HDTenEightyP/NetNews huggingface dataset:
From: lwalsh@nemo (Laura L. Walsh)
Subject: Re: Is Math Hard?
Organization: University of Illinois at Urbana
Date: Sat, 7 Nov 1992 18:04:19 GMT

burtt@comet.nscl.msu.edu (BRIAN BURTT) writes:
>	Having failed at the home education route, my mother tried to
>get me enrolled in a gifted program in a local school district.  They
>were quite happy to have me, but it took TWO AND A HALF YEARS before
>this particular school district was willing to give up its state funds
>for me and let me go on my way.
>	Have others had similar problems in moving elementary 
>school students to more appropriate situations, or was I just 
>particularly unlucky?
>--Brian Burtt
>burtt@lynch.nscl.msu.edu

My mother is working on a history of our family and I came across
a lecture she gave at a conference on the education of the gifted
about our family's attempts to meet my educational needs.  In this 
account she stated that up until 6th grade (in small schools) I 
had done fine, but when I reached 6th grade, housed in a junior 
high, I began to be sloppy and distracted, doing C and D work.  My 
elementary teachers had suggested that I be sent to a gifted 
program available in the neighboring city, but, since it was a 
"special education" program, it was not permitted to attend it 
from outside the district.  So my mother and I moved into an 
apartment in the city, while my father and siblings remained at 
"home".  Even this did not satisfy them, however, when they found 
out that my siblings were going to school in their original schools.
So my parents, at great cost in terms of finances, rented a house
in the city and moved us all there.  All I remember is a great
feeling of re-awakening I experienced there.  I loved my math
class especially, and learning seemed fascinating.  The
following year, in the junior high, there was no "gifted"
program, per se, but some of the classes were "tracked", so
we were permitted to return to our home and my parents paid
tuition for me to attend the city schools.

My own experience with my daughters is familiar to readers
who have been on this group a while.  Our local public 
school simply could not deal with my second grade daughter,
or rather, they dealt with her just fine -- by doing nothing.
She, like me, did not act up, but rather became distracted
and uninterested.  The district's gifted program consists
of a 5 week, 2 hours a week chance to go to the library
for literature class and one or two week summer classes,
which last 1 hour, 3 days a week.  Result:  my husband
ended up teaching her at home after school hours.  In school,
she learned how to burp and how to pretend to be busy
without actually having to do anything -- and she learned
to fill out innummerable too easy worksheets.  This year
she is in a new private school, which I have helped start,
along with other parents equally fed up.  This has been
with great cost for us, not only financially, but time
and energy-wise.  I am doing all of this while trying to
finish grad school myself.  I am satisfied that it is 
beneficial, necessary and worth it, but it certainly isn't
easy.
Laura Walsh
Newsgroups: sci.math,sci.physics,sci.astro,sci.bio,sci.chem,misc.education
From: dsc@gemini.tmc.edu (Doug S. Caprette Bldg. 28 W191 x3892)
Subject: Re: Is Math Hard?
Organization: NASA GSFC CDP VLBI
Date: Fri, 6 Nov 1992 16:07:58 GMT

In article <Bx9uy1.LB0@mentor.cc.purdue.edu> hrubin@mentor.cc.purdue.edu (Herman Rubin) writes:
>In article <1992Nov5.180244.27364@athena.mit.edu> jamess@athena.mit.edu (John A Mess) writes:
>>....
>>     This was a very common problem in the 60's and 70's when public educa-
>>tors wanted to "modernize" the process.  The idea of teaching reading by
>>using phonetic symbols, by leaving out words, and other garbage was often
>>*forced* on public teachers from above.
>
>This happened partly, but you have the whole thing wrong.  Before the 40's
>reading was ALWAYS taught that way.  It was the educationists and school

I think you guys are comparing apples and oranges.  I learned to read and
write c1960 in a Parochial school using Phonics, which I understand was the
normal method used by Public Schools earlier in the century.   In Phonics, one
learns to pronounce the words as written in normal English using the Latin
alphabet.

Phonetics, which a friend of mine had in a Public Scool at the same time 
was a method in which the children were taught to read and write using a
spoecialized alphabet of symbols recently invented for just that purpose.
I gather that they were supposed to later learn written English by translation.

This method seems to have been soon abandoned.  One obvious drawback is that
it restricts early reading to literature specially prepared for the students
taught by this method.

There seems to be some effort being expended to move back to phonics, (Not
Phonetics).  The original studies which supported the switch to the 'look
see' methods have been largely discredited.  

Newsgroups: sci.math,sci.physics,sci.astro,sci.bio,sci.chem,misc.education
From: rfc@allegra.att.com (Robert F. Casey)
Subject: Re: Is Math Hard?
Organization: AT&T Bell Laboratories, Murray Hill, NJ
Date: Sat, 7 Nov 1992 18:42:03 GMT

>>All you have to do is get enough retired engineers, old mathematicians,
>>etc., then put them into the schools with adequate curriculum and support.

My father used to teach (after he retired from his computer work, and before
age 70) arithmetic to college freshmen at the local community college!
Kids who graduated high school who couldn't do arithmetic.  Saw the text,
and it talked about how to do fractions, divide, multiply, and a few
word problems.  One night he was making up a test, and I suggested a word
problem: "I went to the lumber yard and bought a 4 foot by 8 foot sheet
of plywood.  I cut a 2 foot by 2 foot square out of one of the corners.
How much square footage of plywood do I have left over?"  He said that
that would be too hard for them.  I could have done this in 3rd or 4th
grade.  

One time I visited a friend who had a young kid, about 4 to 5 years old,
and the kid was learning to count and such.  My friend asked questions
like "How many hands do you have? feet? noses?  Could be memorized responses
for answers, so I asked "How many tails do you have?"  kid:"Ahhh...
none! zero!"  He had to think a little for that one, probably noone ever
asked that question before.  Then "How many fingers?  Thumbs?"  "OK,
how many fingers do you have that are not thumbs?"  kid: "Ahh.. 10?"
looks at hands "no, ahhh.. 1,2,3,4,5,6,7,8 eight."  Another wierd
question!
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: Sat, 14 Nov 1992 02:36:06 GMT

In article <1992Nov13.170538.14844@hubcap.clemson.edu> mjs@hubcap.clemson.edu (M. J. Saltzman) writes:
>In article <1992Nov13.154406.4800@CSD-NewsHost.Stanford.EDU> pratt@Sunburn.Stanford.EDU (Vaughan R. Pratt) writes:
>>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.
>
>I don't understand your point.  The simplex method solves linear
>programs (but in exponential worst-case time).

I cited a lower bound on a problem.  What does a lower bound on an
algorithm have to do with this?

>Furhtermore, although linear formulations of the TSP require an
>exponential number of constraints, that in itself is not enough to
>ensure that a problem is NP-hard.

I said "exponential time lower bound."  If you have a justification for
translating this to "NP-hard" then you're in an even better position
than me to make my point that the proof must be wrong.

>I found a reference to a 1978 paper by Papadimitriou (in Math
>Programming), which shows that determining if two tours represent
>adjacent vertices of the TSP polytope is itself NP-complete.  Is this
>the result you're thinking of?

See Yannakakis, STOC'88.
-- 
Vaughan Pratt	  		A fallacy is worth a thousand steps.
Newsgroups: sci.math,sci.physics
From: matmcinn@nuscc.nus.sg (Brett McInnes)
Subject: Re: Three-sided coin (ANSWER)
Organization: National University of Singapore
Date: Fri, 13 Nov 1992 09:08:45 GMT

mueller@schaefer.math.wisc.edu (Carl Douglas Mueller) writes:
: In the DOVER book "Fifty Challenging Problems in Probability with Solutions,"
: the 38th problem is called "The Thick Coin."  It is:  "How thick should a coin
: be to have a 1/3 chance of landing on edge."  

Is there any country in the world that issues such thick coins so we
can check this out experimentally? In my travels I found that the
thickest [relative to diameter] coin is the British pound. But that
isn't thick enough.
Newsgroups: sci.math
From: sassoj@rs6413.ecs.rpi.edu (John J. Sasso Jr.)
Subject: Lebesgue measure
Reply-To: sassoj@rpi.edu
Organization: Rensselaer Polytechnic Institute, Troy, NY.
Date: Fri, 6 Nov 1992 22:43:09 GMT


Hi, 

   I am having trouble with two Real Analysis questions, so thought someone
   might help me out.

    Q1.  If a function f is defined a.e. and continuous a.e. on [0,1], it
         Lebesgue measurable?
         (*  I stated that since f is defined & continuous a.e., it is
             Riemann integrable.  There is a theorem which states that 
             if f is defined & continuous and is Riemann integrable, then
             it is Lebesgue integrable ==>> f is Lebesgue measurable.I get
             stuck here since the 'a.e.' property is not present in this
             theorem
           *)

    Q2.   Does the above property hold if f is right-differentiable only?

    Q3.   If Q1 is the set of all rationals in [0,1], and {I[k]} is a finite
          collection of open intervals which contain Q1, show that the sum of
          the Lebesgue measures of I[k] is > 1.


     Thank you for your assistance.

                  John


Newsgroups: sci.math
From: frisch1@athena.mit.edu (Jonathan Katz)
Subject: Re: Simple Diff Eq
Organization: Massachusetts Institute of Technology
Date: Sun, 8 Nov 1992 19:17:25 GMT

In article <13390031@hpspdla.spd.HP.COM>, ric@hpspdla.spd.HP.COM (Ric Peregrino) writes:
|> 
|> Hello sci.math,
|> 
|> I've come by a simple differential equation that I'm interested in:
|> 
|> df(x)/dx - 1/f(x) = 0
|> 
|> Any information or references would be welcome.
|> 
|> No, this is not homework. 
|> 
|> --------------------------------------------------------------------
|> Ric Peregrino   c/o Hewlett Packard Co.    I represent only myself
|> ric@spd.hp.com  1501 Page Mill Rd Bldg 5M  I may be wrong, maybe not
|> 415-857-7526    Palo Alto, CA 94304        Do DC photons exist?
|> --------------------------------------------------------------------

I don't know what kind of information  you're looking for, but the answer is 
f(x)=(2x)^.5 
(the square root of 2x)
-- 
Jonathan Katz 
Newsgroups: sci.math,comp.theory
From: hansb@cs.ruu.nl (Hans Bodlaender)
Subject: Re: NP Completeness Question
Date: Fri, 13 Nov 1992 13:57:22 GMT
Organization: Utrecht University, Dept. of Computer Science

In <BxMu2J.2JD@watserv1.uwaterloo.ca> nrswart@phonon.uwaterloo.ca (Nicholas R. Swart) writes:

>In article <1dpkkeINNad2@mizar.usc.edu> tunal@mizar.usc.edu (Tamer Unal) writes:
>...
>>My guess is that 1. is in of polynomial complexity while 2.
>>is NP-complete.
>>
>>Any pointers, references, appreciated.
>>
>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.
>
>This proves that P=NP and all NP-complete and all other NP problems thus
>have polynomial time algorithms.
>
>So to answer your question, 1 and 2 are probably both polynomial.
>
>Nicholas
>Dept. of Elec. and Comp. Engineering
>University of Waterloo
>Waterloo, Ontario
>CANADA
>N2L 3G1
>
>>-- 
>>Serdar Boztas
>>posting from someone else's account with their permission
>>normally at serdar@fawlty8.eng.monash.edu.au

Ocasionnally, claims of results that P = NP appear. These have upto now all
shown to be incorrect. So far, no-one has been
able to give a correct proof of P=NP or the converse. Any claim of such a
result should be doupted, before its proof is sufficiently verified.
The result of professor Swart is not known to me, and I assume that it has not
been verified by the scientific community, thus I think one should not base
research on the assumption that the result claimed above is correct.

				Hans Bodlaender
				Dept of CS
				Utrecht University, the Netherlands
Newsgroups: sci.math,sci.physics,sci.astro,sci.bio,sci.chem,misc.education
From: gjm11@cus.cam.ac.uk (G.J. McCaughan)
Subject: Re: definition of topological space
Organization: U of Cambridge, England
Date: Fri, 6 Nov 1992 03:53:52 GMT

Here is another axiomatic definition of "topological space", which is
probably more intuitive than the usual one in terms of open sets.

A topological space is a set X of "points", together with (for each point)
a class of subsets of X, called "neighbourhoods" of the point, such that:

1. If N is a nbhd of x then x is in N.
2. The intersection of two nbhds of x is a nbhd of x.
3. Anything containing a nbhd of x is a nbhd of x.

The idea is that N is a neighbourhood of x if it contains all points "close
enough" to x. For instance, the plane (R^2) is a topological space; say that
a set is a neighbourhood of x if it contains some disc centred on x, and the
axioms are easily verified.

This definition is equivalent to the one in terms of open sets. N is a nbhd
of x iff it contains some open set containing x; on the other hand, U is open
iff it is a nbhd of all its points. (This last is quite a good way of thinking
about just what an open set is.)

-- 
Gareth McCaughan     Dept. of Pure Mathematics & Mathematical Statistics,
gjm11@cus.cam.ac.uk  Cambridge University, England.    [Research student]
From: elkies@ramanujan.harvard.edu (Noam Elkies)
Newsgroups: sci.math
Subject: Tangent Re: Crackpot Relatives
Date: 11 Nov 92 02:51:43 GMT
Article-I.D.: husc3.1992Nov10.215144.17331
Organization: Harvard Math Department

In article <1dp92qINNfj5@master.cs.rose-hulman.edu>
goddard@NeXTwork.Rose-Hulman.Edu (Bart E. Goddard) writes:

>At family reunions, I am always called on to do such difficult math as
>counting heads and 2-digit multiplication.  I always lie.  The best way
>to lie is to have a pre-defined way of generating a wrong answer.  I  
>usually just concatenate all the digits in their question into one big
>number:  "Hey, Bart, what's 34 times 51?"  "3 thousand 4 hundred and
>fifty-one".  [...]

Hey, Bart, what's 2^5 times 9^2?  :-)

--Noam D. Elkies (elkies@zariski.harvard.edu)
  Dept. of Mathematics, Harvard University
From: a_rubin@dsg4.dse.beckman.com (Arthur Rubin)
Newsgroups: sci.math
Subject: Re: Three-sided coin
Date: 12 Nov 92 17:05:31 GMT
Organization: Beckman Instruments, Inc.

In <1992Nov10.204733.25206@massey.ac.nz> news@massey.ac.nz (USENET News System) writes:

>I doubt it. Any asymmetrical object will be affected by air resistance
>in a fairly predictable way, so the probability will depend on how far
>the coin falls. One can hope that the bounce will be unpredictable, but
>that depends on the surface the coin falls on and was not specified in
>the problem. If you want to throw a randomising device, you'd better
>stick to Platonic solids.

Semi-regular polyhedra should be adequate.  Actually, I don't know the term
but any solid with the property that, for any two faces, there is a
quasi-Euclidean transformation (rotations + reflections) that maps one to
the other, is sufficient.  (The usual definition of semi-regular requires
that the faces be regular polygons.)  If you want to include non-convex
solids, you define "face" for the purpose of this requirement to be "face
of the convex hull".
--
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: len@math.nwu.edu (Len Evens)
Newsgroups: sci.math
Subject: Re: who should teach calculus?
Date: 13 Nov 92 00:05:28 GMT
Article-I.D.: news.1992Nov13.000528.12551
Organization: Dept of Math, Northwestern Univ

In article <1992Nov12.203923.26575@magnus.acs.ohio-state.edu>, gedgar@magnus.acs.ohio-state.edu (Gerald A Edgar) writes:
> 
> How about: "should algebraists teach calculus?"
> Are they the ones who say, "I have never used hyperbolic functions,
> so we can skip that section"??
> -- 
>   Gerald A. Edgar                Internet:  edgar@mps.ohio-state.edu
>   Department of Mathematics      Bitnet:    EDGAR@OHSTPY
>   The Ohio State University      telephone: 614-292-0395 (Office)
>   Columbus, OH 43210             -292-4975 (Math. Dept.) -292-1479 (Dept. Fax)

-- 
I have been told by professors in engineering departments exactly
the same thing.  If you go around and collect information on what
to leave out from everyone in sight you end up with almost
nothing.  If you collect information on everything which should be
included you get a 3 year calculus sequence.
Leonard Evens      len@math.nwu.edu      708-491-5537
Dept. of Mathematics, Northwestern Univ., Evanston, IL 60208
From: bruck@mathj.usc.edu (Ronald Bruck)
Newsgroups: sci.math
Subject: Re: Erdos number
Date: 13 Nov 1992 10:33:01 -0800
Organization: University of Southern California, Los Angeles, CA
NNTP-Posting-Host: mathj.usc.edu

In article <1992Nov12.224157.23146@infodev.cam.ac.uk> sl25@cus.cam.ac.uk (Steve Linton) writes:
>The definition of Erdos number clearly implies the existence of the Erdos graph,
>in which the number is sinmply distance from Erdos. 
>
>1) observe that this graph is undirected in mathematics, but directed (by the
>order of the author's names on the paper) in most sciences. Does this allow any
>interesting generalisations?
>
>2) are there (among mathematicians) any connected components of size greater than
>one not connected to Erdos.



Here's another question I've always wondered about:  what is Gauss's Erdos
number?

It certainly makes sense to ask such a question, since coauthorship can
extend into the past as well as the future.  The answer might be trivial,
because it is my __impression__ that coauthorship was rare until relatively
recently.  Does anyone know offhand whether Gauss ever coauthored a paper?
(For that matter, where can one find a list of his publications?  Relatively
short, given his motto.)

--Ron Bruck
bruck@mtha.usc.edu preferred
From: akessler@bernard.ma.utexas.edu (Adam Kessler)
Newsgroups: sci.math
Subject: Re: Who are our best mathematicians?
Date: 6 Nov 92 15:21:18 GMT
Organization: University of Texas at Austin Mathematics

>Actually, it's been awhile since I've seen anything substantive from Gauss.
>Is he on sabbatical this year?

I have heard that Hilbert and Gauss are working on some of the problems that
have popped out of the newly discovered contradiction about the interval
[0,1) being irrational (since it lacks a rational point), but having 
rational length.
Newsgroups: sci.math,sci.physics
From: djpegg@utkvx2.utk.edu (PEGG, DAVID J)
Subject: Re: Three-sided coin
News-Software: VAX/VMS VNEWS 1.41    
Organization: University of Tennessee Computing Center
Date: Wed, 11 Nov 1992 22:36:00 GMT

In article <1drt9sINN7hu@darkstar.UCSC.EDU>, ask@ucscb.UCSC.EDU (Andrew Stanford Klingler) writes...
> 
>Coins "flip nicely" because they're nearly two-dimensional symmetric objects.
>If I remember my mechanics correctly, the only stable rotations are about the
>inertial axes with the highest and lowest moments.  In this case that means
>the "vertical" axis and any "horizontal" axis.  I don't recall how to
>compute the angular trajectory of an object with an arbitrary initial
>orientation and spin, but the general answer will not be proportional times
>for proportional solid angles.  If the coin is "nicely flipped" it should
>be proportional times for proportional pure angles, giving a "floating
>through honey" solution h=d.  But as you say, this is far from relevant
>to a real throw.
> 
> 
Don't forget that the coin presents its edge twice as often as a head
or tail. So I'd say a first approximation for "floating thru honey"
would be 2h=d. But then the center o' mass is different. It's taller
and narrower when landing on an edge and thus must land in a smaller
range of angles to settle onto its edge.  
Let's see, we need 120 degrees per face (60 per edge). That gives
1.73h=d where d is diameter. (I think this'll work even without the
honey.)
Newsgroups: sci.math
From: dmsilev@athena.mit.edu (Daniel M Silevitch)
Subject: Re: Help wanted in integration.
Organization: Massachusetts Institute of Technology
Date: Mon, 9 Nov 1992 14:06:18 GMT

In article <1992Nov9.104113.17807@sun0.urz.uni-heidelberg.de>, afm@trillian (Andreas Mueller) writes:
|> UKJW@DKAUNI2.BITNET ("Christoph Schlenker") writes:
|> : Hello,
|> :
|> : I have just typed your integral into a math-prg and the solution
|> : of it is just    0.
|> <stuff deleted>
|> : I hope thats right...                                 Christoph
|> It cannot possibly be right: the integrand is a function >=0,
|> so the integral cannot vanish unless the integrand is identically
|> zero, which it is obviously not.
|>                                 Andreas Mueller
|> 
|> ---------------------------------------------------------
|> Andreas Mueller         afm@vogon.mathi.uni-heidelberg.de
|> Mathematisches Institut
|> Im Neuenheimer Feld 288
|> W - 6900 Heidelberg 1
|> ---------------------------------------------------------

I missed the initial post, but I can offer some insight on why the math
program gave an incorrect result. If the function inside the integral is
strongly periodic (ex. sin^2(32*X) ), and the two limits contain an
integer number of cycles, it is very likely that incorrect results will
be returned, due to the algorithm used by most programs to evaluate
integrals. The most common numeric algorithms are variants of Simpson's
rule. They usually start with 2 or 4 trapezoids, and doube the number of
subdivisions until the answer converges. With the function given above,
integrating from 0 to 2*pi, the first 6 subdivisions will all have the
integral evaluated at roots of the function. The system will see that 6
consecutive estimates are 0, and therefore assume that the integral has
value 0. To get around this, split the integral into two integrals of
differing limits (1/3, 2/3 of the range works well) and sum the results.
Note that this is a consequence of numerical integration algorithms, and
is not present in symbolic math programs.

Daniel Silevitch                           dmsilev@athena.mit.edu
Massachusetts Institute of Technology
Newsgroups: sci.math,misc.education