HDTenEightyP/NetNews huggingface dataset:
From: mkrogers@unix.amherst.edu (MICHAEL K ROGERS)
Subject: Re: Square root of a number
Organization: Amherst College
X-Newsreader: TIN [version 1.1 PL7]
Distribution: na
Date: Wed, 18 Nov 1992 18:26:52 GMT

Carl Douglas Mueller (mueller@schaefer.math.wisc.edu) wrote:
: >In article <1992Nov15.194049.1@woods.ulowell.edu> buxamusaa@woods.ulowell.edu writes:
: >>Please could someone help me with an assignment that I have to do.
: >>It is a very general question, though the answer could be quite lengthy.
: >>"Discuss methods for finding the square root of a number."
: >>What I am looking for are all possible methods/alogrithms for this.
:                             ^^^^^^^^^^^^^^^^^^^^
: 
: There are MANY methods.  For example to find the square root of x.
: 1) Pick a random number r.
: 2) Compute r*r.  
: 3) if r*r <> x goto 1.
: 
: (OK, so this isn't an efficient method.  It is a method.   :-)  )

It is not a method that works.  I would call it an impossible method.
Xref: sparky sci.math:15057 sci.math.num-analysis:3321
From: jorchard@dciem.dciem.dnd.ca (Jeff Orchard)
Newsgroups: sci.math,sci.math.num-analysis
Subject: RSA Scheme for Encryption/Decryption
Date: 16 Nov 92 15:50:16 GMT
Reply-To: jorchard@dretor.dciem.dnd.ca
Followup-To: sci.math
Organization: Defence and Civil Institute of Environmental Medicine

I asked...
>I would like to know the algorithm for encrypting/decrypting codes
>with the RSA scheme.

Here is what I was sent...

From duvallp@hamlet.uncg.edu Wed Nov 11 19:37:52 1992

  You've probably gotten a zillion replies, but ....

  Choose two primes, p and q. Let M = pq, and F = phi(pq) = (p-1)(q-1).
  Choose a number e and let d be the solution to ed = 1 mod F. (You
  have to pick e relatively prime to F.) Publish M and e, keep p,q,F,
  and d secret. If x is the message, 0<x<M, I send y = x^e mod M to 
  you. You then compute y^d mod M. Since x^F = 1 mod M by Fermat's 
  little theorem, (actually Euler's refinement), you get
   y^d = x^ed = x^(kF + 1) = x mod M, and recover the message. 
  There's a good treatment in "Elementary Number Theory and Its
  Applications," by K. Rosen, Addison Wesley. I also seem to remember a
  nice discussion in Knuth's "Art of Computer Programming, Vol.II,"
  but I don't have that in front of me.
     pd


-- 

 Paul Duvall                   Department of Mathematics
 duvallp@hamlet.uncg.edu       University of North Carolina 
 duvallp@uncg.bitnet                    at Greensboro
 duvallp@mcduff.uncg.edu       Greensboro, NC 27412
                               (919) 334 5836   

Jeff Orchard	jorchard@dretor.dciem.dnd.ca
Dept. of National Defence, Toronto, Canada
Newsgroups: sci.math
From: stephen@europa.inmos.co.uk (Stephen Collyer)
Subject: Re: US education system terminology?
Organization: INMOS Limited, Bristol, UK
Date: Mon, 16 Nov 1992 13:37:08 GMT

In article <1992Nov14.224032.13878@eng.umd.edu>, clin@eng.umd.edu (Charles Lin) writes:
|> 
|> In article <1992Nov14.120215.42551@urz.unibas.ch>, kullmann@urz.unibas.ch writes:
|> >
|> >Could someone please enlighten me about the education system in the USA?
|> >My problem is that the European system (if there is such a thing) seems to
|> >differ quite a lot from the US, especially in terminology. What does 'under-
|> >graduate' mean? etc. For comparison I have given an outline of the Swiss


[useful summary of education system in USA deleted]

|> 
|> --
|> Charles Lin
|> clin@eng.umd.edu


This was very helpful. Thanks. Could someone also outline at what ages kids in the
USA learn various mathematical concepts, such as algebra, logs, calculus, mechanics
etc. I get the impression from American maths books that calculus isn't taught at all
until university. Is this right ? Here in the UK, most science/maths students will have
done at least 2 years of calculus by the time they get to University. How do Americans
catch up ?

Steve Collyer.
Newsgroups: sci.math
From: sl14@crux3.cit.cornell.edu (Stephen Lee)
Subject: Complex numbers
Organization: Fantasy Zone Ithaca, Inc.
Date: Mon, 16 Nov 92 07:57:28 GMT

Somebody asked me this problem, but I think I left my complex numbers
behind (or 'gave them back to my high school teachers' as my HS
teachers said) so can anyone give me some pointer on it?

The problem follows:

Let f(z) = (az + b)/(cz + d) with ad - bc =/= 0 and a, b, c, d, z all
complex.  Suppose L is a straight line drawn in the complex plane,
describe what f(L) could be.

Rgds
Stephen

--
Stephen Lee
Internet: sl14@crux2.cit.cornell.edu
From: ramesh@barbados.crd.ge.com (Rajaram  Ramesh)
Newsgroups: sci.math
Subject: Help needed (Problem in integer programming?)
Date: 18 Nov 92 18:49:14 GMT
Organization: GE Corp. Research & Development, Schenectady, NY


I have come across a problem in my research which probably involves 
integer programming. I am looking for any insight into how to go about
tackling this problem.

Given a sequence f(n), n=0,...,M-1.
Given:
1. f(0)=0;
2. f(k)=f(M-k), k >0, k<M
3. f(n) is a positive integer for n > 0.
4. an integer L < M
If it is of any help, f(M/2)=M/2 and f(k) < M/2 for all other k.

I wish to find a subset of indices k_1, k_2, ...  k_L, 
that
minimizes the double summation

sum_{l=1}^L sum_{m=1}^L f((k_l - k_m) mod M)

,i.e.,

f((k_1 - k_1) mod M) + f((k_1 - k_2)mod M) +... + f((k_1 - k_L) mod M) +
f((k_2 - k_1) mod M) + f((k_2 - k_2)mod M) +... + f((k_2 - k_L) mod M) +
.
.
f((k_L - k_1) mod M) + f((k_L - k_2)mod M) +... + f((k_L - k_L) mod M) 



I do not have to necessarily find the optimum solution, 
good sub-optimal solutions are okay.


On the surface, it looks as if a complete search has to be done. If
anyone knows of a trick to avoid this, I'd appreciate it.

Thanks.

Ramesh.
ramesh@crd.ge.com
From: blom@husc15.harvard.edu
Newsgroups: sci.math
Subject: Three-sided coin
Date: 21 Nov 92 00:15:04 GMT
Article-I.D.: husc15.1992Nov20.191504.17650
Organization: Harvard University Science Center

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

--Eric Blom
--Harvard U
From: marwk@levels.unisa.edu.au
Newsgroups: sci.math
Subject: Has FFT been beaten to the finish line?
Date: 21 Nov 92 20:29:30 +1030
Organization: University of South Australia
NNTP-Posting-Host: sirius.itd.adelaide.edu.au
Originator: daemon@sirius.ucs.adelaide.edu.au

I have heard a rumour of a faster algorithm for FT than the FFT and the
rumour even comes with a percentage improvement of 15%.

If this is true could someone please point me to code and/or theory/description
of it.

It will be used to speed up some surveillance interpretation.

--
Raymond Kennington
LECTURER
University of South Australia   | Act in haste and repent at leisure
P.O. Box 1                      | Code too soon and debug forever
Ingle Farm                      | Knobs, knobs everywhere,
South Australia                 |              just vary a knob to think!
From: hanche@ams.sunysb.edu (Harald Hanche-Olsen)
Subject: Re: 1+1/2+1/3+1/4+...+1/n
Organization: University at Stony Brook, NY
Date: Thu, 19 Nov 1992 17:31:51 GMT

>>>>> On Thursday, 19 Nov 1992 13:23:29 CET, Mutter Christoph Johannes
>>>>> <K3032E2@ALIJKU11.BITNET> said:

Chris> Hallo.
Chris> I've a problem. I have to calculate the sum 1+1/2+1/3+1/4+...+1/n.
Chris> The result should be 100. But my computer is far too slow, to solve this
Chris> problem. I need the index n when the sum > 100.0
Chris> And that exactly.
Chris> Has anyone calculated this? (Perhaps on a CRAY|) ?

You won't find your answer by brute force on any present-day computer.
Consider the fact that this sum is fairly close to log(n)+gamma for
large n, where gamma is Euler's constant; it follows that the desired
n is rather close to exp(100-gamma), which has the approximate value
15092688622113788323693563264538101449859497.364099... (according to
Maple).  Some finesse (asymptotic analysis) is clearly called for to
get the exact answer.  Hint: Estimate the area between the step
function 1/[t] (where [t] is the largest integer <= t) and 1/t for t
between n and infinity.

- Harald
Newsgroups: sci.math
From: afm@trillian (Andreas Mueller)
Subject: Re: Solutions to a cubic equation
Organization: University of Heidelberg, Germany
Distribution: usa
Date: Thu, 19 Nov 92 09:55:15 GMT

preece@StPaul.c10sd4.NCR.COM (Bently.Preece) writes:
: 
: markd@locus.com (Mark Dubinsky) writes
: 
:     ... What is the formula for the solutions of a cubic
:     equation
: 
:     x3 + ax2 + bx + c = 0    ?
: 
: sichase@csa3.lbl.gov (SCOTT I CHASE) writes:
<stuff deleted>
:     use the trignometric identity:
<stuff deleted>
: Forget trig identities.  Try (A + B)^3 = 3AB(A + B) + (A^3 + B^3).  Now if
: you can get 3AB = -D and (A^3 + B^3) = -E then A + B will be a solution.
: This is easy to solve.

Well, it is not so easy to forget the trigonometric identities.
Historically, the use of the formula

	(a+b)^3=3ab(a+b)+(a^3+b^3)

was the first attempt to solve the third order equation,
this step is used to reduce to a quadratic equation. But
then it turns out that in case our original equation has
three real roots, the quadratic equation has complex
roots (not real). The roots of the cubic equation could
be obtained if one knew how to get third roots of
complex numbers. In the time when the problem was first 
solved (by Cardano), this was impossible (complex numbers
were impossible then...) so this was called the `casus
irreducibilis', the irreducible case. Later people learnt
to compute third roots of complex numbers. And how
do they do that? Using de Moivre's formula, which
reduces the problem to a trigonometric one. So You
simple cannot forget the trigonometry.

Hope this clears up a few points

				Andreas

---------------------------------------------------
Andreas Mueller         afm@mathi.uni-heidelberg.de
Mathematisches Institut
Im Neuenheimer Feld 288
W - 6900 Heidelberg 1
---------------------------------------------------
Date: Sunday, 15 Nov 1992 21:48:59 EST
From: <RVESTERM@vma.cc.nd.edu>
Newsgroups: sci.math
Subject: ok, i'll bite.

i understand "cryptography".  i understand "np".  someone please
explain the connection.

note: if you think you've already explained it by saying something
like, "finding the private key given the public key is np-complete"
then please don't try explaining again.  thanks.

bob vesterman.

Newsgroups: sci.math,news.answers
From: andrew@rentec.com (Andrew Mullhaupt)
Newsgroups: sci.math
Subject: Re: who should teach calculus?
Date: 13 Nov 92 22:29:25 GMT
Organization: Renaissance Technologies Corp., Setauket, NY.

In article <1992Nov10.223300.19016@murdoch.acc.Virginia.EDU> tep2j@amsun.apma.Virginia.EDU (Todd E. Peterson) writes:
>I am interested in hearing net.opinions on the following:
>
>Is it a good or bad practice to use non-mathematicians to
>teach mathematics courses? 

Generally very bad practice.

>In particular, what about the
>use of engineering faculty to teach engineering calculus
>courses, and other applied mathematics courses?

The best people to teach Calculus to Engineers and Scientists are
mathematicians who are qualified at some level as scientists or engineers
and who (1) know the engineering or science program they are functioning
in, and (2) care about this kind of education. Most of the best people by
this reckoning are in industry where they teach little or not at all.

Later,
Andrew Mullhaupt
From: ramsay@math.ubc.ca (Keith Ramsay)
Newsgroups: sci.math
Subject: Job ratings (was Re: Minimum standards for math "competency")
Date: 24 Nov 1992 01:27:31 GMT
Organization: University of British Columbia, Vancouver, B.C., Canada
NNTP-Posting-Host: gauss.math.ubc.ca
Keywords: math competency education university college standards

In article <1339@kepler1.rentec.com> rjfrey@rentec.com (Robert J Frey) writes:
|       o       The Jobs Almanac's top 5 jobs are all mathematically based:
|		actuary, computer programmer, systems analyst, mathematician
|		and statistician.

In article <1992Nov23.200403.111578@Cookie.secapl.com>
frank@Cookie.secapl.com (Frank Adams) writes:
|It appears that a number of people are doubting this, based on the
|assumption that these are the jobs which [will] have the most jobs opening
|up.
...
|Then again, the Almanac may be using some other criteria entirely.

I suspect that this is based on the same job survey as was cited in
the newspapers, which rated these five jobs highest on some
combination of pay scale, working conditions, stress, possibility for
advancement, and job security. I don't think availability of the job
was among the criteria, just security (once one has it). I dimly
remember wondering whether the method of combining the criteria was
reasonable.

I suspect that mathematics rated well as an occupation because of
tenure (for academic mathematicians), and because it is an indoor job.
By contrast migrant farm work and fishing were near the bottom of the
same list.

Keith Ramsay
ramsay@unixg.ubc.ca
From: gore@pepper.rutgers.edu (Bittu)
Newsgroups: sci.math
Subject: Functions
Keywords: Subexponential
Date: 19 Nov 92 17:14:37 GMT
Organization: Recreation Center, Busch Campus


I am trying to figure out if a certain class of functions is well
defined and also trying to find good nontrivial examples of functions
that belong to this class. The functions can either be assumed to be
from N to N or from [0,oo) to [0,oo) (I am more interested in the N to
N case). Let me define a class "subexp" first:

f is in subexp if for every e > 0, f(n) = o(2^(n^e))
                        this is little oh ^ 

Now define the class subsubexp with the follwing restriction:

For any two functions f and g in subsubexp, their composition must be
in subexp.

Is subsubexp well defined? I know that functions like 2^((log n)^k)
for any k are in subsubexp, but I want better examples. Maybe there
are functions that come out of combinatorial analysis (like the Ramsey
function R(n,n) for instance) that belong to subsubexp.

--Vivek
From: goddard@NeXTwork.Rose-Hulman.Edu (Bart E. Goddard)
Newsgroups: sci.math
Subject: Re: ODE problem...
Date: 19 Nov 1992 14:53:20 GMT
Organization: Computer Science Department at Rose-Hulman
Reply-To: goddard@NeXTwork.Rose-Hulman.Edu (Bart E. Goddard)
NNTP-Posting-Host: g214-1.nextwork.rose-hulman.edu



There should be an award for Robert Israel for consistantly clear,
intelligent posts, which always are about math and always polite.

(I, myself, will have to settle for "Mr. Congeniality".)

However, there is a small error in his solution to the
following problem.  The solutions still works just fine, but one
of the constants is different:


In article <israel.722130237@unixg.ubc.ca> israel@unixg.ubc.ca (Robert  
B. Israel) writes:
> >(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.
>  
> Quite a neat problem!  I hope nobody was sadistic enough to
> assign it as homework.
> 
> First go to polar coordinates: x = r cos(s), y = r sin(s)
> (I'm too lazy to type "theta").
> (1)   r' = (x x' + y y')/r = r cos(t-2s)
     there's a missing "a" here ^

[....]
> -- 
> Robert Israel                            israel@math.ubc.ca

Bart Goddard
Newsgroups: sci.math
From: ruberman@binah.cc.brandeis.edu
Subject: Re: another trivial homology question
Reply-To: ruberman@binah.cc.brandeis.edu
Organization: Brandeis University
Date: Mon, 23 Nov 1992 20:46:43 GMT

In article <1992Nov23.150344.2734@crl.dec.com>, herlihy@crl.dec.com (Maurice
Herlihy) writes: 
>Let D be an n-dimensional simplicial complex that is connected with trivial
>homology groups above dimension 0.  Is D necessarily homeomorphic to an n-disk?


Not necessarily: 
Example 1: 
D might not be simply connected.  For example, let P be
Poincare's homology sphere (= S^3/I* where I* is the binary icosahedral
group), and let D = P - an open 3-ball.  There are similar examples in
every dimension > 2.  Given an example D_n in dimension n with boundary =
S^{n-1}, form S^1 x D_n U D^2 x D^{n-1} = D_{n+1}.  D_{n+1} has the homology
of a ball but the same fundamental group as D_n.  

Example 2: D might be simply connected, but boundary D a homology sphere
with nontrivial fundamental group.  There are examples in all dimensions > 3
due to Mazur.  You can find this at the end of Rolfsen's book Knots and Links.

Example 0: If D and its boundary are both simply connected, D still
might be a counterexample to the Poincare conjecture. The only interesting
dimensions for this are n=3,4.

Daniel Ruberman
From: dik@cwi.nl (Dik T. Winter)
Newsgroups: sci.math
Subject: Re: Discrete Fields
Date: 20 Nov 92 01:17:10 GMT
Organization: CWI, Amsterdam

In article <1992Nov19.153057.18919@news.lrz-muenchen.de> stpa@nws.e-technik.tu-muenchen.de (St. Paul) writes:
 > I'm looking for literature on matrix computation on 
 > discrete fields  (SVD, eigenvalues, QR-decomposition etc. ..).

EVD requires an algebraically complete field.  This is easy to verify (given
a polynomial it is simple to write down a matrix using the coefficients of
the polynomial that has the roots of the polynomial as its eigenvalues).
QR and SVD can be done if you are able to extract the square root of every
number in the field (and this is required).  You simply follow the standard
routines for matrices over R.  But be aware that methods for SVD are
iterative, so you need some metric to determine convergence, and also
some singular values will be in the algebraic completion of the field.

If the matrix has eigenvalues representable in the field in question,
there are methods that might be able to approximate them, but again,
you need a metric.
-- 
dik t. winter, cwi, kruislaan 413, 1098 sj  amsterdam, nederland
home: bovenover 215, 1025 jn  amsterdam, nederland; e-mail: dik@cwi.nl
Newsgroups: sci.math,sci.physics,sci.astro,sci.bio,sci.chem,misc.education
From: hrubin@mentor.cc.purdue.edu (Herman Rubin)
Subject: Re: What can we have for an educational system?
Organization: Purdue University Statistics Department
Date: Sun, 22 Nov 1992 11:24:15 GMT

In article <By3CFt.4HJ@eis.calstate.edu> kmushal@eis.calstate.edu (KAYE MUSHALIK) writes:

			............................

>I had a teacher in high school who had a PhD but couldn't teach worth
>"beans". It was obvious that he knew his subject well but he couldn't 
>convey any excitement to us. I don't claim to be brilliant, but there
>were kids in my class who were and they even had trouble with the subject.
>Yes, it's important to know the subject matter, but it is more important to
>know how to make that subject EXCITING and RELEVANT to the students' lives.

A teacher has to work with both the structure of the subject and also the
background of the students.  Some things can be made exciting by some people,
but not by all.  As for relevance, education is for the future, not the
present, and teaching in a logical manner may require a great deal of 
apparently irrelevant material before the relevance can be seen.

One of the weaknesses of our miseducational system is that there is far too
much of an emphasis on teaching children to memorize what is immediately
applicable in the elementary and secondary schools.  This continues on to
the universities now, and is even reaching the graduate schools.  There 
does not seem to be any immediate relevance of the axiomatic approach to
geometry when it is given, but the child is under great unlearning stress
if computational junk is given at that stage instead of reasoning.

This also holds in other fields.  Is a child forced to do rote taxonomy
in the lower grades any better prepared to understand molecular biology,
or even worse, the problems of biochemistry which involve both physical
and chemical structure of biological materials, later?  Is the child 
who learns ancient physics better able to understand the simpler, but
mathematically involuted, models later?  The answer is almost certainly NO.
-- 
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: ashall@magnus.acs.ohio-state.edu (Andrew S Hall)
Newsgroups: sci.math
Subject: Re: Bozos Synonymous
Date: 16 Nov 92 18:25:14 GMT
Article-I.D.: magnus.1992Nov16.182514.17995
Organization: The Ohio State University

Several people has been beating up on Camille Paglia. Someone even stated that 
Camille belives that math is a masculine way of thinking etc.  I believe you 
have Ms. Paglia's writings confused with the femi-nazis she deplores.

If you have actually READ any of her writing, you would see she insists on a 
scientific eduaction for everyone, incl. liberal arts people. I may not agree 
with her in totally, but I won't sit by and watch her views being 
misrepresented.

It would appear that a lot of people in this group have as little knowledge of
the humanities as humanities people have of science and math. This is sad. It
esp. saddens someone like myself who has gotten a degree in math and molecular
biology and plans to go to grad. school in art history and archaeology.

                                                  Andrew Hall
Newsgroups: sci.math
From: pvonk@scott.skidmore.edu (Pierre VonKaenel)
Subject: Re: Minimum standards for math "competency"
Keywords: math competency education university college standards
Organization: Skidmore College, Saratoga Springs NY, 12866
Date: Mon, 23 Nov 1992 14:06:53 GMT

In article <1992Nov23.021123.22797@linus.mitre.org> crawford@boole.mitre.org (Randy Crawford) writes:
>In article <1339@kepler1.rentec.com> rjfrey@rentec.com (Robert J Frey) writes:
>>
>>	o	The Jobs Almanac's top 5 jobs are all mathematically based:
>>		actuary, computer programmer, systems analyst, mathematician
>>		and statistician.
>
>A greater need is anticipated for systems analysts and mathematicians than for
>nurses or accountants?  First time I've heard that.  Sounds dubious.
>

Yup, that's what the article states, I've seen it.

>>
>>	o	The math scores of the top 1% of American high school students
>>		would place them in the 50th percentile in Japan (that's not
>>		a typo). How can we expect to compete with Japan in high tech
>>		manufacturing?
>
>Hoo boy!  Does this statement need qualification!
>
>In effect, this states that EVERY american student would be below average 
>mathematically in Japan.
>
>I'll step out on a limb here and say: RUBBISH!  Such a statement _has_ to be
>completely wrong.  If the margin between the US and Japan were that great, we'd
>see vast differences between us in virtually every form of technology, including

Perhaps you haven't visited a technical university lately.  I recall
professors complaining that most of their students are oriental, and
where are the American kids?  I'm not sure about the statement above,
but it's quite clear here in education land that American students are
pitifully deficient in math.  Why a good number of them can't add
fractions together or interpret what a percent means.  As to our
brightest.. there are way too few of them!

>
>But perhaps it's just my gross inadequacy in mathematics speaking...
>

-- 
Pierre von Kaenel	| Skidmore College	     | pvonk@skidmore.edu
Math & CS Dept.		| Saratoga Springs, NY 12866 | (518)584-5000 Ext 2391

"Experience is the name everyone gives to their mistakes." Oscar Wilde
Newsgroups: sci.math