HDTenEightyP/NetNews huggingface dataset:
From: hrubin@pop.stat.purdue.edu (Herman Rubin)
Subject: Effects of the schools
Organization: Purdue University Statistics Department
Date: Mon, 9 Nov 1992 13:35:54 GMT

In article <ccDyTB3w164w@allen.com> carolyn@allen.com (Carolyn Allen) writes:
>> 	(P. S. I'm not complaining... I like Michigan State.  I am,
>> however, rather jaded from the years of school for which I have nothing
>> useful to show.  Also, while I haven't done disastrously, my grades
>> here don't reflect my ability well because my high school did NOTHING
>> to teach me the study skills I would need here, so I am trying to
>> teach myself, as usual.)

>...excuse me, but what class is supposed to teach you study skills? 

			...................

With this I agree.  Many of the schools actually do attempt to teach
study skills.  These might improve regurgitation, like the advertized
materials, "Where There's a Will There's an A," but as for understanding,
each must develop essentially on his own, with constructive criticism.
Just as one cannot teach people how to find proofs, one cannot teach
study skills.

>> 	In the U. S., how much money you have to play with is one 
>> BIG factor in determining what you can do.

>...In the U.S. (and elsewhere), how much determination you have is one 
>BIG factor in what you do with the money you have.

>Necessity is the mother of invention...no one said that money inspires 
>creativity, self-discipline or intelligence. You're facing necessity, so 
>count your blessings and cut the jealousy. You have been given a 
>background that can motivate you to great heights if you appreciate it 
>for the kick in the behind it is.

He has been given a background, but he rightly complains about having 
been denied at least 5 years of education by the schools and the effects
of the stultifying atmosphere.  And we should join him in decrying the
waste of talent.
-- 
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)
Xref: sparky sci.math:14842 sci.physics:18763 sci.astro:11913 sci.bio:4108 sci.chem:4531 misc.education:4262
From: lwalsh@nemo (Laura L. Walsh)
Newsgroups: sci.math,sci.physics,sci.astro,sci.bio,sci.chem,misc.education
Subject: Re: What can we have for an educational system?
Date: 11 Nov 92 16:08:32 GMT
Organization: University of Illinois at Urbana

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.
>Allan Adler ara@altdorf.ai.mit.edu

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.

Now back to the elementary school:  School starts (for my daughter
at 8:15), the teachers get a 5-10 minute bathroom break when they 
trade off for recess.  They get 45 minutes at lunch.  School gets 
out at 3:00.  That means 370 minutes of instruction time, about 6 
hours per day.  If we gave them 1 hour of preparation for each 
instructional hour, they would have to live at the school.  But 
elementary teachers don't have to research the material they teach, 
you say?  Wrong!  They actually have to do two different kinds of 
research.  First, they need to know the material and how to present 
it.  Secondly, they have to know the capabilities of each and every 
child they teach and how to reach each one.

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
Xref: sparky sci.math:14616 misc.education:4200
From: carolyn@allen.com (Carolyn Allen)
Newsgroups: sci.math,misc.education
Subject: Re: Is Math Hard?
Date: Sun, 08 Nov 92 22:39:23 EST
Organization: Allen Marketing Group - Raleigh, NC

> 	(P. S. I'm not complaining... I like Michigan State.  I am,
> however, rather jaded from the years of school for which I have nothing
> useful to show.  Also, while I haven't done disastrously, my grades
> here don't reflect my ability well because my high school did NOTHING
> to teach me the study skills I would need here, so I am trying to
> teach myself, as usual.)

...excuse me, but what class is supposed to teach you study skills? I 
thought every kid knows how to learn, some better than others, but if a 
child learns to talk, walk and potty in the right place, that child has 
study skills.  Applying them in complex ways is up to the motivation of 
the individual and you are sitting on a pitty pot, my young man.

> 	In the U. S., how much money you have to play with is one 
> BIG factor in determining what you can do.

...In the U.S. (and elsewhere), how much determination you have is one 
BIG factor in what you do with the money you have.

Necessity is the mother of invention...no one said that money inspires 
creativity, self-discipline or intelligence. You're facing necessity, so 
count your blessings and cut the jealousy. You have been given a 
background that can motivate you to great heights if you appreciate it 
for the kick in the behind it is.
Newsgroups: sci.math
From: dy@shire.math.columbia.edu (Deane Yang)
Subject: Re: What's a manifold?
Organization: Mathematics Department, Columbia University
Date: Mon, 9 Nov 1992 19:34:45 GMT
X-Posted-From: shire.math.columbia.edu
NNTP-Posting-Host: sol.ctr.columbia.edu

As a practicing differential geometer, the atlas definition of
a manifold is the most "natural" (in the long run) and the most
useful. Baez has argued for the scheme definition. This, in
general, has proved less useful, except for those doing
algebraic geometry and those doing Alain Connes' noncommutative
differential geometry (These are both very important areas
of current research).

The problem in teaching this definition, however, is that I also
believe that when you're introducing a new concept to students,
it's important to be completely precise and unambiguous in
your notation, so that students have less to get confused about.
But all this discussion about atlases and maximal atlases
plus all the indices up and down labelling the open sets and the
coordinates makes for a big mess that obscures the essential
ideas.

If I could control how students learn about manifolds from the
start, I think I would follow history (as was described in
an earlier posting). Teach the students about 2-manifolds
and Riemann surfaces first. Riemann surfaces can be motivated
very nicely using complex analysis. Moreover, I think it's
much easier to work with a holomorphic manifold at the start.
Also, since the dimension is 1, there's one less index to
clutter up the notation.
From there, it's not hard to generalize to higher dimensions
and less regularity.

I'm teaching an introduction to manifolds course right now.
What I chose to do is to first define the notation of a
"local manifold", which is simply a manifold that is
diffeomorphic to an open set of Euclidean space.
I have emphasized an analogy with abstract linear algebra,
where a vector space is really the same thing as R^n, but
where we've chosen treat all bases on equal footing.
A local manifold is an open set in R^n, where we treat
all possible coordinate systems on equal footing.

The advantage I see in doing this is that I only
need one coordinate chart at a time and I don't have
to mess around with covers of charts. I'm now developing
the usual foundations of manifolds in this limited setting.

Later, I will observe that local manifolds can be
glued together in the obvious way, and we'll get
the standard notion of a manifold. I'll also
discuss why everything we've done so far generalizes
to manifolds.

When teaching the "local theory of manifolds", which is
what is usually done in an introductory course, I always
find myself emphasizing that the notion of a manifold
is in some sense a nonlinear analogue of the notion of
a vector space.

The problem with this approach is that it assumes the
students have come to terms with abstract linear algebra.

Any suggestions and ideas about what should be taught
in such a course and how the course should be taught
are welcome.

Newsgroups: sci.math
From: pratt@Sunburn.Stanford.EDU (Vaughan R. Pratt)
Subject: Re: Extended Fermat primes
Organization: Computer Science Department,  Stanford University.
Date: Sun, 8 Nov 1992 18:36:18 GMT

In article <1992Nov7.172207.17207@husc15.harvard.edu> blom@husc15.harvard.edu writes:
>Fermat primes have the form
>
>  n
> 2
>2  + 1.
>
>One extension of this form could be
>
>     n
>    2
>(2a)  + 1.
>
>The largest prime of this form I have encountered is
>
>    7
>   2
>120  + 1.
>
>Does anyone know of any larger primes of this form?

Sticking to exponent 128, replacing 120 by 190 and 234 yields the next
two primes.  Nothing more out to 500.
-- 
Vaughan Pratt
Newsgroups: sci.math
From: wjcastre@magnus.acs.ohio-state.edu (W.Jose Castrellon G.)
Subject: Re: Assorted questions and problems
Organization: The Ohio State University,Math.Dept.(studnt)
Date: Mon, 9 Nov 1992 22:44:36 GMT

In article <1992Nov9.191022.12493@Princeton.EDU> tao@potato.princeton.edu (Terry Tao) writes:

>|> >(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?
>

There is still a counterexample:   (0,1)  and   (0,1)  together with a set
order isomorphic to the rationals, all of whose elements you'll call bigger
than the ones of (0,1). However if you assume that both sets are _superdense_
(I dont know the standard term): i.e. for every pair A, B of countable subsets
if every element of A is strictly smaller than every element of B, then there
is a  x  in between; then in this case by a back-and-forth argument (same as
for showing that all dense unbounded countable orderings are isomorphic to Q) 
it turns out to be 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?
>

Still there is a counterexample: One cannot map the first uncountable ordinal
in an order preserving fashion into the real numbers, one can even get a pair 
of dense sets with no order preserving map of anyone into the other [same 
technique].

>Thank you for the large number of responses.
>
>Terry
Newsgroups: sci.math
From: phkahler@vela.acs.oakland.edu ( Paul H. Kahler)
Subject: A REAL 3-sided coin
Organization: Oakland University, Rochester MI.
Date: Wed, 11 Nov 1992 17:27:03 GMT

1) Start with an equilateral right cylinder.
2) Eliminate the possibility of it landing on end by:
    a) tapering the ends to a point (a 3-sided football)
    b) rounding the ends
3) For each side A=1,2,3 put A face down and write A on the bottom
   of the other 2 sides.

When thrown, this die will, of course, have an equal probability of
landing on each of its 3 side. I haven't ever seen one and I don't
know if anyone has ever made one. I just knew such a thing must
exist, it just took a little thought (trivial :-)

Paul
From: andrew@rentec.com (Andrew Mullhaupt)
Newsgroups: sci.math
Subject: Re: feynman story probably not true.
Date: 11 Nov 92 18:16:40 GMT
Organization: Renaissance Technologies Corp., Setauket, NY.

In article <92309.155316RVESTERM@vma.cc.nd.edu> RVESTERM@vma.cc.nd.edu writes:


>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.



>a few days later, i got a mail message from mr. carl feynman, 
>     "it's not true as far as i know.  it's such a good story,


Well, we can make it true if it's not. Where's E. T. Bell when you need him?


Later,
Andrew Mullhaupt
Xref: sparky sci.math:14748 sci.math.symbolic:2941
From: amarmahb@gandalf.rutgers.edu (Amar Mahboob Ali)
Newsgroups: sci.math,sci.math.symbolic
Subject: Re: Help wanted in integration.
Date: 13 Nov 92 03:01:55 GMT
Followup-To: sci.math
Organization: Rutgers Univ., New Brunswick, N.J.


Hi 

First of all I would like to thank everone who tried to solve this
problem for me. And my special thanks go out to Victor Adamchik, John
Cordes and Jeffrey Golden, who actually got the results. Thanks a lot
fellows. 

And for how this integral arose.

nagrwb@vax.oxford.ac.uk writes:

>In article <1992Nov10.031024.4001@wri.com>, victor@tuamotu.wri.com (Victor Adamchik) writes:
>> In article <Nov.6.00.08.18.1992.2647@gandalf.rutgers.edu>  
>> amarmahb@gandalf.rutgers.edu (Amar Mahboob Ali) writes:
>>> 
>>> Hi
>>> 
>>> Can anyone please help me in integrating the following.
>>> 
>>>            infinity
>>> 
>>>                 / 4    2             2
>>>                | x  sin (Pi a x)  sin (Pi b x)
>>>                | ---------------------------- dx
>>>                |    2    2 2   2    2 2
>>>               /   (x  - d )  (x  - c )
>>> 
>>> 	  -infinity       
>>>       
>>> 
>>> Where a,b,c and d are positive intergers.
>>>... stuff deleted

>Been trying to reach the original poster without success. Does he or
>anyone else for that matter know under what circumstances this integral
>arises? Is there a real underlying application? I'd be interested to know.

>Richard. 

This integral arose as result of multiplying the power spectral
densities of two signals. I was trying to calculate the interference
generated by a narrow band TDMA signal in a wide band spread spectrum
CDMA system. It is quite a real world applicaition.

Please feel free to email me if you want more details.

Regards

Amar
Xref: sparky sci.math:14475 sci.physics:18255 sci.astro:11690 sci.bio:4039 sci.chem:4430 misc.education:4155
From: zrepachol@cc.curtin.edu.au
Newsgroups: sci.math,sci.physics,sci.astro,sci.bio,sci.chem,misc.education
Subject: Re: Is Math Hard?
Date: 5 Nov 92 19:48:51 GMT
Organization: Curtin University of Technology

In article <Bx79Lo.LG1@mentor.cc.purdue.edu>, hrubin@pop.stat.purdue.edu (Herman Rubin) writes:
> In article <1992Nov4.044300.15766@cbfsb.cb.att.com> wa2ise@cbnewsb.cb.att.com (robert.f.casey) writes:
> 
> 			........................
> 
>>In 5th grade, we did set theory (at least the simple stuff).  At the time,
>>I couldn't believe that we were doing such easy stuff instead of hard
>>long division and such.  But it seemed that the teacher and the rest of
>>the class had a hard time figuring it out.  And I'm no rocket scientist.
>>Unions, intersections, subsets, and such stuff that turns out to be a bit
>>similar to and gates and or gates in logic design.
> 
> From the experiences when people who had an understanding of mathematics
> taught it, most of the children could get some grasp of the subject.  But
> failure of the attempts to teach the teachers was what killed the new math.
> 

In 6th grade, I was in one of schools in W.A. that did 'new maths'. Set theory,
number theory, topology and a few others. It was great...

It was kill deader than a magot by the parents and teachers who didn't under-
stand it and "... can't see whats it's good for..."

~Paul
From: batchelor@nssdca.gsfc.nasa.gov (Dave Batchelor, Space Phys. Data Facil. 301/286-2988)
Subject: Re: Simple Diff Eq
News-Software: VAX/VMS VNEWS 1.41    
Organization: NASA - Goddard Space Flight Center
Date: Thu, 12 Nov 1992 23:45:00 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?
>--------------------------------------------------------------------

Try f(x) = (2x)^(1/2)
Cheers,
])ave
------------------------------------------------------------------------------
Dr. Dave Batchelor   Space Science Data Operations Office   Mail Code 632
NASA Goddard Space Flight Center  Greenbelt  MD  20771  USA
batchelor@nssdca.gsfc.nasa.gov
Xref: sparky sci.math:14538 sci.physics:18332 sci.astro:11735 sci.bio:4058 sci.chem:4454 misc.education:4168
From: andy@ccwf.cc.utexas.edu (Andrew Hackard)
Newsgroups: sci.math,sci.physics,sci.astro,sci.bio,sci.chem,misc.education
Subject: Re: Is Math Hard?
Date: 6 Nov 92 22:05:06 GMT
Article-I.D.: ut-emx.83160
Followup-To: sci.math,sci.physics,sci.astro,sci.bio,sci.chem,misc.education
Organization: The University of Texas at Austin, Austin TX

hrubin@pop.stat.purdue.edu (Herman Rubin) writes:

>The system is broke.  There is no way that we can get enough competent
>teachers NOW.  These teachers can only dumb down thinking children.  
>That is why there is no hope of getting an adequate public school system.

It ill behooves me to comment on the first half of this, since I'm going
to be a teacher next year (ideally, a competent one, though I'm loathe 
to make that claim myself).  However, I'm curious, Mr. Rubin: what
alternative school system do you propose?

(This wasn't meant as a flame; I'm honestly not sure what you have in
mind.)

--
--Andrew Hackard                                 If I spoke for UT, this post
  andy@ccwf.cc.utexas.edu                        would make even less sense.
Xref: sparky sci.math:14784 misc.education:4250
From: elg@elgamy.uucp.taronga.com (Eric Lee Green)
Date: 10 Nov 92 20:25:50 CDT
Newsgroups: sci.math,misc.education
Subject: Re: Is Math Hard?
Distribution: world
Organization: Eric's Amiga 2000 @ Home

From article <ccDyTB3w164w@allen.com>, by carolyn@allen.com (Carolyn Allen):
> ...excuse me, but what class is supposed to teach you study skills? I
> thought every kid knows how to learn, some better than others, but if a

Obviously you are not a teacher :-).

Study skills, like almost all human skills, are learned skills. The fact
that they are not generally taught in class is irrelevant. Study skills are
part of the repertoire of middle-class upbringing. Those of us who attended
weaker school systems and did not have the luxury of a middle-class
upbringing had to learn study skills on our own, with varying success.

Accusing someone of "sloth" is unwarranted in this case. I believe that you
owe an apology to someone.

As a teacher in an inner-city school I see, every day, skills my students
are missing that my middle-class nephews learned as a matter of course in
their homes. I resent you calling my kids "lazy" simply because they did
not have the same advantages as you. Some (few) of my parents may be
"lazy". But my kids work their tails off, thank you. The fact that nobody
ever taught them productive ways of doing so isn't an indictment of the
kids, but, rather, an indictment of their education.

 Eric Lee Green  elg@elgamy.taronga.com   Dodson Elementary
 (713) 664-6446                             Houston, TX
                "Kids are kids, no matter what"
From: smith@gramian.harvard.edu (Steven Smith)
Newsgroups: sci.math
Subject: Re: Michael Spivak
Date: 5 Nov 92 15:25:29 GMT
Article-I.D.: gramian.SMITH.92Nov5102529
	<1992Nov3.123113.17059@husc3.harvard.edu>
	<1992Nov5.074221.8111@math.toronto.edu> <Bx8xz4.67L.1@cs.cmu.edu>
Organization: Harvard Robotics Lab, Harvard University

> I too am interested in getting hold of Spivak's text-book on
> Calculus.  Any info to this end would be much appreciated.

I believe (?) that you may order this book directly from Publish or
Perish, Inc.  Send a brief note with your address to
spivak@math.rice.edu and ask for an order form to be sent to you.
I've ordered books from Publish or Perish before, and have always been
satisfied -- especially when a defective copy was promptly replaced.

Steven Smith
From: weemba@sagi.wistar.upenn.edu (Matthew P Wiener)
Newsgroups: sci.math
Subject: Re: Axioms of set theory, infinity and R. Rucker
Date: 8 Nov 92 15:43:45 GMT
Reply-To: weemba@sagi.wistar.upenn.edu (Matthew P Wiener)
Organization: The Wistar Institute of Anatomy and Biology
In-reply-to: schiller@prl.philips.nl (schiller c)

In article <1992Nov6.133138.16642@prl.philips.nl>, schiller@prl (schiller c) writes:
>Reading the book "infinity and the mind" by Rudy Rucker
>(by the way, it is delighting),

Based on his science fiction, which I have found unreadable in large
doses (too much gee-whiz), I had low expections for IATM.  I'm pleased
to say that I was completely wrong.  It's an excellent book.

>Which of these is the infinity specified in the
>axioms of set theory ?

The basic ZFC axioms specify only the smallest infinity, aleph_0.
From this, one derives within ZFC aleph_1, aleph_2, ....

>		        Is it important to decide this
>question ? Does this have any effect on set theory ?

However, not only are there higher infinities, there are also what may
be called "stronger" infinities.  These can be thought of as being
unreachable from below under axiomatic expansion.  For example, aleph_0
can not be reached by finite operations done on finite sets.  Similarly,
the stronger cardinals mentioned in IATM cannot be reached from below,
even using infinitary ZFC operations on infinite, yet smaller, sets.

What's especially intriguing is that these stronger infinities form,
more or less, a hierarchy of strength.  Near the bottom is something
called an inaccessible cardinal.  Near the middle is something called
a measurable cardinal.  Near the top is something called a supercompact
cardinal.  Letting I, M, S denote the existence axiom for the respective
cardinals, we can form set theories ZFC+I, ZFC+M, ZFC+S.  Then we have
that ZFC+I is stronger than ZFC, in the sense that it is impossible
to prove there are any inaccessible cardinals just using ZFC, and the
same for ZFC+M versus ZFC+I, and for ZFC+S versus ZFC+M.  Yet the reverse
holds in each case.  There is definitely more mathematics that can be
proven in the stronger axiom systems.

In fact, this can be made very concrete.  There are, thanks to the work
of Matiyasevich and Jones, all but explicit diophantine equations that
can be proven to have no solution only in a stronger set theory.  It is
remotely conceivable that Fermat's last theorem even is an example of
such a diophantine equation.

(Here's a boo in the the general direction of M&J: why not give the
simpler exponential diophantine equations also?)
-- 
-Matthew P Wiener (weemba@sagi.wistar.upenn.edu)
Newsgroups: sci.math