HDTenEightyP/NetNews huggingface dataset:
From: crawford@boole.mitre.org (Randy Crawford)
Subject: Re: Minimum standards for math "competency"
Keywords: math competency education university college standards
Organization: The MITRE Corporation, McLean, VA
Date: Mon, 23 Nov 1992 02:11:23 GMT

In article <1339@kepler1.rentec.com> rjfrey@rentec.com (Robert J Frey) writes:
>[...] an alternate question: What mathematics will students need when they get
>out into the world REGARDLESS of what is or is not required in your or any 
>other university?
>
>The answer in that case is clear. They need a lot more than they're getting!
[...]

>If you want I can snail mail you a copy of the presentation. Here however are a
>few facts:
>
>	o	The Jobs Almanac's top 5 jobs are all mathematically based:
>		actuary, computer programmer, systems analyst, mathematician
>		and statistician.

A greater need is anticipated for systems analysts and mathematicians than for
nurses or accountants?  First time I've heard that.  Sounds dubious.

>
>	o	The math scores of the top 1% of American high school students
>		would place them in the 50th percentile in Japan (that's not
>		a typo). How can we expect to compete with Japan in high tech
>		manufacturing?

Hoo boy!  Does this statement need qualification!

In effect, this states that EVERY american student would be below average 
mathematically in Japan.

I'll step out on a limb here and say: RUBBISH!  Such a statement _has_ to be
completely wrong.  If the margin between the US and Japan were that great, we'd
see vast differences between us in virtually every form of technology, including
patents and major prizes for scientific research, which we don't.  We'd find
ten Japanese students for every American in every non-american and non-japanese
university, which (I'll bet) we don't.

But perhaps it's just my gross inadequacy in mathematics speaking...

>
>My recommendations to you are as follows: 
>
>	o	Hit 'em with facts, HARD. Good sources: Lester Thurow, Head to
>		Head, Morrow, 1992; and National Academy Press, A Challenge of
>		Numbers: People in the Mathematical Sciences, 1990. These 
>		contain extensive references which will point you further.

More power to references.

-- 

| Randy Crawford        crawford@mitre.org        The MITRE Corporation
|                                                 7525 Colshire Dr., MS Z421
| N=1 -> P=NP           703 883-7940              McLean, VA  22102
Xref: sparky sci.math:15441 sci.physics:19521 sci.astro:12327 sci.bio:4211 sci.chem:4798 misc.education:4469
From: hanche@ams.sunysb.edu (Harald Hanche-Olsen)
Newsgroups: sci.math
Subject: Re: 1+1/2+1/3+1/4+...+1/n
Date: 23 Nov 92 17:21:10 GMT
	<HANCHE.92Nov19123151@ptolemy.ams.sunysb.edu>
	<BxzMuB.6Gr@cantua.canterbury.ac.nz>
	<1992Nov21.125910.24073@linus.mitre.org>
Organization: University at Stony Brook, NY

>>>>> On Sat, 21 Nov 1992 12:59:10 GMT, bs@gauss.mitre.org (Robert D.
>>>>> Silverman) said:

bs> In article <BxzMuB.6Gr@cantua.canterbury.ac.nz>
bs> jsv@math.canterbury.ac.nz (Julian Visch) writes:

bs> :> evalf(sum(1./n,n=1..15092688622113788323693563264538101449859496));
bs> :99.999999999999999999999999999999999999999999942747074071711130782[...]

bs> Just HOW did Maple produce this sum?

With the help of the Psi function, the heart of which does the
following (this is computing Psi(x) -- I have simplified a bit and cut
several branches that are not taken for the values of x and Digits
considered here):

    z := evalf(x);
    t := Digits-trunc(z);
    s := ln(z);
    z := 1/z;
    t := -1/2*z;
    z := z^2;
    y := 1;
    for k from 2 by 2 while s+t <> s do
        s := s+t; y := y*z; t := -bernoulli(k)*y/k
    od;
    RETURN evalf(s)

bs> How do you know it is right?

You don't, of course, unless you repeat the computation independently.

bs> I'm not saying it is wrong, but I am suspicious.

As you should always be :-)

bs> Using H_n = log(n) + gamma + O(1/n) [even getting many error terms
bs> via Bernoulli polynomials won't give explicit constants on the
bs> errors], is NOT sufficient.

Ummm.  Can't suitable constants be determined, you say?  Then this
calculation seems to be in trouble all right...

- Harald
From: dvf@kepler.unh.edu (David V Feldman)
Newsgroups: sci.math
Subject: Re: Bieberbach Conjecture (was Re: Assorted questions...)
Date: 15 Nov 1992 03:24:24 GMT
Organization: University of New Hampshire  -  Durham, NH
NNTP-Posting-Host: kepler.unh.edu

At the time the Bieberbach conjecture was proved, I heard mention that
de Branges was planning to publish a revised and substantially expanded
edition of his book on Square Summable Power Series.  To the best of
my knowledge, no such thing as ever appeared.  Does anyone have any
information about this?

David Feldman
University of New Hampshire
d_feldman@unhh.unh.edu
Newsgroups: sci.math,sci.physics
From: rryan@panix.com (Rob Ryan)
Subject: Re: 3-sided coin
Date: Tue, 17 Nov 1992 13:50:16 GMT
Organization: Panix, NYC

In <1e98b8INN6s@manuel.anu.edu.au> butler@rschp2.anu.edu.au (Brent Butler)
writes:

>The solution to this problem is simple.  When a coin is flipped it
>will *come to rest* in a position that represents a minimum in its
>(gravitational) potential energy.  For a real coin this means one
>of its two faces with equal probability - it will never *come to
>rest* on its edge even though it has a finite area because this is
>a metastable state.

Yes, it will come to rest at a minimum, but it doesn't have to be an
absolute minimum, but rather a local minimum would do as well.  Resting on
edge is a relative minimum and is therefore possible.  You can think of the
bouncing coin as a form of gradient descent.  With a coin of standard
dimensions, so little energy is necessary get it out of that local minimum
that it is extremely unlike to settle there, but when you make the coin
wider, it becomes more likely.

>Our three sided coin, therefor, should be 1 coin diameter thick. This 
>is where the center of mass is at equal heights in each of the three
>states and so each configuration represents an equally likely
>stable state for the coin to *come to rest* after a toss.

Incidentally, what if the coin is 0.9999 coin diameter thick.  By your
argument above, since resting on the side would become a "metastable"
state, it would never come to rest on it's side, would it?

Are you applying some non-standard interpretation of "come to rest"?
Can you elaborate upon your argument here?

-- 
 Rob Ryan
    Internet:   rryan@panix.com or Robert_Ryan@brown.edu
    Bitnet:     ROBR@BROWNVM
    Compu$erve: 70324.227@compuserve.com
From: hdev@dutiag.tudelft.nl (Hans de Vreught)
Newsgroups: sci.math
Subject: Re: jump in price of journals
Date: 19 Nov 92 00:30:59 GMT

mroussel@alchemy.chem.utoronto.ca (Marc Roussel) writes:

>Of course, once they start raising their prices, more libraries drop
>their subscriptions, and so on.  With any luck, this is a signal of an
>impending shakeout in scholarly publications.

Don't you believe that. The one part of Elsevier that was booming was
scholarly publications. Our need to write publications, simply means that
either many journals or very thick journals are needed. Either way, your
university must pay the prices.
--
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.
From: jack@dcs.glasgow.ac.uk (Jack Campin)
Newsgroups: sci.math
Subject: Re: Topology and CS?
Date: 19 Nov 92 17:46:35 GMT
Reply-To: jack@dcs.glasgow.ac.uk (Jack Campin)
Organization: COMANDOS Project, Glesga Yoonie

tenny@euclid.uucp (Nathan Tenny) wrote:
> I'm given to understand that both point-set and low-dimensional topology
> are of some interest in computer science....
> The problem: I have a nodding acquaintance with CS, but not enough to read
> papers in it.  The literature I've found on topology and CS seems to be
> written from the CS end.
> Could anyone give me a couple of suggestions about where to start reading, or
> possibly even a quick braindump on the subject?

One application area that is described, so far, in a fairly mathematical
way is the use of locales in concurrency theory - try Vickers' "Topology
via Logic" (Cambridge Univ Press) for starters.  Another place to look is a
paper by Hopcroft in the Journal of the ACM a few years ago, on the
mathematics CS now needs, that describes applications of algebraic topology
to robot motion planning (this is way removed from anything I have detailed
knowledge of, so maybe someone has better references).  A classical
application, now rather inactive as a research field, is Scott's use of T0
spaces in domain theory (try the Scott et al book "A Compendium of
Continuous Lattices").

-- 
--  Jack Campin    room G092, Computing Science Department, Glasgow University,
17 Lilybank Gardens, Glasgow G12 8RZ, Scotland   TEL: 041 339 8855 x6854 (work)
INTERNET: jack@dcs.glasgow.ac.uk or via nsfnet-relay.ac.uk    FAX: 041 330 4913
BANG!net: via mcsun and uknet     BITNET: via UKACRL    UUCP: jack@glasgow.uucp
From: jbaez@riesz.mit.edu (John C. Baez)
Newsgroups: sci.math,sci.physics
Subject: Re: RSA Encryption
Keywords: cryptography, primes
Date: 23 Nov 92 01:25:10 GMT
Organization: MIT Department of Mathematics, Cambridge, MA

In article <1992Nov22.224208.12455@galois.mit.edu> jbaez@riesz.mit.edu (John C. Baez) writes:
>In article <1992Nov22.011016.6268@CSD-NewsHost.Stanford.EDU> pratt@Sunburn.Stanford.EDU (Vaughan R. Pratt) writes:
>
>>Apropos of which, here is my proof that P=NP.  (I came up with it
>>around 1972, if you have an earlier source then it's not mine after
>>all.)  Computers double in speed every 18 months or so, whence any
>>exponential time problem can be solved in linear time by waiting the
>>requisite number of months for the problem to become solvable in one
>>month and then starting the computation.  This counts the waiting time,
>>and has the additional advantage that you can use your computer on
>>something else while waiting.
>
>Very interesting.  Like Lewis Carroll's jokes, there is a real fact
>lurking in this one.  *If* the world's future was predictable in
>polynomial time from initial data, and *if* P was not equal to NP, one
>could use the contrapositive of Pratt's joke to prove that the rate of
>speed of computers cannot double each 18 months or so forever.

Whoops.  One only needs that polynomial time is not equal to exponential
time, not that P is not equal to NP.  The former is known to be true.
Newsgroups: sci.math
From: palais@binah.cc.brandeis.edu
Subject: Re: Another fundamental group question
Reply-To: palais@binah.cc.brandeis.edu
Organization: Brandeis University
Date: Sat, 21 Nov 1992 03:17:12 GMT

>>
In article <1eejigINNaqm@agate.berkeley.edu> fogel@rosarita.berkeley.edu (Micah
E. Fogel) writes:
>
>       I once saw in this newsgroup an article describing a space that was
>supposed to have fundamental group equal to some non-discrete group (I think
>it was the reals, but the rationals is also possible).  Or was I just dreaming?
>>
See the footnote on page 11 of Vaughan Jones recent book Subfactors and
Knots (CBMS Regional Conf. Series #80) published by AMS---for a real 
life example.
Newsgroups: sci.math
From: rusin@mp.cs.niu.edu (David Rusin)
Subject: Re: jump in price of journals
Organization: Northern Illinois University
Date: Fri, 20 Nov 1992 19:13:40 GMT

In article <1992Nov19.210512.27600@alchemy.chem.utoronto.ca> mroussel@alchemy.chem.utoronto.ca (Marc Roussel) writes:
>In article <1992Nov19.193647.24279@CSD-NewsHost.Stanford.EDU>
>rivin@SAIL.Stanford.EDU (Igor Rivin) writes:
>>Again, with the current state of
>>funding, I find it hard to believe that many libraries will find the
>>$200 to pay for North Holland/Elsevier books (easily triple Springer
>>prices for comparable titles).
>
>     We shouldn't unfairly single out Elsevier. 

Right. I'd be happy to knock Gordon and Breach in particular, except I'll
bet that a lot have people have just given up and cut the G+B subscriptions.
Advice to young readers: be sure to publish your best results in journals
which people are going to continue to subscribe to -- that excludes journals
with high or rapidly rising prices.

dave rusin@math.niu.edu, ever griping about journal costs.

Newsgroups: sci.math
From: rasiaie@magnus.acs.ohio-state.edu (Reza Asiaie)
Subject: Potential Theory
Organization: The Ohio State University
Date: Mon, 16 Nov 1992 04:57:01 GMT

Hello,
I would appreciate if anyone could help me with the following problem:
I would like to determine the Green's function for an area bounded
between 2 concentric spheres, for any n.

Please replay directly to my email address:

rasiaie@magnus.acs.ohio-state.edu
Newsgroups: sci.math
From: mueller@schaefer.math.wisc.edu (Carl Douglas Mueller)
Subject: Re: Geometrical parking problem.
Reply-To: mueller@schaefer.UUCP (Carl Douglas Mueller)
Organization: Univ. of Wisconsin Dept. of Mathematics
Date: Thu, 19 Nov 92 15:35:36 GMT

In article <Bxys1K.4Fo@watdragon.uwaterloo.ca> deghare@daisy.uwaterloo.ca (Dave Hare) writes:
>In article <1992Nov18.143131.25971@schaefer.math.wisc.edu> mueller@schaefer.UUCP (Carl Douglas Mueller) writes:
>>>>
>>>>A car of length L reverses into a parking space without touching the kerb.
>>>>Has anyone calculated the minimum theoretical length of the parking space?
>>  Actually, there is no MINIMUM.  The length of the car is not quite enough,
>> but the length of the car plus epsilon (for any positive epsilon) is enough.
>
>Is everybody taking into account the fact that rear wheels don't (generally)
>turn?

  Yes.
>
>Dave Hare

Carl Mueller
Newsgroups: sci.math
From: hubertc@cs.berkeley.edu (Hung-Hsien Hubert Chang)
Subject: mathematical software for number theory
Organization: CS Dept. Snakepit - Do Not Feed.
Date: Fri, 20 Nov 1992 21:28:47 GMT

Hi! I would like to know the ftp site of efficient mathematical 
software on calculating pi, e , ..etc  with precision up to say, 
500 digits or more.( depending how much time one wants 
the machine to calculate) As efficient as possible.

Thank you.

Hubert
From: wang@apache.dtcc.edu (Wang Gang)
Newsgroups: sci.math
Subject: Can anyone solve this problem?
Date: 18 Nov 1992 11:30:19 -0500
Organization: Delaware Technical & Community College
Distribution: usa
NNTP-Posting-Host: apache.dtcc.edu


Newsgroups: sci.math
From: levine@symcom.math.uiuc.edu (Lenore Levine)
Subject: Re: Bozos Synonymous
Organization: University of Illinois at Urbana
Date: Mon, 16 Nov 1992 15:15:23 GMT

cxm7@po.CWRU.Edu (Colin Mclarty) writes:


>In a previous article, levine@symcom.math.uiuc.edu (Lenore Levine) says:

>>
>>You think that "crop circles" character is something. Wait till
>>you read "Sexual Personae" by Camille Paglia! Lots of complete
>>nonsense about how mathematics is done, and mathematicians 
>>think! 
>>
>>I defy this lady to explain why the derivative of x^2 is 2x. Meanwhile
>>she's making zillions, and I'm scrambling for pennies in graduate
>>school.
>>
>>
>	I'm sure this is the first time anyone has complained about
>Paglia's views on math.  What were they?  I read the book but the math
>must have escaped me in the rush.  (You probably are right that she
>couldn't explain deriviatives of polynomials.)

>Colin

She seems to be saying:

1. That mathematics represents a "masculine" way of thinking.

2. That there never will be, or ought to be, any more
   women doing research mathematics than there have been
   historically. (Almost none.) 

I think you'd have to look long and hard to find a research
mathematician who would agree with these two sentences...

Lenore Levine
levine@symcom.math.uiuc.edu

P.S. Speaking of bozos, hasn't Timothy Leary been talking an awful
lot about computers? I defy him to write a BASIC program listing
the primes from 1 to 100.

But wouldn't you love to listen to a Timothy/Camille debate? (Maybe
on "The Future of Technology in the 21st Century...")
From: mccolm@darwin.math.usf.edu. (Gregory McColm)
Newsgroups: sci.math
Subject: Re: Erdos number
Date: 17 Nov 92 18:40:59 GMT
Organization: Univ. of South Florida, Math Department

In article <EIJKHOUT.92Nov12213622@cupid.cs.utk.edu> eijkhout@cupid.cs.utk.edu (Victor Eijkhout) writes:
>
>   In article <1992Nov11.001750.12213@mailhost.ocs.mq.edu.au> gerry@macadam.mpce.mq.edu.au (Gerry Myerson) writes:
>   >
>   >
>   >In article <1992Nov2.231234.19251@smds.com>, sammy@smds.com (Samuel Murphy) writes:
>   >> 
>   >> In article <1992Oct29.170517.7780@email.tuwien.ac.at> zach@csdec1.tuwien.ac.at writes:
>   >> >In article <petersen.720366033@rzcspc1>, petersen@rzcspc1.informatik.uni-hamburg.de (Holger Petersen) writes:
>   >
>   >[definition of Erdos number, deleted]
>   >
>   >> So, are there any non-mathematicians with such a number? 
>   >
>   >Yes. John Clough, Professor of Music at SUNY, Buffalo, wrote a paper in the 
>   >Monthly with me some years ago, thereby acquiring an Erdos number of 4. 
>

Erdos once said that Einstein's Erdos number was 2 or 3, 
I forget which.

-----Greg McColm
--
SHAMELESS AD:  Math PhDs in Analysis, Discrete Math./Th. of Comp., Num. Anal., 
Prob., are invited to apply to the Math. Dept. of Univ. of S. Florida for 
research/teaching positions that may be available: contact K. L. Pothoven at 
mathdept@math.usf.edu. Deadline 2/1/93. USF is a politically correct employer.
Organization: Johannes Kepler University Linz - Computing Center
Date: Thursday, 19 Nov 1992 13:23:29 CET
From: Mutter Christoph Johannes <K3032E2@ALIJKU11.BITNET>
Newsgroups: sci.math
Subject:    1+1/2+1/3+1/4+...+1/n

Hallo.
I've a problem. I have to calculate the sum 1+1/2+1/3+1/4+...+1/n.
The result should be 100. But my computer is far too slow, to solve this
problem. I need the index n when the sum > 100.0
And that exactly.
Has anyone calculated this? (Perhaps on a CRAY|) ?
Thanks.

Chris. ------------
Newsgroups: sci.math
Subject: Re: ODE problem...
From: a_rubin@dsg4.dse.beckman.com (Arthur Rubin)
Date: 19 Nov 92 17:01:34 GMT
Organization: Beckman Instruments, Inc.

In <1992Nov17.205237.21447@athena.mit.edu> frisch1@athena.mit.edu (Jonathan Katz) writes:

>The following ODE problem came up recently.
>I know how to solve it by the power series method, but was wondering
>if anyone could figure out an easier way of solving it (maybe a nice
>substitution?).
>(x and y are functions of t, a is a constant)
>x'=(a)(x)cost+(a)(y)sint
>y'=(a)(x)sint-(a)(y)cost.
>It may be worth noting that, viewing this as a matrix problem:
>x'=Ax,
>A^2=I.

>I don't know if that helps.

I used a completely different approach than Robert.  If you write:

z = x + i y, then the equation becomes:

      i t  _
z' = E     z

Playing with this for a while, and guessing that solutions z exist which
are a sum of only 2 expontials in t, we can derive the general solution:

Let c be one of the square roots of (a^2-1/4).

C(t) = / cosh(|c| t)      , c real != 0
       | 1                , c = 0
       \ cos(|c| t)       , c pure imaginary

S(t) = / sinh(|c| t)/|c|  , c real != 0
       | t                , c = 1
       \ sin(|c| t)/|c|   , c pure imaginary


x0(t) = C(t) cos(t/2) + S(t) (a cos(t/2) + sin(t/2)/2)
x1(t) = -C(t) sin(t/2) + S(t) (a sin(t/2) + cos(t/2)/2)

y0(t) = C(t) sin(t/2) + S(t) (a sin(t/2) - cos(t/2)/2)
y1(t) = C(t) cos(t/2) + S(t) (-a cos(t/2) + sin(t/2)/2)

Then x=C0 x0 + C1 x1 and y=C0 y0 + C1 y1 form the general solution.





--
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.
From: werner@pell.anu.edu.au (Werner Nickel)
Newsgroups: sci.math
Subject: Re: A Question About Fundamental Group
Date: 23 Nov 92 12:52:36
Organization: Australian National University
	<arvola.722107812@sol>
NNTP-Posting-Host: 150.203.15.67
In-reply-to: arvola@sol.acs.unt.edu's message of Wed, 18 Nov 1992 17:30:12 GMT

arvola@sol.acs.unt.edu (Arvola William) writes:

   >>Consider a bunch of infinitely many (countable) circles with a
   >>point in common. The radii of these circles make a sequence like
   >>{1/n}. What is the fundamental group of this space? Any comments
   >>or referenc would be so helpful!

   >Sometimes known as the "Hawaiian earing space".
   >Its fundamental group has coutably many generators (one for each circle)
   >and no relations.  (I.e., it is a free non-Abelian group on countably 
   >many generators.)  

   I don't think that it is as simple as this.  Take, for example,
   a loop running around a subcollection of the circles whose radii
   converge like the sequence {1/2^n}.  Since this (sub)sequence is
   summable this loop represents an element of the fund group which
   is not a finite product of the generators that were proposed.

The fundamental group of the Hawaiian earring can be described as follows.
Number the circles by the natural numbers and let p_i be a single
loop around circle number i. Then all closed paths are (possibly
infinite) products of the p_i and their inverses. The only (obvious)
restriction is that each loop p_i (or its inverse) occurs only a finite
number of times in a product.
One way to describe this in a precise algebraic way is to construct the
fundamental group of the Hawaiian earring as a subgroup of an inverse limit
of the free group on n generators with n going to infinity. The details
are spelled out in the paper I quoted earlier in this newsgroup.

Werner Nickel
Mathematics Research Section
Australian National University
From: werner@pell.anu.edu.au (Werner Nickel)
Newsgroups: sci.math
Subject: Re: A Question About Fundamental Group
Date: 20 Nov 92 15:05:29
Organization: Australian National University
NNTP-Posting-Host: 150.203.15.67
In-reply-to: amirishs@acf9.nyu.edu's message of 18 Nov 92 04:06:28 GMT

In article amirishs@acf9.nyu.edu (shaahin amiri sharifi) writes:

   Consider a bunch of infinitely many (countable) circles with a
   point in common. The radii of these circles make a sequence like
   {1/n}. What is the fundamental group of this space? Any comments
   or referenc would be so helpful!

The fundamental group of this topological space, known as the Hawaiian
earing, is derived in the following paper:

J.W. Morgan, I. Morrison:
A van Kampen Theorem for Weak Joins
Proc. London Math. Soc. (3), 53 (1986), 562-576

Werner Nickel
Mathematics Research Section
Australian National University
Newsgroups: sci.math