HDTenEightyP/NetNews huggingface dataset:
From: gilligan@bldrdoc.gov (Jonathan M. Gilligan)
Newsgroups: sci.math,sci.physics,sci.astro,sci.bio,sci.chem,misc.education
Subject: Re: What can we have for an educational system?
Date: 12 Nov 92 19:50:19 GMT
Followup-To: sci.math
Organization: National Institute of Standards and Technology

In article <lwalsh.721498112@news.cso.uiuc.edu> lwalsh@nemo (Laura L. Walsh) writes:
>I agree.  Think about teaching a class in a university.  Typically,
>the class meets 3 times a week for 50 minutes.  The instructor will
>spend about an hour preparing for each class (photocopying, getting
>references, checking the texts, etc.).  The class meets for 16 weeks
>in the semester.  The instructor teaches a maximum of 2 courses a
>semester.  Bathroom breaks are permitted, as is lunch with colleagues.

Funny... when I was in my last year of grad school, I simply could not
get my advisor into the lab to help me with the lasers until after 6
in the evening (he came in at 8 to 8:30 in the morning) or on the
weekends (well, maybe for an hour or so during a weekday if it was
really important) because he was spending so much time preparing for
class. He was teaching (for the first time) a junior-level E&M class
and related lab and spent about 8 hours a day five days a week
preparing for lectures, preparing experiments for the lab, teaching,
or meeting with students.

Other years, he wasn't so busy because he wasn't teaching two courses
for the first time, but he usually spent several hours a day preparing
lectures.

Research was what the hours from 6 to 11 pm and weekends and
university vacation time were for.

>I recognize that the above leaves out the research functions of
>the university instructor.  But the point is that the TEACHING
>obligations are enormous for elementary school teachers.  They
>are extremely busy when they are working and they NEVER have
>enough time to do the job that we, and usually they, would like
>to do.  I will grant that many are not actually competent to
>do it, we have had personal experience with that last year, but
>I don't think we will retain competent teachers when the working
>conditions are so difficult and the pay is so meager.
>Laura Walsh

You are essentially right on these points, but having a PhD would be
more appropriate in a high-school setting than an elementary one.  I
speak as a Physics PhD and an ex-high-school teacher. When I was
teaching, one of my colleagues in English had a PhD, as did one in
French and one in history. The specialization that accompanied those
degrees was not of immediate relevance to teaching, but the depth of
understanding of the field that came from working so intensely in it
for several years.

---Jon

-- 

Disclaimer --- The government probably disagrees with my opinions.
From: ramsay@unixg.ubc.ca (Keith Ramsay)
Newsgroups: sci.math
Subject: Re: What's a knot? (inspired by "What's a manifold?")
Date: 7 Nov 1992 02:11:58 GMT
Organization: University of British Columbia, Vancouver, B.C., Canada
Distribution: sci
NNTP-Posting-Host: unixg.ubc.ca

In article <COLUMBUS.92Nov6105242@strident.think.com> 
columbus@strident.think.com (Michael Weiss) writes:
|I would summarize almost all the discussion in favor of the atlas
|definition of a manifold in one phrase:
|
|	proofs drive definitions
|
|in other words, old, "intuitive" definitions are replaced by new "abstract"
|definitions when the new definitions turn out to be more convenient for the
|logical development of the subject.

This is also one of the main points of _Proofs_and_Refutations_ by
Imre Lakatos. His example is the concept of "polyhedron".

Keith Ramsay                "Tender victuals"
ramsay@unixg.ubc.ca
Newsgroups: sci.math,sci.physics,sci.astro,sci.bio,sci.chem,misc.education
From: clin@eng.umd.edu (Charles Lin)
Subject: Re: What can we have for an educational system?
Date: Wed, 11 Nov 92 21:07:15 GMT
Organization: College of Engineering, Maryversity von Uniland, College Park
Originator: clin@delta.eng.umd.edu


In article <ARA.92Nov11034458@camelot.ai.mit.edu>, ara@zurich.ai.mit.edu (Allan Adler) writes:
>
>
>As I have pointed out on other occasions, if they would improve the
>working conditions, they could have PhD's teaching in the public schools.
>I don't mean improve them a little. I mean offer working conditions that
>would make a PhD happy and the glut of unemployed and underemployed
>PhD's will beat down the doors of the schools trying to get in.
>
>The working conditions say most eloquently how little the public cares
>about education.

   Exactly what do you mean by working conditions?  I just saw something on
CNN last night about how public schools in California are overcrowded.  Obviously,
these conditions are not exactly amenable to good learning (though I suspect
some other countries tolerate just as bad conditions and still produce
good students) and it isn't what a Ph.D. would like to teach in, but
even with improvements in teaching facilities (heating/AC, enough desks,
janitorial services, equipment, etc.), there's still the matter of
teaching.

   I had a high school teacher tell me that his biggest problems were
discipline and having the parents care.   We blame a lot of the problems
on the school, but by necessity, these schools have a fairly poor teacher
to student ratio.  In addition, the teaching profession is hardly respected.
Not enough parents take enough time to actually get involved in the
education of their children.   Parents don't even have to be well-educated
for their children to succeed as long as they believe in the value of education
and keep telling their children that it is something they ought to strive for.

   In fact, the high school teacher told me that when he was TA'ing (he
was on sabbatical and was teaching a course in math to pay part of his
expenses for a Ph.D.) a course in basic math, the students in this course
were much better behaved than his high school students who may have been
brighter.   Ph.D.'s would beat down doors if they felt that students
are interested in learning, but if they are not, are they prepared to
motivate them to learn?  In a college, students are paying to learn,
and if they want to waste their money by not trying, profs. don't have
to worry since these students will probably not cause disciplinary problems.

   To change the education situation in American will take a great deal
of changing of cultural beliefs, and this may be harder to do than
doling out money to improve schools.

--
Charles Lin
clin@eng.umd.edu
Newsgroups: sci.math
From: hrubin@pop.stat.purdue.edu (Herman Rubin)
Subject: Re: To express Q(x)/P(x) into continued fraction
Organization: Purdue University Statistics Department
Date: Thu, 5 Nov 1992 18:05:18 GMT

In article <1992Nov5.064414.28859@griffin.itc.gu.edu.au> jchen@sct.gu.edu.au (Jinghong CHEN) writes:

>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.

As stated, it cannot be done, because Q(x)/P(x) approaches a non-zero limit
as x -> infinity in general.  So you would have to add a constant.  

Even in this case, it usually cannot be done, and if the last a were dropped,
the quotient would have to be odd.  You have only n+1 a's and 2n constants.
However, for almost all such fractions, you can get the expression if
an additive constant is allowed before each fraction.  One way to do this,
and other similar things, is by brute force; see the book by Khovanskii
and Khovanskii.  In exceptional cases, it may be necessary to use higher
degree polynomials before each fraction.  In most problems, doing it by
brute force is about as easy as any other method.
-- 
Herman Rubin, Dept. of Statistics, Purdue Univ., West Lafayette IN47907-1399
Phone: (317)494-6054
hrubin@pop.stat.purdue.edu (Internet, bitnet)  
{purdue,pur-ee}!pop.stat!hrubin(UUCP)
From: andrew@rentec.com (Andrew Mullhaupt)
Newsgroups: sci.math
Subject: Orthogonal Polynomials
Keywords: Multivariate Orthogonal Polynomials Jacobi Matrix
Date: 4 Nov 92 23:42:27 GMT
Organization: Renaissance Technologies Corp., Setuket, NY

The recurrence relation for univariate orthogonal polynomials can be
written as a tridiagonal symmetric (i.e. Jacobi) matrix eigen-problem.

What (if any) is the analogous result for multivariate polynomials?

Later,
Andrew Mullhaupt
Newsgroups: sci.math
From: pratt@Sunburn.Stanford.EDU (Vaughan R. Pratt)
Subject: Re: Mercator Projection
Organization: Computer Science Department,  Stanford University.
Date: Tue, 10 Nov 1992 04:38:05 GMT

In article <1992Nov10.024331.10080@galois.mit.edu> jbaez@riesz.mit.edu (John C. Baez) writes:
>Hmm, maybe I'm confused.  Let t be the angle from the equator
>(latitude) and x the distance from the equator on the Mercator
>projection.  (The Mercator projection projects draws a line from the center
>of the earth through the surface of the earth and then to an imaginary
>cylinder running north-south into which the earth fits snugly, right?)
>Then x = sec t.  But if you want to know the amount by which linear
>dimensions are multiplied *right at latitude t* you need dx/dt = sec^2
>t.  Areas would then go as sec^4 t.  (Here you need to note that
>east-west lengths are getting scaled the same way as north-south
>lengths, i.e. that the Mercator projection is conformal.)  

No projection matches this description.  The horizontal dimension
necessarily scales as sec(t).  The vertical dimension of the projection
you describe (globe center through point onto cylinder, as described
for example by the Encyclopedia Britannica) scales as sec^2(t) as you
say, but for a net area of sec^3(t).  The real Mercator projection
scales vertically by sec(t) *in order* to be conformal.  As previous
posters have pointed out, the Mercator projection is the unique
conformal projection with straight meridians; equivalently the unique
projection sending rhumb lines (lines of constant bearing) to straight
lines of the corresponding slope.

Sec^4(t) would make Greenland look 20 times bigger than South America!
-- 
Vaughan Pratt
Newsgroups: sci.math
From: lombardo@ghost.dsi.unimi.it (franco lombardo)
Subject: Functions for n-valued logic
Keywords: n-valued logic
Organization: Computer Science Dep. - Milan University
Date: Thu, 12 Nov 1992 16:16:37 GMT

Hi!
I have this problem:
i have a function f:{0,1/2,1}^3--->{0,1/2,1}^3 completely described
by a table and i  want to express it using the operators of
a three-valued Lukasiewicz logic: and, or, not and
Lukasiewicz implication.
Would you like to help me?
			   Franco Lombardo.
		      lombardo@ghost.dsi.unimi.it
From: ahanysz@spam.ua.oz (Alexander Hanysz)
Newsgroups: sci.math
Subject: Re: symbolic derivation of polynomial roots
Summary: That's cheating!
Date: 11 Nov 92 23:56:16 GMT
Organization: Department of Pure Mathematics, University of Adelaide

In article <5412@daily-planet.concordia.ca> mckay@alcor.concordia.ca (John McKay) writes:
>
>My understanding is that the roots of ANY polynomial in Q[x] 
>can be expressed in terms of radicals. What is the trick?
>You may need infinitely many of them.

Well, if you're going to be like that then you don't even need radicals!
Any real number can be expressed in terms of integers and arithmetic
operations.  You just need infinitely many of them.  It does seem to
trivialise the issue somewhat.

								Alex.

From: ric@hpspdla.spd.HP.COM (Ric Peregrino)
Date: Fri, 6 Nov 1992 00:30:12 GMT
Subject: Simple Diff Eq
Organization: HP Stanford Park - Palo Alto, CA
Newsgroups: sci.math


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?
--------------------------------------------------------------------
Xref: sparky sci.math:14913 sci.physics:18820
From: pratt@Sunburn.Stanford.EDU (Vaughan R. Pratt)
Newsgroups: sci.math,sci.physics
Subject: Re: Three-sided coin
Date: 13 Nov 92 16:11:46 GMT
Organization: Computer Science Department,  Stanford University.

In article <1992Nov13.065340.28950@CSD-NewsHost.Stanford.EDU> pratt@Sunburn.Stanford.EDU (Vaughan R. Pratt) writes:
>Here's Joe's simplest construction of a fair n-sided die for n >= 5.
>Cylindrify (prismify) a regular n-agon.

In an email message to me Peter Hamer turned my own argument (favoring
1/sqrt(3) over 1/sqrt(8) as Thickness/Diameter for 1/3 chance of a coin
landing on edge) about dependence on initial conditions against the
above.  One might say his point was that there ain't no such thing as a
fair launch.

So here's a die to contradict TANSTAAFL, namely one for which a fair
launch is easy.  For n=6, just take an ordinary lead pencil.  This
generalizes readily to n >= 3.
-- 
Vaughan Pratt	  		A fallacy is worth a thousand steps.
Date: Wednesday, 4 Nov 1992 15:53:16 EST
From: <RVESTERM@vma.cc.nd.edu>
Newsgroups: sci.math
Subject: feynman story probably not true.

a little while ago, somebody posted a story to this effect: for a
certain physics exam at caltech, students were allowed to use any
reference material that they could carry in to the room.  one
enterprising guy supposedly carried richard feynman in.

around the same time that this story was posted, a bunch of people
in another conference, alt.culture.tuva, were claiming to know
ralph leighton, who co-authored some books with richard feynman.
i posted a message in alt.culture.tuva asking them to ask mr. leighton
if he knew whether the story was true or not.

a few days later, i got a mail message from mr. carl feynman, richard
feynman's son.  it included my posting in alt.culture.tuva, and said,

     "it's not true as far as i know.  it's such a good story,
      i would think that my father would have told it to me if
      it were true, and this is the first i heard of it.  however,
      it is not inconceivable."

i thought you'd like to know.

bob vesterman.
From: weemba@sagi.wistar.upenn.edu (Matthew P Wiener)
Newsgroups: sci.math
Subject: Re: Trivial! (was: Re: Help X^2 == Y mod N)
Date: 5 Nov 92 19:48:50 GMT
Reply-To: weemba@sagi.wistar.upenn.edu (Matthew P Wiener)
Organization: The Wistar Institute of Anatomy and Biology
In-reply-to: tycchow@riesz.mit.edu (Timothy Y. Chow)

In article <1992Nov5.170945.1740@galois.mit.edu>, tycchow@riesz (Timothy Y. Chow) writes:
>>Wiener wandered away in deep thought and returned 20 minutes
>>later to announce triumphantly that it was indeed trivial.

>I've heard this exact same story told about Hardy and von Neumann and
>various other mathematicians.  Is there any hope of figuring out if such
>an event actually occurred and if so who it was?

Yes.  I admit I did it.  End of discussion.
-- 
-Matthew P Wiener (weemba@sagi.wistar.upenn.edu)
Newsgroups: sci.math
From: cory@riemann.math.mun.ca (Cory C. Pye)
Subject: Re: Simple Diff Eq
Organization: Chem Dept., Memorial University of Newfoundland
Date: Mon, 9 Nov 1992 12:17:23 GMT

In article <1992Nov8.191725.14856@athena.mit.edu> frisch1@athena.mit.edu (Jonathan Katz) writes:
>In article <13390031@hpspdla.spd.HP.COM>, ric@hpspdla.spd.HP.COM (Ric Peregrino) writes:
>|> I've come by a simple differential equation that I'm interested in:
>|> 
>|> df(x)/dx - 1/f(x) = 0
>|> 
>
>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)

That should read 'an' answer. A family of solutions exists, namely

f(x) = (2(x+c))^.5

where c is any constant.
-Cory Pye

-- 
Cory Pye, grad student in Theoretical Chemistry.
From: gjm11@cus.cam.ac.uk (G.J. McCaughan)
Newsgroups: sci.math
Subject: Re: Axioms of set theory, infinity and R. Rucker
Date: 7 Nov 92 17:19:17 GMT
Organization: U of Cambridge, England

In article <BxBpwq.LFM@mentor.cc.purdue.edu> hrubin@mentor.cc.purdue.edu (Herman Rubin) writes:

>However, one does not need the axiom of choice.  The ordinal numbers, defined
>as in Godel, for example, do not need that axiom for the definition.  Then
>for any set x, the Hartogs function of x, which is the set of all ordinal
>numbers of size smaller than or equal to x, is an ordinal number not of such
>a size.  This must contain the natural numbers if x is not a finite set, so
>any kind of infinite set is adequate.

Oh yes. Thanks; I was a little worried about saying that you couldn't always
find a countable set with "there exists an infinite set" and no AC, but I
couldn't see a way to get one. I'd forgotten Hartogs' theorem completely.

>It is not possible to have a smaller infinite set than the natural numbers,
>but it is possible to have infinite sets of a size incomparable to that of
>the natural numbers.

Yes, I know. I didn't want to be overcomplicated in answering a simple
question like this one, though.

-- 
Gareth McCaughan     Dept. of Pure Mathematics & Mathematical Statistics,
gjm11@cus.cam.ac.uk  Cambridge University, England.    [Research student]
Newsgroups: sci.math
From: rjk@world.std.com (robert j kolker)
Subject: Oldy but Goody Geometry Problem
Keywords: Euclidean Geometry, Triangle
Organization: The World Public Access UNIX, Brookline, MA
Date: Fri, 13 Nov 1992 23:57:05 GMT

I am looking for a classic style proof to the following:

The plumb lines of a plane triangle meet in a single point. Plumb line is
the line dropped orthagonally from a vertex to the opposite side.

The algebraic proof in analytical fashion is trivial, but I can't for the
life of me get a classic Greek style proof. If you can help please e-mail.

Much thanx.

Bob Kolker
 

Newsgroups: sci.math
From: tao@fine.princeton.edu (Terry Tao)
Subject: Assorted questions and problems 
Organization: Princeton University
Date: Sun, 8 Nov 1992 18:16:31 GMT

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.

(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?

(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?

please answer by email.

Terry
 
Newsgroups: sci.math,sci.physics,sci.astro,sci.bio,sci.chem,misc.education
From: onar@hsr.no (Onar Aam)
Subject: Re: 2-dimensional grading system (was Re: What can one do for the bright?)
Organization: Rogaland University Centre
Date: Mon, 9 Nov 1992 17:11:41 GMT


>In article <1992Nov5.070342.6288@hsr.no>, onar@hsr.no (Onar Aam) writes:
>
>|> What the hell are you guys talking about?(!) This is EXACTLY why I proposed the
>|> 2D grading system in the first place. With today's grading system you only get
>|> one grade which includes both effort and grasp. With this system the employer
>|> wouldn't know whether his employee has brains or not. With a 2D system, however,
>|> the employer gets that vital information. 
>
>What are YOU talking about? The question that was being addressed is WHY WOULD
>ANYBODY CARE ABOUT THE EFFORT PUT IN CLASSES? It is additonally unclear whether
>A's would go to those people who put in the least effort, or if you would give
>A's to the people who are dumb and couldn't learn it in twice the time that other
>people could, but gave up a social life so they could get an A on the academic
>part.
>
>Jason W. Solinsky

Are you an employer? I find that very unlikely. Employers are in most cases
interested in people who are willing to work, not in some brilliant-but-lazy guy.
Someone with a grade: effort=A , understanding=C is probably VERY much wanted
by an employer. 



Onar.
   

Newsgroups: sci.math
From: pratt@Sunburn.Stanford.EDU (Vaughan R. Pratt)
Subject: Re: definition of topological space
Keywords: Topology; Open sets; Continuity
Organization: Computer Science Department,  Stanford University.
Date: Thu, 5 Nov 1992 16:55:30 GMT

In article <1992Nov5.094404.15550@infodev.cam.ac.uk> rgep@emu.pmms.cam.ac.uk (Richard Pinch) writes:
>Incidentally, {1,2,3} {} {1} is a perfectly good family of open sets
>for a topology on {1,2,3}: but it has nothing to do with epsilons and
>deltas.

Well, not nothing at all.  Any topology determines the nearness
relation:  point x is NEAR set Y when x does not belong to Y but does
belong to every closed set containing Y (i.e. to the CLOSURE of Y).

(The points near the INTERIOR of X (= complement of closure of
complement of X) constitute the FRONTIER of X.  The BOUNDARY of X is
the portion of its frontier lying within X, equivalently those points
near the complement of X.  So the frontier of X is the boundary of X
plus all points near X.)

Applying this to the example, 1 is a hermit (is near no set) while 2 is
near {1}, {3}, and {1,3}, and 3 is near {1}, {2}, and {1,2}.  (So x
being near singleton {y} need not imply that y is near singleton {x}.)

This is the topologically abstract expression of the general idea of
epsilon-delta.
-- 
Vaughan Pratt				There's no truth in logic, son.
From: weemba@sagi.wistar.upenn.edu (Matthew P Wiener)
Newsgroups: sci.math
Subject: Re: Axioms of set theory, infinity and R. Rucker
Date: 11 Nov 92 19:35:17 GMT
Reply-To: weemba@sagi.wistar.upenn.edu (Matthew P Wiener)
Organization: The Wistar Institute of Anatomy and Biology
In-reply-to: ara@zurich.ai.mit.edu (Allan Adler)

In article <ARA.92Nov11024751@camelot.ai.mit.edu>, ara@zurich (Allan Adler) writes:
>What is the reference to this recent work of Matiyasevich and Jones?

I remember a research announcement in BULL AMS, early 80s, with an
explicit universal diophantine equation.

>Also, I've never understood what a supercompact cardinal is. Would you
>like to explain the concept?

(In my campaign for ASCII fake Greek, I will use % for kappa and $ for
lambda and @ for alpha.  P%[X] denotes the set of %-sized subsets of X)

A cardinal % is called measurable if there exists a non-trivial %-additive
ultrafilter on it.  This is equivalent (via an ultrapower of the whole
universe construction) to the assertion that there is an elementary
embedding j:V->M such that %<j(%) and % is the first cardinal moved,
and M^@ is contained in M for @<%.  Not all filters have quite the
right properties for this construction--you have to work with what are
called normal ultrafilters.  There is also a notion, based on the desire
for compactness theorems for infinitary logic, of strongly (and weakly)
compact cardinals.  In terms of ultrafilters, it works out that a cardinal
% is strongly compact if for all $>%, P%[$] has a non-trivial %-additive
ultrafilter. One would like to carry out the same normalization construction
as for measurable cardinals, but the proof just doesn't happen.  So a
supercompact cardinal is _defined_ like the strongly compacts, but with
the additional requirement that P%[$]'s filter is normal from the beginning.
This leads, for any $>%, to elementary embeddings j:V->M such that % is
the first cardinal moved, j(%)>$, and furthermore M^$ is contained in M.

The general consensus seems to be that measurable cardinals are fairly
reasonable beasties, with good inner-model theory, but that supercompacts
are beyond any true comprehension.  One indication of this is the recent
taming of AD, at a level well below supercompact.
-- 
-Matthew P Wiener (weemba@sagi.wistar.upenn.edu)