HDTenEightyP/NetNews huggingface dataset:
Date: Tuesday, 10 Nov 1992 14:44:32 EST
From: <RVESTERM@vma.cc.nd.edu>
Newsgroups: sci.math
Subject: Re: Relatives with Crackpot Proofs

why don't you just tell him where his proof went wrong? sheesh.

just say, "this step here is wrong, because blah blah blah."
you don't have to be derisive about it, and tell the guy how
dumb his proof is.  just tell him why it's wrong.

also, pretending that it's right, or that you don't see a mistake,
could be even worse.  if you do that, then he sends his "proof" off
to a bunch of people he doesn't know; thus, a bunch of people who
may very well have no qualms in saying, "this is the stupidest piece
of garbage i've ever seen."

jeez, come on.  do you really need other people's advice in order
to be honest?

bob vesterman.
Newsgroups: sci.math
From: cyeomans@ms.uky.edu (Charles Yeomans)
Subject: Re: a first year grad student freaks out.
    <DREIER.92Nov10235243@durban.berkeley.edu>
Date: Thu, 12 Nov 1992 15:48:05 GMT
Organization: University Of Kentucky, Dept. of Math Sciences

In article <DREIER.92Nov10235243@durban.berkeley.edu> dreier@durban.berkeley.edu (Roland Dreier) writes:
>In article <92314.170255RVESTERM@vma.cc.nd.edu> <RVESTERM@vma.cc.nd.edu> writes:
>   i'm a first year grad student.  i can do most of the homework assigned
>   to me.  i can pass tests i have to take.  i can usually understand
>   proofs of theorems that we're studying, given some thought.  i think
>   that with a lot of work, i can pass my orals.
>
>   however, what's the deal with this thesis thing? what happens if you
>   simply cannot prove whatever your advisor assigned?
>
>   bob vesterman.
>
>Guess what, kid.  It's even harder than that.  Consider yourself
>extremely lucky if your advisor even gives you a question.  More
>likely, not only are you gonna have to solve a problem, you're gonna
>have to find the problem yourself.  But the advantage of this is that
>you can usually find a problem you can solve if you look hard enough.
>It's still not easy to come up with a problem you can do and also that
>interests other people enough so that they're willing to give you a
>degree.
>
>--
Andre Weil couldn't solve his thesis problem either.  He got a degree
with a partial result.

Charles Yeomans
cyeomans@ms.uky.edu
yeomans@austin.onu.edu
From: chasebd@NeXTwork.Rose-Hulman.Edu (Brian D Chase)
Newsgroups: sci.math
Subject: Where to get Michael Spivak's Calculus text?
Date: 6 Nov 1992 23:43:16 GMT
Organization: Computer Science Department at Rose-Hulman
Distribution: usa
Reply-To: chasebd@NeXTwork.Rose-Hulman.Edu (Brian D Chase)
NNTP-Posting-Host: g310a2.nextwork.rose-hulman.edu
Keywords: Spivak, calculus


I'm curious as to where I could obtain a copy of Spivak's book.  I've a  
friend whose calculus course last year was taught using Spivak's text and he  
thought very highly of it.  On a few occassions I had an opportunity to look  
it over and I'd planned on buying a copy but their school's bookstore no  
longer carries it.  Can anybody help me out with this one?

--
------------------------------------------------------------------
  Brian D. Chase        Internet: chasebd@nextwork.rose-hulman.edu
(they call him Sid)           ph:  (812)877-8679
  Rose-Hulman IT, Box#258, 5500 Wabash Ave, Terre Haute, IN 47803
=================[ bit a byte O' bitter batter ]==================
Newsgroups: sci.math,misc.education
From: wkl1@Ra.MsState.Edu (Wing-Keong Loke                                               the consummate chronic prevaricator)
Subject: Re: Is Math Hard?
Organization: Mississippi State University
Date: Mon, 9 Nov 1992 05:14:28 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.)
>
>> 	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.

	Sure, but determining what you do and what you CAN do is two
different thing.  The former needs determination, guts etc., the
later *may* very well need heap big $$$.
>
>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.

	Is it worth it to Rodney King that he got the hell beat out of
him now that he's got a chance of...say..."earning" $10,000 for every
beating that he got?  
	Is it worth the while to have Anita Hill so disgracefully treated
that there is now a treefold increase of women in the congress?

	But that is not to say that I totally disagree with you.  Sometimes
I think the way you do to, that cathartic events are beneficial.  In fact, I
believe they are largely beneficial.  But when someone feels so strongly
about some injustice done to him/her, I don't think it's wise to denigrate
his/her experience.
	Some people/experiences you just have to be there and see or
experience for yourself to understand how galling they are.  It's just
too easy to judge others on the little stuff that they tell you.  Sometimes
you're right, sometimes no.
	I think when someone expresses some pain/anger/discontent, we better
listen carefully--not that I ever do even half the time, just roll over
complaints/hurt feelings/etc.  Pretty insuferable, huh?  ;-)

Newsgroups: sci.math,sci.physics
From: stephen@europa.inmos.co.uk (Stephen Collyer)
Subject: Re: Three-sided coin
Organization: INMOS Limited, Bristol, UK
Date: Thu, 12 Nov 1992 14:46:04 GMT

In article <1992Nov10.032643.10467@galois.mit.edu>, jbaez@riesz.mit.edu (John C. Baez) writes:
|> In article <5413@daily-planet.concordia.ca> mckay@alcor.concordia.ca (John McKay) writes:
|> >
|> > von Neumann was asked, when about to enter a taxi,
|> >
|> >"How thick should a coin be to have equal (=1/3) probability
|> > of landing on its head,tail,or edge?"
|> >
|> >He turned, told the taxi where to go, then answered and was 
|> >away.
|> >
|> >Surprisingly, making "reasonable" assumptions, this can be
|> >done in your head.
|> 
|> Well, this question has been seriously batted about before on sci.math
|> and sci.physics, and the consensus was that there is simply not enough
|> information to answer it.  So I eagerly await what von Neumann's answer
|> was supposed to have been - and what "reasonable" (note quotes!)
|> assumptions go into it. 
|> 
|> My best shot at answer invoked an idea from stat mech, namely,
|> equipartition.  This says that the solution occurs when the *energy* of
|> standing upright equals the energy of lying on edge.  Guess this means
|> the radius should equal half the thickness of the coin, or if you
|> prefer, the diameter should equal the thickness.

This seems wrong to me. Consider the cases where the coin is balanced on the
edge between the head and the cylindrical section. It can fall either way,
ending up on its on its head or its cylinder. Similarly for the other edge,
it can end up on its tail or its cylinder. This would seem to weight the 
chances towards ending up on its cylinder, rather than its head or tail, 
if the diameter = thickness. 

Also if diameter = thickness, then A (tail) = A (edge) = 1/4 A (cylinder)
(A = surface area) and surface area here is surely the determining factor.

I guess we want to have A (tail) = A (edge) = A (cylinder) which occurs
when thickness = 1/2 radius. 

|> 
|> However, I became convinced that in an actual coin toss conditions are
|> not such that the equipartition principle is applicable.

Steve Collyer.
Newsgroups: sci.math
From: jbaez@riesz.mit.edu (John C. Baez)
Subject: What is trivial?
Organization: MIT Department of Mathematics, Cambridge, MA
Date: Sat, 7 Nov 92 18:27:59 GMT

In article <1992Nov6.194950.18823@cs.yale.edu> choo@cs.yale.edu (Young-il Choo) writes:
>If I remember correctly, the trivium consisted of 
> grammar
> rhetoric (which included logic) and 
> poetics (or poetry, though today this would be more like "writing" or
>   "composition")
>
>[From Dorothy Sayers' "Tools of Learning"]

Webster's unabridged dictionary sides with my recollection of the
trivium as grammar, rhetoric and logic.  Perhaps Sayers is using her
poetic license.  :-)
From: brock@NeXTwork.Rose-Hulman.Edu (Bradley W. Brock)
Newsgroups: sci.math
Subject: Re: Surface area of ellipsoid
Date: 6 Nov 92 20:28:38 GMT
Article-I.D.: master.1dekhmINNnf5
Reply-To: brock@NeXTwork.Rose-Hulman.Edu (Bradley W. Brock)
Organization: Computer Science Department at Rose-Hulman
NNTP-Posting-Host: g210b-1.nextwork.rose-hulman.edu

In article <1992Nov5.142635.25873@mnemosyne.cs.du.edu> fburton@nyx.cs.du.edu  
(Francis Burton) writes:
> That's about as far as my math goes, and I am having trouble finding
> an expression for the surface area of an ellipsoid where a, b and c
> are ALL UNEQUAL. Why is it that the expression for surface area
> becomes so complicated when a sphere is squashed, in marked contrast
> to the equivalent volume formulae?

In some sense you have asked for a generalization of a classical problem: what  
is the formula for the perimeter of an ellipse?  The answer involves the  
so-called complete elliptic integral of the second kind, E(k).  (The incomplete  
or indefinite elliptic integral in some sense is a generalization of the  
function arcsin(x).)   The study of these integrals naturally leads to elliptic  
curves, the natural Riemann surface on which these integrals live.  For further  
information pick up any book on elliptic integrals.

--
Bradley W. Brock, Department of Mathematics
Rose-Hulman Institute of Technology  | "Resist not evil.... Love your
brock@nextwork.rose-hulman.edu       |  enemies."--Jesus of Nazareth
From: eijkhout@cupid.cs.utk.edu (Victor Eijkhout)
Newsgroups: sci.math
Subject: Re: Erdos number
Date: 13 Nov 92 02:36:22 GMT
	<1992Nov12.104155.7564@ms.uky.edu>
Organization: /pearl/homes/eijkhout/.organization
NNTP-Posting-Host: cupid.cs.utk.edu
In-reply-to: cyeomans@ms.uky.edu's message of Thu, 12 Nov 1992 15:41:55 GMT


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

With me the case is the other way around: my Erd"os number is three
through an electronics engineer who co-authored with Richard Guy.
His two is probably a lower bound, unless Erd"os himself wrote
about non-mathematical subject.

Victor.
From: lry1219@cfdd40.boeing.com (Larry Yeagley)
Newsgroups: sci.math
Subject: Re: Geometry text wanted
Summary: Recommendations for geometry texts
Date: 5 Nov 92 16:12:07 GMT
Organization: Boeing Computer Services, Seattle - CFD lab

In article <epang.720783520@sfu.ca>, epang@fraser.sfu.ca (Eugene Pang) writes:
> I would appreciate some recommendations for good introductory geometry texts
> (or reference books) which covers Euclidean [and I guess] projective
> geometry-- eg collineation & maps on planes, like the plane of 16 pts.
> 
> Any suggestions?
> 
> Thanks in advance.


The following two books are quite comprehensive in their treatment of geometry.
In addition, their bibliographies are also quite good.

   "Introduction To Geometry" (2nd Ed.) by H. S. M. Coxeter

   "Geometry I" by Marcel Berger
      There is a second volume to this - presumably called "Geometry II". These
      are available in both French & English editions.
From: speedy@vax.oxford.ac.uk
Newsgroups: sci.math
Subject: Visiting Res Fellowship
Date: 11 Nov 92 17:35:30 GMT
Organization: Oxford University VAX 6620

Herewith notice of a visiting fellowship that may be of interest
to scientists of various disciplines.  I am sending it to a number
of groups on NETNEWS.  Please bring it to the attention of any
suitable colleagues.  Replies to Dean's secretary at the address 
below - not by e-mail, please! Please indicate where you saw the
advert.

Andrew Speedy
Tutor in Biological Sciences
Christ Church
Oxford

---------------------------------------------------------------------
ADVERTISEMENT


CHRIST CHURCH,  Oxford



Dr Lee Visiting Research Fellowships in the Sciences


The college proposes to elect Visiting Fellows, in the Natural
Sciences and Mathematics, for up to nine months in the period
September 1993 to August 1994.

The Fellowships are intended to enable distinguished senior
scholars to pursue their own research as members of the college
community, and they will be expected to reside in Oxford during
the period of tenure.    Fellows must make their own research
arrangements with Oxford laboratories.

Each Fellow will be entitled to free family accommodation, a
study-room in college and free dinners.   Return fares from the
place of residence will be paid for each Fellow and his/her
family.   Limited stipends may also be offered, depending on
individual circumstances.

Further details may be obtained from The Dean's Secretary, Christ
Church, Oxford OX1 1DP, and applications should be received not
later than
12 December 1992.
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 06:05:43 GMT

In article <7868@charon.cwi.nl> dik@cwi.nl (Dik T. Winter) writes:
>In article <1992Nov8.214329.27209@CSD-NewsHost.Stanford.EDU> pratt@Sunburn.Stanford.EDU (Vaughan R. Pratt) writes:
> > Turns out if you try to calculate this using the 1986 Encyclopedia
> > Britannica you get sec^3(t).  The reason is that EB defines the
> > Mercator Projection to be the result of projecting the globe from its
> > center onto the cylinder tangent to the equator.  If this were true the
> > vertical direction would scale not by sec(t) but by the derivative of
> > tan(t), namely sec^2(t).
>
>EB is right.

I think you're alone on this one.  Alan Paeth mentioned in an earlier
post that this was a common but incorrect assumption.

>It is not immediately obvious that the Rand McNall map is conformal;
>is it?  The Mercator projection is.  But I do not think that straight
>lines on the Rand McNall map are lines of constant bearing.

You are right that Mercator is conformal.  Since the horizontal
dimension necessarily scales as sec(t) to keep the meridians vertical,
an easy check for conformality is to measure the vertical scale and
verify that it scales as sec(t).  If you get anything else your map
cannot be conformal.  Rand McNally measures out to sec(t), surprisingly
accurately (even more accurate than my Wil Tirion Sky Atlas 2000.0!).
-- 
Vaughan Pratt
Newsgroups: sci.math,sci.math.symbolic
From: victor@tuamotu.wri.com (Victor Adamchik)
Subject: Re: Help wanted in integration.(correction)
Organization: Wolfram Research, Inc.
Date: Tue, 10 Nov 1992 16:07:24 GMT


There is a misprint in my previous message. The numeric coefficient
there should be 1/4 instead of 1/16. And the right answer is:

if 0 < a <= b then (a*(c^2 + d^2)*Pi^2)/(4*(c^2 - d^2)^2)
if 0 < b <= a then (b*(c^2 + d^2)*Pi^2)/(4*(c^2 - d^2)^2)


--
Victor Adamchik
victor@wri.com

Xref: sparky sci.math:14914 misc.education:4281
From: hrubin@pop.stat.purdue.edu (Herman Rubin)
Newsgroups: sci.math,misc.education
Subject: Re: What can we have for an educational system?
Summary: Teachers have to know what they are teaching
Date: 13 Nov 92 15:46:06 GMT
Article-I.D.: mentor.Bxnvsv.Itr
Organization: Purdue University Statistics Department

In article <26302@optima.cs.arizona.edu> lal@cs.arizona.edu (The Morning Sun) writes:
>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.


>Having Ph.D's teach in public schools is not going to help.
>A Person with a PhD, has done research in a particular area
>which is probably totally irrevelant to his teaching.

>Theorem : PhD implies good teacher

>[thats your assumed theory]

		[Examples deleted.]

In every one of the examples, the PhD was in a different area.  A PhD
in English Literature is not likely to be successful at teaching mathematics.
It is more likely that a PhD can move even a fair amount from his/her area
and be able to more than keep up with the class, but this is difficult.

The school system abounds in having teachers teaching what they do not know.
It is notorious to have athletic coaches teaching mathematics or science.
In the primary grades, almost none of the teachers has any understanding
of mathematics, and consequently can only teach arithmetic manipulations.
-- 
Herman Rubin, Dept. of Statistics, Purdue Univ., West Lafayette IN47907-1399
Phone: (317)494-6054
hrubin@snap.stat.purdue.edu (Internet, bitnet)  
{purdue,pur-ee}!snap.stat!hrubin(UUCP)
Newsgroups: sci.math
From: jbaez@riesz.mit.edu (John C. Baez)
Subject: Re: Trivial! (was: Re: Help X^2 == Y mod N)
Organization: MIT Department of Mathematics, Cambridge, MA
Date: Thu, 5 Nov 92 21:05:04 GMT

In article <1992Nov5.031326.11279@CSD-NewsHost.Stanford.EDU> pratt@Sunburn.Stanford.EDU (Vaughan R. Pratt) writes:
>In article <1992Nov5.001930.24516@galois.mit.edu> jbaez@riesz.mit.edu (John C. Baez) writes:
>>Some of you may remember the post in which I described a system of logic
>>with a predicate T such that T(P) means "P is trivial".  T(P) -> P
>>but not vice-versa.  (Well, in real life T(P) does not imply P, but
>>we're just joking around here.)  T(P) -> T(T(P)), though.
>
>Isn't T->TT contradicted by the example of Norbert Wiener?  After being
>challenged about T(P) for some P that probably no one remembers any
>more, Wiener wandered away in deep thought and returned 20 minutes
>later to announce triumphantly that it was indeed trivial.
>
>Or did you mean Trivial(P) -> Triumphantly(Trivial(P))?
>
>(MIT is the official repository of Wiener stories, so I fully expect a
>suitable counterstory from John.)

I'll have to make up an apocryphal one.  Upon his return, the students
asked if it was *trivially* true that his statement was trivial.  Wiener
wandered off for another couple of hours and returned saying, yes, it
was indeed trivial.  

I've gotten 2 emails so far reminding me of this joke, actually.  My
opinioni is that this joke is funny precisely because it violates the
principle that T(P) -> T(T(P)).  

I was also reminded that T(P) -> T(T(P)) is one of the properties that a
provability predicate must satisfy to derive Loeb's theorem.  This says
that (P -> T(P)) -> P.

I.e., "this statement is provable," suitably mathematized by
Goedel-number, is in fact provable.  

Similarly, "if this statement is true, it's trivial" is trivial.  
(Now I am joking again, just in case anyone's having trouble keeping
things straight.)   Why?  Let P = "if this statement is true, it's
trivial."  If P is true, then if P is true, it's trivial.  In other
words, if P is true, it's trivial!  We have just shown that P is true.
So it follows trivially that P is trivial.

Newsgroups: sci.math
From: awpaeth@watpix.uwaterloo.ca (Alan Wm Paeth)
Subject: Re: Mercator Projection
Organization: University of Waterloo
Date: Mon, 9 Nov 1992 22:51:51 GMT

In article <1992Nov8.214329.27209@CSD-NewsHost.Stanford.EDU> pratt@Sunburn.Stanford.EDU (Vaughan R. Pratt) writes:

 > [...questions on the derivation and use maps / conformal (complex) maps...]

The Mercator projection has no simple geometric analog. Being cylindrical
(meridians/lines of longitude map onto parallel, vertical lines on the chart)
it is often incorrectly assumed to be developed from a sphere and tangent
cylinder model.

The mapping function is the integral of the secant, called (in my CRC) the
inverse Gudermannian. Its most common formula is

    f(x) = ln (tan (x/2 + Pi/4))

The Taylor expansion (about zero) of the function and its inverse have
identical terms, though one contains alternating signs, the other all
positive. This property can be used to explain the Gudermannian's use of
interrelating trigonometric and hyperbolic formulae without the use of
an imaginary unit. (I view the function as the real portion yanked from a
complex analytical function and hence a conformal map). The series are both
odd and resemble arcsin(x) and sin(x) through the cubic term.

Conformal maps preserve angle measure (and their handedness). For instance, the
Stereographic map is the image of the complex function f(z) = z^(-1). It is
conformal and by convention has a proper orientation ("up" on the chart is
"north" along the sphere) at its point of projection. But elsewhere, the
``compass rose'' must be rotated. Because the Mercator projection is
cylindrial, "north" is upwards up along any meridian anywhere on the chart. So
being both conformal and cylindrical are necessary and sufficient to product a
chart on which compass heading may be plotted directly. This was Mercator's
intent in his derivation (not his real name, BTW) and explains the chart's
widespread nautical application.

Because of the excessive scale distortions near the pole, transverse or
oblique projections may rotate the pole onto the equator or another arbitrary
position. Transverse Mercator projections have geodetic applications. Oblique
projections may be used to produce long-haul give over-the-pole charts with
little distortion along a select great circle route, though for general
aeronautical use Lambert's (second) conformal conic is more widely used.

Most of what I've written above is excerpted from my entry appearing in
_Graphics Gems_ (Academic Press, 1990, Andrew Glassner, ed.), written with the
scientist/mathematician in mind. The volume includes the derivation and
accompanying figures for a number of common charts, including representative
conformal and equal-area varieties.

    /Alan Paeth
    Computer Graphics Laboratory
    University of Waterloo
Newsgroups: sci.math.num-analysis