HDTenEightyP/NetNews huggingface dataset:
From: yeomans@austin.onu.edu (Charles Yeomans)
Subject: Re: SIMTEL-20 symbolic mathmatica software
Date: Thu, 17 Dec 1992 16:34:20 GMT
Organization: Ohio Northern University

In article <1992Dec16.194957.27147@pony.Ingres.COM>, nitin@Ingres.COM (Nitin Borwankar) writes:
> 
> I believe ( and I may not have this exact to the letter ) that the commercial
> use of the Internet is within the original goals of the NSF *as long as it
> supports research and education*.
> Very loosely speaking products supporting research and education could be
> discussed and still remain within the original guidelines.
> Clearly discussion of symbolic mathematical packages is of interest primarily
> to students, academics and research scientists and engineers.
> 
> Given this, There doesn't appear to be a problem with discussing either
> SymbMath or Maple or even letting everyone know of its features when someone
> asks for it.
> 
> The fact that there is a *free* version of some such package is definitely
> worth knowing. If the developer is available for comments via the net, all
> the better. This definitely serves research and education.
> 
> If there is something personal the original poster has against the developer
> of SymbMath he should address it personally by e-mail, rather than start
> a flame war here.
> 
> The original tone of the complaint about commercial posting had an edge to it
> that did appear a bit attacking.
> 
> Let's focus on helping each other and if someone blatantly begins advertising
> without being solicited for info, they are likely to be negatively affected
> rather than positively, since people tend to stay away from them.
> 
> Speaking for myself, I did find all the above messages valuable.
> 
I am, as far as I know, the original complainer.  I have nothing personal 
against Huang.  What does annoy the shit out of me is that someone posted
a request for a location for SIMTEL and this Huang replied, as he has done
to many other posters - "I suggest you try SymbMath", followed by info about
how to purchase it.  What he did NOT do is to answer the poster's question
about SImtel.  Furthermore, he appears to have added several other newsgroups
to the follow-up line for no discernible reason other than to advertise his 
product.

There is no free version of SymbMath - it is, at the least, shareware.  As any
shareware developer will tell you, shareware is usually not free.  AT the 
very least, Huang could have identified himself as the author of this product
he was recommending.  But he didn't do that either.

I wouldn't describe what I did as attacking Huang.  "Attacking" might include
sending copies of his posings to the sysop at his site with a request to
ask Huang to stop his uninvited advertising - or to at least be straightforward
about what his intentions are.

Charles Yeomans



Newsgroups: sci.math
From: pratt@Sunburn.Stanford.EDU (Vaughan R. Pratt)
Subject: Re: Philosophy of Pi
Organization: Computer Science Department,  Stanford University.
Date: Fri, 11 Dec 1992 20:25:21 GMT

In article <1gakiiINN2mp@master.cs.rose-hulman.edu> goddard@NeXTwork.Rose-Hulman.Edu (Bart E. Goddard) writes:
>
>Actually, I count by Pi's, so I have trouble dealing with integers, even
>though they seem to pop up everywhere.  My banker insists on being  
>closed-minded and intolerant about all this, but it's my numerical  
>orientation:-)

No wonder.  You should be seeing a baker, not a banker.

Are pop-up's anything like pop-overs?
-- 
Vaughan Pratt				All knowledge resides in the going odds
Newsgroups: sci.math,rec.puzzles
From: bcash@crchh410.BNR.CA (Brian Cash)
Subject: Re: Marilyn Vos Savant's error?
Reply-To: bcash@crchh410.BNR.CA (Brian Cash)
Organization: Bell-Northern Research Ltd.
Date: Wed, 16 Dec 1992 07:40:32 GMT

Oops!  I figured out what I did wrong.
I took Boy+Girl to be the same prob. as Boy+Boy and Girl+Girl.
It should be twice as much, making the prob = 1/3, not 1/2.
I was looking at single person cases rather than group cases.
Sorry!  Forget the last post.


Brian /-|-\
Newsgroups: sci.math
From: mcfarlan@corona.math.washington.edu (Thomas J. McFarlane)
Subject: Re: Difference between "show" and "prove"
Organization: University of Washington, Mathematics, Seattle
Date: Mon, 14 Dec 1992 20:32:18 GMT

In article <Bz9GAt.D5y@mentor.cc.purdue.edu> hrubin@pop.stat.purdue.edu (Herman Rubin) writes:
>In article <Bz7KyK.297@ulowell.ulowell.edu> cdeloge@cs.ulowell.edu (Carolyn Deloge) writes:

>>What is the difference between "show" and "prove"?

>In mathematics, there is no difference.

Moreover, "theorem" etymologically means "something to behold."
So one should preferably "show" a theorem.

Tom McFarlane

Newsgroups: sci.math,comp.edu,misc.education
From: hrubin@pop.stat.purdue.edu (Herman Rubin)
Subject: Re: Student attitudes
Organization: Purdue University Statistics Department
Date: Fri, 18 Dec 1992 21:50:12 GMT

In article <1992Dec17.222321.23782@dsuvax.dsu.edu> dbreiden@dsuvax.dsu.edu (Danny Breidenbach) writes:
>In article <Bz21G2.CHo@mentor.cc.purdue.edu> hrubin@pop.stat.purdue.edu (Herman Rubin) writes:
>>The math departments are quite willing to teach concept courses to reasonably
>>prepared students.  Reasonable preparation is the ability to use symbols to
>>formulate problems, to know what a function is, and to understand what is and
>>what is not a proof.  

>Some members of math departments are willing to teach them to students who 
>aren't reasonably prepared with reasonable success.  Of course, a lot of
>other people get annoyed that these members first help the students learn
>about using symbols, formulating problems, and what a function is.  But once
>that is done -- the concepts come along pretty quickly.  It happens all over.
>Even at Purdue ...

One can reach relatively few students can learn how to use functions
intelligently without a reasonable formal notion of function, and even
fewer can manage the idea of proof by induction if it is used for the
first time in a calculus course.  In addition, the students have the
attitude that what is important in the course is to know how to plug
in the appropriate memorized formulas.

>>When the physicists and engineers tell the math departments that they want
>>their students to know what derivatives and integrals ARE, to understand
>>their use in word problems, instead of how to calculate them, the
>>mathematicians will produce these courses.  I see no signs of this
>>happening.  

>When asked -- they will tell you.  They were asked by people at Purdue ...
>and guess what they said?    No, I don't have the answers and all the data
>on hand -- but I doubt you'd have a hard time finding it if you ask the
>right people.  And hell --- why not talk to a physicist or engineer over
>lunch and find out what one of them thinks?

At most universities, and I know that this happens at Purdue, people from
other departments ARE consulted on service courses.  I believe that there
are, or at least there have been, representatives from engineering on the
Calculus Committee.  One can find engineers and physicists who would like
the math department to give such a course, but not too many.  Also, they
would have to support real remedial courses in high school algebra and
either geometry or a logic course with proofs, remedial in the sense that
they assume not that the student did not learn in--all of the students in
science and engineering supposedly have had this in high school--but that
their high school courses paid too little, or even no, emphasis to these
non-computational topics.
-- 
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: goddard@NeXTwork.Rose-Hulman.Edu (Bart E. Goddard)
Newsgroups: sci.math
Subject: Re: Pi base e, and e base Pi.
Date: 15 Dec 92 15:31:53 GMT
Reply-To: goddard@NeXTwork.Rose-Hulman.Edu (Bart E. Goddard)
Organization: Computer Science Department at Rose-Hulman
NNTP-Posting-Host: g214-1.nextwork.rose-hulman.edu

In article <1992Dec15.041507.18194@serval.net.wsu.edu>  
wvanweer@wsuaix.csc.wsu.edu (Wayne VanWeerthuizen) writes:
> Is there an efficient method for calculating pi base e, or e  
base pi 
> to an arbitrary number of digits?
> 
> What are the first 40 digits of each?
> 
> -- 
In Mathematica I typed:

RealDigits[N[E,40],N[Pi,40]]

{{2, 2, 0, 2, 1, 2, 0, 1, 0, 0, 2, 1, 1, 1, 1, 2, 2, 0, 
 
   0, 1, 1, 0, 1, 2, 0, 1, 0, 0, 0, 2, 0, 1, 1, 2, 0, 2, 
 
   2, 1, 0, 1, 2, 0, 0, 1, 1, 1, 2, 1, 0, 1, 2, 1, 1, 0, 
 
   2, 1, 1, 2, 1, 2, 1, 2, 2, 0, 1, 1, 0, 3, 0, 0, 2, 2, 
 
   0, 0, 2, 0, 0, 0, 0, 0}, 1}
Which means 2.20212...
and:

RealDigits[N[Pi,40],N[E,40]]

{{1, 0, 1, 0, 1, 0, 0, 2, 0, 2, 0, 0, 0, 2, 1, 1, 1, 1, 
 
   2, 0, 0, 2, 0, 1, 0, 1, 1, 2, 0, 0, 0, 1, 0, 1, 0, 2, 
 
   0, 2, 0, 0, 0, 1, 1, 1, 0, 1, 2, 0, 2, 0, 0, 1, 0, 1, 
 
   2, 0, 0, 0, 2, 0, 0, 1, 1, 0, 1, 1, 2, 0, 1, 0, 1, 2, 
 
   1, 0, 0, 1, 0, 0, 0, 2, 1, 0, 0, 1, 0, 0, 2, 1, 1, 0, 
 
   1}, 2}
Which means 10.101002...

Bart
Newsgroups: sci.math
From: pratt@Sunburn.Stanford.EDU (Vaughan R. Pratt)
Subject: Re: Philosophy of Pi
Organization: Computer Science Department,  Stanford University.
Date: Sat, 12 Dec 1992 22:15:57 GMT

In article <1gd4dbINNm9q@gambier.rick.cs.ubc.ca> t4d192@rick.cs.ubc.ca (Bruce Paul Dow) writes:
>
>Actually there's a related point I haven't been able to grasp
>intuitively. How about that -other- number: e
>
>It's just that Euler identity... I can't seem to wave my hands
>around in the right way to imagine what it means to multiply
>e (or any number) by itself an imaginary number of times!
>
>Okay, I know we can justify raising a base to an irrational
>exponent using logarithms, but it doesn't seem to me to justify
>the same thing for imaginary exponents.
>
>Of course, I have seen the Taylor series proof of Euler's
>identity but I can't seem to pull any intuitive feeling out 
>of it. It seems to me as well that having proved Euler's
>identity, you then have a strong link between e and Pi.
>Is this not so? I was wondering whether anyone knew how strong
>this link might be and whether we can express e and Pi in terms
>of each other in any useful way?

(Why isn't this on the FAQ?)

You have to like series a whole lot to find them an intuitive way to
understand why exp(ix) traces out a circle in the complex plane.

The only property of exp that we need to show this is that exp is a
fixpoint of the derivative operator D.  So let's carry out the argument
for any fixpoint Df = f.  Then we must have D f(ix) = i f(ix).  That
is, the velocity of the point f(ix) moving around on the complex plane
under the control of the real variable x is just the vector f(ix)
(construed as a line segment from the origin to the point f(ix))
rotated 90 degrees counterclockwise.  Hence the point always moves at
right angles to the line segment from the origin to the point.  But
this can only happen for motion around a circle with center the
origin.  That's it.

Exercise: Show that f(ix) goes round at a steady speed.  Infer that the
fixpoints of D are exactly the functions a exp(ix) where a is given by
the (arbitrarily chosen) starting position of the circular motion at
x=0.

>In engineering we seem to get enough math to be able to use it
>to solve problems but it's not deep enough to get comfortable
>with it. By the way I just found out today I passed the
>Partial Differential Equations exam after writing it for the
>third time.
>
>Congrats, flames, comments?

Congrats are definitely in order!
-- 
Vaughan Pratt				Actions have consequences
From: fc03@ns1.cc.lehigh.edu (Frederick W. Chapman)
Newsgroups: sci.math
Subject: Challenge Problem:  2-D Harmonic Functions
Date: 13 Dec 92 19:15:21 GMT
Organization: Lehigh University


Here is a problem which I hope will interest/challenge sci.math readers.  I
do not believe it to be trivial (though I might be wrong).


SUMMARY:

Show that any linear, constant-coefficient partial differential operator
which annihilates all harmonic functions in 2 variables must be a multiple
of the 2-dimensional Laplacian.  (The converse is of course trivially
true.)


DETAILS:

Let L = (d/dx)^2 + (d/dy)^2 denote the 2-dimensional Laplacian, let G be an
open connected subset of R^2, and let

                H(G) = { u | u:G --> R is C^2 and Lu = 0 },

the space of harmonic functions on G.  It is true that functions in H(G)
are not merely C^2, but in fact C^{oo} (since L is a hypoelliptic
operator).  Let R[d/dx, d/dy] denote the R-algebra of linear,
constant-coefficients partial differential operators on functions of two
variables.  For brevity, let D = (d/dx, d/dy).  Define

         A(G) = { P(D) in R[D] | P(D)u = 0 for all u in H(G) },

the ideal in R[D] of operators which annihilate all harmonic functions
on G.

(1) Show that A(G) is independent of G.
(2) Show that A = (L), the principal ideal in R[D] generated by L.


HINTS:

(a) Get the theory of functions of a complex variable into the act.
(b) Think about harmonic polynomials.


I'll be interested to see if anyone gets this, and by what methods.
I'll post my solution in a week or so.


Fred Chapman
PDE Puzzler
-- 
 
o ------------------------------------------------------------------------- o
|  Frederick W. Chapman, User Services, Computing Center, Lehigh University |
|    Campus Phone:  8-3218     Preferred E-mail Address:  fc03@Lehigh.Edu   | 
o ------------------------------------------------------------------------- o
| The day after the day after tomorrow is the last day before the rest of   |
| our country's future a week from the day before the day before yesterday! |
Newsgroups: sci.math,comp.edu,misc.education
From: dwilkins@maths.tcd.ie (David Wilkins)
Subject: Re: Student attitudes
Organization: Dept. of Maths, Trinity College, Dublin, Ireland.
Date: Mon, 14 Dec 1992 12:36:28 GMT

In article <11DEC199208420044@cycvax.nscl.msu.edu> burtt@cycvax.nscl.msu.edu (BRIAN BURTT) writes:
>> 
>An idea for a college/university large enough to offer several calculus
>sections:
>	Split the calculus sequence into three parts:
>	a) a sequence oriented to physical scientists and engineers that
>targets the math useful to them-- this is essentially freshman calculus
>as we know it
>	b) a sequence oriented to economists, business students, statisticians,
>etc., which give them calculus without relying on "physics" problems
>that are what calc textbooks normally have
>        c) a sequence oriented to mathematicians, that covers the theoretical
>aspects of calculus and offers a very early introduction to proofs and 
>developing maturity of mathematical thought.
>	Before I get flamed:  I not advocating either insulating scientists
>totally from mathematical theory, or mathematicians from the applications
>of their work.  I just think the classes should be a little more relevant
>to those who take them.
>	I am a student, not an educator, so I'm no expert and welcome
>comments and criticism.

The above is an almost exact description of the system that operates
here.  Main differences: students in the theoretical physics degree
programme take the courses in with the mathematicians, not the natural
scientists; the statisticians are put in with the engineers, not the
economists and business students; the computer scientists are given
separate courses; there are separate service courses for the scientists
and for the engineers.

As regards whether we are `large enough' to operate the system we
do operate, our department consists of 15 permanent full-time teachers,
two part-time teachers, and one full-time teacher on a 9 month contract.
As such, we cover pure mathematics, theoretical computer science, classical
applied mathematics and theoretical physics.  We teach all courses
taken by undergraduate mathematicians with the exception of courses
in statistics and more practical aspects of computer science (taught
by the respective departments of statistics and computer science).
We teach over half of the courses taken theoretical physicists
(from introductory analysis and abstract algebra to quantum
mechanics and general relativity).  We also teach the separate
`service' courses for natural scientists, engineers and computer
scientists, and staff from the economics department cover the
courses for economists, social scientists and business students.

DRW
From: baez@guitar.ucr.edu (john baez)
Newsgroups: sci.math
Subject: another math trivia puzzle
Date: 14 Dec 92 00:16:04 GMT
Organization: University of California, Riverside

Which famous mathematician wrote: "I had graduated from the Ecole Normale
and I did not know what an ideal was, and only just knew what a group was!
This gives you an idea of what a young French mathematician knew in 1930."
Xref: sparky sci.math:17068 rec.puzzles:7983
Newsgroups: sci.math,rec.puzzles
Subject: Re: Marilyn Vos Savant's error?
From: wft@math.canterbury.ac.nz (Bill Taylor)
Date: Thu, 17 Dec 1992 01:04:19 GMT
Organization: Department of Mathematics, University of Canterbury

In article <MARTIN.92Dec15232645@lyra.cis.umassd.edu>, martin@lyra.cis.umassd.edu (Gary Martin) writes:

|> Take a bag with a bazillion pennies and a bazillion nickels.  Randomly
|> draw 100 coins and put them in a much smaller bag.  Randomly draw
|> 99 coins from the smaller bag.  Having observed that 99 of them are
|> pennies, what is the probability that the remaining coin is a nickel?
|> If it were a nickel, then 99 times out of 100 you would have seen it
|> already, so having seen 99 pennies would have been a freak occurrence.
|> But if it were a penny, then the event you just observed would be a
|> certainty.  We have two hypotheses to choose from: one which makes 
|> our observation inevitable and one which makes it a freak accident.
|> Which hypothesis is more likely?

If this last line is meant to imply it's overwhelmingly more likely that we had
100 pennies in the small bag, this is yet another boo-boo in this most boo-boo
infested of all hoary threads.

The fact is, we were overwhelmingly more likely to have had just 99 pennies in 
the small bag to begin with, than 100.  The probabilities are almost exactly
binomial(100 , .5) , in fact, if a bazillion is as big as it sounds.

The probability of getting an observed 99 pennies from a 100-penny bag is much
bigger than getting 99 pennies from a 99-penny bag, of course; but this exactly
cancels the other bias.

P(100 pennies in small bag     | at least 99)     100
---------------------------------------------- =  ---
P(just 99 pennies in small bag | at least 99)      1

and...

P(observe first 99 coins are pennies | 100-penny bag)    100
----------------------------------------------------- =  ---
P(observe first 99 coins are pennies |  99-penny bag)     1

These combine by the usual conditional probabilty calculation to give

P(unobserved coin is a penny | 1st 99 are pennies) = 1/2 ,

which is the common sense result, deducible in a few seconds. This all has little
to do with the original problem, however, where (in effect) the 99 observables
are chosen deliberately rather than randomly.

-------------------------------------------------------------------------------
              Bill Taylor              wft@math.canterbury.ac.nz
-------------------------------------------------------------------------------
 Galaxies - results of chaotic amplification of quantum events in the big bang.
 Free will- the result of chaotic amplification of quantum events in the brain.
-------------------------------------------------------------------------------
From: blom@husc15.harvard.edu
Newsgroups: sci.math
Subject: Integral Puzzle (Evil)
Date: 18 Dec 92 06:00:48 GMT
Organization: Harvard University Science Center

If you're bored or want to see just how much Calculus you REALLY know, try
integrating 1/(x^7+1) from 0 to infinity.  It's a lot harder than it looks. 
Now, can you put that into some form that does not use trig functions?

*Satanic grin, demonic giggling*

Eric Blom
Harvard U
Newsgroups: sci.math
Subject: Re: Integral Puzzle (Evil)
From: a_rubin@dsg4.dse.beckman.com (Arthur Rubin)
Date: 18 Dec 92 16:32:04 GMT
Organization: Beckman Instruments, Inc.

In <1992Dec18.010048.18658@husc15.harvard.edu> blom@husc15.harvard.edu writes:

>If you're bored or want to see just how much Calculus you REALLY know, try
>integrating 1/(x^7+1) from 0 to infinity.  It's a lot harder than it looks. 
>Now, can you put that into some form that does not use trig functions?

alpha = Pi/7

ans = alpha/Sin(alpha) = Beta(1/7,6/7) / 7
--
Arthur L. Rubin: a_rubin@dsg4.dse.beckman.com (work) Beckman Instruments/Brea
216-5888@mcimail.com 70707.453@compuserve.com arthur@pnet01.cts.com (personal)
My opinions are my own, and do not represent those of my employer.
My interaction with our news system is unstable; please mail anything important.
From: huuskone@klaava.Helsinki.FI (Taneli Huuskonen)
Newsgroups: sci.math
Subject: Re: Centillion etc. (was Re: Negative Zero)
Date: 14 Dec 92 16:15:49 GMT
Organization: University of Helsinki

In <djoyce.724343714@black.clarku.edu> djoyce@black.clarku.edu (Dave Joyce) writes:

>[...]  I don't
>know if the unit (namely, one) would have to be named after some famous
>counter or mathematician such as Ahmes, Thales, Pythagoras, or Archimedes.
>Imagine using "megapyth" or "megaarch" instead of "million". 

What's wrong with "megaone"?  :-)
-- 
Taneli Huuskonen |   finger huuskonen@cc.helsinki.fi   | Garanteely speling
-----------------|-------------------------------------| & grammer errur free
 Did I claim | S e va'gy tala'n me'g jobban boldogi't  |---------------------
 something?  | Mint ha ott volne'k, ahol lenni va'gyok.  -Peto"fi Sa'ndor
Newsgroups: sci.math,rec.puzzles
From: hiraga@Csli.Stanford.EDU (Yuzuru Hiraga)
Subject: Integral Puzzle (Cute, not Evil)
Organization: Stanford University CSLI
Date: Sat, 19 Dec 1992 01:12:44 GMT


Let f be any function such that:
	* for 0<=x<=1; 0<=f(x)<= a

	  /1
	* |  f(x)dx = A
	  /0
where a and A are given constants (obviously, A<=a).

What are the maximum and minimum values that

	/1       2
	|  {f(x)}  dx
	/0

can take?
The values can be easily induced, but come up with
a simple (cute) proof.

-Yuzuru Hiraga
From: andrew@rentec.com (Andrew Mullhaupt)
Newsgroups: sci.math
Subject: Re: more math puzzles
Date: 15 Dec 92 22:58:54 GMT
Organization: Renaissance Technologies Corp., Setauket, NY.

In article <24341@galaxy.ucr.edu> baez@ucrmath.ucr.edu (john baez) writes:
>1)  Which famous mathematician wrote "The introduction of numbers as
>coordinates... is an act of violence"?

Rene Descartes

Later,
Andrew Mullhaupt
From: radcliff@csd4.csd.uwm.edu (David G Radcliffe)
Newsgroups: sci.math
Subject: Function Terminology
Date: 11 Dec 1992 19:27:57 GMT
Organization: UW-Milwaukee Math Department
NNTP-Posting-Host: 129.89.7.4

Suppose I have a function f: A --> B, and C is a subset of B which
contains the image set of f.  I define a function g: A --> C by
setting g(a) = f(a) for all a in A.  Usually, f and g can be considered 
as the same function, but sometimes the distinction is important.

Is there a standard term or notation for this?

--
David Radcliffe                                
radcliff@csd4.csd.uwm.edu
Newsgroups: sci.math
Subject: Compass and ruler construction - circles tangent to lines and circle
From: xarjp@levels.unisa.edu.au
Date: 11 Dec 92 19:48:44 +1030
Organization: University of South Australia

The following geometic construction would be useful in the derivation
of violin outlines. 

Given two orthogonal lines AB and CD, intersecting at E, and a circle R
containing E, construct the two circles tangent to R, and tangent to AB
at E.

A "ruler and compassess" construction for AutoCAD or similar is desired.

Analytic results are of course easy to derive, but I cant see the
compass and ruler construction to find the centres of the circles
(which must lie on CD obviously).

ANy pointers gartefully received (email is OK). Alternatively, what is the
classic reference (I assume fairly old) for such constructions?

Cheers, Rob Potter

Newsgroups: sci.math,rec.puzzles,alt.usage.english