HDTenEightyP/NetNews huggingface dataset:
From: mroussel@alchemy.chem.utoronto.ca (Marc Roussel)
Subject: Re: jump in price of journals
Organization: Department of Chemistry, University of Toronto
Date: Wed, 18 Nov 1992 16:56:25 GMT

In article <djoyce.722095513@black.clarku.edu> djoyce@black.clarku.edu
(Dave Joyce) writes:
>We've had to cut subscriptions to journals because of the big price hike
>primarily in European journals.  We just can't afford an average 25% increase.
>Some are much worse.  Our two Kluwer journals, Compositio Math. and J.
>Automated Reasoning, went up 65.5% and 35.1%, respectively.  North Holland
>(Elsevier) journals went up an average of 30%, but Theoretical Comp. Sci. went
>up 48.1% ($2679 from $1808).  Springer journals up 25% to 30%, Pergamon &
>Wiley up 25% to 50%.  What do they think we're made of, gold?

     I wouldn't be at all surprised if these price hikes were caused
by libraries dropping subscriptions because of financial constraints.
Of course, once they start raising their prices, more libraries drop
their subscriptions, and so on.  With any luck, this is a signal of an
impending shakeout in scholarly publications.

				Marc R. Roussel
                                mroussel@alchemy.chem.utoronto.ca
Newsgroups: sci.math
From: rivin@SAIL.Stanford.EDU (Igor Rivin)
Subject: Re: jump in price of journals
Organization: Computer Science Department,  Stanford University.
Date: Thu, 19 Nov 1992 19:36:47 GMT

In article <hdev.722133059@dutiag> hdev@dutiag.tudelft.nl (Hans de Vreught) writes:
>mroussel@alchemy.chem.utoronto.ca (Marc Roussel) writes:
>
>>Of course, once they start raising their prices, more libraries drop
>>their subscriptions, and so on.  With any luck, this is a signal of an
>>impending shakeout in scholarly publications.
>
>Don't you believe that. The one part of Elsevier that was booming was
>scholarly publications. Our need to write publications, simply means that
>either many journals or very thick journals are needed. Either way, your
>university must pay the prices.

Maybe the abysmal job situation in math is causing people to write
more papers now (to improve their chances). Presumably, as people
leave mathematics, for lack of employment, there may indeed be a
shakeout in scholarly journals. 

As for Elsevier, their prices are absolutely insane, and obviously
targeted at libraries, not people. Again, with the current state of
funding, I find it hard to believe that many libraries will find the
$200 to pay for North Holland/Elsevier books (easily triple Springer
prices for comparable titles).
From: cxm7@po.CWRU.Edu (Colin Mclarty)
Newsgroups: sci.math
Subject: Re: Bozos Synonymous
Date: 15 Nov 1992 23:54:56 GMT
Organization: Case Western Reserve University, Cleveland, OH (USA)
Reply-To: cxm7@po.CWRU.Edu (Colin Mclarty)
NNTP-Posting-Host: slc5.ins.cwru.edu


In a previous article, levine@symcom.math.uiuc.edu (Lenore Levine) says:

>
>You think that "crop circles" character is something. Wait till
>you read "Sexual Personae" by Camille Paglia! Lots of complete
>nonsense about how mathematics is done, and mathematicians 
>think! 
>
>I defy this lady to explain why the derivative of x^2 is 2x. Meanwhile
>she's making zillions, and I'm scrambling for pennies in graduate
>school.
>
>
	I'm sure this is the first time anyone has complained about
Paglia's views on math.  What were they?  I read the book but the math
must have escaped me in the rush.  (You probably are right that she
couldn't explain deriviatives of polynomials.)

Colin
From: israel@unixg.ubc.ca (Robert B. Israel)
Newsgroups: sci.math
Subject: Re: comparison problem
Date: 18 Nov 92 23:55:01 GMT
Organization: The University of British Columbia
Distribution: usa
NNTP-Posting-Host: unixg.ubc.ca

In <1992Nov18.161028.11906@seas.gwu.edu> chihy@seas.gwu.edu (Chih-Hsun Yao) writes:

>Hi, everyone:
>        I got problem with following question:

>Describe an algorithm that finds the largest and second largest integer in a
>set of (2^m) integers using at most m+(2^m)-2 comparisons.
>(Hint: Consider binary tree tournament)

>        My problem is following: if I use the way of binary tree tournament,
Sounds awfully like homework, so I'll just give a hint: the second largest
is compared to the largest at some point in the tournament.
-- 
Robert Israel                            israel@math.ubc.ca
Department of Mathematics             or israel@unixg.ubc.ca
University of British Columbia
Vancouver, BC, Canada V6T 1Y4
From: jxh@math.ksu.edu (James C. Hu)
Newsgroups: sci.math
Subject: Re: Three-sided coin
Date: 21 Nov 1992 16:09:24 -0600
Organization: Dept. of Mathematics, Kansas State University
NNTP-Posting-Host: hilbert.math.ksu.edu

blom@husc15.harvard.edu writes:
>I came late to this thread, but it sounds like you are looking for a
>coin that would land 1/3 of the time on either face and 1/3 of the
>time would stabilize on its side.  For this to be so the width of the
>coin should equal its radius.  I don't see why you would need to try
>different sizes.

I am not sure this would work.

But what about a straight, three-sided banana like shape?

What about a cube, where the opposite faces are treated as the same
face?

Or, is that cheating?
-- 
James C. Hu (jxh@math.ksu.edu), 1804 Denholm Dr., Manhattan, KS 66502
I speak for me, the whole me, and nothing but for me.  So help me me.
Newsgroups: sci.math
From: Jim.Buddenhagen@launchpad.unc.edu (Jim Buddenhagen)
Subject: dodecahedron on S3
Organization: University of North Carolina Extended Bulletin Board Service
Date: Tue, 17 Nov 1992 20:59:20 GMT

Given a (regular pentagonal faced) dodeahedron of edge  e  living on
a 3-sphere of radius r,  how does one compute the dihedral angle in
terms of (say)  s = e/r ?

--
   The opinions expressed are not necessarily those of the University of
     North Carolina at Chapel Hill, the Campus Office for Information
        Technology, or the Experimental Bulletin Board Service.
           internet:  laUNChpad.unc.edu or 152.2.22.80
Newsgroups: sci.math,sci.physics
From: leife@ii.uib.no (Leif Erik R. Hauge)
Subject: Hypercube/k-cube
Organization: Institutt for Informatikk, UiB, Bergen, Norge
Date: Thu, 19 Nov 92 10:03:11 GMT

Question about Hypercubes/k-cubes.
---------------------------------

Can someone please help me in finding relevant
litterature which outlines basic properties of
the hypercube/k-cube.

(My view of a k-cube is a graph where vertices
correspond to the binary k-tuples and the edges
connect those vertices having a Ham. distance
of 1)

Thanks,

	Erik

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


Newsgroups: sci.math
From: janes@dhhalden.no (JAN EIVIND STILLINGEN)
Subject: A picture of Allan M. Turing
Organization: Ostfold College
Date: Mon, 23 Nov 1992 14:24:08 GMT

To those of you who answered my question of pictures of M. Turing;
(our mailserver crashed - I lost your names, so I'll have to post it here)

Thank you for the info, and I've now placed two .TIF-files of the man
on
    ftp.dhhalden.no in directory uploads/gifs

One is a portrait, the other is a special one with Turing showing
off his physical talents.

JES
Newsgroups: sci.math
From: umatf071@unibi.hrz.uni-bielefeld.de (0105)
Subject: the rang of cographs
Date: Sun, 22 Nov 92 19:19:21 GMT
Organization: Universitaet Bielefeld
Keywords: cograph, rang

Cographs are the graphs formed from a single vertex under the closure
of the operations of union and complement. Another characterization of 
cographs is that they are the undirected graphs with no induced paths
on four vertices (P_4). (see: Corneil, ..., SIAM J Comput 14 (1985) 926)

Let A(G) be the adjacency matrix of the graph G.

Conjecture:
  For a cograph G there is
  rg( A(G) ) = the number of different nonzero columns of A(G).

Are there other classes of graphs with this property?

Torsten Sillke
From: somos@ces.cwru.edu (Michael Somos)
Newsgroups: sci.math
Subject: Re: Minimum standards for math "competency"
Date: 23 Nov 1992 23:28:34 GMT
Organization: Computer Engineering and Science, Case Western Reserve University
NNTP-Posting-Host: george.ces.cwru.edu
Keywords: math competency education university college standards


Is everyone else fed up with this thread too?  There have always
been and always will be students who don't have any clue when it
comes to mathematics?  Aren't you just quibbling over the relative
percentages?  And finally, if the situation is really so bad, then
why are there so many people with a lot of mathematical knowledge
who are underemployed or unemployed?  For details look at recent
issues of Notices of the AMS.  Something is very wrong, but it is
not what people are saying it is.  

Also realize that there is no consensus on this.  There is a wide
variety of opinions.  If everyone agreed on what the problem was,
there would be rapid progress on solving it.  This is absolutely
not the case now.  I won't bore you with any of my own opinions,
but point out that this has nothing to do with mathematics per se.
It is a general cultural problem and pervades many areas.  Let us
drop this thread, and let us enjoy mathematics while we can.  At
least that is what I think this news group is for.  There are many
other news groups for other kinds of discussion.   Shalom, Michael
--
Michael Somos <somos@alpha.ces.cwru.edu> (* No, I don't work for CWRU *)
From: rusin@mp.cs.niu.edu (David Rusin)
Newsgroups: sci.math
Subject: Re: Are teachers paid enough? (Was Re: Is Math Hard?)
Date: 16 Nov 92 19:12:55 GMT
Organization: Northern Illinois University

In article <hdev.721903573@dutiaj> hdev@dutiaj.tudelft.nl (Hans de Vreught) writes:
>mccolm@darwin.math.usf.edu. (Gregory McColm) writes:
>>One thing not being mentioned:  American teachers have been 
>>underpayed for a VERY LONG time.
>
>What are the wages generally encountered at the US education system?
>I can give you the Dutch equivalents. Over here a year salary consist of 12
>moth salaries + 8% holiday allowance. Furthermore I will assume $1 = f1.75
>(which is almost correct +/- one or two cents). I'm not 100% sure about the
>salary scales of Nursery and First level education (but I believe they are
>right).
>
>Nursery education (below kindergarten)   $24861 - $38576
>First level education                    $24861 - $42924
>Second level education (high school)     $26150 - $57424
>Assistent professor                      $26150 - $57424
>Associate professor                      $50944 - $62489
>Full professor                           $53588 - $100614

Thank you for posting this, but cross-cultural comparisons are likely
to be enormously complicated (see below). For what it's worth:...

I'm not really sure what makes a good comparison population, but I can give you
the 1st and 3rd quartile salaries of US Math faculty. This is the 1992 data
for "Group II" departments (e.g. the top state university in many states):
Assistant professor                       $37500 - $42500
Associate professor                       $42500 - $47500
Full professor                            $52500 - $72500
Readers of the Notices of the Amer Math Soc will see I have had to fudge
data a bit, but this should be in the spirit of things.

I don't have, and would like to see, data for US teachers at other levels.
I can promise you that the 1st and 3rd quartiles are very far apart. I know
two high school math teachers within 30 miles of my home, both new to the
job. One earns $18000, the other $40000 (more than our newly hired PhDs) 

>These numbers might look much higher than in the States but over in Europe
>social security and income tax are way over what is normal in the States. But
>that is of course completely indepemdent of the education profession. Over
>here in Europe teaching is also an underpaid profession.

(US Income taxes are low by EC standards; but remember medical care is not
state funded here, and wise employees are funding their own retirement.
My take-home pay is about 75% of my salary, after federal and state income
taxes, social security, medical insurance, personal retirement and medical
funds, and a few other minor deductions.)
From: scotts@math.orst.edu (Scott Settlemier)
Newsgroups: sci.math
Subject: Biting spheres
Date: 21 Nov 92 00:07:02 GMT
Article-I.D.: talon.1ejuj6INNi9s
Distribution: world
Organization: Oregon State University Math Department
NNTP-Posting-Host: moondance.math.orst.edu

If you've a sphere S of radius R, how many non-empty
bites on average need you make with a sphere of radius
r to remove a fraction 0<=x<=1 of the sphere S?

Where a non-empty bite of a sphere S with a sphere s is
S\s for s randomly centered but not disjoint from S.

(Related is the plain vanilla bite where s can be disjoint
from the bitten S, but not from the original unbitten S.
How many bites required on average?)
Newsgroups: sci.math
From: umatf071@unibi.hrz.uni-bielefeld.de (0105)
Subject: prime boxes of the Y-pentomino
Date: Fri, 20 Nov 92 19:25:50 GMT
Organization: Universitaet Bielefeld
Keywords: tiling

                                      Torsten Sillke, Bielefeld
List of all prime rectangles and boxes for the Y-pentomino (.:..).
A 'p' following a number indecates a prime box.

Rectangles with the Y-pentomino:

10: 5p, 10, 14p, 15, 16p, 19, 20, 21, 23p, 24, 25, 26, 27p, 24-27 + 5*n
15: 10, 14p, 15p, 16p, 17p, 19p, 20, 21p, 22p, 23p, 24-33 + 10*n
20: 5, 9p, 10, 11p, 13p, 14, 15, 16, 17p, 14-17 + 5*n
25: 10, 14, 15, 16, 17p, 18p, 19, 20, 21, 22p, 23p, 24, 25, 26, 27
30: 5, 9p, 10, 11p, 13p, 14, 15, 16, 17, 14-17 + 5*n
35: 10, 11p, 13p, 14, 15, 16, 17, 18p, 19, 20, 21, 22, ...
40: 5, 9, 10, 11, 13, 14, 15, 16, 13-16 + 5*n
45: 9p, 10, 11p, 13p, 14, 15, 16, ...
50: 5, 9, 10, 11, 12p, 13, 9-13 + 5*n
55: 9p, 10, 11, 12p, 13, 14, 15, 16, ...
60: 5, 9, 10, 11, 12p, 13, 14, 15, 16, ...
65: 9, 10, 11, 12p, 13, 14, 15, 16, ...
70: 5, 9, 10, 11, 12p, 13, 14, 15, 16, ...
75: 9, 10, 11, 12p, 13, 14, 15, 16, ...
80: 5, 9, 10, 11, 12p, 13, 14, 15, 16, ...
85: 9, 10, 11, 12p, 13, 14, 15, 16, ...
90: 5, 9, 10, 11, 12p, 13, 14, 15, 16, ...
95: 9, 10, 11, 12p, 13, 14, 15, 16, ...
100: 5, 9, 10, 11, 12, 13, 14, 15, 16, ...  /no new prime
/all primes found

Strips (one side open) with the Y-pentomino:
 5p, 6p, 8p, 9p, 10, 11, 12, 8-12 + 5n
 
Strips (two sides open) with the Y-pentomino:
 2p, 4, 5p, 4-5 + 2n

Boxes with the Y-pentomino:
2 5: 6p, 8p, 10, 11p, 12, 13p, 14, 15p, 10-15 + 6n
3 5: 4p, 8, 9p, 10, 11p, 8-11 + 4n
4 5: 3p, 4p, 5p, 3-5 + 3n
5 5: 4p, 5p, 6p, 7p, 4-7 + 4n
6 5: 2p, 4, 5p, 4-5 + 2n
7 5: 4, 5p, 6, 7p, 4-7 + 4n
8 5: 2p, 3, 2-3 + 2n
9 5: 3p, 4, 5, 3-5 + 3n
k 5: 2, 3, 2-3 + 2n  (k>=10) see 2 5: k, and 3 5: k

2 10: 4p, 5, 6, 7p, ...
3 10: 4, 5, 6p, 7p, ...

2 15: 4p, 5p, 6, 7p, ...
3 15: 4, 5, 6p, 7p, ...
/all primes found

Impossible hyperboxes with the Y-pentomino:
 2*..*2*3*..*3*n (and strip on side open)
 2*..*2*3*..*3*5*5

When did I get the results:
New (August 1992)
10*23, 10*27, 15*17, 15*19, 15*21, 20*13, 20*17
    (September 1992)
30*11, 30*13, 25*17, 35*11, 45*11, 45*9, 55*9, 35*13, 45*13
    (October 1992)
15*23, 18*25, 18*35, 3*5*9, 3*5*11, 5*5*6, 5*5*7, 5*7*7, 2*7*10, 3*6*10, 2*7*15
    (November 1992)
3*7*10, 3*7*15

Annotations:
  15*15  16 solutions without H-symmetry
  20*13   1 solution  without H-symmetry

Question:
=========
-- What are the prime rectangles for the one-sided 
Y-pentomino (.:..), L-pentomino (:...), and P-pentomino (::.)?
The case of the L-tetromino is solved.
Known prime rectangles:
  Y-pentomino: 5*10
  L-pentomino: 2*5
  P-pentomino: 2*5

-- Why is there no 8*5n rectangle tileable with Y-pentominoes?

-- Where are the prime hyperboxes?
-- Is there anyone interested?
Newsgroups: sci.math
From: mueller@schaefer.math.wisc.edu (Carl Douglas Mueller)
Subject: Re: Geometrical parking problem.
Reply-To: mueller@schaefer.UUCP (Carl Douglas Mueller)
Organization: Univ. of Wisconsin Dept. of Mathematics
Date: Wed, 18 Nov 92 14:31:31 GMT

In article <1992Nov18.101107.29182@infodev.cam.ac.uk> rgep@emu.pmms.cam.ac.uk (Richard Pinch) writes:
>In article <1992Nov17.225821.6579@augean.eleceng.adelaide.edu.AU> 
>dabbott@augean.eleceng.adelaide.edu.AU (Derek Abbott) writes:
>>
>>A car of length L reverses into a parking space without touching the kerb.
>>Has anyone calculated the minimum theoretical length of the parking space?
>
>Yes, it's the length of the car.  The commutator of two rotations is
>a translation, so you can drive sideways by making very small moves of
>the form LRLR.
 
  Actually, there is no MINIMUM.  The length of the car is not quite enough,
 but the length of the car plus epsilon (for any positive epsilon) is enough.
>
>Richard Pinch
>

   Carl Mueller (mueller@math.wisc.edu)
From: tim@maths.tcd.ie (Timothy Murphy)
Newsgroups: sci.math
Subject: Re: Prime test algorithm
Date: 18 Nov 92 02:34:53 GMT
Organization: Dept. of Maths, Trinity College, Dublin, Ireland.

rkaivola@mits.mdata.fi (Risto Kaivola) writes:

>>blom@husc15.harvard.edu writes:
>> [asks information on C-language packages for doing big number arithmetics
>   and some special things]

>>The best package seems to be Arjen Lenstra's arbitrary precision
>>arithmethic package written in C, based on what I've read.

Is this better than the GNU package gmp,
available from prep.ai.mit.edu ,
and many other archives?

-- 
Timothy Murphy  
e-mail: tim@maths.tcd.ie
tel: +353-1-2842366
s-mail: School of Mathematics, Trinity College, Dublin 2, Ireland
From: andrew@rentec.com (Andrew Mullhaupt)
Newsgroups: sci.math
Subject: Re: a first year grad student freaks out.
Date: 13 Nov 92 22:24:49 GMT
Organization: Renaissance Technologies Corp., Setauket, NY.

In article <1992Nov11.223722.29808@galois.mit.edu> jbaez@riesz.mit.edu (John C. Baez) writes:
>
>>In article <92314.170255RVESTERM@vma.cc.nd.edu> <RVESTERM@vma.cc.nd.edu> writes:
>You think *you've* got it bad!  I'm a mathematics professor with nobody
>to assign me things to prove!

I can fix this for you in no time, John.

Later,
Andrew Mullhaupt
From: israel@unixg.ubc.ca (Robert B. Israel)
Newsgroups: sci.math
Subject: Re: ODE problem...
Date: 23 Nov 92 22:51:38 GMT
Organization: The University of British Columbia
NNTP-Posting-Host: unixg.ubc.ca

In <1992Nov20.184102.14068@athena.mit.edu> frisch1@athena.mit.edu (Jonathan Katz) writes:

>T
>Lines: 30

>>The following ODE problem came up recently.
>>I know how to solve it by the power series method, but was wondering
>>if anyone could figure out an easier way of solving it (maybe a nice
>>substitution?).
>>(x and y are functions of t, a is a constant)
>>x'=(a)(x)cost+(a)(y)sint
>>y'=(a)(x)sint-(a)(y)cost.

>Hi, I was the one to originally pose this problem, and I'm glad to see the
>interest it has sparked.
>Thanks to all those who sent email.

>However, while playing with this system, I came upon a neat 'trick' which no one
>has yet pointed out.

>multiply the first equation by y and the second by x.  Then add the two equations
>together, getting:
>yx'+xy'= xy(acos(t)+asin(t))
>letting f=xy, note that this simplifies to:
>f'=f(acos(t)+asin(t)) which is easily solvable.

>Now subtract the two equations, and divide the resulting equation by y^2.  Then
>let g=x/y, and the equation becomes:
>g'=some function of g  (sorry I don't have my work in front of me, but it's
>simple enough to carry out)

Huh? y x' + x y' = a (x^2 + y^2) sin(t)
On the other hand,  y x' - x y' = a (2 x y cos(t) + (y^2 - x^2) sin(t))
so g' = a(2 g cos(t) + (1 - g^2) sin(t)) (which isn't particularly pleasant
to solve).

-- 
Robert Israel                            israel@math.ubc.ca
Department of Mathematics             or israel@unixg.ubc.ca
University of British Columbia
Vancouver, BC, Canada V6T 1Y4
Newsgroups: sci.math
From: rouben@math9.math.umbc.edu (Rouben Rostamian)
Subject: Re:    1+1/2+1/3+1/4+...+1/n
Organization: University of Maryland Baltimore Campus
Date: Thu, 19 Nov 1992 16:42:39 GMT

In article <92324.132329K3032E2@ALIJKU11.BITNET> Mutter Christoph Johannes <K3032E2@ALIJKU11.BITNET> writes:
>I've a problem. I have to calculate the sum 1+1/2+1/3+1/4+...+1/n.
>The result should be 100. But my computer is far too slow, to solve this
>problem. I need the index n when the sum > 100.0
>And that exactly.  Has anyone calculated this? (Perhaps on a CRAY|) ?

Here is a program that you may find useful.  It has been completely
debugged on my personal cray.

sum = 0
for k=1 to 10^44
   sum = sum + 1/k
end
print sum

:-)
Newsgroups: sci.math
From: palais@binah.cc.brandeis.edu
Subject: Re: Has FFT been beaten to the finish line?
Reply-To: palais@binah.cc.brandeis.edu
Organization: Brandeis University
Date: Sat, 21 Nov 1992 16:23:38 GMT

>>    I have heard a rumour of a faster algorithm for FT than the FFT
>>    and the rumour even comes with a percentage improvement of 15%.
>>    If this is true could someone please point me to code and/or 
>>    theory/description of it. 

   I don't know whether this is related to what you heard, but there has 
recently been developed a fast WAVELET transform, which is asymptotically
a lot better than the FFT (its O(n) as opposed to O(n log n) for the FFT).
Newsgroups: sci.math
From: dak@messua.informatik.rwth-aachen.de (David Kastrup)
Subject: Re: Square root of a number
Organization: Rechnerbetrieb Informatik  /  RWTH Aachen
Date: 17 Nov 92 18:02:18 GMT

buxamusaa@woods.ulowell.edu writes:


>Please could someone help me with an assignment that I have to do.
>It is a very general question, though the answer could be quite lengthy.
>"Discuss methods for finding the square root of a number."

>What I am looking for are all possible methods/alogrithms for this.

>Please respond to either directly to me (preferably) or via the net.

One nice possibility is the bitwise algorithm similar to binary
division.

Suppose that your result will be in some register called result, your
modulus (root^2 + modulus = argument, root = floor(sqrt(argument)) )
is in a register called modulus, and your argument is in a register called
spill.

One iteration consists of shifting two (MSB) bits from spill into
modulus (LSB) (of course this is a left shift), and then trying to subtract
4 times result+1 from modulus. If you can, you do it and shift a one into
results LSB position, if you can't, you don't, and shift a 0.

Repeat until spill is used up. result with then have half as many bits
as the argument had.
From: edgar@function.mps.ohio-state.edu (Gerald Edgar)
Newsgroups: sci.math
Subject: Re: closed forms
Date: 23 Nov 1992 07:56:50 -0500
Organization: The Ohio State University, Dept. of Math.
NNTP-Posting-Host: function.mps.ohio-state.edu

In article <1992Nov22.100111.42575@urz.unibas.ch> kullmann@urz.unibas.ch writes:
>Another question that could belong here: How does one proof that there is
>no closed form expression of \int(exp(-x**2))? 

This is a result of Liouville.  More generally, he proved:

  THEOREM:  Let g and y be algebraic functions of x, with g nonconstant.
  If integral exp(g) y dx is an elementary function of x, then it has
  the form  exp(g) w + C, where w is a rational function of x, y, and g.

A function is "elementary" if it is obtained from algebraic operations,
trig and inverse trig functions, exponential and logarithmic functions,
or combinations of these (including composition and inverse function).
(There is a more technical definition...)

Examples of the application of the theorem are:
  integral exp(-x^2) dx is not elementary
  integral exp(x)/x dx is not elementary
  integral dx/log x  is not elementary.

A book on this classical theory is:  _Integration in Finite Terms_
by J. F. Ritt (1948).  The background required is complex analysis.
There are also some more recent books, which take a more algebraic
approach, but I do not have those references handy.


Note.  Derivation of the fact that integral exp(-x^2) dx = exp(-x^2) w + C
for rational function w is impossible:  First, w must satisfy the
differential equation  w' - 2x = 1.  Deduce that w has no (finite) poles, so
w is a polynomial.  Obtain a contradiction by comparing the degrees of
polynomials.
-- 
  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)
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