HDTenEightyP/NetNews huggingface dataset:
From: msb@sq.sq.com (Mark Brader)
Subject: Re: feynman story probably not true.
Organization: SoftQuad Inc., Toronto, Canada
Date: Fri, 6 Nov 92 07:01:48 GMT

> 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. ...
>      "It's not true as far as I know... However, it is not
>      inconceivable." [says Feynman's son]

Two other variations on this theme have been mentioned in alt.folklore.-
urban in the past.  One is that the rule was as quoted above, but the
student taking the exam carried in an unnamed graduate student or
professor in the same field.  The other is that the rule was simply
"You can bring Feynman to the exam", meaning a textbook of his; no
mention of having to *carry* "Feynman"; and the rest is obvious.

Any further discussion should be in alt.folklore.urban, if you can stand it.
-- 
Mark Brader			"*Nature*, Mr. Allnutt, is what we are put in
SoftQuad Inc., Toronto		 this world *to rise above*."
utzoo!sq!msb, msb@sq.com				-- The African Queen

This article is in the public domain.
Newsgroups: sci.math,comp.theory
From: gjm11@cus.cam.ac.uk (G.J. McCaughan)
Subject: Re: NP Completeness Question
Organization: U of Cambridge, England
Date: Fri, 13 Nov 1992 13:46:42 GMT

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

>Professor E.R. Swart of the Computer Science Department at the University
>of Guelph, has recently developed a polynomial-sized linear programing
>formulation of the graph isomorphism problem and he has been able to show
>that with minor modifications, this same formulation can be used to solve
>the Hamilton tour, clique and other subgraph isomorphism problems.
>
>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.

This *is* a joke, isn't it?

-- 
Gareth McCaughan     Dept. of Pure Mathematics & Mathematical Statistics,
gjm11@cus.cam.ac.uk  Cambridge University, England.    [Research student]
Newsgroups: sci.math,misc.education
From: dal3@cbnewsg.cb.att.com (dale.e.parson)
Subject: Re: Is Math Hard?
Organization: AT&T
Date: Mon, 9 Nov 1992 22:30:47 GMT

In article <1992Nov7.031019.147@julian.uwo.ca> roberts@gaul.csd.uwo.ca (Eric Roberts) writes:
>
>	I have been in the same situation as you. By the time I got
>to grade 9, I was studying advanced calculus, but I was forced to attend
>the grade 9 math programm where I was taught arithmetics and basic algebra;
>similiar in most other subjects. Unfortunately in Canada, it seems to be 
>absolutely impossible to be accepted to university without having a 
>highschool diploma, or get one without spending four years in that 
>institution. It was always my impression, that the situation was difference 
>in the US, for I have heard of people being accepted by the universities 
>(Harvard), without attending highschool at all (for example William James 
>Sidis and Wiener), maybe that is no longer true.
>  	 
>
>							Eric
> 

There are U.S. universities that are recruiting home learners & others
that are discriminating against them. As home learning success stories
become public knowledge I expect the amount of discrimination to diminish.
This much I can promise you: home schooling families take learning very
seriously, working hard at a practical level every day. When we--children
& parents--decide that college admission is the next step we wish to take
in our self-directed education, woe to the college administrator who decides
to stand in our way. It will take a lot more than some small minded 
bureacrats to stop the self-determined educational paths that our children
have followed into early adulthood. Count on it.


Dale Parson, Bell Labs, dale@mhcnet.att.com

 ---------------------------------------------------------------------- 
|    "These words are too solid, they don't move fast enough           |
|     to catch the blur in the brain that flies by, and is gone..."    |
 ----------------------------------------------------------------------
|     Suzanne Vega                                                     |
 ----------------------------------------------------------------------

Newsgroups: sci.math
From: kasdan@cs.columbia.edu (John Kasdan)
Subject: Re: W.S. Anglin's comments on history of math
Organization: Columbia University Department of Computer Science
Date: Sun, 8 Nov 1992 20:59:35 GMT

In article <djoyce.721078379@black.clarku.edu> djoyce@black.clarku.edu (Dave Joyce) writes:
>In the issue of _The Mathematical Intelligencer_ that just came out there is a
>seven page article in the opinion column by W. S. Anglin entitled "Mathematics
>and History."
>
>Anglin complains that calculating devices, including algorithms for
>calculation, don't receive enough attention in history of mathematics
>books.  Some barely mention them.  I agree calculation is important
>in mathematics' history, but the one place in his article I find weakest
>is his arguments for the importance of calculations.  Of the four ways he
>lists in which calculating devices have proved essential for progress in
>pure mathematics only one (the involvment of computers in the proof the the
>four color theorem) seems very strong.
>

I haven't read the article, but the uses of computation in "real"
mathematics is a topic that seems interesting.  On a major level, I
believe the Birch Swinerton-Dyer conjecture was largely based on
computations, both hand and mechanized.  At a much more modest level,
Buchweitz' example of a complement of a semi-group which is not a
Weirstrass gap sequence was found by a computer.  I would expect that
some of the work in the classification of simple groups was done by
computer, but I don't know.  Does anyone have any info on that?

>
>
>
>-- 
>David E. Joyce				Dept. Math. & Comp. Sci.

/JK

Newsgroups: sci.math
From: gerry@macadam.mpce.mq.edu.au (Gerry Myerson)
Subject: Re: Erdos number
Originator: gerry@macadam.mpce.mq.edu.au
Organization: School of MPCE, Macquarie University, Australia.
Date: Wed, 11 Nov 1992 00:17:50 GMT



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. 

> What is the largest number known?
> 
> Sam Murphy
> sammy@smds.com   

Gerry Myerson
Newsgroups: sci.math,comp.theory
From: mjs@hubcap.clemson.edu (M. J. Saltzman)
Subject: Re: NP Completeness Question
Organization: Clemson University, Clemson SC
Date: Fri, 13 Nov 1992 17:05:38 GMT

In article <1992Nov13.154406.4800@CSD-NewsHost.Stanford.EDU> pratt@Sunburn.Stanford.EDU (Vaughan R. Pratt) writes:
>In article <BxMu2J.2JD@watserv1.uwaterloo.ca> nrswart@phonon.uwaterloo.ca (Nicholas R. Swart) writes:
>>Professor E.R. Swart of the Computer Science Department at the University
>>of Guelph, has recently developed a polynomial-sized linear programing
>>formulation of the graph isomorphism problem and he has been able to show
>>that with minor modifications, this same formulation can be used to solve
>>the Hamilton tour, clique and other subgraph isomorphism problems.
>
>Papadimitriou showed in 1975 an exponential lower bound on
>simplex-based solutions of the travelling salesman problem.  Since
>linear programming solves simplex problems (and indeed has polynomial
>time solutions), the above account renders the claim very unconvincing
>by making no mention of an additional trick.

I don't understand your point.  The simplex method solves linear
programs (but in exponential worst-case time).  On the other hand,
linear programming is in P, as shown by Khachian (the ellipsoid
method) and Karmarkar (interior point methods).

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.  The matching (edge cover) problem
has an exponential number of constraints, yet it is solvable in
polynomial time.

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?

>-- 
>Vaughan Pratt	  		A fallacy is worth a thousand steps.

-- 
		Matthew Saltzman
		Clemson University Math Sciences
		mjs@clemson.edu
From: ledwards@leland.Stanford.EDU (Laurence James Edwards)
Newsgroups: sci.math
Subject: definition of topological space
Date: 5 Nov 92 03:38:35 GMT
Organization: DSG, Stanford University, CA 94305, USA

The definition of a topological space is:

    :a set with a collection of subsets satisfying the conditions that 
    both the empty set and the set itself belong to the collection, the 
    union of any number of the subsets is also an element of the collection, 
    and the intersection of a finite number of the subsets is an element 
    of the collection

What is the purpose of this definition? To the naive reader (such as myself)
it would seem that just about any set along with one of its subsets and the
empty set would be a topological space, e.g. it would semm to me that:

{1,2,3} {} {1}

is a topological space. What am I missing here? In one math dictionary
it is stated that this definition allows one to establish the notion of
continuity as it applies to functions between topological spaces ...
I don't see how. Can anyone clue me in?

Thanks for any help,

Larry Edwards
From: jorchard@dciem.dciem.dnd.ca (Jeff Orchard)
Newsgroups: sci.math
Subject: Re: Simple Diff Eq
Date: 10 Nov 92 14:02:04 GMT
Distribution: na
Organization: Defence and Civil Institute of Environmental Medicine

Newsgroups: sci.math
Subject: Re: Simple Diff Eq
Summary: 
Reply-To: jorchard@dretor.dciem.dnd.ca
Distribution: na
Organization: Defence and Civil Institute of Environmental Medicine
Keywords: 

>(Jonathan Katz) writes:
>>(Ric Peregrino) writes:
>>|> 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
>
>     Careful there!  That should be f(x) = sqrt(2x + c) where c is
>     chosen to satisfy the initial or boundary conditions.
>
>				     Marc R. Roussel

Careful again... the actual answer is

	f(x) = +- sqrt(2x+c)    (Positive OR Negative)

(Picky, picky!!!)  :-)

Jeff Orchard	jorchard@dretor.dciem.dnd.ca
Dept. of National Defence, Toronto, Canada
Newsgroups: sci.math
From: jk87377@cc.tut.fi (Juhana Kouhia)
Subject: Re: Apology about f'(g(x))
Organization: Tampere University of Technology
Date: Sat, 7 Nov 92 21:09:01 GMT


In article <1992Nov2.161555.13669@CSD-NewsHost.Stanford.EDU>
pratt@Sunburn.Stanford.EDU (Vaughan R. Pratt) writes:
>
>In article <1992Nov2.115020.11332@linus.mitre.org> bs@gauss.mitre.org
>(Robert D. Silverman) writes:
>>
>>Look guys. f(g(x)) is a function of x, say h(x). Now, f'(g(x)) means
>>the derivative of this function with respect to x. That is to say
>>f'(g(x)) = h'(x)
>
>You:             f'(g(x)) = (f o g)'(x).
>Everyone else:   f'(g(x)) = (f' o g)(x)


I didn't see that following format was written in article here yet:

Silverman should write (f(g(x)))' instead of f'(g(x)).
(f(g(x)))' is, of course, the allready mentioned (f o g)'(x).

Juhana Kouhia
Xref: sparky sci.math:14583 misc.education:4182
From: burtt@cycvax.nscl.msu.edu (BRIAN BURTT)
Newsgroups: sci.math,misc.education
Subject: Re: Is Math Hard?
Date: 8 Nov 92 00:21:00 GMT
Organization: NSCL Michigan State University
News-Software: VAX/VMS VNEWS 1.41


>	I have been in the same situation as you. By the time I got
>to grade 9, I was studying advanced calculus, but I was forced to attend
>the grade 9 math programm where I was taught arithmetics and basic algebra;
>similiar in most other subjects. Unfortunately in Canada, it seems to be 
>absolutely impossible to be accepted to university without having a 
>highschool diploma, or get one without spending four years in that 
>institution. It was always my impression, that the situation was difference 
>in the US, for I have heard of people being accepted by the universities 
>(Harvard), without attending highschool at all (for example William James 
>Sidis and Wiener), maybe that is no longer true.
>  	 
> 
>							Eric
> 

	While being significantly ahead of my fellow elementary school,
I wasn't a prodigy like the aforementioned.  Another factor:  my mother
(single parent) worked hard through my childhood to provide such 
humdrum items as medical insurance and groceries.  So, rather than going
to Harvard or Chicago, I am going to a state university where I can
get a significant portion of my expenses paid for by scholarships, etc.
	(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.)
	In the U. S., how much money you have to play with is one 
BIG factor in determining what you can do.
	--Brian Burtt
	Undergraduate major in physics and mathematics
	Michigan State University
	burtt@lynch.nscl.msu.edu
Newsgroups: sci.math
From: pratt@Sunburn.Stanford.EDU (Vaughan R. Pratt)
Subject: Re: Boolean Algebras
Organization: Computer Science Department,  Stanford University.
Date: Sat, 14 Nov 1992 02:55:04 GMT

In article <Bxo1Hw.6qA@dcs.ed.ac.uk> mxh@dcs.ed.ac.uk (Martin Hofmann) writes:
>In article <42536@gremlin.nrtc.northrop.com>, jbarnett@nrtc.northrop.com (Jeff Barnett) writes:
>> 
>> Is there a free boolean algebra such that the cardinality of
>> the algebra (not the cardinality of its generators) is that
>> of the continuum?
>> 
>> Jeff Barnett
>
>I guess the powerset of the natural numbers ordered by inclusion provides an example.

For any infinite X, the power set of X, and for that matter the set of
all finite and cofinite subsets of X, are Boolean algebras with atoms.
Hence they cannot be free Boolean algebras.

(In any equationally defined class, the free algebra F(X) on a set X
consists of the equivalence classes of those formulas whose variables
are drawn from X.  Claim: for Boolean algebras, if X is infinite F(X)
has no atoms.  Proof: Let the equivalence class [p] be an atom where p
is some (necessarily finite) Boolean formula, and let Q be a Boolean
variable not appearing in p.  Then 0 < p&Q < p, contradicting [p]'s
atomicity.)
-- 
Vaughan Pratt	  		A fallacy is worth a thousand steps.
From: columbus@strident.think.com (Michael Weiss)
Newsgroups: sci.math
Subject: Re: What is a knot?
Date: 9 Nov 92 10:02:48
Organization: Thinking Machines Corporation, Cambridge MA, USA
NNTP-Posting-Host: strident.think.com
In-reply-to: jbaez@riesz.mit.edu's message of Sat, 7 Nov 92 21:25:57 GMT

In article <1992Nov7.212557.24399@galois.mit.edu> jbaez@riesz.mit.edu (John
C. Baez) writes: 

   Actually, it turns out to be very good to work with framed oriented links.
   Then we have the marvelously erudite

   5') Hom(0,0) in the free tortile tensor category generated by a single
   object.

Now that's more like it.  (How come they didn't tell me about this at
Community Boating when I learned to tie a bowline?)
Newsgroups: sci.math
From: lady@uhunix.uhcc.Hawaii.Edu (Lee Lady)
Subject: Re: Curvature of a Line in Space
Followup-To: sci.math
Summary: The curvature is the rate at which is tangent vector is turning.
Keywords: curvature
Organization: University of Hawaii (Mathematics Dept)
Date: Fri, 13 Nov 1992 06:21:55 GMT

In article <1992Nov5.014717.9834@nas.nasa.gov> asimov@wk223.nas.nasa.gov (Daniel A. Asimov) writes:
>    ....    The curvature vector can be defined as the second
>derivative of the position vector *with respect to arclength*.
>Then, the magnitude of this vector is the curvature.
>With respect to an arbitrary parametrization, you will not in general
>get the same thing.

More intuitively, the curvature is the rate at which the tangent vector 
is turning as one moves along the curve at a speed of 1.  In other
words, if we take the tangent vector at two values  s  and  s+h  of the
arc length and denote the angle between them by  delta_theta, then the
curvature is the limit of  delta_theta/h  as  h goes to 0.

For a curve in the plane, this is easy to see.  In that case, we can let
theta  denote the angle between the unit tangent vector and the
horizontal.  (The unit tangent vector is the first derivative of the
position vector with respect to arc lenth.)  Since the unit tangent
vector has length 1 it then has components  (cos theta, sin theta).   
Differentiating with respect to  s  using the chain rule shows that the
magnitude of its derivative equals the derivative of theta, i.e. the
rate at which the tangent vector is turning.

I believe that you can adapt this proof for a curve in three space by
projecting the curve onto its osculating place at the point in question.
Not being a differential geometer, though, I'm not prepared to offer
details of a proof.  

--
It is a poor sort of skepticism which merely delights in challenging
those claims which conflict with one's own belief system.  
                                                          --Bogus quote 
lady@uhunix.uhcc.hawaii.edu         lady@uhunix.bitnet
From: mkrogers@unix.amherst.edu (MICHAEL K ROGERS)
Newsgroups: sci.math
Subject: Re: 2-dimensional grading system (was Re: What can one do for the
Date: 10 Nov 92 16:00:50 GMT
Organization: Amherst College
X-Newsreader: TIN [version 1.1 PL6]

: "Cogito, ergo Sum." - Descartes

How does this explain *your* existence?  :) :) :)
From: holmes@garnet.idbsu.edu (Randall Holmes)
Subject: Re: Electoral college (was Re: Bill Clinton and Complex Analysis : -))
Organization: Boise State University
Date: Fri, 6 Nov 1992 19:00:25 GMT

In article <israel.720991427@unixg.ubc.ca> israel@unixg.ubc.ca (Robert B. Israel) writes:
>In <1992Nov4.054813.20137@CSD-NewsHost.Stanford.EDU> rivin@SAIL.Stanford.EDU (Igor Rivin) writes:
>
>>Does the electoral college actually help in fairness? I was under the
>>impression that it was a purely political compromise to augment
>>states' rights, so it would interesting if it actually serves an a
>>posteriori purpose...
>
>Fairness is a very subjective term, but it may be of interest to note
>that Perot received enough votes to give him an absolute majority of
>the electoral college.  You just have to rearrange the existing voters
>(keeping national totals for each candidate fixed as well as total votes
>in each state) so that he gets just over 1/3 the votes in each of a 
>set of states having just over half the electoral votes, and Bush and
>Clinton each get just under 1/3 in those states.  In the other states, he
>needs no votes.  In a system with electoral votes proportional to 
>voters, you thus need only about 1/6 of the total votes to get a
>majority this way.  Where it's not perfectly proportional, you can
>get by with less if you pick the "over-represented" states.  Exercise:
>using the actual data, find the actual minimum number of votes needed.
>
>To get a plurality, rather than a majority, in the electoral college,
>you just need about 1/9, rather than 1/6. 
>
>This is not entirely a fanciful exercise. It could quite easily happen
>that a candidate with fairly strong appeal in one half of the country and
>little in the other would be elected despite finishing a poor third in
>popular vote.

Lincoln was elected with a rather small plurality for this reason, if
I recall correctly.  (He had the largest popular vote, but nothing
like a majority).
 
>
>-- 
>Robert Israel                            israel@math.ubc.ca
>Department of Mathematics             or israel@unixg.ubc.ca
>University of British Columbia
>Vancouver, BC, Canada V6T 1Y4


-- 
The opinions expressed		|     --Sincerely,
above are not the "official"	|     M. Randall Holmes
opinions of any person		|     Math. Dept., Boise State Univ.
or institution.			|     holmes@opal.idbsu.edu
Organization: Arizona State University
Date: Thursday, 5 Nov 1992 12:16:54 MST
From: Hans DeBano <KGHDB@ASUACAD.BITNET>
Newsgroups: sci.math
Subject:    Re: Who are our best mathematicians?


>> baez@ucrmath.ucr.edu (john baez) writes:
> choy@skorpio.usask.ca (I am a terminator.) writes:

>> When asked how he was so good at mathematics, Gauss reputedly said "I just
>> think about it all the time."  With the emphasis, of course, on ALL.

> All in all, "think" is quite vague. Is there an algorithm being followed
> at least some of the time? Does Gauss hop from idea to idea? Does he
> freak out and spend all day every day on a problem?

Actually, it's been awhile since I've seen anything substantive from Gauss.
Is he on sabbatical this year?
Newsgroups: sci.math
From: sibley@math.psu.edu (David Sibley)
Subject: Re: group theory for HS students
Organization: Department of Mathematics, Pennsylvania State University
	<04VSB5M6@cc.swarthmore.edu>
	<PRENER.92Nov7191213@prener.watson.ibm.com>
Distribution: sci
Date: Sun, 8 Nov 1992 13:58:01 GMT

>If math courses had the training of mathematicians as their only
>purpose, then the ordering would be more like what you suggest.  On
>the other hand, there is an urgent need to provide, say, physics
>students, with calculus at an even faster rate than is usually done.

When I was a grad student at Caltech many years ago, there was a rumor
that the math department had received a request along these lines from
the physics department.  It seems they were reorganizing freshman
physics and could do it the way they really wanted to, providing only
that the calculus courses be reorganized a bit as well.  They wanted
freshman calculus taught so that Green's theorem in the plane would be
covered by the end of the second week.

David Sibley
sibley@math.psu.edu
Newsgroups: sci.math
Subject: Re: 2-dimensional grading system (was Re: What can one do for the bright?)
From: a_rubin@dsg4.dse.beckman.com (Arthur Rubin)
Date: 10 Nov 92 23:08:41 GMT
Organization: Beckman Instruments, Inc.

In <1992Nov10.53953.20423@ms.uky.edu> msunde01@mik.uky.edu (Mark  Underwood) writes:


>OK, I will admit (even agree) that the selection from NM Semifinalist to  
>Finalist is a manner of popularity contest.  However, the selection of  
>Semifinalists is merely a measure of success on standardized tests, where  
>at least the selection of Finalist takes into consideration the  
>recommendations of teachers and one's ability to write a good, short B.S.  
>"Why I deserve this" essay . . . and therefore is more of a measure of the  
>student than the Semifinalist measure.  I, too, have friends (several) who  
>were more deserving of my scholarship than I.  I did not mean to imply  
>that the difference was so great or that they were not deserving, just  
>that there WERE rather difficult (if subjective, and they WERE subjective)  
>selection criteria for the Finalist standing, and that it was not merely a  
>formality of sorts.  BTW let's drop this, as it really isn't that  
>important and certainly doesn't relate to the group.

I was turned down for Finalist status because I went directly from high
school to graduate school.
--
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.
Newsgroups: sci.math