HDTenEightyP/NetNews huggingface dataset:
From: ara@zurich.ai.mit.edu (Allan Adler)
Newsgroups: sci.math
Subject: Re: Abel's proof of the insolubility of the quintic
Date: 3 Sep 92 18:50:04 GMT
Article-I.D.: camelot.ARA.92Sep3135004
Organization: M.I.T. Artificial Intelligence Lab.

In article <1992Sep2.204229.12330@news.cs.brandeis.edu> ruberman@binah.cc.brandeis.edu writes:

   Does anyone know a reference for a modern treatment of Abel's
   proof of the insolubility of the quintic?  A high-school student 
   recently came to me, having learnt the solutions to the lower degree
   equations, and hoping to understand the higher degree case as well.
   He tried to read Abel's memoir (translated into English in the venerable
   Source book in Mathematics).  Understandably, he didn't get too far
   since Abel's paper is rather dense and obscure to an untutored reader.
   (For instance he doesn't take any pains to explain what the meaning
   of `a solution in radicals to the general quintic' would actually mean.)

   One suggestion to this student is to read enough about groups and fields
   to learn the rudiments of Galois Theory.  There is a book of H. Edwards
   which more or less travels this route.  On the other hand, Abel's proof
   is quite elementary, and can in principle be explained to a high-school
   student.  (I said in principle!)  I am looking for a source for such an
   explanation; any pointers would be greatly appreciated.

   Daniel Ruberman
   Department of Mathematics
   Brandeis University
   Waltham MA 02254

   ruberman@binah.cc.brandeis.edu
   ruberman@brandeis.bitnet


When I taught at Brandeis, I presented Abel's paper to my algebra class.
If Brandeis hadn't fired me, you could just send the student to me now. ;-)

I still have my notes from the course and I am planning to write up
the analysis I made of Abel's paper sometime. At that time, you are
welcome to have a copy.

But I am just wondering: why don't you read the paper yourself and
figure out what is going on yourself? It would set a wonderful
example for your student and it would make you more capable of
helping him/her read the original.

Allan Adler
ara@altdorf.ai.mit.edu
From: bradtke@greed.cs.umass.edu
Newsgroups: sci.math
Subject: A matrix anti-derivative puzzle
Date: 29 Aug 92 13:44:54 GMT
Reply-To: bradtke@greed.cs.umass.edu ()
Distribution: usa
Organization: University of Massachusetts, Amherst


I have a problem involving the anti-derivative of a matrix function.
I would like to find a function F such that 

dF/dw = - G'w

or

dF/dw = (G - G')w,

where G is a nonsymmetric matrix, and w is a vector.
The quadratic form F = w'Gw gives, of course, dF/dw = (G+G')w.

Although if hasn't helped me any, the following may help you.
The particular G I am concerned with is of the
form
G = H' (I-sP) Y H, where H is of dimensions (n by m), s is a scalar between
0 and 1, P is the transition probability matrix of a Markov chain, and
Y = diag(y), where y is the vector of limiting state residence
probabilities of the ergodic Markov chain.

Thanks for any time you may put into this.  Even if you only get a few
partial results, I'm interested in seeing those.  Maybe putting those
together will achieve a complete answer.

I'll share the results will all that are interested.

Steve

bradtke@cs.umass.edu
From: bach@jalapeno.cs.wisc.edu (Eric Bach)
Newsgroups: sci.math
Subject: Re: Polygon point enclosure
Date: 27 Aug 92 18:57:40 GMT
Organization: University of Wisconsin, Madison -- Computer Sciences Dept.

>>> I'm looking for a method to determine if a point is enclosed
>>> by a polygon. Any help would be greatly appreciated.
>
>>Well, here's one approach. Imagine a ray (=half-line) coming off from the point
>>in some direction. Count how many of the sides of the polygon it goes through.
>>(If it goes *along* any of those sides you're in trouble and should try another
>>direction.) If it's an odd number the point is inside the polygon; if it's an
>>even number the point is outside the polygon.
>
>This algorithm is in _Algorithms_ by Robert Sedgewick, Addison-Wesley
>(1983), pp 315-318.  (I believe there is a second edition out, but I
>don't have it.) 

	The last time I taught the algorithms course, I discovered
	that the algorithm in the second edition (p. 354) fails on
	an equilateral triangle whose vertices are the 3 roots of
	unity. (Are you listening, Bob?)  Not exactly "general position,"
	but...

	In response to this, I presented another algorithm, based
	on computing "pseudo winding numbers" using the "pseudo angle"
	defined on p. 353.  The rough idea is that you only care about
	the homology class of your cycle, and this can be figured out
	using O(n) rational operations.  I am curious if this is "known"
	(i.e. written up somewhere).  Next time it would be nice to give a
	reference!

	-Eric Bach
	 bach@cs.wisc.edu
From: columbus@strident.think.com (Michael Weiss)
Newsgroups: sci.math
Subject: Re: Parallel axiom.
Date: 27 Aug 92 10:53:25
Organization: Thinking Machines Corporation, Cambridge MA, USA
	<1992Aug27.115903.10390@waikato.ac.nz>
NNTP-Posting-Host: strident.think.com
In-reply-to: maj@waikato.ac.nz's message of 26 Aug 92 23:59:03 GMT

In article <1992Aug27.115903.10390@waikato.ac.nz> maj@waikato.ac.nz writes:

   I have always felt that Euclid's form is superior because it contains
   no mention of the mysterious undefined concept 'parallel'. And how
   are we supposed to have any intuition of what 'parallel' means in the
   various possible geometries that may exist without the axiom. I don't
   think Playfairs Axiom plays fair in the least. It has always struck
   me as question begging.

   -- 
   Murray A. Jorgensen [ maj@waikato.ac.nz ]    University of Waikato
   Department of Mathematics and Statistics     Hamilton, New Zealand      

Definition: two lines are parallel if they have no points in common.
What's mysterious about that?

If you want to be really picky, or are a fan of first order logic, consider
a theory containing unary predicates "point(x)" and "line(x)", and a binary
predicate "on(x,y)", which I will write in the infix form "x on y".  Then
the parallel predicate is defined:

           def
   x || y  ===   line(x) and line(y) and not (exists z)[point(z) and z on x
                 and z on y]


Incidentally, I am fairly sure that Playfair was not the first to introduce
"Playfair's" form of the parallel postulate, though I don't remember
offhand who was.

So far as intuition goes, are you familiar with Poincare's model of the
non-euclidean plane?  I grant you that a purely axiomatic treatment is apt
to prove a bit unsatisfying, although that's all that Bolyai had to work
with.
From: sichase@csa1.lbl.gov (SCOTT I CHASE)
Newsgroups: sci.math
Subject: Re: Solitaire games
Date: 4 Sep 92 21:27:06 GMT
Organization: Lawrence Berkeley Laboratory - Berkeley, CA, USA
Distribution: na
Reply-To: sichase@csa1.lbl.gov
NNTP-Posting-Host: 128.3.254.196
News-Software: VAX/VMS VNEWS 1.3-4   

In article <NICKH.92Sep3143716@VOILA.VENARI.CS.CMU.EDU> nickh@CS.CMU.EDU (Nick Haines) writes:
> I play a game with triplets of digits (such as one finds on 99% of
> British numberplates),

This reminds me of the "annual puzzle" which appears each January in the 
alumnus section of Technology Review, in a math/games column which appears
in each issue.  (MIT grads get a special insert with class news, MIT 
propaganda, etc.)

Problem:  Construct all the numbers from 1 to 100 using all four digits
of the year (in our case: 1,9,9,2),preferably in order, by interposing
apropriate operators.  For example,

1  = 1**992
2  = 1**99 * 2 
3  = 1**99 + 2
7  = (1**9)*9 - 2 
16 = 1*(9+9) - 2

and so forth.  If you've never tried it before, give it a whack.  Warning:
the best solution does *not* include all 100 numbers in most (if not all) years.

-Scott
--------------------
Scott I. Chase			"The question seems to be of such a character
SICHASE@CSA2.LBL.GOV		that if I should come to life after my death
				and some mathematician were to tell me that it
				had been definitely settled, I think I would
				immediately drop dead again."      - Vandiver
Newsgroups: sci.math
From: asimov@wk223.nas.nasa.gov (Daniel A. Asimov)
Subject: Re: HELP! Inscribed Circle...
Organization: NAS, NASA Ames Research Center, Moffett Field, CA
Date: Fri, 28 Aug 92 17:58:17 GMT

In article <1992Aug28.121042.28144@nrtpa038.bnr.ca> Re:HELP! Inscribed Circle... writes:
>To anyone who might have read the previous posting
>where I requested assistance with a lat-long problem;
>it was mentioned in a response that a comment I made 
>was kind of derogatory. I regret that it was taken in that manner,
>I assure you it was actually meant as a compliment. I 
>am not very good at mathematics, and the discussions on
>this thread are usually beyond my depth.  My apologies to
>anyone I offended...
>
>Bob - thanks for your assistance.
>
>Madeleine Thomas
------------------------------------------------------------

I want to assure you that that I thought the use of the term
"math whiz" *was* rather complimentary.  

I am a mathematician, and have been for many years, and I
*never* have heard of any other time someone objected to
the use of that term.

I can't help noticing that you are being so circumspect that
you didn't even quote what the offending term was, in your post
above.  In my opinion, there is *nothing* to worry about.
And by the way, thanks for contributing an interesting problem
to this newgroup.

--Dan Asimov
asimov@nas.nasa.gov

Mail Stop T045-1
NASA Ames Research Center
Moffett Field, CA 94035-1000
(415) 604-4799
Newsgroups: sci.math
From: sdyck@ccu.umanitoba.ca (Sheldon Dyck)
Subject: Re: Looking for faulty proof that 0=1.
Organization: University of Manitoba, Winnipeg, Canada
Date: Wed, 2 Sep 1992 23:58:40 GMT

In <1992Sep2.172220.12362@klaava.Helsinki.FI> amnell@klaava.Helsinki.FI (Marko Amnell) writes:

>I looked in Spivak's _Calculus_ and found a similar bogus proof:

>Let x=y.  Then
> 
>       x^2=xy,
>   x^2-y^2=xy-y^2,
>(x+y)(x-y)=y(x-y),
>       x+y=y,
>        2y=y,
>         2=1.

>So, given your proof, I conclude that 2=0 !  ;-)

Here is another proof that 2=0, this one involes complex numbers.

    1 = Sqrt[1]
      = Sqrt[ (-1) * (-1) ]
      = Sqrt[ (-1) ] * Sqrt[ (-1) ]
      = i * i
      = i^2
      = -1

Hence we conclude that 2=0. 
Where is the error in the "proof".  :^)

+=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=+=-=-=-=-=-=-=-=-=-=-=-=-=-=+
| Sheldon Dyck    <sdyck>                     | 58 Pincarrow Road         |
| Department of Mathematics,                  | Winnipeg, Manitoba.       |
| University of Manitoba.                     | Canada,  R3Y-1E3.         |
| e-mail: sdyck@ccu.UManitoba.CA              | (204)-488-6990            |
+=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=+=-=-=-=-=-=-=-=-=-=-=-=-=-=+
Newsgroups: sci.math
From: hporopudas@tnclus.tele.nokia.fi
Subject: Re: Proof of God's Existence
Organization: Nokia Telecommunications.
Date: Wed, 2 Sep 1992 06:48:37 GMT


In article <1992Sep1.123533.14058@relay.nswc.navy.mil>,
bwallet@apssgi.nswc.navy.mil (Brad Wallet) writes:
> In article <1992Sep1.090011.1@tnclus.tele.nokia.fi>,
hporopudas@tnclus.tele.nokia.fi writes:
> |>
> |> In article <17ui6kINNsft@matt.ksu.ksu.edu>, bubai@matt.ksu.ksu.edu
> |> (P.Chatterjee) writes:
> |> > I was told by somebody that there is a mathematical proof of God's existence;
> |> > was wondering if somebody could shed some light on the same.
> |> >
> |> > Thanks. Looking forward to the response.
> |>
> |>    I think that God's existence is an axiom. He says in the Holy Bible (Second
> |>  book of Moses 3:14-15 in Old Testament and also in Johannes 8:28-29 in New
> |>  Testament) that He is "Existence Himself".
> |>    If someone is arguing that "Existence Himself" does not exist, I think that
> |>  at the same time he/she is arguing that he/she himself/herself does not exist.
> |>
> |>               Hannu.
>
> Mr. Space Potato has left/was run off sci.physics and has found a new home.
> Please, before this gets started, take it to alt.talk.does.not.belong.here.

  Can't we ever get rid of these unbusinesslike comments.

                   Hannu.
From: maj@waikato.ac.nz
Newsgroups: sci.math
Subject: Re: Parallel axiom.
Date: 27 Aug 92 11:59:03 +1200
Distribution: world
Organization: University of Waikato, Hamilton, New Zealand

In article <1992Aug25.170135.504@csc.canterbury.ac.nz>, wft@math.canterbury.ac.nz (Bill Taylor) writes:
> Euclid's parallel axiom, in its original form, seems very cumbersome....
> ----------------------------
> "Two lines that have a third line crossing them, will meet on that side of
> the third line for which the interior angles together sum to less than
> two right angles."
> ----------------------------
> Though it presumably has some advantage in logical purity, I can't help
> thinking Euclid made a serious pedagogical error to choose this form of
> the axiom. (It takes quite a bit of reading even to see what it says, 1st time).
> 
> As is well-known, it is the strikingly non-obvious nature of this version
> that led to centuries of struggles to prove it, and eventually led to the
> discovery of non-Euclidean geometries.
> 
> There are many well-known logically equivalent forms.   My own favourite is
> `Playfairs Axiom'  (a very honest-sounding name for a straightforward and
>  ~~~~~~~~~~~~~~~    clear-cut axiom;  how terribly British !)
> 
> "There is exactly one parallel to any given line through any point not on it." 
> ----------------------------------------------------------------------------
> In my opinion, this version has all the intuitive clarity that those searchers
> were missing.  I suspect, if Euclid had hit on this form of the axiom, there
> would have been no great search for a proof, with incalculable consequences
> for the history of mathematics.     But that is neither here nor there.
[rest deleted]

I have always felt that Euclid's form is superior because it contains
no mention of the mysterious undefined concept 'parallel'. And how
are we supposed to have any intuition of what 'parallel' means in the
various possible geometries that may exist without the axiom. I don't
think Playfairs Axiom plays fair in the least. It has always struck
me as question begging.

-- 
Murray A. Jorgensen [ maj@waikato.ac.nz ]    University of Waikato
Department of Mathematics and Statistics     Hamilton, New Zealand      
__________________________________________________________________
'Tis the song of the Jubjub! the proof is complete,
if only I've stated it thrice.'
Newsgroups: sci.math
From: Ulf.Lunde@kvatro.no (Ulf Lunde)
Subject: Wanted: Numerical method
Organization: Kvatro A/S, Trondheim, Norway
Distribution: sci
Date: 4 Sep 92 09:58:30

Given a set of numbers, say {47, 79, 167, 223, 359, 439, 727, 839, 3 967} or
{383, 467, 659, 883, 1 583, 2 099, 2 287, 2 687, 3 119, 3 583}, how does one go
about in finding a smooth (polynomial) function f(x) which outputs those 
numbers for different (not necessarily neighbouring) integer values of x?  
Preferably a polynomial of low order and with a positive first coefficient.
E.g., given the set of numbers:  
 
   {8 297 644 387, 12 478 210 777, 16 658 777 167, 29 200 476 337} 

I would like the procedure to yield:

   f(x) = 4180566390x + 4117077997.

--
Ulf Chr Lunde		  Phone: +47 752 0090       Bank acct no: 5270.10.56183
KVATRO A/S, Pirsenteret	  Fax: +47 752 0140              (deposits welcome! :-)
N-7005 Trondheim, NORWAY. E-mail: Ulf.Lunde@kvatro.no
From: suthan@cs.hw.ac.uk (Manickam Umasuthan)
Newsgroups: sci.math
Subject: Algebraic Geometry Book
Date: 29 Aug 92 13:29:20 GMT
Organization: Dept of Computer Science, Heriot-Watt University, Scotland

Dear Netters,

I shall be very much THANKFUL if someone could give me the full details 
(price, ISBN number etc) of the book "Algebraic Geometry for 
Scientists and Engineers" by S.S. Abhyankar , American Mathematical Society.
so as to enable me to get a copy of it.

THANKS VERY MUCH
-- 
-------
M.Umasuthan, 				:: EMAIL:  suthan@uk.ac.hw.cs
Dept. of Computing & Electrical Engineering,
Heriot-Watt University, Riccarton, Edinburgh EH14 4AS, U.K.
From: faustus@ygdrasil.CS.Berkeley.EDU (Wayne A. Christopher)
Newsgroups: sci.math
Subject: Question about polyhedra
Date: 30 Aug 92 20:36:42 GMT
Article-I.D.: agate.17rbgqINNscd
Organization: University of California, Berkeley
NNTP-Posting-Host: ygdrasil.cs.berkeley.edu

I need some information that must be in a book somewhere, but I can't
seem to find it.  The question is this: for the various platonic
solids, in particular the dodecahedron and the icosahedron, if the
length of an edge is 1 and the polyhedron is centered about the origin,
what are the coordinates of the vertices?  (For some convenient orientation.)
Any references or numbers would be very much appreciated.  Thanks,

	Wayne
Newsgroups: sci.math
From: sshws@convx1.lerc.nasa.gov (Herb Schilling)
Subject: Question on divergence of series given condition
Organization: NASA Lewis Research Center
Date: Fri, 4 Sep 1992 17:40:51 GMT


We think there is a theorem ( By Weierstrauss ? ) on this subject
but we cannot find
it. Can anyone out there tell us if the following is true? 

=======================================================================

  If the terms, a  , of a series have the following property:
                 n

         a                               A
          n+1                1            n
        ------ =    1   -  -----   +   -----    as n -> oo
         a                   n           n
          n



    where A    ->   0 as n -> oo
           n




  then does sum of the a    diverge  ?
                        n 


 Thanks in advance for the help.
-- 
Herb Schilling , NASA Lewis Research Center , 21000 Brookpark Road, MS 142-5
Cleveland, Ohio 44135 . (216) 433-8955       sshws@convx1.lerc.nasa.gov
Newsgroups: sci.math
From: rairan@ecf.toronto.edu (RAI Ranjan)
Subject: Re: p prime, p divides ab => pdivides a or b
Keywords: Contrapositive
Organization: University of Toronto, Engineering Computing Facility
Date: Wed, 2 Sep 1992 19:06:10 GMT

In article <BtyqL2.9A8@ecf.toronto.edu> rairan@ecf.toronto.edu (RAI Ranjan) writes:
>In article <Btyo8q.E63@ux1.cso.uiuc.edu> ceblair@ux1.cso.uiuc.edu (Charles Blair) writes:
>>
>>   My recollection is that a number theory course I took presented
>>this as a difficult result, only proved after doing some stuff
>>with the Euclidean algorithm.  Is there a proof which avoids that?
>
>  So to prove p|(ab) => p|a or p|b, we just show that if p does not 
>divide a AND p does not divide b, then p does not divide ab.  By the
>Fundamental Theorem of Arithmetic this is obvious.  Euclid's algorithm is
>not necessary.  Indeed, the proof of the extended Euclidean algorithm
>depends on this result, I think.

YIKES!!!  Ignore all this stuff above - it's all WRONG!  I have gotten the
whole thing in reverse.  You try to be smart...

I can just here them now:  Engineers!  HA! HA! HA! HA! :-)
-- 
Ranjan Rai                             <rairan@ecf.toronto.edu> 
Engineering Science 9T3                <rairan@eecg.toronto.edu>
University of Toronto
From: jxh@math.ksu.edu (James C. Hu)
Newsgroups: sci.math
Subject: Re: Homework Problems
Date: 30 Aug 1992 12:33:05 -0500
Organization: Dept. of Mathematics, Kansas State University
Distribution: na
NNTP-Posting-Host: hilbert.math.ksu.edu

mueller@schaefer.math.wisc.edu (Carl Douglas Mueller) writes:

> ... I wonder if there is a rule on this group that we do not help
> people with things that look too much like homework problems.  ...

Yes, it is generally considered "bad form" to ask the net for help on
homework.  I s'pose you could keep track of who did the asking, and
match it against those who apply for graduate schools or jobs... :-)
But, a mail message to the offending individual would probably be
sufficient (but not necessary).

So how is everyone?

Obligatory Math:
Found any interesting new ways to prove that .9999... = 1?  Figured
out any clever proofs for Fermat's Last Theorem?  Do you know the
value of the currently largest known prime?  Does this mean we know
all the primes inbetween it and the previously largest known prime?
If Well Ordering and Induction are equivalent, then why is it that
Indeuction is almost always used in undergraduate courses, while Well
Ordering is almost always ignored?

Later,
-- 
James C. Hu (jxh@math.ksu.edu), 1804 Denholm Dr., Manhattan, KS 66502
"If it was so, it might be; and if it were so, it would be; but as it
isn't, it ain't.  Thats logic." - Lewis Carroll
Opinions expressed are mine.  Let me know if they are someone else's.
Newsgroups: sci.math
From: kcj@matilda.vut.edu.au (Kate)
Subject: Permutation problem
Organization: Victoria University of Technology
Date: Fri, 4 Sep 1992 01:06:25 GMT

Can someone tell me the formula for getting the number
of permutations of any group of numbers that add up to a certain number. e.g.
how many permutations of length 5 add up to 20?

Thanks,

Kate

-- 
Kate Juliff                           | kcj@matilda.vut.edu.au
Victoria University                   | phone +61 3 4814720   
P.O. BOX 14428,                       | fax   +61 1 6902011 
MELBOURNE MAIL CENTRE, AUSTRALIA 3000 |
From: elkies@ramanujan.harvard.edu (Noam Elkies)
Newsgroups: sci.math
Subject: Re: Abel's proof of the insolubility of the quint
Date: 3 Sep 92 16:24:49 GMT
Article-I.D.: husc3.1992Sep3.122450.15337
Organization: Harvard Math Department

In article <87834@netnews.upenn.edu>
weemba@sagi.wistar.upenn.edu (Matthew P Wiener) writes:

>I spent my undergraduate days under the misconception that the proof of
>the simplicity of A_5 was overly complicated and uninformative.  Then I
>came across the proof in Rotman: identify the conjugacy classes of A_5,
>and notice the impossibility of any of them forming a partition for a
>size that non-trivially divides 60.

This nice proof is reasonably well-known, but can one get a proof
of the simplicity of all A_n (n>4) from such ideas?

--Noam D. Elkies (elkies@zariski.harvard.edu)
  Dept. of Matehmatics, Harvard University
Newsgroups: sci.math
From: ramsay@unixg.ubc.ca (Keith Ramsay)
Subject: Re: Proof of God's Existence
Organization: University of British Columbia, Vancouver, B.C., Canada
Date: Wed, 2 Sep 1992 07:46:22 GMT

In article <John_Jenkins-010992224544@kip-32.taligent.com> 
John_Jenkins@taligent.com (John H. Jenkins) writes:

>This is from E.T. Bell's "Men of Mathematics":

[Story about Diderot and Euler]

>I love the story -- but since Bell tells it, I suppose it's probably
>apocryphal (even if de Morgan *is* his source).  :-(

It has been passed down for a long time, but it is almost certainly
apocryphal. For example, Bell's remark:

>This was easy because all mathematics was Chinese to Diderot.

is known not to be true; Diderot had written some scientific papers.
(I forget the details on this).

Keith Ramsay
ramsay@unixg.ubc.ca
Newsgroups: sci.math
From: malton@qucis.queensu.ca (Andrew Malton)
Subject: Re: Solitaire games
Organization: Computing & Information Science, Queen's University at Kingston
Date: Fri, 4 Sep 1992 15:47:34 GMT

>My game with license plates is to try to find a word that contains the
>letters of the license plate in order, not necessarily consecutively.
>For example, XPV -> expressive.  My license plate used to have XPF; I never
>did think of one for that.

My wife and I play this game too, but in Polish, which is much easier, since
it has solutions to common (around Kingston) strings like SZR and CLJ.
We usually add the constraint that no consonants should be added at the
beginning.
-- 
Prof. Andrew Malton                  | Office (613) 545 6526
Dept. of Computing and Info. Science | FAX    (613) 545 6513
Queen's University                   | malton@qucis.queensu.ca
Kingston, Ontario, Canada K7L 3N6    | 
Newsgroups: sci.math