HDTenEightyP/NetNews huggingface dataset:
From: frisch1@athena.mit.edu (Jonathan Katz)
Subject: Generalizing Prime Numbers
Organization: Massachusetts Institute of Technology
Date: Sun, 8 Nov 1992 19:19:48 GMT

I was wondering if anyone knows about any method of generalizing the concept of
prime numbers to the complex plane.
Is there more than one way to generalize it?
Any help on the would be appreciated.
-- 
Jonathan Katz 
From: selee@hpcc01.corp.hp.com (Lee Say Eng)
Date: Fri, 13 Nov 1992 09:17:09 GMT
Subject: Need HELP !
Organization: the HP Corporate notes server
Newsgroups: sci.math


I have been trying without much success to find the amount of
damage that a machine part will suffer when it is impacted by 
a moving body.  I understand that when the kinetic energy of
the moving body exceeds the maximum elastic strain energy of
the machine part, the part will (if we neglect the inertia of
the part and the energy dissipated during impact) either suffer
some permanent deformation or be crushed at the location where
the cross-sectional area is minimum.   I however do not know
how to find by how much the part will be crushed in such a case.
It could be found experimentally but it would also be beneficial
to be able to theoretically predict things.  The material is
pretty brittle but to simplify things, it might be easier to
ignore failure by crack propagation.  Any help will be greatly
appreciated.   


		     ********
		     * mass *  |  Free falling mass
		     *  m   *  |  from height h 
		     ********  V


                               |
                               |
                               V
		       ****  ---  Distance that will
          Machine     *    * ---  be crushed ??
           Part      *      *  ^
                    *        * |
                   *          *
              ___ *___________ * _____
	      ////////////////////////
		    Rigid Base
                 
  
  Data known regarding machine part:  
  
		Dimensions/geometry 
		Young's Modulus, E
		Compressive strength
		Ultimate tensile strength

Thanks in advance,

Alan Phang

alan@hpmalr50.mal.hp.com






                       
Xref: sparky sci.math:14727 sci.math.symbolic:2939
From: cordes@ac.dal.ca (John Cordes)
Newsgroups: sci.math,sci.math.symbolic
Subject: Re: Help wanted in integration.
Date: 10 Nov 92 17:16:03 -0400
Organization: Dalhousie University, Halifax, Nova Scotia, Canada

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.
>> 
>> 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 didn't see the original posting, but just wanted to throw in the
comment that there are _no_ poles on the real axis. The sine functions in
the numerator vanish (linearly) at integer values of x, thus cancelling the
vanishing denominators. Contour integration should handle the evaluation of
your integral without too much difficulty (1st deform the integration
contour away from the real axis, avoiding the points c,d; then introduce
the complex exponential forms for the sine functions and expand the
products in the numerator; close the contour appropriately for the various
pieces, and do a little residue calculus). 

  If in fact the integrand _did_ have double poles on the real axis (the 
integration contour) the integral would be divergent. When there are only 
simple poles a finite value can be extracted by the Cauchy principal value 
procedure.

BTW, I haven't done the contour integration outlined above so have no
particular reason to doubt the solution found using Mathematica as given in
the next few lines. As I write this, however, inspection of the integral
posed suggests to me that it should be finite even for c=d, so I am
suspicious of the answer given. 

> 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 


John Cordes, Dept. of Physics,
Dalhousie University, Halifax, N.S.,
Canada  B3H 3J5       Internet: cordes@ac.dal.ca
Date: Monday, 9 Nov 1992 17:02:55 EST
From: <RVESTERM@vma.cc.nd.edu>
Newsgroups: sci.math
Subject: a first year grad student freaks out.

i'm a first year grad student.  i can do most of the homework assigned
to me.  i can pass tests i have to take.  i can usually understand
proofs of theorems that we're studying, given some thought.  i think
that with a lot of work, i can pass my orals.

however, what's the deal with this thesis thing? what happens if you
simply cannot prove whatever your advisor assigned?

bob vesterman.
Newsgroups: sci.math
From: victor@watson.ibm.com (Victor Miller)
Subject: Re: An Interesting Function
Date: Thu, 12 Nov 1992 15:48:34 GMT
Reply-To: victor@watson.ibm.com
Disclaimer: This posting represents the poster's views, not necessarily those of IBM
Organization: IBM, T.J. Watson Research Center

>>>>> On Wed, 11 Nov 1992 18:37:05 GMT, sasrdt@shewhart.unx.sas.com (Randall D. Tobias) said:
Randall> Originator: sasrdt@shewhart.unx.sas.com
Randall> Nntp-Posting-Host: shewhart.unx.sas.com


Randall> In article <1992Oct29.001255.35683@Cookie.secapl.com>, frank@Cookie.secapl.com (Frank Adams) writes:
Frank> Consider the function W(n) = sum(0<i<n,mod(n,i)).  The problem is to find an
Frank> asymptotic expression for W(n).
Frank>
Frank> It is pretty clear that W(n) = O(n^2).  In fact, we can write
Frank> W(n)=c n^2 + o(n^2).  The question is, what is c?  I know the answer, and
Frank> will post it later if no one gets it.
Frank>
Frank> I think in fact W(n) = c n^2 + O(n), but I can't prove it.  It seems that
Frank> W(n) /= c n^2 + d n + o(n); the O(n) stuff "wanders around".

Randall> Well?  I got as far as empirically verifying the

Randall>    W(n) /= c n^2 + d n + o(n)

Randall> for n up to 100000 or so.  But i haven't got the number theory know-how
Randall> to go much further.  Pretty function, though.

Randall> -- 

Randall> Randy Tobias          SAS Institute Inc.     sasrdt@unx.sas.com
Randall> (919) 677-8000 x7933  SAS Campus Dr.         72450.2545@compuserve.com
Randall> (919) 677-8123 (Fax)  Cary, NC   27512-8000  norat@aol.com

Randall>  ... just my $(-exp(2*sqrt(-1)*arcos(0))/(((2**(2 + 1)) - 1)**2 + 1)).

The answer is W(n) = (1 - 1/12 \pi^2) n^2 + O(n log n).  This may be
seen as follows:

W(n) = \sum_{i=1}^n (n - i [n/i]) = n^2 - \sum_{i=1}^n i [n/i].

The latter sum is = \sum_{i=1}^n \sum_{k=1, i|k}^n i =
\sum_{k=1}^n\sum_{i|k} i = \sum_{k=1}^n \sigma(k), where \sigma(k) is
the sum of the divisors of k.  By Hardy and Wright Theorem 234 (page
266 in the Fourth edition), the latter sum is = (1/12) \pi^2 + O(n log n).


--
		Victor S. Miller
		Bitnet: VICTOR at WATSON
		Internet: victor@watson.ibm.com
		IBM, TJ Watson Research Center
		"Great artists steal; lesser artists borrow" Igor Stravinsky
Newsgroups: sci.math
From: rjk@world.std.com (robert j kolker)
Subject: Problem in Category Theory (elementary)
Summary: A little problem for amusement
Keywords: Category theory
Organization: The World Public Access UNIX, Brookline, MA
Date: Sun, 8 Nov 1992 01:38:54 GMT

Find a category with an arrow (morph) that is epic and monic but not an
isomorphism.

Bob Kolker
From: chrisman@purina.berkeley.edu (chrisman)
Newsgroups: sci.math
Subject: Re: What can we have for an educational system?
Date: 9 Nov 1992 20:28:46 GMT
Organization: U.C. Berkeley Math. Department.
Distribution: usa
NNTP-Posting-Host: purina.berkeley.edu

>baldwin@csservera.scs.usna.navy.mil (J.D. Baldwin) writes:
>some work, perhaps even some training is required for most of us to become
>good teachers.  Personally, I wouldn't mind knowing a little more
>developmental and cognitive psychology; I especially would like to learn
>something about these subjects if I were to teach younger children.  I
>have developed a set of rules of thumb which seem to get me through
>undergraduate teaching assignments, but there is no science to my
>approach.  While I reserve the right to disagree with someone else's
>theories, I would at least like to know what the evidence is and what
>other people's thinking has produced before I claim that I know anything
>about how children and adults learn anything.

I also would like some "training".  As with most skills, one can improve
one's skill at teaching by making use of other people's experience.
If I had my choice, this "training" would consist of hearing about
other teachers' rules of thumb and hearing about how they handled 
particular students under particular situations - in short, gaining
their personal experience.

Why aren't education courses like that?  In my experience, teachers of
education courses try to make teaching into a _science_ (as baldwin 
would have it), putting out lots of unsubstantiated generalizations as 
"theorems" of developmental and cognitive psychology.  I can learn
more about teaching from a one-hour conversation with a good teacher
than I can learn in a ten-hour education course or seminar.

Newsgroups: sci.math
From: hrubin@mentor.cc.purdue.edu (Herman Rubin)
Subject: Re: group theory for HS students
Organization: Purdue University Statistics Department
Distribution: sci
Date: Sat, 7 Nov 1992 13:34:09 GMT

In article <ARA.92Nov6191321@camelot.ai.mit.edu> ara@zurich.ai.mit.edu (Allan Adler) writes:

>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.

I raise the question as to whether students learn anything after high
school algebra, before they take abstract algebra, which is even relevant
to learning group theory.  The only possibility is a good course in logic,
including the predicate calculus and a discussion of proof, and such a
course can be taught at any time after a reasonable attainment of reading
ability is achieved.  Anyhow, most students taking abstract algebra now
have not had such a course.

In the rest of an abstract algebra course, there is a slight use made of
matrix algebra as an example of rings, and this even occurs as an example
of groups on vector spaces.  But this is not essential.
-- 
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: rfc@allegra.att.com (Robert F. Casey)
Subject: Re: Helping to Change Public Education (was Re: Is Math Hard?)
Organization: AT&T Bell Laboratories, Murray Hill, NJ
Date: Sat, 7 Nov 1992 19:13:19 GMT

In article <1992Nov6.221230.10779@athena.mit.edu> jamess@athena.mit.edu (John A Mess) writes:
>In article <Bx9uy1.LB0@mentor.cc.purdue.edu> hrubin@mentor.cc.purdue.edu (Herman Rubin) writes:
>     Apples and oranges!  A high school student is not an Asian graduate
>student.  I certainly hope *any* graduate student is doing more than memor-
>izing proofs.  But you also are wrong about proofs.  A truly beautiful
>proof isn't simply operations.  The published proof is kind of a schematic
>for the initiate to go from a to b concisely.  Proofs by contradiction are
>a marvelous kind.  You must know why the contradiction holds.  Understanding
>the spirit of a proof will allow someone to make more headway in rederiving
>it than simply having memorized the steps once.

I must have missed something somewhere in my math clases, because to me
proofs don't mean anything to me.  It also seemed that everything was
proven true anyway, so why do it?  As if the math teacher was going to
lie about something? :-)
Though once the teacher was going to "prove that 2=3"
Proof:
prove that 2=3
ok a=b
ax=bx
ok, now set x=0
now you can set a=2 and b=3 and have it work
so, 2=3

But you can't divide by zero.  I ask "where did you divide? All I
see is multiplying by zeros?"
Teacher said something unclear, I thought "screw it, proofs are BS anyway".
This was in freshmen year in high school.
Newsgroups: sci.math
From: dbriggs@zia.aoc.nrao.edu (Daniel Briggs)
Subject: Re: Caltech, Re: Feynman story
Organization: National Radio Astronomy Observatory, Socorro NM
Date: Tue, 10 Nov 92 01:19:31 GMT

In article <BxGxDL.8u1@watcgl.uwaterloo.ca>
  awpaeth@watpix.uwaterloo.ca (Alan Wm Paeth) writes:
>>a little while ago, somebody posted a story to this effect: for a
>>certain physics exam at caltech, students were allowed to use any
>>reference material that they could carry in to the room.  one
>>enterprising guy supposedly carried richard feynman in.
>
>I heard the story at Caltech in Spring 1975. Feynman was never mentioned --
>it concerned a geology final with a grad student lugged in. The story is
>somewhat plausable, given that (a) Caltech students are famous for pranks and
>(b) open-book exams are quite common there.

It sounds like the first story combines elements of the grad student story
and a different Feynman story.  Namely, an open book physics exam, (probably
a take home exam -- I don't remember), where the students were allowed to
use "Feynman".  (A standard physics reference is _The Feynman Lectures on
Physics_, volumes I. II. & III.  Often collectively called "Feynman" or
"the red books".)  Supposedly the student contacted Richard Feynman, either
by phone or by walking into his office.  There might well be some elements
of truth to the story.

Dan Briggs    Caltech BS '86, '87

-- 
| Daniel Briggs  (dbriggs@nrao.edu)                      |  USPA B-14993
| New Mexico Tech / National Radio Astronomy Observatory |      DoD #387
| P.O. Box O / Socorro, NM 87801   (505) 835-7391        | 
Support the League for Programming Freedom   (info from lpf@uunet.uu.net)
From: brihut@pro-palmtree.socal.com (Brian Hutchings)
Newsgroups: sci.math
Subject: also, at the same event,
Date: Fri, 6 Nov 92 19:52:47 PST
Organization: The Palmtree BBS - 310/453-8726 - Santa Monica, CA

they'll be showing the SDI-cum-ET video
that the shuttle took last November; if
it was SDI-surviellance, then
the guy at NASA that "leaked" it just happenned to be fired,
shortly after it was broadcast, live, by our Dan Quayle.

Newsgroups: sci.math
From: msunde01@mik.uky.edu (Mark  Underwood)
Subject: Re: 2-dimensional grading system (was Re: What can one do for the 
    bright?)
Reply-To: msunde01@mik.uky.edu
Organization: University Of Kentucky, Dept. of Math Sciences
Date: Tue, 10 Nov 1992 05:39:53 GMT

In article <1992Nov8.190639.12667@serval.net.wsu.edu>  
kfarmer@wsuaix.csc.wsu.edu (keith farmer;S10000) writes:
> In article <1992Nov8.071756.2228@athena.mit.edu> solman@athena.mit.edu  
(Jason W Solinsky) writes:
> >In article <1992Nov3.091430.4135@hsr.no>, onar@hsr.no (Onar Aam)  
writes:
> >
> >|> As a current student (Electrical Engineering if you're curious AND a  
> >|> National Merit Finalist (read: Seimifinalist with "formalities" done  
> >|> NOT! - but that's a different argument I'm perfectly willing to let  
> >|> slide)
> >
> >Well I'm not. Please DO read National Merit Finalist as National Merit
> >Semifinalist with formalities. The difference between the two is that
> >semifinalists are chosen objectively and finalists are all  
semi-finalists
> >who fit the stereotypes that the organizers have in mind for the  
nation's
> >brightest individuals. This cut of 5% of all semifinalists is highly
> >subjective and effectively meritless.
> >
> >Jason W. Solinsky
> >National Merit Finalist
> 
> I turned down my Merit Scholarship (yes, the $2000) to U Chicago in an
> attempt to gewt a life. I've no regrets. What Solinsky say is true. Know
> a Semi-finalist friend of mine: I count him brighter than me... I just
> take tests better.
> 
> Keith


OK, I will admit (even agree) that the selection from NM Semifinalist to  
Finalist is a manner of popularity contest.  However, the selection of  
Semifinalists is merely a measure of success on standardized tests, where  
at least the selection of Finalist takes into consideration the  
recommendations of teachers and one's ability to write a good, short B.S.  
"Why I deserve this" essay . . . and therefore is more of a measure of the  
student than the Semifinalist measure.  I, too, have friends (several) who  
were more deserving of my scholarship than I.  I did not mean to imply  
that the difference was so great or that they were not deserving, just  
that there WERE rather difficult (if subjective, and they WERE subjective)  
selection criteria for the Finalist standing, and that it was not merely a  
formality of sorts.  BTW let's drop this, as it really isn't that  
important and certainly doesn't relate to the group.


--
Mark Underwood
EE Student, University of Kentucky
Lab Assistant, UK Library Microlabs
Internet address:  msunde01@mik.uky.edu

"Cogito, ergo Sum." - Descartes
Newsgroups: sci.math
From: mroussel@alchemy.chem.utoronto.ca (Marc Roussel)
Subject: Re: What is catastrophe theory?
Organization: Department of Chemistry, University of Toronto
Distribution: utsa
Date: Thu, 12 Nov 1992 20:30:19 GMT

In article <1992Nov12.054448.26967@ringer.cs.utsa.edu>
gokhman@ring05.cs.utsa.EDU (Dmitry Gokhman) writes:
>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.

     If you read Zeeman's book and some of Thom's work, I think
you'll see the problem.  The impression one gets is that some C.T. folk
would like to explain everything with it, from ship capsizing (where there
is a genuine catastrophe, both in the mathematical sense and otherwise)
to prison riots and wars (where the underlying dynamics, if there is one,
is unknown and almost certainly isn't as simple as it is portrayed in
these works).  The technical parts of Zeeman's book are very clear
however, which is why I suggested that the original poster consult it.

				Marc R. Roussel
                                mroussel@alchemy.chem.utoronto.ca
From: ara@zurich.ai.mit.edu (Allan Adler)
Newsgroups: sci.math
Subject: Re: Relatives with Crackpot Proofs
Date: 11 Nov 92 08:26:40 GMT
Article-I.D.: camelot.ARA.92Nov11032640
Organization: M.I.T. Artificial Intelligence Lab.

Keith Goldfarb wants to know how to avoid being buttonholed by 
a relative who thinks he has a proof of Fermat's Last Theorem.

This is obviously a matter of great delicacy. But it is by no means
unique. Is it really so different when you are buttonholed by a
colleague who is excited by something you have no interest or
understanding of but the importance of which you strongly suspect
is being greatly exaggerated? True, we have to get along with relatives
for the rest of our or their lives, but the profession is not such
a big world and a department is sometimes as cozy as a nuclear
family. Again, is it really so different from arriving in a new
department and being told by the local feudal lord that you are 
strongly advised to drop your own research interests and start
working on something more to his/her liking? 

It seems likely that the skills one uses to deal with such professional
situations can be adapted to the case at hand.

I won't offer specific suggestions, but if you are interested in 
experimenting, you might obtain some other crackpot proofs or merely
false proofs of FLT or any other unsound mathematics and send it to him
for his opinion.

The origin of this suggestion is an experience I had a number of years
ago when I wound up staying at the Quaker meeting house on Decatur
in Washington, DC many years ago. The situation was such that a lot
of people were able to stay there with very few questions asked and
some very crazy people started drifting in and represented maybe 10% of
the population in the house, if not more. It was clear to me that they
were completely nuts (see my autobiography for the details) but what
I found remarkable was that they could each tell that the rest were
nuts. So why not try this observation out on your crackpot relative?

Allan Adler
ara@altdorf.ai.mit.edu
From: regard@hpsdde.sdd.hp.com (Adrienne Regard)
Newsgroups: sci.math
Subject: Equation needed
Date: 5 Nov 1992 11:58:31 -0800
Organization: Hewlett Packard, San Diego Division
Distribution: USA
NNTP-Posting-Host: hpsdde.sdd.hp.com


Hi,

I apologise if this has been discussed here before -- I am not a regular 
reader of sci.math.

I'm looking for a statistical equation that would express the probabilities
in the game LETS MAKE A DEAL.  I assume you've all seen it:  Monty Hall
gives a person a choice of three doors.  One door contains a grand prize
and the other two doors contain goats.  The person picks a door (say, door
1).  Then Monty opens one of the unpicked doors to reveal a goat (say, door
3).  Then Monty offers the person the chance to switch from their door (1) 
to the remaining door (2).  The person has a better chance of winning the
grand prize if he switches, but I don't know how to write the equation to
express the probabilities, and I've got a very excited friend who wants
proof on this subject.  Can anyone help me?

e-mail to regard@hpsdde.sdd.hp.com or post to this net.  Thanks,

Adrienne Regard
Newsgroups: sci.math
From: choo@cs.yale.edu (Young-il Choo)
Subject: Re: Trivial! (was: Re: Help X^2 == Y mod N)
Organization: Yale Univ Computics
	<1992Nov5.061236.3595@nuscc.nus.sg>
	<1992Nov5.204018.3311@galois.mit.edu>
Date: Fri, 6 Nov 1992 19:49:50 GMT

In article <1992Nov5.204018.3311@galois.mit.edu> jbaez@riesz.mit.edu (John C. Baez) writes:

J> In article <1992Nov5.061236.3595@nuscc.nus.sg> tim@iss.nus.sg (tim poston) writes:

>No mathematics is trivial;
>the trivium was grammar and rhetoric and I forget what;
>roughly, the mediaeval equivalent of a Bachelor's.
>
>Mathematics (along with harmony and two others I forget)
>was part of the quadrivium;
>equivalent of that peculiar US invention,
>the PhD.

J> Yes, if I remember correctly the trivium was logic, rhetoric and
J> grammar, while the quadrivium was arithmetic, geometry, harmony and
J> women's studies.  (Guess which one doesn't fit - and should be
J> astronomy.)

J> So - logic is trivial!  Mathematics is quadrivial!

If I remember correctly, the trivium consisted of 
 grammar
 rhetoric (which included logic) and 
 poetics (or poetry, though today this would be more like "writing" or
   "composition")

[From Dorothy Sayers' "Tools of Learning"]

-- Young-il
Xref: sparky sci.math:14786 misc.education:4251