banach spaces, though!)).  

>(3) Assume the axiom of choice and the axiom of the continuum.  Is it true that two chains (totally ordered sets) which
>both have the cardinality of the continuum have a one-to-one and onto order
>preserving mapping betweem them?

What is "totally ordered"?  If you simply mean "linearly ordered" the
answer is no; let one set be R and the other be R copies of Z stacked on
top of each other, or the first ordinal with cardinality of the
continuum.  If you mean "well-ordered" the answer is yes and you only
need AC.  


Xref: sparky sci.math:14669 misc.education:4220