HDTenEightyP/NetNews huggingface dataset:
From: "Christoph Schlenker" <UKJW@DKAUNI2.BITNET>
Subject: Re: Help wanted in integration.
Organization: University of Karlsruhe, Germany
Date: Fri, 6 Nov 1992 14:42:34 GMT

Hello,

I have just typed your integral into a math-prg and the solution
of it is just    0.
The integral is:
        2     2                     2          2     2
 (-1/4 a -3/4c )a ln(x-a)          a      (1/4a +3/4c ) a ln(x+a)
(------------------------ - 1/4 ------- + -----------------------
           F                    E (x-a)             F

          2             2  2                   2
         a          c(3a +c ) ln(x-c)         c
 -1/4 ------- + 1/4 ----------------- - 1/4 -------
      E (x+a)              F                E (x-c)

         2  2                   2
     c(3a +c ) ln(x+c)         c         4
-1/4 ----------------- - 1/4 -------) sin x
            F                E (x+c)
with
   4    2 2    4
E=a  -2a c  + c

     6     4  2      4 2    6
F= -c  -3 a  c  + 3 c a  + a

I hope thats right...                                 Christoph
From: hdev@dutiag.tudelft.nl (Hans de Vreught)
Newsgroups: sci.math
Subject: Re: who should teach calculus?
Date: 13 Nov 92 00:01:45 GMT

gedgar@magnus.acs.ohio-state.edu (Gerald A Edgar) writes:
>How about: "should algebraists teach calculus?"
>Are they the ones who say, "I have never used hyperbolic functions,
>so we can skip that section"??

Funny.
How about: "should calculus teachers teach algebra?"
Are they the ones who say, "I have never used finite fields,
so we can skip that section"??
--
Hans de Vreught                          | John von Neumann:
hdev@dutiaa.tudelft.nl                   | Young man, in mathematics
Delft University of Technology (TWI-ThI) | you don't understand things,
The Netherlands                          | you just get used to them.
Newsgroups: sci.math
Subject: Re: Assorted questions and problems
From: a_rubin@dsg4.dse.beckman.com (Arthur Rubin)
Date: 10 Nov 92 23:22:21 GMT
Organization: Beckman Instruments, Inc.

In <96778@netnews.upenn.edu> weemba@sagi.wistar.upenn.edu (Matthew P Wiener) writes:

>In article <1992Nov8.181631.13298@Princeton.EDU>, tao@fine (Terry Tao) writes:

>>(3) Assume the axiom of choice and the axiom of the continuum.  Is it
>>true that two chains (totally ordered sets) which both have the
>>cardinality of the continuum have a one-to-one and onto order
>>preserving mapping betweem them?

>Of course not.  It's almost embarrassing to mention the counterexamples,
>but here goes: (0,1) and [0,1].  The question you meant to ask, I assume,
>was if the orderings were dense.  In that case, a back and forth argument
>shows the two are isomorphic.  I'm pretty certain you need CH for this--I
>think Shelah has the contrary model.

You mean "(countably) complete" rather than "dense", don't you?
Q x R and R x Q clearly aren't isomorphic; and I don't think you need CH if
it is "complete".
--
Arthur L. Rubin: a_rubin@dsg4.dse.beckman.com (work) Beckman Instruments/Brea
216-5888@mcimail.com 70707.453@compuserve.com arthur@pnet01.cts.com (personal)
My opinions are my own, and do not represent those of my employer.
My interaction with our news system is unstable; please mail anything important.
Newsgroups: sci.math
From: regeorge@magnus.acs.ohio-state.edu (Robert E George)
Subject: Re: DERIVATIVE OF X^X
Organization: The Ohio State University
Date: Fri, 6 Nov 1992 20:45:39 GMT

In article <13421@ecs.soton.ac.uk> dbc@ecs.soton.ac.uk (Bryan Carpenter) writes
:
[deletions]
>
>I think ``first principles'' ought to allow you to take
>
>      Lim     (1 + y/n)^n
>    n -> inf
>
>as the definition of e^y.  So, if y = log x and n is infinitely large
>(if you know what I mean),
>
>    x = (1 + y/n)^n
>
>so
>
>    y = n (x^(1/n) - 1)
>
>and you can put h = 1/n (so to speak).  It gets the right answer, anyway.
>
[deletions]

I can see a potential problem with putting h = 1/n in cases where
the limit did not exist. If you know the derivative (limit) does exist,
then the limit of
       f(x + a ) - f(x)
              n
      ------------------       (*)
             a
              n

where an --> 0 *will* equal f'(x). If the derivative doesn't exist,
there can be problems: To give a simple example, let
f = abs. value, x = 0, and a   = 1/n
                            n

Then  the limit as n -->  oo of (*) will equal 1, giving one the false
notion that f is differentiable at x = 0.
Now it may well be possible to *show* that a particular function is
differentiable at a point x. Then one can use (*) to find the derivative.


Robert George
(speaking only for myself)

"The very essence of individual freedom is equal justice under a rule of
law, a law to which every man shall be subject and which no executive
can modify."
    Senator Robert Taft , March 11, 1944
From: djoyce@black.clarku.edu (Dave Joyce)
Newsgroups: sci.math
Subject: W.S. Anglin's comments on history of math
Date: 6 Nov 92 19:32:59 GMT
Organization: Clark University (Worcester, MA)

In the issue of _The Mathematical Intelligencer_ that just came out there is a
seven page article in the opinion column by W. S. Anglin entitled "Mathematics
and History."

He has various complaints mainly about books written on the history of
mathematics.  I agree wholeheartedly with most of his observations, find some
others worth thinking about, and disagree with few.

He addresses the interesting question of how the historian should tackle the
scarcity of women mathemations, among other questions.  But, it seems to me he
fails with his solutions (either don't mention the gender of individuals
discussed, say women were right in not studying mathematics, or don't mention
individuals at all).  Maybe that section of the article was written tongue in
cheek.

Anglin complains that calculating devices, including algorithms for
calculation, don't receive enough attention in history of mathematics
books.  Some barely mention them.  I agree calculation is important
in mathematics' history, but the one place in his article I find weakest
is his arguments for the importance of calculations.  Of the four ways he
lists in which calculating devices have proved essential for progress in
pure mathematics only one (the involvment of computers in the proof the the
four color theorem) seems very strong.

Overall, I recommend the article and look forward to reading responses to it.



-- 
David E. Joyce				Dept. Math. & Comp. Sci.
Internet:  djoyce@black.clarku.edu	Clark University
BITnet:    djoyce@clarku		Worcester, MA 01610-1477
Newsgroups: sci.math
From: jdhossei@nyx.cs.du.edu (Joshua Hosseinoff)
Subject: Isetl 3.0 on AIX 3.2 / RS6000
Organization: Nyx, Public Access Unix @ U. of Denver Math/CS dept.
Date: Tue, 10 Nov 92 04:15:29 GMT

Has anyone managed to compile Isetl 3.0 on an AIX?  I've got
the source code and no matter what I try it will not compile.
If anyone has a working executable or a list of changes for AIX
it would be much appreciated.  Thank You.

Joshua Hosseinof  - hosseino@yu1.yu.edu  -
   -  or jdhossei@nyx.cs.du.edu  - or eaw7100@acf.nyu.edu

Newsgroups: sci.math
From: asteindl@mch2ws2.tuwien.ac.at (Alois Steindl)
Subject: Re: definition of topological space
Organization: Inst. f. Mechanics II, TU Vienna
	<1992Nov5.094404.15550@infodev.cam.ac.uk>
	<1992Nov6.092037.7676@leland.Stanford.EDU>
	<1992Nov6.101258.3345@infodev.cam.ac.uk>
Date: Fri, 6 Nov 1992 13:12:57 GMT

Hi,
I think that the possibilities differ, if compact sets are involved:
If one covers some region with closed sets, there need not be a finite
collection of those sets to cover the region. 
Since there are a lot of proofs which use this compactness property,
one would have to invent a new type of continuity: the (usual) one mapping
open sets back to open sets.

Hope this is correct and helpful.
Alois
--

___________________________________________________________________________

Alois Steindl,			Tel.: (0222) 58801 / 5529	
Inst. for Mechanics II,		Fax.: (0222) 5875863
TU Vienna,
A-1040 Wiedner Hauptstr. 8-10	
___________________________________________________________________________
Newsgroups: sci.math
From: hrubin@mentor.cc.purdue.edu (Herman Rubin)
Subject: definitions vs. characterizations (inspired by "What's a manifold?")
Organization: Purdue University Statistics Department
Distribution: sci
Date: Sat, 7 Nov 1992 14:18:05 GMT

In article <1df8leINNolm@iskut.ucs.ubc.ca> ramsay@unixg.ubc.ca (Keith Ramsay) writes:
>In article <COLUMBUS.92Nov6105242@strident.think.com> 
>columbus@strident.think.com (Michael Weiss) writes:
>|I would summarize almost all the discussion in favor of the atlas
>|definition of a manifold in one phrase:

>|	proofs drive definitions

>|in other words, old, "intuitive" definitions are replaced by new "abstract"
>|definitions when the new definitions turn out to be more convenient for the
>|logical development of the subject.

>This is also one of the main points of _Proofs_and_Refutations_ by
>Imre Lakatos. His example is the concept of "polyhedron".

The problem is that we are using definitions instead of characterizations.
There are dozens of definitions of "group" and of "topological space."
The concepts of group and topological space do not depend on which subset
of their properties we choose to use to characterize them.

In other situations, the definitions are at best stultifying.  The general
notion of indepandence in probability is that of obtaining no probability
information about some of the objects from information about others.  This
is not how one tests for independence, as it is extremely complicated to
use directly.  The usual "definition", namely, probabilities of intersections
equal products of probabilities, is a much simpler test.  But as a definition,
it conveys little.
-- 
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,misc.education
From: hrubin@mentor.cc.purdue.edu (Herman Rubin)
Subject: Teaching mathematics  Was: Re: group theory for HS students
Organization: Purdue University Statistics Department
Distribution: sci
Date: Sun, 8 Nov 1992 13:09:02 GMT

In article <PRENER.92Nov7191213@prener.watson.ibm.com> prener@watson.ibm.com (Dan Prener) writes:
>In article <04VSB5M6@cc.swarthmore.edu> rbrown1@cc.swarthmore.edu (Randolph Gregory Brown) writes:

>   [ ... ]

>>            Math teaching suffers from a chronalogical problem -- just
>>because calculus was invented (discovered if you really want) before
>>group theory doesn't mean that it should be learned beforehand.

>The conventional order of the mathematics curriculum isn't based on the
>history of mathematics.  It is a compromise to accomodate a heterogeneous
>audience.

It is not just a compromise, it is a surrender to the fact that the "students"
are now brainwashed into routine.  A substantial majority of those taking
college mathematics do not even know what a proof is, nor can they formulate
word problems.

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

>So the compromise gives everyone a quick jolt of calculus, then gets on
>with other stuff.  Real analysis courses are an explicit recognition that
>that first jolt of calculus wasn't really part of the orderly training
>of mathematicians.

This was done right after WWII, with the calculus course usually being
done in 1 year, including multivariate.  Then the student went directly
into abstract algebra and real analysis.  But it did not take long for
the dumbing to set in.

But the chonological order even was abandoned in favor of computation
against concepts.  Axiomatic geometry is no longer required, and many
cannot even get it.  Nor are the universities willing to consider this
as something to be remedied, nor are they willing to assume this anywhere.

I doubt that any student is in a better position to understand "abstract"
mathematics after calculus than before.  The general concept of measure
and integration is about 5000 years old, although only formulated a
century ago.  It can be taught to someone who understands algebraic
notation, but is very difficult for those who have had a calculus course.

At this time, there is little, if any, logic in the mathematics curriculum.
Learning to compute, unless it is presented as merely this, makes learning
even what the computations mean more difficult.  If we must teach arithmetic
without concepts, make it clear that this is what is being done.  If we must
teach calculus manipulations without understanding, make this clear also.
And point out explicitly that learning to compute may very well make it 
much harder to understand, and remove the computing from the prerequisites
for the conceptual courses.
-- 
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)
From: wjcastre@magnus.acs.ohio-state.edu (W.Jose Castrellon G.)
Newsgroups: sci.math.research
Subject: Re: combinatorial set theory
Date: 12 Nov 92 22:07:52 GMT
Article-I.D.: magnus.1992Nov12.220752.28346
Organization: The Ohio State University,Math.Dept.(studnt)
Originator: dan@symcom.math.uiuc.edu
X-Submissions-To: sci-math-research@uiuc.edu
X-Administrivia-To: sci-math-research-request@uiuc.edu

In article <1992Nov11.164014.14768@tolten.puc.cl> cgutierr@mat.puc.cl (Claudio Gutierrez) writes:

>
>I need the following result (that can be of comon sense)
>
>Exists a family of sets *A* = { Ai}_{i \in \omega}
>such that  there is a family
>*F* of infinite subsets of *A* with |*F*|=2^{\omega}
>with the properties:
>  i) Each B \in *F* has F.I.P. (The intersection of a 
>	finite numbers of elements of each B \in *F*  is non empty.
> ii) For all B \in *F* , the intersection of all the
>	elements of B is empty.
>iii) For all B={B1,B2,...} \in *F*, B'={B'12,B'2,...} \in *F*
>	there exists n \in |N  such that
>	Intersection{B1,...,Bn} and  Intersection{B'1,..,B'n}
>	are dosjoint.
>

Yes, there is such a family: Let  A_(i,n) be the set of numbers  = i (mod 2^n),
and call  A  the (countable) set of all such  A_(i,n) 's .  Now to get the
uncountable family  B , take all the subsets of  A  that are totally ordered
by inclusion (one can take just the ones that are maximal chains, to make it
easier to visualize).  To see that there are  2^Aleph_0  of them, and that
i, ii and iii hold, note that  N  is the disjoint union of two elements of A
(even and odd numbers), and each of these is again the disjoint union of two
elements of  A ... so one can go along  2^Aleph_0 many paths and choose one
of the two possible sets to get the elements of  B : ordered by inclusion, 
finite intersection non-empty, total intersection empty  and two different 
elements of  B  will start to have pairwise disjoint elements from the moment 
their paths differ, forcing  iii to hold.

I wonder what application you have in mind for this, is it a forcing argument?
Newsgroups: sci.math.research
From: hammond@math.albany.edu (William F. Hammond)
Subject: Primes like 40487
X-Submissions-To: sci-math-research@uiuc.edu
Organization: University of Illinois at Urbana
X-Administrivia-To: sci-math-research-request@uiuc.edu
Date: Tue, 10 Nov 1992 18:41:10 GMT

My unverified computations with PARI [an excellent computer library
slanted toward number theory, by C. Batut, D. Bernardi, H. Cohen and
M. Olivier] show that  40487  is the only odd prime  p  smaller than
2^31  (about 2.147*10^9) for which the smallest positive primitive
root  c  is NOT a topological generator of the p-adic integers, i.e.,
for which  c  is a solution of the congruence  c^(p-1) = 1 mod p^2.

Does anyone else know other primes having this property?  I have
looked at several lists of solutions of the congruence a^(p-1) = 1
mod p^2 for small values of  a  with  p  quite a bit larger than
2^31, including an unpublished one furnished by Peter Montgomery,
without finding another example.

If the phenomenon known as "approximation" makes it reasonable to view
the selection of c as a random selection among the various primitive
roots mod p^2 for p in a finite set of primes, then it is reasonable
to conjecture that there should be infinitely many of these primes.

The same line of reasoning would suggest that the probability of one's
not finding such a prime between  x  and  y  (with  x < y)  is about
log(x)/log(y) .

----------------------------------------------------------------------
William F. Hammond                   Dept. of Mathematics & Statistics
518-442-4625                         SUNYA, Albany, NY 12222 (U.S.A.)
hammond@math.albany.edu               FAX: 518-442-4731
----------------------------------------------------------------------


Newsgroups: sci.math.research
From: ozan@nada.kth.se (Ozan \Vktem)
Subject: Noetherian sub k-algebras of k[x,y]
Originator: ozan@dront.nada.kth.se
Reply-To: ozan@nada.kth.se (Ozan \Vktem)
Followup-To: poster
X-Submissions-To: sci-math-research@uiuc.edu
Organization: Royal Institute of Technology, Stockholm, Sweden
X-Administrivia-To: sci-math-research-request@uiuc.edu
Date: Tue, 10 Nov 1992 08:40:40 GMT
Keywords: Noetherian

Let A be a k-subalgebra of k[x,y], i.e the polynomial ring in two variables
over a given field k. Now, if A is Noetherian is A finitely generated as
k-algebra?

I have a ''semi solution'' which is far from complete and too complicated.
Therefore I'm grateful for any suggestions and please also reply by e-mail
(ozan@matematik.su.se).

                                                     Thanks in advance,
                                                       Ozan Oktem

Newsgroups: sci.math.research
From: chernoff@garnet.Berkeley.EDU (Paul R. Chernoff)
Subject: Re: Geometry Conjecture
X-Submissions-To: sci-math-research@uiuc.edu
Organization: University of California, Berkeley
X-Administrivia-To: sci-math-research-request@uiuc.edu
Date: Fri, 6 Nov 1992 21:23:05 GMT

In article <1d9q1sINN9ms@darkstar.UCSC.EDU> sutin@helios.ucsc.edu (Brian Sutin) writes:
>I need the following result (which may be common knowledge):
>
>Let D be a region of R^3 with a reasonable boundary S and let dS be any
>measure on the surface of D.  If
>
>    INT(S){ 1/|x - y| dS(y) } = 1	for all x in D,
>
>then D must be an R^3 ball.
>

This is certainly false if dS is allowed to be *any* measure.  For
let S be any nice closed surface in R^3. Think of S as a conductor and
let dS represent an equilibrium distribution of positive charge on S;
then the field inside S is 0 and the potential is constant.  (For the case
of an ellipsoid, where it is shown explicitly that dS is a positive measure,
see Kellogg, Foundations of Potential Theory, pp 188-191.)


-- 
# Paul R. Chernoff                       chernoff@math.berkeley.edu     #
# Department of Mathematics              ucbvax!math!chernoff           #
# University of California               chernoff%math@ucbvax.bitnet    #
# Berkeley, CA  94720                                                   #

Newsgroups: sci.math.research
From: cgutierr@mat.puc.cl (Claudio Gutierrez)
Subject: combinatorial set theory
X-Submissions-To: sci-math-research@uiuc.edu
Organization: Pontificia Universidad Catolica de Chile
X-Administrivia-To: sci-math-research-request@uiuc.edu
Date: Wed, 11 Nov 1992 16:40:14 GMT

Keywords: 

I need the following result (that can be of comon sense)

Exists a family of sets *A* = { Ai}_{i \in \omega}
such that  there is a family
*F* of infinite subsets of *A* with |*F*|=2^{\omega}
with the properties:
  i) Each B \in *F* has F.I.P. (The intersection of a 
	finite numbers of elements of each B \in *F*  is non empty.
 ii) For all B \in *F* , the intersection of all the
	elements of B is empty.
iii) For all B={B1,B2,...} \in *F*, B'={B'12,B'2,...} \in *F*
	there exists n \in |N  such that
	Intersection{B1,...,Bn} and  Intersection{B'1,..,B'n}
	are dosjoint.

Newsgroups: sci.math.research
From: kgrant@alfred.ccs.carleton.ca (Ken Grant)
Subject: Topology problem
X-Submissions-To: sci-math-research@uiuc.edu
Organization: Carleton University
X-Administrivia-To: sci-math-research-request@uiuc.edu
Date: Wed, 11 Nov 1992 02:44:07 GMT

Topology problem:
If X is the continuous image of a countable successor ordinal with the
order topology by a map with all fibers finite, then is there a
compact Hausdorff topology finer than the topology of X ?

(If so then X countable T1, X the cts image of a compact Hausdorff
space ==> X is the cts image of a compact Hausdorff space under a
bijective map.
Is there a counterexample for X uncountable?)

Ken Grant.




Newsgroups: sci.math.research
From: eemn@cc.newcastle.edu.au (Brett Ninness)
Subject: Game theory question
X-Submissions-To: sci-math-research@uiuc.edu
Organization: University of Newcastle, AUSTRALIA
X-Administrivia-To: sci-math-research-request@uiuc.edu
Date: Sat, 7 Nov 1992 13:14:52 GMT


I've got a problem, which I think could probably be easily solved by 
someone who knows about Game theory or quadratic programming.  The
problem is that I have a quadratic cost function 

f(x,w) = x^T M(w) x

where both the matrix M(w) and the vector x are variable. The
individual elements x_k of x must satisfy linear constraints

|x_k| < epsilon.

The matrix M(w) varies with the real variable w in a well known
structured way.  What I want to know is what is the sup over x of the 
inf over w of f(x,w) ?  I don't know anything about game theory, but I
think this is the sort of problem tackled by it.

Can someone give me some help and/or point me towards a relevant
reference ?

Brett Ninness
Dept. Elec. Eng.
University of Newcastle
AUSTRALIA




Newsgroups: sci.math.research
From: schramm@wisdom.weizmann.ac.il (Schramm Oded)
Subject: A Conjecture About Packings of Balls
X-Submissions-To: sci-math-research@uiuc.edu
Organization: University of Illinois at Urbana
X-Administrivia-To: sci-math-research-request@uiuc.edu
Date: Fri, 6 Nov 1992 08:33:32 GMT

For a finite ball packing P in R^3, let 

a(P)=2(number of tangencies)/(number of balls),

then a(P) is the average number of contacts that a ball in P
has.

Conjecture: sup a(P) = 12.

Let A = sup a(P).  Taking large portions of the infinite
cannonball packing shows that A >= 12.  On the other hand,
the following argument shows that A <= 24.  For each contact
c in the packing, let b(c) be the smaller ball from the
two in contact there, or an arbitrary one if the two are equal.
Since in a packing of equal sized balls at most 12 balls can
contact a single ball (I believe this was stated by Newton,
where can a proof be found?), the correspondence
b : contacts -> balls
is at most 12 to 1.  Therefore A<=24.

I think I can improve the naive argument above to get something
better than A<=24, but I don't expect to reach A=12.

Is this problem known?  Any related results?

Oded


oschramm@wisdom.weizmann.ac.il
From: schoen@ghost.dsi.unimi.it
Newsgroups: sci.math.research
Subject: An inequality fo INCOMPLETE GAMMA functions
Date: 12 Nov 92 10:36:25 GMT
Article-I.D.: ghost.1992Nov12.103625.27794
Organization: Computer Science Dep. - Milan University
Originator: dan@symcom.math.uiuc.edu
X-Submissions-To: sci-math-research@uiuc.edu
X-Administrivia-To: sci-math-research-request@uiuc.edu
X-Char-Esc: 29
X-Charset: ASCII

Let $\gamma(a,x) = \int_0^x exp(-t) t^{a-1} dt$ be the incomplete gamma
function. Is it true that
	$\gamma(a,x) <= \gamma(a+0.5,x)$ ?
(or, at least, for which range of x and a values does the inequality
hold?)
Thank you.
-- 
+---------------------------------------------------------------------------+
| Fabio Schoen                                  e-mail:                     |
| Dipartimento di Scienze della Informazione    schoen@ghost.dsi.unimi.it   |
| via Comelico 39/41 - room    S235             schoen@imiucca.csi.unimi.it |
Newsgroups: sci.math.research