HDTenEightyP/NetNews huggingface dataset:
From: edgar@function.mps.ohio-state.edu (Gerald Edgar)
Newsgroups: sci.math
Subject: Re: Relatives with Crackpot Proofs
Date: 10 Nov 1992 08:15:40 -0500
Organization: The Ohio State University, Dept. of Math.
NNTP-Posting-Host: function.mps.ohio-state.edu


There is a new book called MATHEMATICAL CRANKS by Underwood Dudley.
[Actually, the book is quite entertaining.]
He has some suggestions of the proper way to deal with "fermatists",
as he calls them, and other cranks.  But I don't think he relates
any cases of a cranky relative.


-- 
  Gerald A. Edgar                Internet:  edgar@mps.ohio-state.edu
  Department of Mathematics      Bitnet:    EDGAR@OHSTPY
  The Ohio State University      telephone: 614-292-0395 (Office)
  Columbus, OH 43210             -292-4975 (Math. Dept.) -292-1479 (Dept. Fax)
Newsgroups: sci.math
From: tycchow@athena.mit.edu (Timothy Y Chow)
Subject: Why Atlases?  (was: Re: What is a manifold?)
Organization: None.  This saves me from writing a disclaimer.
Date: Thu, 5 Nov 1992 20:58:54 GMT

Vaughan Pratt asks why the complicated notion of atlas is essential,
since it seems to involve just as much arbtirariness as a retract
definition.

In my previous articles I glossed over the distinctions between
topological and smooth manifolds.  In the case of topological manifolds
I think the embedding-independent definition is well-motivated.  (Feel
free to disagree, of course.)  There isn't any of the arbitrariness of
the choice of open charts that there is in the case of smooth manifolds:
we just require that at EVERY point there is SOME neighborhood that's
homeomorphic to R^n.

In the case of differentiable manifolds, however, there is a certain
arbitrariness in choosing an atlas.  The arbitrariness can be removed by
requiring the set of charts to be maximal, but this doesn't really answer
the question of why this definition is superior to the retract definition 
that Vaughan Pratt suggests.

I think the point is that a lot of basic theorems about smooth manifolds
require you to work with coordinate neighborhoods of points.  In order
to apply the inverse function theorem or other techniques from calculus,
you need to identify a small portion of the manifold with an open set in
Euclidean space.  Since you need the existence of such things all the
time, you might as well build it into the definition.  Even with the
retract definition, at some point you're going to have to prove that
you can take coordinate neighborhoods.

To some extent it is just a matter of taste whether you begin with the
existence of global tubular neighborhoods and prove the existence of
local coordinate neighborhoods or proceed the other way around.  In
favor of the standard approach I think it can be said that it is more
in keeping with the approach in modern mathematics of defining objects
as intrinsically as possible, i.e., without having to create a habitat
for them to live in before allowing them to exist, but focusing on the
object itself as much as possible.  IMHO this is a more natural way to
define mathematical objects.

Incidentally, another way to avoid the apparent arbitrariness of the
choice of charts for the atlas is to define a smooth manifold by
specifying, instead of these little overlapping charts, the sheaf of
differentiable functions on the manifold.  This is more in the spirit
of scheme theory, but I think we're starting to digress here.
From: dvf@kepler.unh.edu (David V Feldman)
Newsgroups: sci.math
Subject: Re: Univariate polynomial equations and the FAQ
Date: 11 Nov 1992 03:23:17 GMT
Organization: University of New Hampshire  -  Durham, NH
NNTP-Posting-Host: kepler.unh.edu

In article <1992Nov10.100903.18040@sun0.urz.uni-heidelberg.de> gsmith@urania.uucp (Gene W. Smith) writes:

[stuff deleted]

>Are you saying, fix some m, and consider all polynomials of the 
>form
>
>x^n + a_m x^m + a_(m-1) x^(m-1) + ... + a_0, a_i in Q?  
>
>If so, then for m > 1 and n > 4, we have nonsolvable extensions of Q.
>
>If I am reading what you wrote below correctly, you are interested in
>extensions which have Tschernhausen transformations into a form with
>a_i beyond a certain point 0.  We can see that over Q there is an
>immediate problem getting rid of the a_2 term.  If the extension in
>question is totally real, the sums of the squares of the roots is
>positive.  If we have eliminated the trace term already, we see
>immediately that a_2 must be positive.

[stuff deleted]

Sorry for the equation that was hard to read.  As requested, I shall
try to restate my question clearly and unambiguously:

Let  K_m  be the smallest extension of Q with the property that K_m
contains all roots of all polynomials

x^n + a_m x^m + a_{m-1} x^{m-1} + ... + a_0, a_i in  K_m .

Assuming that K_m is not the algebraic closure of Q, let s(m) be the
degree of the smallest algebraic number *not* in K_m.  What
can be said about s(m) as a function of  m ?  Classical Galois theory
and pre-Galois theory of equations give s(0)=5.  Tschernhausen
transformations give s(m)>m+2.  I am afraid that this is all I know
at the moment.
>-- 
>     Gene Ward Smith/Brahms Gang/IWR/Ruprecht-Karls University 
>               gsmith@kalliope.iwr.uni-heidelberg.de

David Feldman
Newsgroups: sci.math
From: jbaez@riesz.mit.edu (John C. Baez)
Subject: Re: a first year grad student freaks out.
Organization: MIT Department of Mathematics, Cambridge, MA
Date: Thu, 12 Nov 92 21:46:57 GMT

In article <BxKu9s.BAw@news.udel.edu> cornwall@bach.udel.edu (Ray J Cornwall) writes:

>For those of us who wish to do research (cause we'll get our names in
>really cool journals! :) can you give us some pointers on how to come
>up with such topics?
>I've been trying to be more aggressive with my studies in math, to
>look for such ideas, but I have a feeling I'm barking up the wrong
>tree looking in textbooks and looking for my favorite topics here.
>Where are some good sources of information, and what are some good
>questions to ask myself?
>(I know, Bad English on the last part...sorry...)

There are an essentially infinite number of good research topics so for
me to name any particular topic would be very misleading.  Textbooks are
not especially good for finding out what's NOT known that SHOULD be, as
you note.  By far the best are good colloquia and seminars, conferences,
advanced math classes and chats with mathematics bigshots.  That's how I
keep up with the "current state of ignorance" and always have piles of
problems on my plate.  Of course, in the final analysis one has to come
up with problems oneself because one needs to come up with problems one
can do.  Often it's best to first figure out something one can do and
then see if it solves some problem or other!  But keeping in touch with
other mathematicians is the prime way to find undeveloped areas of math
where there are plenty of obviously interesting questions to ask that
haven't been answered yet.  

Second best, when compared to interaction with real humans, is reading
journals.  I spend large hunks of time doing this.  Don't read anything
boring, though (that automatically knocks out 99% of the stuff).  Start
with something you are interested in, look it up in Math Reviews and
find some papers that talk about it.  Pay special attention to what the
papers are *trying to do but not quite succeeding in* -- most papers do
not definitively settle the question that motivated them, so reading
them gives you an idea of what people are struggling to do but haven't
done yet.  Conference proceedings are often especially good about
admitting that X, Y, and Z are still poorly understood.  Read some
papers making sure not to get bogged down in stuff you don't understand
-- don't spend too much time on any *one* paper until you are *sure* it
will repay the effort.  At first, it's much more important to skim your
way through lots of stuff in order to get the lay of the land in
whatever subject you are checking out!  Grad students are often way too
obsessive about understanding every single sentence before they move on
to the next.
From: leyfre@McRCIM.McGill.EDU (Frederic Leymarie)
Newsgroups: sci.math
Subject: Re: Michael Spivak
Date: 6 Nov 92 16:56:55 GMT
Organization: McGill Research Centre for  Intelligent Machines


In article <BxAuv1.11D@dcs.glasgow.ac.uk>, jack@dcs.glasgow.ac.uk
 (Jack Campin) writes:
|> palais@binah.cc.brandeis.edu wrote:
|> > A number of people have asked how to order Spivak's "Calculus".
|> > It is published by his own company, Publish or Perish Inc.

|> > Publish or Perish Inc.
|> > 3701 West Alabama 450-130
|> > Houston, TX,   77027
|> > 713  524  5515 

|> What else do they publish?  All I've seen is Spivak's own huge 5-volume
|> differential geometry notes (this must be the biggest single-author
|> mathematics text ever written).

Here are some other books they publish:

	"Spaces of Constant Curvature", Wolf, 5th ed.
	"Knots & Links", Rolfsen, new corr. print.
	"User's Guide to Spectral Sequences", McCleary
	"Submanifolds & Isometric Immersions", Dajczer et al.


BTW, there are single-authored maths. text around of similar size;
Darboux' "Theorie Generale des Surfaces" in 4 vols. comes to mind
(over 2200 pages...)


|> I've got the 1967 W.A. Benjamin edition of "Calculus", and the answers
|> volume - is the 1980 Publish or Perish one any different?  Why did W.A.
|> Benjamin drop it?

Well, the 1980 version is the SECOND edition. It must be different.
-- 
Frederic Leymarie -- leyfre@mcrcim.mcgill.edu
McGill University, Electrical Eng. Dept., McRCIM,    |	Tel.: (514) 398-8236
3480 University St., Montreal, QC, CANADA, H3A 2A7.  |	FAX:  (514) 398-7348
Newsgroups: sci.math
From: phkahler@vela.acs.oakland.edu (KAHLER PAUL H.)
Subject: Re: Soccer ball question
Organization: Oakland University, Rochester MI.
Date: Fri, 6 Nov 1992 06:03:10 GMT

Someone wanted to know a ratio on a soccer ball. I assume this means with
flat polygons for faces. If that is the case then:

RadiusOfCircumscribedSphere / SideLength = 2.877583464...

Anyone want to confirm this number?

Paul


ps. It is 'trivial' :-)
Xref: sparky sci.math:14536 alt.politics.elections:22967
From: brock@NeXTwork.Rose-Hulman.Edu (Bradley W. Brock)
Newsgroups: sci.math,alt.politics.elections
Subject: Re: Electoral college (was Re: Bill Clinton and Complex Analysis : -))
Date: 6 Nov 1992 20:48:26 GMT
Organization: Computer Science Department at Rose-Hulman
Reply-To: brock@NeXTwork.Rose-Hulman.Edu (Bradley W. Brock)
NNTP-Posting-Host: g210b-1.nextwork.rose-hulman.edu

In article <israel.720991427@unixg.ubc.ca> israel@unixg.ubc.ca (Robert B.  
Israel) writes:
> 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. 

Which is not that far removed from how Lincoln won in 1860 with a plurality of  
only 40%.  I might add that Rutherford B. Hayes and Benjamin Harrison both won  
despite finishing second in the popular vote.

--
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: magdi@uxh.cso.uiuc.edu (Magdi N Azer)
Newsgroups: sci.math
Subject: Dissertations
Date: 11 Nov 92 18:09:45 GMT
Organization: University of Illinois at Urbana


	Now that we have scared a first year grad student to death, perhaps
let's give the poor guy some mode information.

	First of all, nobody expects you to be understad everything there is to
know right now.  Research, particularly as it relates to a Ph.D is something
that takes years to become proficient at.  I'm just finishing a Ph.D (not in
math, but in Mechanical Engineering) and only in the last two months or so have
I felt comfortable with my approaches to problem solving.

	The best bit of advice I could give you (even though you didn't ask for
any) is to begin now reading the journals that are relevant to your field of
interest.  There are so many journals and publications these days that it is
difficult to keep up as much as one would like, but by starting early you have
the advantage of seeing how others in your field have attacked certain
problems.  In time, you may see errors in their approach or areas for further
study, and this is the exciting part.  When you don't have to say something
because that is what you arvisor told you, you are on the way to developing
independence.

	Finally, try to set milestones for yourself.  After you finish taking
classes, it is easy to get bogged down on your degree progress and because
research has benefits that are always in the future, it is easy to feel as if
you are not worthwhile as a person, or that you are stupid simply because
progress is going slower thatn you want.  This is something I think we have all
faced at one time or another.  

	Best of luck

Magdi N. Azer
magdi@uxh.cso.uiuc.edu
Newsgroups: sci.math
From: ledwards@leland.Stanford.EDU (Laurence James Edwards)
Subject: Thank you: Re: definition of topological space
Organization: DSG, Stanford University, CA 94305, USA
Date: Fri, 6 Nov 92 21:18:46 GMT

Thanks to some very lucid replies my lack of understanding and
confusion on this matter has been thoroughly eradicated.

Thank you all very much!

Larry Edwards
 
Newsgroups: sci.math,sci.physics,sci.astro,sci.bio,sci.chem,misc.education
From: sethb@fid.morgan.com (Seth Breidbart)
Subject: Re: 2-dimensional grading system (was Re: What can one do for the bright?)
Organization: my opinions only
Date: Sun, 8 Nov 1992 20:15:55 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. 

One minor point:  I've read hundred (thousands?) of resumes,
and interviewed many candidates.  I have no idea what grades any of
them received.

Seth		sethb@fid.morgan.com
From: sundar+@cs.cmu.edu (Sundar Vallinayagam)
Newsgroups: sci.math
Subject: Re: Michael Spivak
Date: 5 Nov 92 14:09:04 GMT
Article-I.D.: cs.Bx8xz4.67L.1
Organization: School of Computer Science, Carnegie Mellon


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

Thanks!
-- 
**************************************************
ramli@orca.ele.uri.edu
**************************************************
From: keith@celia.UUCP (Keith Goldfarb)
Newsgroups: sci.math
Subject: Relatives with Crackpot Proofs
Date: 9 Nov 92 20:25:29 GMT
Reply-To: celia!keith@usc.edu (Keith Goldfarb)
Organization: Rhythm & Hues, Inc., Hollywood

Does anybody have any good suggestions about how to deal with
crackpot "proof"s from relatives and friends?  A relative of
mine cornered me at a party recently and gave me a copy of
his "proof" of FLT.  He'd like me to give him some feedback.
I told him that he should just mail away a few copies to some
real experts (trying my hardest to get out of it) and he said
that he had done that, but he wanted my feedback as well.

Of course, his document had no value at all, it was a classic
case of a crackpot proof as we've all see them.  Now, I don't
want to start another discussion about crackpot proofs in general,
but rather what should be done when the person pushing the proof
is personally known, and known well.  When I next see this guy,
he's going to ask me what I thought, and I really don't know how
I should deal with it.

Maybe Dear Abby would have some suggestions?

K.
-- 
Keith Goldfarb              Rhythm & Hues               Claudia is Everywhere.
celia!keith@usc.edu         ...mlogic!celia!keith  
I got nothing.  Too bad.                                Some pink toes
But I'm happy 'cause that's all I have.                 Some black toes
From: lady@uhunix.uhcc.Hawaii.Edu (Lee Lady)
Newsgroups: sci.math
Subject: Re: Problem in Category Theory (elementary)
Summary: Epimorphisms which are not surjections.
Keywords: Category theory  epimorphism
Date: 8 Nov 92 23:52:26 GMT
Followup-To: sci.math
Organization: University of Hawaii (Mathematics Dept)

In article <BxDJ8v.DCw@world.std.com> rjk@world.std.com (robert j kolker) writes:
>Find a category with an arrow (morph) that is epic and monic but not an
>isomorphism.

At the very least, one should stick to concrete categories to make the
problem at all interesting.  Even so, there are lots and lots of concrete
categories with epimorphisms which are not surjections, thus providing
easy examples for the question.  

1)  Let  X  be a set which is not a singleton.  Give  X  the discrete
topology.  Let  Y  be the same set with the indiscrete topology and let 
f:X --> Y  be the identity map, considered as a morphism in the category
of topological spaces.  (Unlike the rest of the examples,  f  is not only
an epimorphism but is in fact surjective.)  

2)  Let  f:Q --> R  be the inclusion map from the rationals into the
reals.  This is an epimorphism in the category of Hausdorff spaces
since  Q  is dense in  R.  (Two continuous maps from  R  into a Hausdorff
space which agree on  Q  have to be the same.)  

3)  In the category of rings with identity, let  f:Z --> Q  be the
inclusion map from the integers into the rationals.  This is an
epimorphism in the category of rings.  

4) In the category of *torsion free* abelian groups let  f:Z --> Q  be
the inclusion map.  This is an epimorphism since if two homomorphisms
from  Q  into a torsion free group agree on the element  1  they must be
the same.  

--
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: mjd@saul.cis.upenn.edu ("[*] Last of the Dinosaurs")
Newsgroups: sci.math
Subject: Noncommutative division rings sought
Date: 5 Nov 92 21:58:08 GMT
Followup-To: poster
Organization: Eaters of Wisdom


Other than the quaternions, what's an example of a noncommutative
division ring?  (Division ring == ring + multiplicative inverses).

Please email if you want to give an answer or if you want me to send you
the list of answers I receive.
--

                And for to se, and eek for to be seye
Mark-Jason Dominus 	  			    mjd@central.cis.upenn.edu
From: tep2j@amsun.apma.Virginia.EDU (Todd E. Peterson)
Newsgroups: sci.math
Subject: who should teach calculus?
Date: 10 Nov 92 22:33:00 GMT
Article-I.D.: murdoch.1992Nov10.223300.19016
Reply-To: tep2j@amsun.apma.Virginia.EDU (Todd E. Peterson)
Organization: University of Virginia

I am interested in hearing net.opinions on the following:

Is it a good or bad practice to use non-mathematicians to
teach mathematics courses?  In particular, what about the
use of engineering faculty to teach engineering calculus
courses, and other applied mathematics courses?

                             ________________
Todd E Peterson              |\  /\  /\  /\  /|     phone 804 982 2909
Dept of Applied Math         |_\/__\/__\/__\/_|     fax   804 982 2972
Thornton Hall, UVa           | /\  /\  /\  /\ |     email tep2j@virginia.edu
Charlottesville VA 22903     |/__\/__\/__\/__\|
Newsgroups: sci.math,misc.education
From: roberts@gaul.csd.uwo.ca (Eric Roberts)
Subject: Re: Is Math Hard?
Organization: Univ. of Western Ontario, London, Canada
Date: Sat, 7 Nov 1992 03:10:19 GMT

In article <6NOV199218493271@comet.nscl.msu.edu> burtt@comet.nscl.msu.edu (BRIAN BURTT) writes:
>(In response to Mr. Parson's comments on home education...)
>In my particular circumstance, which I think reflects that of some other 
>people out there:
>	As of about fifth or sixth grade, I was quite of ahead of my 
>mother (my single parent, who BTW graduated high school and has almost
>two years of college behind her) in knowledge of science, math, and history,
>and by the time I reached high school in most other academic subjects.
>She wanted to "home educate" me, letting me teach myself, which I have 
>always done quite well.  Of course, the local school district was not
>at all interested in letting this happen.  (They weren't concerned about
>the quality of my education, because I was already far past what they
>could teach me in classes that, for example, sixth graders were taught
>at a second grade level.  They wanted to be sure they continued to get 
>the money from the state of Michigan that they were granted for each 
>enrolled student.  These are statements of officials and teachers of 
>the school district.)
>	The only thing I remember learning from my first five years
>is arithmetic.  Almost everything else I knew years before it was 
>taught in school.
>	Having failed at the home education route, my mother tried to
>get me enrolled in a gifted program in a local school district.  They
>were quite happy to have me, but it took TWO AND A HALF YEARS before
>this particular school district was willing to give up its state funds
>for me and let me go on my way.
>	Have others had similar problems in moving elementary 
>school students to more appropriate situations, or was I just 
>particularly unlucky?
>
>--Brian Burtt
>Undergraduate major in physics and mathematics
>Michigan State University
>burtt@lynch.nscl.msu.edu

	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
 
Newsgroups: sci.math
From: jbaez@riesz.mit.edu (John C. Baez)
Subject: Re: What is a knot?
Organization: MIT Department of Mathematics, Cambridge, MA
Date: Tue, 10 Nov 92 03:31:22 GMT

In article <COLUMBUS.92Nov9100248@strident.think.com> columbus@strident.think.com (Michael Weiss) writes:
>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?)

Perhaps they weren't very well educated.  Actually this is the sort of
thing I hoped Pratt would bounce back with when I teased him about folks
who can't tie their shoelaces until it is explained in
category-theoretic terms.
Newsgroups: sci.math