HDTenEightyP/NetNews huggingface dataset:
From: blom@husc15.harvard.edu
Newsgroups: sci.math
Subject: RE: closed forms
Date: 21 Nov 92 00:10:07 GMT
Article-I.D.: husc15.1992Nov20.191007.17649
Organization: Harvard University Science Center

No, there is no closed form expression for n!.  There are infinite expansions
which are asymptotic and very good.  Yes, the factorial is defined for the
reals.  n! = gamma(n+1), where the gamma function expands asymptotically as

  n-1/2
 n     sqrt(2 pi) e^(-n + 1/12n^2 - 1/30n^4 ...)

or something like that.

--Eric Blom
--Harvard U
Newsgroups: sci.math
From: hanche@ams.sunysb.edu (Harald Hanche-Olsen)
Subject: Re: Geometrical parking problem.
Organization: University at Stony Brook, NY
	<1992Nov18.101107.29182@infodev.cam.ac.uk>
	<1992Nov18.143131.25971@schaefer.math.wisc.edu>
Date: Thu, 19 Nov 1992 00:38:27 GMT

>>>>> On 18 Nov 92 14:31:31 GMT, mueller@schaefer.math.wisc.edu (Carl Douglas Mueller) said:

Carl> 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.
Carl>  
Carl>   Actually, there is no MINIMUM.  The length of the car is not
Carl> quite enough, but the length of the car plus epsilon (for any
Carl> positive epsilon) is enough.

Essentially correct, though the picture is a little bit more
complicated: The two vector fields at disposal are one (S) for turning
the steering wheel and one (D) for driving back and forth.  The
sideways slide is [D,[D,S]] if I remember it right.  There is a nice
(and very amusing) account in, I think, a book by Nelson (in the
Princeton lecture note series?  I have it in my office the other side
of the Atlantic ocean -- a bit hard to look from here).

I suspect Derek may have had a much simpler situation in mind though:
Apparently the car is not allowed to drive forward?  It should be
quite easy to solve by going the other way: Start parked by the curb,
turn the steering wheel as far as it will go, and drive out.  Once the
trajectory of the car is computed, place a car ahead as close as
possible, and you've got your answer.

- Harald
Newsgroups: sci.math
From: swillden@news.ccutah.edu (Shawn Willden)
Subject: Re: Minimum standards for math "competency"
Organization: University of Utah Computer Center
X-Newsreader: Tin 1.1 PL3
Date: Tue, 24 Nov 92 01:12:16 GMT

somos@ces.cwru.edu (Michael Somos) writes:
: 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

No, I don't think we're "quibbling over the relative percentages."
The present discussion concerns (among other things) the validity of
an article that claims that 99% of American students would be considered
below average in Japan (I'm ignoring the discussion about Asian American
students vs. Asian students, which should be dropped).  Those percentages
are downright frightening if true.

: 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.  

This is a different issue entirely.  We aren't talking about the 
demand for people with a lot of mathematical knowledge, we're 
talking about the requirement of an industrialized society that 
all individuals have an understanding of basic mathematical 
concepts -- something that is just not true in America today.
 
: 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

I disagree that posession of a definition of the problem implies
rapid progress toward a solution.  Sometimes solutions aren't that
easy to come by.  A mathematician above all others should know
that :).

[ Other (somewhat valid) complaints about the crosspost to sci.math
  deleted. ]

: --
: Michael Somos <somos@alpha.ces.cwru.edu> (* No, I don't work for CWRU *)

Now, to see if I can turn this thread in a more useful direction, here
are some questions.

	1)	Do you disagree that innumeracy is a problem?
	
Now, supposing the answer to that question is no:

	2)	What math do you think an "average" citizen should
		know?
	3)	What math skills should an employer be able to expect of 
		a college graduate?

--
Shawn Willden
swillden@icarus.weber.edu
Newsgroups: sci.math
From: jbaez@riesz.mit.edu (John C. Baez)
Subject: Re: Another fundamental group question
Organization: MIT Department of Mathematics, Cambridge, MA
Date: Fri, 20 Nov 92 21:50:49 GMT

I said "attach 1-cells" but meant "attach 2-cells" - i.e., discs.
From: burt@aupair.cs.athabascau.ca (Burt Voorhees)
Newsgroups: sci.math
Subject: Re: Bozos Synonymous
Date: 18 Nov 92 04:35:13 GMT

>cxm7@po.CWRU.Edu (Colin Mclarty) writes:


>>   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.)

>She seems to be saying:

>1. That mathematics represents a "masculine" way of thinking.

>2. That there never will be, or ought to be, any more
>   women doing research mathematics than there have been
>   historically. (Almost none.)

Just to jump in on this thread, one could make a good argument for point 1,
and for just the opposite of point 2.  Here goes.

Basic assumption: statistically speaking suppose that we assume there are
sex based differences in cognitive skills.  There is at least some
evidence for this, although untangling it from a ton of cultural
prejudices is not easy.

Since math was developed mainly by men it would be natural to suppose
that it would tend to favor those cognitive skills at which men tended
to excel.

Conclusion: At the present time in history math represents a "masculoine"
way of thinking.  But..........

Doesn't this really indicate that math, as practiced at present, is
incomplete?  That as more women enter the field we will see some major
changes in math?

>I think you'd have to look long and hard to find a research
>mathematician who would agree with these two sentences...

No, unfortunately not.  Mathematicians tend to be rather sexist.

>Lenore Levine
>levine@symcom.math.uiuc.edu

burt voorhees
From: 8321207d@levels.unisa.edu.au
Newsgroups: sci.math
Subject: Math Practice
Date: 17 Nov 92 14:32:30 +1030
Organization: University of South Australia
NNTP-Posting-Host: sirius.itd.adelaide.edu.au
Originator: daemon@sirius.ucs.adelaide.edu.au


Hi There

I am about to finish my undergraduate studies this year. I will be
working as a code-cutter for a small computing company. I have a
very strong interest in Mathematics and intend doing further study
when various financial committments have been met. The problem that
I envisage is that lack of use of the Math skills learnt thus far
will cause my ability and confidence to do 'Mathematics' to become
rusty.

It would be useful for me to keep refreshing my Mathematics in some
way. One suggestion has been for me to find some interesting and hard
Maths problems to work on. My question is where?

I would therefore be extremely grateful for any suggestions or advice
relating to my situation. It should be kept in mind that because of a
full-time work committment (& family as well) I can hardly take on a
task which entails a time requirement beyond what I have available.

What areas of Maths have I found interesting: number theory, diff eqns,
hydrodynamics, calculus of variations, numerical maths.

My e-mail address until the end of semester (approx 2 weeks) is:
8321207d@lv.levels.unisa.edu.au

Many thanks for any help
#! rnews 308
From: 8809787l@levels.unisa.edu.au
Newsgroups: soc.culture.iranian
Subject: Testing: payam from the Spell Checker project
Date: 17 Nov 92 14:34:59 +1030
Organization: University of South Australia

Doostan this is just a test.

#! rnews 1372
From: 9022327n@levels.unisa.edu.au
Newsgroups: unisa.help
Subject: Re: Help needed with X and Linux on an ibm PC!
Date: 17 Nov 92 19:33:03 +1030
Organization: University of South Australia

In article <19324.2b0825c8@levels.unisa.edu.au>, 9128057f@le!%w1whGGMk{st pg@3vels.unisa.edu.auwrites:
> Greetings everyone!
>
>   This is an unshamefull plea for help!!  I've managed to get Linux 0.98
> running on my 486/33 (SLS distribution) but after successfully installing
> the complete base system + X11 I have run into problems with trying to get
> X11 to run!
>
>   The problem, quite simply, is that I don't know where to start with
> Xconfig!  Some of the docs talk about setting it up but it all tended to
> go a bit above my head (monitor frequencies, video card freq. etc) ...

Have a look in X386/doc/video.tutorial. It explains how to calculate
the horizontal and vertical timing. You will need to run the clock.exe
program to find the clock frequencies of your video card.

>   So, if ANYONE can help me with getting X running it would be greatly
> appriciated!  My system config follows ...
>
>
>   486sx/33mhz, 4mb ram (soon to be 8)

You will have to upgrade to 8MB or add a swap partition. X386 needs 5MB
to run one xterm window.

#! rnews 903
From: xarjp@levels.unisa.edu.au
Newsgroups: rec.music.early
Subject: Re: lute (do it your self)
Date: 18 Nov 92 17:45:14 +1030
Organization: University of South Australia

In article <BOGUSZ.92Nov12170235@albert1.fuw.edu.pl>, bogusz@fuw.edu.pl (Wojtek Bogusz) writes:
> 
>  I am dreaming about lute from year or so. And all of this discussion
etc etc
>  Wojtek Bogusz
> 

If you want to build your own (and you might get addicted), and you will
have to build a few (some people say as many as 50) before you get it
right, then beg, borrow or steal a copy of 

Ronald Zachary Taylor - "Make and Play a Lute"

ISBN 085242 813 8, published by Argus Books Ltd, Wolsey House, Wolsey Road,
Hemel Hempstead, Herts HP2 4SS, United Kingdom.

Good luck,
Rob Potter (still trying)

#! rnews 560
From: xarjp@levels.unisa.edu.au
Newsgroups: rec.music.early
Subject: The Lute of Pythagoras
Date: 18 Nov 92 18:04:08 +1030
Organization: University of South Australia

In Sept 92 issue of Strad - Letters - David Woodrow protests a critique
of his book "The Shape of Stadivari Forms And Violins". He refers to
* the Lute of Pythagoras *, as described in a book by Pickering.

Anyone know the book referred to? If so can they email me the full
reference?
Thanks, hopefully
Rob Potter

#! rnews 1226
From: yawcl@levels.unisa.edu.au
Newsgroups: comp.os.ms-windows.apps
Subject: EXCEL!!! Simple yet lethal question...
Date: 18 Nov 92 20:10:26 +1030
Organization: University of South Australia

Hi... this is for all those excel macro programming enthusiast out there...

How do you do an add texts from two cells into one cell....
( An actual formula for a macro would really be helpful... )

I know it sounds trivial... But I'm ripping hairs out over here....

I know that the same procedure can be done in Lotus with the 
string + string command.... But Excel doesn't have a string command...

And I haven't been able to find an inverse "parse" command....

If that hasn't got you yet... Does Excel's macro programming tool actually
have a limit on embeded "AND" and "OR" commands....
It got really stuffy at me once when I tried to "OR" two "AND" statements
together.... ( Although... the formula was getting a bit long... by this 
point...) Bear in mind they work brilliantly apart....

Paul Leong ..
E-mail : yawcl@ntx.city.unisa.edu.au

ps. Somebody should start a competition for finding the most puzzeling
questions for an application.....


Newsgroups: sci.math
From: frisch1@athena.mit.edu (Jonathan Katz)
Subject: ODE problem...
Organization: Massachusetts Institute of Technology
Date: Tue, 17 Nov 1992 20:52:37 GMT

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.
It may be worth noting that, viewing this as a matrix problem:
x'=Ax,
A^2=I.

I don't know if that helps.
From: skipa@milton.u.washington.edu (Skip Albertson)
Newsgroups: sci.math
Subject: HELP: Empirical Orthogonal Functions (EOFs)...
Summary: HELP: Empirical Orthogonal Functions...
Keywords: HELP, EOFs, Empirical Orthogonal Functions
Date: 18 Nov 92 03:13:03 GMT
Article-I.D.: milton.skipa.722056383
Organization: University of Washington


I'm trying to sample a scalar field (say temperature) with
the minimum number of evaluations (field stations) to gain
a reasonible representation of the field.  A friend suggested
I try Empirical Orthogonal Functions (or some such thing)...
haven't had time to make it to the library yet, thought I'd
solicit help here...

If I over-sample the field (take N random readings) and then
attempt to find the relative independance of each sample by
diagnolizing the N x N matrix formed by the product:

(x1*x1  x1*x2  x1*x3 ... x1*xN)
(x2*x1  x2*x2  ....           )
(....                    xN*xN)

where x1 to xN are the N evaluations of the field, will the
relative values of the eigenvectors tell me which stations
I can drop?

Is this what my friend could have meant?

Thanks in advance,

alberts@apl-em.apl.washington.edu
Newsgroups: sci.math
From: crb11@cus.cam.ac.uk (Colin Bell)
Subject: Re: math encyclopedias
Organization: U of Cambridge, England
Date: Wed, 18 Nov 1992 14:07:05 GMT

In article <Bxqq6H.Ezt@world.std.com>, wdr@world.std.com (William D Ricker) writes:
|> George Gadelkarim (gjg@Cadence.COM) writes:
|> >I noticed somebody mention one published by MIT about three 
|> >months ago. I believe it was for $150. Does anybody know its 
|> >name. Does anybody know of a similar or better one?
|> 
|> I have three different MIT Press publications which try to be an
|> encyclopedia of math, plus one other.
|> 
|> From the German:
|>     Behnke, H. et al., eds.	Fundamentals of Mathematics.  Three
|> volumes. Volume I: Algebra, Volume II : Geometry, Volume III :
|> Analysis.  Was hardback, now I think in paper only.  Each volume is a
|> sequential survey; random access is quite difficult, if you don't
|> really mostly remember the subject anyway.
|>

Is there a new edition of this out? I have a copy (acquired secondhand for
ten pounds) but it's rather out of date in some respects (my edition was
originally published in German in 1958 I think, and the translation of about
five years later brings some things up to date but not all)

-- 
-
Colin Bell, CRB11@CUS.CAM.AC.UK
Department of Pure Mathematics, University of Cambridge.
Newsgroups: sci.math
From: mab@wdl39.wdl.loral.com (Mark A Biggar)
Subject: Re: Square root of a number
Organization: Loral Western Development Labs
Date: Wed, 18 Nov 1992 21:26:20 GMT

 The geometric constructions of square roots is quite nice.

Assuming you have a line segment of length X and a line segment of length 1.
Consturct a segment of length X+1.  Construct a circle with that segment as
its diameter.  Construct a perpendicular 1 unit from the edge of the circle
(i.e. at the point between the X lenght segment and the 1 lenght segment) on
the diameter.  The distance between the diamenter and the point where the
perpendicular intersect is the square root of X.  I will try to draw a diagram
to the limits of Ascii.
                         +
                         |
                         |
                         |
                         | sqrt(X)
                         |
                         |
                         |
   +---------------------+---------+
              X               1

imagine there is a semicircle in above diagram

The above construction can be found in Euclid.

--
Mark Biggar
mab@wdl1.wdl.loral.com





Newsgroups: sci.math,tum.questions
From: masa@nws.e-technik.tu-muenchen.de (Matthias Sauer		)
Subject: Minimum number of lines that cover a set of points
Organization: Leibniz-Rechenzentrum, Muenchen (Germany)
Date: Tue, 17 Nov 1992 16:38:00 GMT


I am looking for an algorithm for the following problem:

    Given a set P of points in the plane find a minimal 
    number of straight lines such that every p in P is
    on at least one of these lines.

I am almost sure that there is some standard algorithm for this problem,
but I could not find any. Please send an e-mail to:
     sauer@nws.e-technik.tu-muenchen.de
or post an article in sci.math or tum.questions

So long, and thanks for all the fish!
From: RVESTERM@vma.cc.nd.edu
Newsgroups: sci.math
Subject: Re: Geometrical parking problem.
Date: 18 Nov 92 21:41:43 GMT

there is no minimum length of the parking space.  consider a car of
length l and no width.  consider a parking space such that cars park
perpindicular to the curb rather than parallel to it.

bob vesterman.
Newsgroups: sci.math
From: dob@ccr-p6.ccr.jussieu.fr (Dominique BERNARDI p3512)
Subject: Re: Prime test algorithm
Organization: Universites P. & M. Curie / D. Diderot
Date: Tue, 17 Nov 1992 16:36:15 GMT

If you just want to be reasonably sure that your number
is prime "for all practical purposes" The Miller-Rabin test
is more than adequate. The only problem is to have a good
multiprecision package. One possibility would be our "PARI"
package, available in C source code, for exemple from
math.ucla.edu in /pub/pari

If, on the other hand, you want a rigorous proof, with
"evidence" you can oppose to others that your number is
indeed prime, you should take a look to ECPP (Elliptic
Curve Prime ?) written by Francois Morain,
available by anonymous ftp from
ftp.inria.fr
in directory /INRIA

ecpp.V3.4.1.tar.Z

D. B.

Newsgroups: sci.math
From: frisch1@athena.mit.edu (Jonathan Katz)
Subject: closed forms
Organization: Massachusetts Institute of Technology
Date: Sun, 22 Nov 1992 20:19:25 GMT

>Another question that could belong here: How does one proof that there is
>no closed form expression of \int(exp(-x**2))?
>Peter

Good question.  I hope someone will post an answer.  Otherwise, please send me
the answer via email.
Thanks
---
Jonathan
Xref: sparky sci.math:15423 comp.edu:1935
From: mccolm@darwin.math.usf.edu. (Gregory McColm)
Newsgroups: sci.math
Subject: Re: a first year grad student freaks out.
Date: 13 Nov 92 16:41:36 GMT
Organization: Univ. of South Florida, Math Department

In article <DREIER.92Nov10235243@durban.berkeley.edu> dreier@durban.berkeley.edu (Roland Dreier) writes:
>In article <92314.170255RVESTERM@vma.cc.nd.edu> <RVESTERM@vma.cc.nd.edu> writes:
>   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.
>
>Guess what, kid.  It's even harder than that.  Consider yourself
>extremely lucky if your advisor even gives you a question.  More
>likely, not only are you gonna have to solve a problem, you're gonna
>have to find the problem yourself.  But the advantage of this is that
>you can usually find a problem you can solve if you look hard enough.
>It's still not easy to come up with a problem you can do and also that
>interests other people enough so that they're willing to give you a
>degree.
>


Since the PhD is supposed to be granted to future researchers, 
many advisors regard the ability to find (or make up) a good 
problem as an initial test.  Some people, eg the late Richard 
Feynman, refused to take students who did not have their own 
problems.

Don't worry too much about not being able to solve a problem 
that you attack.  This often happens (it happened to me:  my 
major project for my PhD was to prove a conjecture of my 
advisor's;  6 years after getting my PhD, the problem is 
still open).  What you want is a problem which will lead you 
to good results (Poincare advised people always to have a 
very hard problem in mind to guide one's research) which 
can be presented in lieu of your desired but unforthcoming 
proof of Fermat's Last Theorem (FLT is a good example of a 
hard problem which many people tried to solve, developing 
much good mathematics in the process).

-----Greg McColm
--
SHAMELESS AD:  Math PhDs in Analysis, Discrete Math./Th. of Comp., Num. Anal., 
Prob., are invited to apply to the Math. Dept. of Univ. of S. Florida for 
research/teaching positions that may be available: contact K. L. Pothoven at 
mathdept@math.usf.edu. Deadline 2/1/93. USF is a politically correct employer.
Newsgroups: sci.math
Subject: Isolate HELP
From: Steve_Grant@kcbbs.gen.nz (Steve Grant)
Date: 17 Nov 92 13:47:20 GMT
Organization: Kappa Crucis Unix BBS, Auckland, New Zealand

Hello, 
     can some one please isol t in this equation for me please:

-(24COS(2.05-4379.t).pi)-42COS(3.5-7596.t).pi=0

Hopefully the result will have n in it since this is the first derivative 
of a sum of sines and I want to find the x axis values of the crests. 
PS x is t.

Steve Grant

Newsgroups: sci.math
From: "norman danner" <ndanner@kiwi.ucs.indiana.edu>
Subject: Re: Undergraduate textbooks
Organization: Indiana University, Bloomington
Date: Mon, 23 Nov 1992 20:50:43 -0500

In article <2B11196B.8137@news.service.uci.edu> dpick@math.uci.edu (Daniel Pick) writes:
>...How do we get better
>texts into the classroom, or conversely, how do we discourage publishers
>from printing this stuff?  I, for one, refuse to buy these kinds of texts.

I think this is probably about the best way.  Just don't buy them.  AND
DON'T USE THEM IN YOUR CLASSES.  I'm of the opinion that at my undergrad
institution, the vast majority of professors just used whatever book was
recommended by the dep't, instead of looking for something worthwhile
(the recommended ones were usually trash, like Ross).  So maybe if all
professors were to spend a little time researching the possible books
for a course, and only used decent ones, publishers and potential authors
would get the idea.  Yes, I'm aware that "decent" is very subjective,
but I think everyone probably gets the idea I'm trying to get across here.
And I'm also aware that this involves a time committment which some
professors may feel is too great.  My response to that is that they shouldn't
be teaching (or their department shouldn't advertise itself as a
teaching institution).

-- 
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
From: tim@maths.tcd.ie (Timothy Murphy)
Subject: Re: Fermat's Last Theorem and the FAQ
Organization: Dept. of Maths, Trinity College, Dublin, Ireland.
Date: Tue, 24 Nov 1992 03:24:16 GMT

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


>Meanwhile, here is my proof that there
>are no odd x,y such that for an even n >=2,
>(A)                             (x**n) + (y**n) = (z**n) for an integer z:

I didn't understand your proof.
But isn't the result obvious anyway.
It is sufficient to prove it for n = 2,
since x^n = (x^{n/2})^2 ;
and in that case it is obvious by working modulo 4,
since odd^2 = 1 mod 4, even^2 = 0 mod 4.

-- 
Timothy Murphy  
e-mail: tim@maths.tcd.ie
tel: +353-1-2842366
s-mail: School of Mathematics, Trinity College, Dublin 2, Ireland
Newsgroups: sci.math