HDTenEightyP/NetNews huggingface dataset:
From: hdev@dutiag.tudelft.nl (Hans de Vreught)
Newsgroups: sci.math
Subject: Re: who should teach mathematics?
Date: 12 Nov 92 23:13:59 GMT

hrubin@pop.stat.purdue.edu (Herman Rubin) writes:

>In article <1992Nov10.223300.19016@murdoch.acc.Virginia.EDU> tep2j@amsun.apma.Virginia.EDU (Todd E. Peterson) writes:

>>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?

>If they can teach it mathematically, it would be appropriate to have
>them do so in the mathematics department. 

Actually over here at my university every department is an enginering
department, including the mathematics department. So, almost al math is given
by engineers. When you study math here, you study it mathematically: starting
with the axioms. So what's the big difference? Well, the topics that are
covered during a math study over here are more focussed on problems you
encounter as an engineer. The specific topics in math that are taught here are
at the same level as the level you will encounter at a non-enginering math
department of other universities.

In principle a subject must be taught by a fully qualified person (i.e. a
person with a degree on the subject he / she teaches). If he has an Arts /
Science / Engineering background isn't that important, as long he presents his
stuff the right way.
--
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.
Xref: sparky sci.math:14622 sci.physics:18472 sci.astro:11789 sci.bio:4087 sci.chem:4484 misc.education:4204
From: solman@athena.mit.edu (Jason W Solinsky)
Newsgroups: sci.math,sci.physics,sci.astro,sci.bio,sci.chem,misc.education
Subject: Re: 2-dimensional grading system (was Re: What can one do for the bright?)
Date: 8 Nov 92 12:05:06 GMT
Organization: Massachusetts Institute of Technology

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. 

What are YOU talking about? The question that was being addressed is WHY WOULD
ANYBODY CARE ABOUT THE EFFORT PUT IN CLASSES? It is additonally unclear whether
A's would go to those people who put in the least effort, or if you would give
A's to the people who are dumb and couldn't learn it in twice the time that other
people could, but gave up a social life so they could get an A on the academic
part.

Jason W. Solinsky
Newsgroups: sci.math
From: benjie@quack.sac.ca.us (Android)
Subject: Internet Math Club
Organization: The Duck Pond public unix: +1 408 249 9630, log in as 'guest'.
Date: 12 Nov 1992 00:55:46 UTC

This is only an idea.  Please don't yell at me if you don't like it.

How about starting an Internet Math Club for people who are non-math
major and interested in math.  For high school kids for example.

Benjie

-- 
     BBB		Benjie Chen
    BCCCB 		benjie@quack.sac.ca.us
    BCCCB		No Axiomatic System Could Produce All Number-
     BBB		Theoretical Truths, Unless It Is Inconsistent.
From: sl25@cus.cam.ac.uk (Steve Linton)
Newsgroups: sci.math
Subject: Re: Erdos number
Date: 12 Nov 92 22:41:57 GMT
Organization: U of Cambridge, England

The definition of Erdos number clearly implies the existence of the Erdos graph,
in which the number is sinmply distance from Erdos. 

1) observe that this graph is undirected in mathematics, but directed (by the
order of the author's names on the paper) in most sciences. Does this allow any
interesting generalisations?

2) are there (among mathematicians) any connected components of size greater than
one not connected to Erdos.
Newsgroups: sci.math
From: gokhman@ring05.cs.utsa.EDU (Dmitry Gokhman)
Subject: Re: What is catastrophe theory?
Reply-To: gokhman@ring05.cs.utsa.EDU (Dmitry Gokhman)
Organization: Univ of Texas at San Antonio
Distribution: utsa
Date: Thu, 12 Nov 1992 05:44:48 GMT

In article <1992Nov12.034022.3378@alchemy.chem.utoronto.ca>, mroussel@alchemy.chem.utoronto.ca (Marc Roussel) writes:
>      Most well-equipped academic libraries should have E.C. Zeeman's
> "Catastrophe Theory".  Parts of it are very readable, others less so.
> Be careful of some of the outrageous claims made in that book for
> catastrophe theory however.  Catastrophes are interesting things, but
> C.T. has not turned out to be the mathematical "theory of everything"
> that Zeeman and Thom sometimes seem to think it should be.
>      There is also a very recent book (by Arnol'd?).  It claims to be
> about the noncontroversial parts of C.T.  Since I haven't read it, I
> can't comment further on its suitability for an interested layman.
> 
> 				Marc R. Roussel
>                                 mroussel@alchemy.chem.utoronto.ca

It's not a theory of everything, it's a theory of dynamical systems
producing discontinuous results from continuous input.
It is not at all clear to me what the so-called controversy is all
about.  The theorems come with proofs.  Somebody please enlighten
me.
-- 
/////////////////////////////////////////////////////////////////////
- Mr. Gumby    * \oo7    Dmitry Gokhman -> gokhman@ringer.cs.utsa.edu
   says:        `/v/-*   
MY BRAIN HURTS  J  L             YOUR AD HERE!
/////////////////////////////////////////////////////////////////////
Xref: sparky sci.math:14499 sci.math.symbolic:2917 sci.math.num-analysis:3247
From: huang@deakin.OZ.AU (Weiguang Huang)
Newsgroups: sci.math,sci.math.symbolic,sci.math.num-analysis
Subject: RE: Where to find PD symbolic math packages (FQA)
Date: 7 Nov 1992 00:35:13 +1100
Organization: Deakin University, Victoria, Australia
Distribution: world
NNTP-Posting-Host: sol.deakin.oz.au

	I suggest you consider SymbMath.
	It has three versions: Shareware, Student, and Advanced. The 
shareware version is available from SIMTEL20 archives on anonymous FTP sites 
(wsmr-simtel20.army.mil as /calculator/sm211a.zip, rana.cc.deakin.oz.au as 
/huang/sm211a.zip, etc) or by e-mail from listserv@ndsuvm1.bitnet. 
Newsgroups: sci.math
From: news@massey.ac.nz (USENET News System)
Subject: Re: definition of topological space
Organization: Massey University
Date: Sun, 8 Nov 92 21:10:02 GMT

In article <1992Nov6.035352.26163@infodev.cam.ac.uk>, gjm11@cus.cam.ac.uk (G.J. McCaughan) writes:
> 
> Here is another axiomatic definition of "topological space", which is
> probably more intuitive than the usual one in terms of open sets.
> 
> A topological space is a set X of "points", together with (for each point)
> a class of subsets of X, called "neighbourhoods" of the point, such that:
> 
> 1. If N is a nbhd of x then x is in N.
> 2. The intersection of two nbhds of x is a nbhd of x.
> 3. Anything containing a nbhd of x is a nbhd of x.
> 
> This definition is equivalent to the one in terms of open sets. N is a nbhd
> of x iff it contains some open set containing x; on the other hand, U is open
> iff it is a nbhd of all its points. (This last is quite a good way of thinking
> about just what an open set is.)
> 

Not quite, you need

4. Any nbhd N of x contains another nbhd M of x which is a nhbd of
each of its points.

This implies that there are open neighbourhoods.

It is probably the extra complication here which suggested working
with open sets. (It could also be that it seemed more elegant to have
an absolute condition - open, without regard to any specific point -
rather than a relative condition - a neighbourhood of a specific point).

One way of allowing one to work with neighbourhoods rather than
open sets while not complicating the axioms (until there is motivation
to do so) is to use the Frechet V-space notion.

A Frechet V-space is a set such that each point is equipped with a
neighbourhood system. There are no axioms, but definitions are carefully
phrased so that 1, 2 and 3 are unecessary. E.g. x is a point of accumulation
of a set A i, if, whenever N is a nbhd of x, then N-{x} contains
a point of A; while x is in the interior of A if there exists a nbhd N of x
such that N U {x} is contained in A. (If we take as an axiom that x is
in none of its nbhds, then we could use N instead of N-{x}, if x is in
all its nbhds, then we could use N instead of N U {x}).

It turns out that the axiom 4 is needed to avoid the following. With the
obvious definition of boundary, define the interior of a set to be the
set without the boundary, and the closure, to be the set together with
the boundary. The interior of the interior and the closure of the closure
are not necessarily the interior and closure unless axiom 4 holds. 
(In fact Frechet defines the interior to be the largest open subset and the
closure to be the smallest closed subset). Without axiom 4, the interior and
closure (as I defined them, not as Frechet did) are not open (closed).
Xref: sparky sci.math:14725 sci.math.num-analysis:3277
From: jorchard@dciem.dciem.dnd.ca (Jeff Orchard)
Newsgroups: sci.math,sci.math.num-analysis
Subject: HELP on RSA scheme for Encryption/Decryption
Date: 10 Nov 92 21:08:14 GMT
Reply-To: jorchard@dretor.dciem.dnd.ca
Followup-To: sci.math
Distribution: na
Organization: Defence and Civil Institute of Environmental Medicine

I would like to know the algorithm for encrypting/decrypting codes
with the RSA scheme.  I took it in first year algebra, but I sold my
textbook and can't remember for the life of me how it went.

Could someone out there with better resources (or better memory)
help me?

Thank you in advance!

Jeff Orchard    jorchard@dretor.dciem.dnd.ca
Dept. of National Defence, Toronto, Canada
Newsgroups: sci.math
From: schevon@cbnewsi.cb.att.com (Cathy Schevon)
Subject: Omega function
Organization: AT&T
Date: Fri, 6 Nov 1992 20:11:44 GMT
Keywords:  omega, e

I recently ran across a solution to an equation in Maple that
involves the omega function, w(x), that satisfies

	w(x) e ^ (w(x)) = x

Is this a known function, and has it been studied to death like
I suspect?

Please email any info to schevon@mhcnet.att.com.  If there is
interest, I'll summarize the responses and post to the list.
Thanks!!
-- 
-----------------------------------------------------------------
Cathy Schevon					  schevon@att.com
#include <disclaimer.h>			...!attmail!houxa!schevon
Project: To join Flying Funeral Directors of America
Newsgroups: sci.math
From: andreas@appel012.hydromech.uni-hannover.de ()
Subject: nonlinear PDE
Organization: RRZN
X-Newsreader: Tin 1.1 PL4
Date: Tue, 10 Nov 1992 10:42:57 GMT


Does anyone know about literature (articles etc.) about _systems_ of
partial differential equations? Especially I'm interested in
nonlinear PDE.

--
------------------------------------------------------------------------------
Andreas Dunker                  andreas@appel012.hydromech.uni-hannover.de
In der Steinriede 7             andreas@veeble.han.sub.org
D-3000 Hannover 1
West Germany                    2B  |  ! 2B  (W. Shakespeare)
------------------------------------------------------------------------------
Newsgroups: sci.math
From: mroussel@alchemy.chem.utoronto.ca (Marc Roussel)
Subject: Re: What is catastrophe theory?
Organization: Department of Chemistry, University of Toronto
Date: Thu, 12 Nov 1992 03:40:22 GMT

In article <1992Nov11.180552.14797@progress.com> neil@progress.COM
(Neil Galarneau) writes:
>I have heard of something called catastrophe theory.
>I am looking for recommendations on articles/books (in English!) readable by a
>non-math major.

     Most well-equipped academic libraries should have E.C. Zeeman's
"Catastrophe Theory".  Parts of it are very readable, others less so.
Be careful of some of the outrageous claims made in that book for
catastrophe theory however.  Catastrophes are interesting things, but
C.T. has not turned out to be the mathematical "theory of everything"
that Zeeman and Thom sometimes seem to think it should be.
     There is also a very recent book (by Arnol'd?).  It claims to be
about the noncontroversial parts of C.T.  Since I haven't read it, I
can't comment further on its suitability for an interested layman.

				Marc R. Roussel
                                mroussel@alchemy.chem.utoronto.ca
Xref: sparky sci.math:14812 sci.math.symbolic:2954
From: nagrwb@vax.oxford.ac.uk
Newsgroups: sci.math,sci.math.symbolic
Subject: Re: Help wanted in integration.
Date: 11 Nov 92 16:40:14 GMT
Organization: Oxford University VAX 6620

In article <1992Nov10.031024.4001@wri.com>, victor@tuamotu.wri.com (Victor Adamchik) writes:
> In article <Nov.6.00.08.18.1992.2647@gandalf.rutgers.edu>  
> amarmahb@gandalf.rutgers.edu (Amar Mahboob Ali) writes:
>> 
>> Hi
>> 
>> Can anyone please help me in integrating the following.
>> 
>>            infinity
>> 
>>                 / 4    2             2
>>                | x  sin (Pi a x)  sin (Pi b x)
>>                | ---------------------------- dx
>>                |    2    2 2   2    2 2
>>               /   (x  - d )  (x  - c )
>> 
>> 	  -infinity       
>>       
>> 
>> Where a,b,c and d are positive intergers.
>>... stuff deleted

Been trying to reach the original poster without success. Does he or
anyone else for that matter know under what circumstances this integral
arises? Is there a real underlying application? I'd be interested to know.

Richard. 
-- 
** R.W. Brankin -- Numerical Algorithms Group Ltd. -- nagrwb@vax.ox.ac.uk **
**   suggestions for sig. welcome   --   will need   include<std.discl>   **
From: israel@unixg.ubc.ca (Robert B. Israel)
Newsgroups: sci.math
Subject: Electoral college (was Re: Bill Clinton and Complex Analysis)
Date: 12 Nov 92 23:18:17 GMT
Organization: The University of British Columbia
NNTP-Posting-Host: unixg.ubc.ca

The historical discussion here has been interesting, but my original
post was of a more mathematical nature.  There are two related problems,
which might be interesting for a course on discrete optimization:

(A) How many electoral votes could Perot have taken, given the number of
votes he received?  Here I'm allowing votes to be moved around, subject to
keeping fixed the total national votes for each candidate, and the total
number of votes cast in each state. 

(B) How many votes must a candidate in a 3-way race receive in order to
get a majority in the electoral college?  Again I'm assuming the total
number of votes cast in each state is fixed.

Both of these can be formulated as "knapsack problems".  Written as an
integer linear programming problem, (A) is

maximize
   sum_{i=1..51} e_i x_i
subject to
   sum_{i=1..51} v_i x_i <= P
   all x_i in {0,1}

Here i ranges over the 50 states plus District of Columbia, e_i is the number
of electoral votes for state i, v_i is the number of votes needed to win state
i (= [(V_i + 4)/3], where V_i is the total number of votes cast in state i,
and [] is the greatest-integer function), and P is the total vote for Perot.
We interpret x_i = 1 as meaning Perot wins state i, 0 that he doesn't.  In
states with x_i = 1, Perot gets v_i votes and the rest are split as evenly
as possible among the other two candidates.  The remaining votes are 
allocated to the other states, arbitrarily except for totals.

Similarly, (B) is the problem
minimize
  sum_{i=1..51} v_i x_i
subject to
  sum_{i=1..51} e_i x_i >= 270
  all x_i in {0,1}

I used data from the New York Times (not-quite-complete returns, but at least
99% in almost all states), and solved the problem using LINDO.  Note that
P = 19,237,247, or 19.02% of the votes cast.

Results: 
(A) Perot takes 338 electoral votes (62.8% of the total), winning all 
states except Fla, Ill, La, Md, Mass, Mich, Minn, Mo, NJ, Ohio, Pa, Va and Wis.
(B) 14,802,010 votes (14.64% of the total), winning all states except 
Colo, Conn, Fla, Ill, Kans, Mass, Mich, Minn, Mo, NJ, NY, Ohio, Pa, Texas, Va, 
and Wis.

 
-- 
Robert Israel                            israel@math.ubc.ca
Department of Mathematics             or israel@unixg.ubc.ca
University of British Columbia
Vancouver, BC, Canada V6T 1Y4
From: wsadjw@rw7.urc.tue.nl (Jan Willem Nienhuys)
Newsgroups: sci.math
Subject: Re: Michael Spivak
Date: 5 Nov 92 16:39:37 GMT
Reply-To: wsadjw@urc.tue.nl
Organization: Eindhoven University of Technology, The Netherlands

In article <1992Nov4.153711.11167@cs.mcgill.ca> jerry@cs.mcgill.ca (Gerald (Jerry) KUCH) writes:
>>a "Michael Spivak."  Does anyone know if this is the differential geometer  
>>Spivak?
>
>Oh, please.... "say it ain't so...."  :-(
>
>I'm really curious to know if it is the same Spivak...  having seen the NLP's
>whacko infomercial last week, which advocated Transcendental Meditation as

There is a Michael Weinless, Ph.D., dean of the math department of
Maharishi International University in Fairfield Iowa, who will go down
in my personal history as editor of a "scientific" journal that
had (1) an exposition of John Hagelin explaining that the yet to
be found unifield field theory is the same as the Unified Field (regd.
trademark of T.M.) of Maharishi and (2) a very long exposition by
a retired Indian lawyer who, having learnt his mathematics at the feet
of Maharishi, proved FLT, basically by observing the contradiction that
the half open interval [0,1) lacks a rational point (so is irrational),
but has a rational length, hence contradiction. (There were two more
whacko proofs.)
Mind you, this "scientific" journal has two screenings for papers: 
first three referees and then the editors themselves.

JWN
Newsgroups: sci.math
From: ara@zurich.ai.mit.edu (Allan Adler)
Subject: group theory for HS students
Organization: M.I.T. Artificial Intelligence Lab.
Distribution: sci
Date: Sat, 7 Nov 1992 00:13:21 GMT


In my high school, I was taught in 11th grade what a group is and what
a field is. I was somewhat shocked recently to learn that there are
accredited universities (e.g. the one in my neighborhood in  RI)
which apparently do not offer undergraduate courses in abstract algebra
and where graduate students do not learn what a group is until their
second year. 

I would be interested in having the names and authors and publishers
of books that teach abstract algebra and which say explicitly that they
are aimed at high school students.

My purpose is twofold:
(1) to persuade some grad students that it was not God who decided that
    you need a BA in math and a year of grad school before learning what
    a group is.
(2) to provide materials that they stand a chance of being able to read.

Allan Adler
ara@altdorf.ai.mit.edu
From: ndanner@kiwi.ucs.indiana.edu (norman danner)
Newsgroups: sci.math
Subject: Re: a first year grad student freaks out.
Date: 12 Nov 92 23:26:27 GMT
Organization: Indiana University, Bloomington

In article <1992Nov12.053255.23048@nntp.uoregon.edu> tenny@euclid.uucp (Nathan Tenny) writes:
>...Based on
>a talk at a conference...

Actually, I think this is probably one of the best first places.  Go to
seminars, talks, etc.  Often they are geared more towards a high-level
description of a person's research, and you don't have to have been studying
the topic for three years to get a feel for what is being talked about.
You're likely to find something being discussed that sparks your interest.

-- 
Norman Danner                    | The only difference between mathematicians
The Semantic Nihilist            |  and philosophers is that mathematicians
ndanner@indiana.edu              |      throw away their scratch paper.
-----------------------------------------------------------------------------
Newsgroups: sci.math,sci.math.symbolic
From: victor@tuamotu.wri.com (Victor Adamchik)
Subject: Re: Help wanted in integration.
Organization: Wolfram Research, Inc.
Date: Tue, 10 Nov 1992 03:10:24 GMT

In article <Nov.6.00.08.18.1992.2647@gandalf.rutgers.edu>  
amarmahb@gandalf.rutgers.edu (Amar Mahboob Ali) writes:
> 
> Hi
> 
> Can anyone please help me in integrating the following.
> 
>            infinity
> 
>                 / 4    2             2
>                | x  sin (Pi a x)  sin (Pi b x)
>                | ---------------------------- dx
>                |    2    2 2   2    2 2
>               /   (x  - d )  (x  - c )
> 
> 	  -infinity       
>       
> 
> Where a,b,c and d are positive intergers.
> 
> This function has double poles on the real axis. Hence theorems
> related to computing such definite integrals dont seem to help me,
> as they allow at the most a simple pole on the real axis. Is there
> some other theorem that I can use? I would appretiate the least bit of
> help on this.
> 
> I am begining to think that there is no closed form solution. 
> Please help.
> 
> Thanks
> 
> Amar

I evaluated your integral in the closed form and
hope the following answer is a correct for integer a,b,c and d:

if 0 < a <= b then (a*(c^2 + d^2)*Pi^2)/(16*(c^2 - d^2)^2)
if 0 < b <= a then (b*(c^2 + d^2)*Pi^2)/(16*(c^2 - d^2)^2)

I checked numerically (the precision was 6 digits) it for 
c = 2; d = 1; a = 3; b = 4
c = 2; d = 1; a = 7; b = 4
and
c = 2; d = 4; a = 3; b = 4
 
If you are interested to look at the proof send me email. I have
used Mathematica to get that result.

--
Victor Adamchik
victor@wri.com

Newsgroups: sci.math
From: sjp@occs.cs.oberlin.edu (Sue Patterson)
Subject: reference in invariant theory wanted
Organization: Oberlin College Computer Science
Date: Wed, 11 Nov 1992 20:09:51 GMT
X-Posted-From: occs.cs.oberlin.edu
NNTP-Posting-Host: sol.ctr.columbia.edu

I'm looking at a problem in invariant theory of finite groups.  I know that
_somebody_ must have thought about it before!  Can anybody give me a reference?

Sorry if my exposition is too elementary, I've only looked at one undergrad
text on the subject, and I don't know how much of their notation is standard.

The situation is as follows:  Given a finite matrix group G, we find the
subring of C[x_1, ... x_n] consisting of polynomials invariant under G.
Call this subring R.  We can find polynomials in n variables f_1, ... f_m
so that R is the set of polynomials over C in the f_i, so  R = C[f_1, .. f_m].
This can always be done.

In some cases, any invariant polynomial can be written uniquely as a polynomial
in these generating invariants.  However, this isn't always the case, and
so we get interested in nontrivial expressions of 0 as a polynomial in the
generating invariants.  In C[y_1, ... y_m] we look at the syzygy ideal
consisting of polynomials g so that g(f_1, ... f_m) = 0.  If this ideal 
isn't 0, then we have no unique way of writing our invariants in terms of the
generators.

My question is, when can we go backwards?  In other words, if we have a
prime ideal, can we find a group such that this ideal is a syzygy ideal
of its invariants?

If anybody has any references on this subject, I'd appreciate it.

Please reply via e-mail, and I'll post responses to the group if there's
interest.

--Sue
sjp@occs.cs.oberlin.edu
--
 ---------------------------------------------------------------------------
|  "To have beauty is to have only that,   |        Sue Patterson           | 
|          but to have goodness            |  patterso@occs.cs.oberlin.edu  |
|        is to be beautiful, too           |    
    |
|              -- Sappho                   |   #include <std.disclaimer>    |
 ---------------------------------------------------------------------------