HDTenEightyP/NetNews huggingface dataset:
From: zeleny@husc10.harvard.edu (Michael Zeleny)
Newsgroups: sci.math,sci.logic
Subject: Re: The Continuum Hypothesis:  Must it be {True or False}
Date: 25 Dec 92 01:42:49 GMT
Organization: The Phallogocentric Cabal

In article <1992Dec25.011158.2712@sifon.cc.mcgill.ca>
rags@triples.math.mcgill.ca (Robert A. G. Seely) writes:

>The practice of quoting in full is one of M Zelany's most irritating
>characteristics - about 75% of the post referred to here was quote.  
>Of course, he is not by any means alone in this - PLEASE SUMMARIZE or at the
>very least leave the quote to the END of your reply.  (And mark it as such,
>so we are not even tempted to scan it if we recall the points.)
>I find too often I have to hit the "K" key because some folk prefer the "F"
>to the "f" key (I am using trn - translate to your own news reader's
>conventions - the sense I hope is clear:  responding with quote rather than
>without.)  Bah humbug....

By contrast, the one thing I find most irritating, -- after the
preponderance of functional illiterates, incapable of spelling six
letters of my last name, -- is the metadiscussions, whose instigators
excoriate the putative shortage of one's substantive contribution to a
given thread, whilst conveniently ignoring the abject nonexistence of
their own.

>On the other hand, maybe that is an indication they are doing me a favour
>;-}

I am so happy you decided to reciprocate.

>Happy hol's to all,

Likewise.

>- rags

cordially,
mikhail zeleny@husc.harvard.edu
"Le cul des femmes est monotone comme l'esprit des hommes."
From: dbradley@symcom.math.uiuc.edu (David Bradley)
Newsgroups: sci.math
Subject: G=Ab Gp. H<G => G/H embedds in G, don't use Hom(G,Q/Z)
Date: 22 Dec 92 02:41:03 GMT
Organization: Math Dept., University of Illinois at Urbana/Champaign

This has probably been discussed before, but could someone please 
nudge me in the right direction on this one?  It's not homework.

Let G be an abelian group and H a subgroup.  Then G has a subgroup
isomorphic to G/H.  I managed to prove this using the isomorphism
G ~ Hom(G,Q/Z), but surely there is a more direct proof, perhaps 
based on the structure theorem for finite abelian groups.  This is
embarassing.  

-D.M.Bradley
From: frandag@math.ksu.edu (Francis Fung)
Newsgroups: sci.math
Subject: Re: Mathmatics
Date: 23 Dec 1992 01:23:56 -0600
Organization: Dept. of Mathematics, Kansas State University
NNTP-Posting-Host: hilbert.math.ksu.edu

A companion book which I forgot to mention in my previous post
is Saunders Mac Lane's book "Mathematics: Form and Function"
which seems to be a nice overview of what's going on.
Francis Fung
From: arodgers@dcs.qmw.ac.uk (Angus H Rodgers)
Newsgroups: sci.math
Subject: Re: Mathmatics
Date: 23 Dec 92 17:01:08 GMT
Organization: Computer Science Dept, QMW, University of London

In <1h941vINNjoq@hilbert.math.ksu.edu>
frandag@math.ksu.edu (Francis Fung) writes:

>Then there is Topology. You will probably want to know some point-set topology
>to get started; some is covered in the analysis books. For more, there is 
>Munkres' "Topology" and an assortment of Dover books. Be warned that no 
>topology book is perfect, and a lot of them are pretty mediocre.

True. You will certainly have to refer to several books, but if you
have to buy just one, the shortlist should contain:

       General topology / Stephen Willard.
       Reading (Mass.) : Addison-Wesley, 1970.

as well as the classics by Kelley and Bourbaki.
--
Gus Rodgers,  Dept. of Computer Science, |  [Profound thought for 1993]
Queen Mary & Westfield College, Mile End |     "Philishave is about
Road, London, England.   +44 71 975 5241 |      personal choice" 
E-mail (JANET):   arodgers@dcs.qmw.ac.uk |             -- TV advert
From: cd187@cleveland.Freenet.Edu (Aye Naing)
Newsgroups: sci.math
Subject: need help in calculus problem.
Date: 3 Jan 1993 08:31:21 GMT
Organization: Case Western Reserve University, Cleveland, Ohio (USA)
NNTP-Posting-Host: hela.ins.cwru.edu


Hello everybody

This may be an easy problem for most of the netter here. But
I have a difficult time to solve it. So please help me with
any idea to solve it. The problem is

The following equations describe a curve parameterized by 't'
F(x,y,t)=0
G(x,z,t)=0
H(y,z,t)=0
Find the equation of the tangent line.

Thank you.

A N

Newsgroups: sci.math,alt.books.technical
From: dhart@bronze.ucs.indiana.edu (dave hart)
Subject: Re: Projecting a vector onto a plane
Organization: Indiana University
Date: Wed, 30 Dec 1992 21:40:34 GMT

In article <1992Dec17.161552.7160@sophia.smith.edu> orourke@sophia.smith.edu (Joseph O'Rourke) writes:
>In article <1992Dec17.150409.13943@bert.eecs.uic.edu> barnes@bert.eecs.uic.edu (Craig Barnes) writes:
>>
>>How do I project an arbitrary
>>vector on to a plane defined by two other vectors?
>
>Call the arbitrary vector V, and the two vectors in the plane A and B.
>Here is one method.  Compute a normal N to the plane by crossing
>A and B:  N = A x B.  Make this a unit normal n.  Project V onto this 
>normal with the dot product: d = V . n.  Now your unknown vector U
>plus (d n) must give V.  So U = V - d n.


	You could also look at it as a "least squares" problem [finding best
approximation in plane spanned by A, B]. You want V = x_1 * A + x_2 * B, for scalar
x_i, or X*x = V, where X is the matrix with columns A, B and x is the vector of x_i's.
The standard least squares "solution" [see for example Strang's Applied Math] is 
the solution of tX*X*x = tX*V, so
	x = (tX*X)^(-1)*(tX*V), where tX means transpose X,
and U = X*x = etc.  [and actually computing an inverse to solve is *bad form* ;-]
	I haven't done an operation count on it, lately...
From: arodgers@dcs.qmw.ac.uk (Angus H Rodgers)
Newsgroups: sci.math
Subject: Re: Names and pictures
Date: 23 Dec 92 16:39:10 GMT
Organization: Computer Science Dept, QMW, University of London

In <hubert.724997920@mike> hubert@mike.ucsb.edu (Hung-Hsien Chang) writes:

>>> I think it would be nice if the mathematical papers  published on 
>>> journals contain the pictures of the authors as well. So people 
>>> will know the authors not just by name.

[...]

>Sometimes it would be admiration and respect. Also it is much more friendly
>( if the author's picture is not angry-looking. ) when name is associated 
>with faces. 

But think how many group portraits Erdos would have to have taken.
--
Gus Rodgers,  Dept. of Computer Science, |  [Profound thought for 1993]
Queen Mary & Westfield College, Mile End |     "Philishave is about
Road, London, England.   +44 71 975 5241 |      personal choice" 
E-mail (JANET):   arodgers@dcs.qmw.ac.uk |             -- TV advert
Newsgroups: sci.math
From: ghica@fig.citib.com (Renato Ghica)
Subject: a + bx + cx^2 + dx^3
Originator: ghica@duck
Organization: Citibank IBISM
Date: Mon, 21 Dec 1992 20:00:13 GMT




does anyone know of a c/c++ algorithm to solve equations of 
this type for a range of x's ? At some ftp site maybe?

thanks.

-rg
-- 

"You're a cold one, Mr. GRINCH! Your head is full of
spiders nd your teeth are made of wood!"

Newsgroups: sci.math
From: ninassup@athena.mit.edu (Nikos I Nassuphis)
Subject: fuzzy minimization
Organization: Massachusetts Institute of Technology
Date: Tue, 22 Dec 1992 01:43:56 GMT

A friend of mine has to do a project involving the
minimization of a cost function of many variables (some
of which are integers and some reals)

The added constraint is that he has to use "fuzzy logic"

I am at a loss about this. Is there anyone out there
who has seen anything similar ?

Thanks
ninassup@athena.mit.edu



Xref: sparky sci.math:17595 rec.puzzles:8195
From: srw@horus.ps.uci.edu (Steven White)
Subject: Re: Marilyn Vos Savant's error?
Newsgroups: sci.math,rec.puzzles
Reply-To: srw@horus.ps.uci.edu (Steven White)
Organization: University of California, Irvine
Distribution: na
Date: 2 Jan 93 19:59:39 GMT

In article <1992Dec31.203934.1@stsci.edu>, zellner@stsci.edu writes:
|> >   1) You meet a man on the street and ask him how many children he has.
|> >      He replies "two, and one is a boy."  What is the probability that
|> >      his other child is also a boy?
|> >
|> >   2) You meet a man on the street and ask him how many children he has.
|> >      He replies "two, and the older one is a boy."  What is the
|> >      probability that his other child is also a boy?
|> >
|> >The answer to problem 1 is 1/3, while the answer to problem 2 is 1/2.
|> 
|> > The answer to both is 1/2.  One child whose gender is not known, and 
|> > two choices for that gender.  It's a 50-50 proposition.
|> 
|> Nope.  Let's re-phrase it a bit.  Suppose the man says 
|>   
|>   A.  "I have two children, and one of them is right over there."  
|> or
|>   B.  "I have two children, and the older one is right over there."
|> 
|> You look and see a boy.  What's the chances that they are both boys?
|> Enumerate the cases:
|> 
|>    Boy - Boy
|>    Boy - Girl
|>    Girl- Boy
|>    Girl- Girl
|> 
|> Each of those cases is assumed to have exactly the same frequency
|> in the total of all two-children families.
|> 
|> In case B you can rule out the latter two combinations, and you are 
|> left with probability 1/2.  But in case A you can only rule out the 
|> fourth combination, and the probability is 1/3. 
|> 

You forgot to label your table. You wanted it to be

  Older   Younger
  -----   -------
  Boy   -   Boy
  Boy   -   Girl
  Girl  -   Boy
  Girl  -   Girl

Then your logic seems to hold. But if I label the table:

  Kid             Kid
Over there       Elsewhere
  -----          -------
  Boy         -   Boy
  Boy         -   Girl
  Girl        -   Boy
  Girl        -   Girl
Then case A gives probability 1/2 and case B gives 1/3.
In other words, this argument fails. Neither wording is the
same as "at least one of them is a boy".

The correct answer is 1/2 for A and B.

					Steve White

Xref: sparky sci.math:17571 sci.math.symbolic:3347 sci.math.stat:2689
From: deghare@daisy.uwaterloo.ca (Dave Hare)
Subject: Re: Two problems
Organization: University of Waterloo
Date: Wed, 30 Dec 1992 21:46:10 GMT

In article <1992Dec30.185116.29392@maths.tcd.ie> tim@maths.tcd.ie (Timothy Murphy) writes:
>israel@unixg.ubc.ca (Robert B. Israel) writes:
>
>>Suppose there are n couples.  
>>I'll assume that the men are seated in numerical order, so husband 
>>#i+1 is two places to the right of #i.
>
>I like your silent assumption of perfect etiquette!
>Thinks: must revise my idea of California ...

No need.  The "ca" stands for "Canada".  (And the "ubc" stands for 
"University of British Columbia".)

Dave Hare
Newsgroups: sci.math
From: jasonp@bungie.prime.com (Jason Pascucci)
Subject: Mathmatics
Organization: Prime Computer R&D
Date: Tue, 22 Dec 1992 21:17:16 GMT

Hi,

Yes, this might be a strange request, however please
indulge me.

I would like to obtain the firm grasp of 'higher-math'
without spending time in school for a Doctorate in Mathmatics. 

I would like suggestions and commentary as to a fairly 
straightforward, and (as much as possible) all-encompassing
'coursework' for an individual, starting, basically,
from Calculus (which I have a fair grasp of, but
some review I expect will help), and going through
the same topics as would a (for example) Doctorate of 
Mathmatics, without the 'overhead'.  

I'm looking for easily obtainable books and papers, 'standard'
college textbooks only as a last resort, unless they are 
exceptionally well written. 

Mostly, I'm looking for direction, I guess. I would like to 
expand my knowledge base, and don't have the patience to 
go through a degree program. I would also like to work at my 
own pace, which is why I'm interested predomenantly in books. 
My learning curve is fairly strong, with high comprehension 
from reasonable reading speeds and minimal need for repetition 
to leave an impression of an idea. It helps if there
is a good background with material...such as the thought-process
which lead to it's discovery and subsequent development...
as opposed to the 'it works this way, memorize it' method. 
(Admittedly, it's quite possible that there is nothing out
there which uses this learning curve...but it would be nice.
I also realize that there is a lot of 'it works this way, memorize
it' involved in mathmatics, but a good presentation might seek
to soften this...)

Any responses will be sincerely appreciated. Thank you
for your time.

--
Jason R. Pascucci
jasonp@primerd.prime.com
From: bubai@matt.ksu.ksu.edu (P. Chatterjee)
Newsgroups: sci.math
Subject: Need guidance on Reference for Probability and Measure Theory
Date: 24 Dec 1992 17:02:21 -0600
Organization: Kansas State University
NNTP-Posting-Host: matt.ksu.ksu.edu

Hi,

I have just completed two semesters of analysis at the level of Ross and
Bartle/Sherbert. I would appreciate getting some input on the ideal text
to give me an intro to Probability and Measure Theory.

Thanks.
Xref: sparky sci.math:17478 sci.physics:21834
From: samuel@front.se
Newsgroups: sci.math,sci.physics
Subject: Re: Three-sided coin
Date: 29 Dec 92 01:25:45 GMT
Organization: Samuel Gustaf Siren

Trying to solve this problem, i derived the following formula which 
[hopefully] gives the correct probability that the coin will end up on the 
'edge' provided that it is thrown IN A BOWL OF LIQUID WITH VERY HIGH 
VISCOSITY :

  h = height of coin (diameter = 1)
  p = probability that coin will end up on the edge (on the bottom of the bowl)

              h
    p =  -----------
         sqrt(h^2+1)

If the coin is infinitely thin  : h = 0,  p = 0.
If the coin is infinitely thick : h = oo, p = 1.
So far the formula seems to be correct...
Setting p = 1/3 (probability for head, tail, and 'edge' = 1/3) gives 
h = 1/sqrt(8), which seems to be rather thin. Anyway, until someone has proven
the opposite, I belive that the formula is a good approximation in the 'bowl
of viscos liquid' case. 

However, I don't think that the formula is useful in the case of a coin that
bounces up and down on the surface to which it is thrown.
For small values of h, the formula can be approximated with p = h, which
can't be correct. If we had a coin with h = 0.1 (which is a very common
value), then 10% of the tosses would result in 'edge' (provided that the coin
is ideal), which obviosly is an erroneous value.

Does this mean that a correct formula would have to include the viscosity of
the air and/or the 'bounce-factor' (Sorry, I don't know the correct word) 
between the coin and the surface ? The first may maybe be approximated to 0,
but I think that the latter must be included in the formula.

/SS
-- 
+----------------------+--------------------------------------+
|                      |        / \                           |
| Samuel Gustaf Siren  |      __!_/_                          |
| SAMUEL@front.se      |    / \ |  / \                        |
|                      |   |/  || | \__oW)----------          |
| All opinions and     |   !! / /\ \                          |
| questions are my     |     / /  \ \                         |
| own /SS              |    //    //                          |
|                      |   /|    ((                           |
+----------------------+--------------------------------------+
Xref: sparky sci.math:17477 sci.physics:21833
From: samuel@front.se
Newsgroups: sci.math,sci.physics
Subject: Re: Three-sided coin
Date: 28 Dec 92 21:19:25 GMT
Organization: Samuel Gustaf Siren

In article <jim.721702281@st-michael>, jim@cs.UAlberta.CA (Jim Easton) writes:

> Given that it is possible to bounce from one state to another it
> is more probable to bounce out of a high energy state to a lower
> energy state than it is the reverse.  I claim that the lowest energy
> state is the most probable and therefore conclude that the three states
> should be equal in energy.
> 
> That implies that the thickness is equal to the diameter.

I agree with you to a certain extent. However, if the thickness is equal to the
diameter, then wouldn't (assuming that your energy-state-theory is correct) the
coin behave similar to a cube, where the sides of the coin correspond to two
sides of the cube and the 'edge' of the coin corresponds to FOUR sides of the
cube. This would imply that the probability for head id 1/6, tail 1/6 and
'edge' 4/6 = 2/3. I'm not sure that I'm entirely correct on this one, but I'm
almost sure that the probability for 'edge' would be significantly higher than
the one for head or tail, given that the thickness is equal to the diameter. 
/SS
-- 
+----------------------+--------------------------------------+
|                      |        / \                           |
| Samuel Gustaf Siren  |      __!_/_                          |
| SAMUEL@front.se      |    / \ |  / \                        |
|                      |   |/  || | \__oW)----------          |
| All opinions and     |   !! / /\ \                          |
| questions are my     |     / /  \ \                         |
| own /SS              |    //    //                          |
|                      |   /|    ((                           |
+----------------------+--------------------------------------+
From: mingos@vax.oxford.ac.uk
Newsgroups: sci.math
Subject: Re: multiples of 9 - THANKS!!
Date: 21 Dec 92 09:14:22 GMT
Organization: Oxford University VAX 6620

In article <1992Dec19.175256.10919@vax.oxford.ac.uk>, mingos@vax.oxford.ac.uk writes:
> 
> Thanks to all of you who responded to my query about multiples of 9!!
>  I started to thank people individually, but in the end it became a toss up
> between thanking everyone, and writing my christmas cards...!
> 
>  I've now got more proofs than I expected, many different, but all on the same
> basic approach.
>   The solution was along the lines that I'd gone, and ended up as easier to
> prove than I expected.  However, I didn't manage to get a proof myself, which
> is why I'm a chemist, and you guys are mathematicians.  
> 
>   Thanks to everyone who responded, I really appreciate your time and effort
> 
> 				Cheers,
> 
> 					Gavin
> 


  Okay, I forgot to send in the proof.  A couple of people have since mailed me
to ask for it, so here goes as far as I get it.

  *    Suppose you have a number a_n a_n-1 a_n-2...a_0, which is a multiple 
  *    of 9, where a_n is the value of the nth power of ten.   
  *    In that case, the number can be written as
  *     
  *       a_n(10^n) + a_n-1(10^n-1) +....+ a_0                       *1
  *
  *    The sum that we are interested in is 
  *
  *       a_n + a_n-1 + a_n-2 + ........a_0                          *2
  *
  *    subtracting *2 from *1, we get
  *
  *      a_n(10^n -1) + a_n-2(10^(n-1) - 1) + ....a_0(1 - 1)         *3
  *
  *    on the RHS of this equation, each coefficient of a_n must equal
  *    a multiple of 9  since 10^n - 1 = 9, 99, 999, 9999, etc, depending on
  *    the value of n.
  *
  *       therefore,   *2 - *1  = *3, and since *1 is divisible by 9 by
  *    definition, and *3 is divisible by 9 as shown, then *2 must also be
  *    divisible by 9.
  *       ie the sum of the individual digits in a number divisible by 9 is 
  *    also divisible by 9.
  *  
  *       The number *2 must be smaller than *1, and so if the process is
  *    repeated on *2, we get a smaller number still, which is also divisible
  *    by 9.  The process must therefore converge on the smallest non-zero
  *    number divisible by 9, ie 9 itself.
 
 The above process can obviously be modified to be applicable to any number
n in base n+1. 


    					Gavin


     
Newsgroups: sci.math,news.answers
From: dutcher@seas.gwu.edu (Sylvia Dutcher)
Subject: Re: Pi and math in general
Organization: George Washington University
Date: Mon, 28 Dec 1992 02:09:44 GMT

In article <18935@mindlink.bc.ca> Clayten_Hamacher@mindlink.bc.ca (Clayten Hamacher) writes:
>Can someone post some information on how to calculate Pi please. (preferably
>something more precise than 22/7)
>
Try "A History of Pi" by Peter Beckman, ISBN 0-312-38185-9,
St. Martin's Press, N.Y.  (List price $8.95).  This book contains
lots of different methods.  It omits my personal favorite, a continued
fraction method worked up by Bill Gosper at M.I.T. years ago...
In all methods, the way is to note that something converges to pi or one
of its multiples.  Some series, for example, or the number of marbles 
dropped into a big circle.  Then calculate that.

>Also, can someone who teaches (or has just gone through some beginning
>(university level) math courses recomend some reading for me. I would like to
>progress a little faster than my school as they are still reviewing
For calculus, Buck's Calculus is great for quick students.  For
younger folk, "A History of Mathematics" by Neuman is a great series
of reads (although somewhat dated in some areas)..
Newsgroups: sci.math
From: victor@watson.ibm.com (Victor Miller)
Subject: Re: need proof:  (1 + 1/n)^n ==> e
Date: Wed, 30 Dec 1992 15:47:55 GMT
Reply-To: victor@watson.ibm.com
Disclaimer: This posting represents the poster's views, not necessarily those of IBM
	<1992Dec29.094842.3685@CSD-NewsHost.Stanford.EDU>
Organization: IBM, T.J. Watson Research Center

The following simple proof comes from "Inequalities" by P. Korovkin,
Blaidell Scientific paperbacks.

set x_n = (1+1/n)^n, and y_n = (1+1/n)^{n+1}.

We show that x_n is monotone increasing and y_n is monotone
descreasing.  Since x_n < y_n we find that they both approach a common
limit, which we call e.

Proofs:

We use the inequality of the arithmetic and geometric mean, in the
following form:

(a b^n)^{1/(n+1)} <= (a + n b)/(n+1).

If we let a=1, and b = (1+1/n), and raise both side to the (n+1)st
power, we find:

x_n <= ((1 + n(1+1/n))/(n+1))^{n+1} = (1+1/(n+1))^{n+1} = x_{n+1}.

Now set z_n = (1-1/n)^n. As above, we set a=1, and b=(1-1/n), we get

z_n <= ((1 + n(1-1/n))/(n+1))^{n+1} = (1 - 1/(n+1))^{n+1} = z_{n+1}.

Now observe that y_n = 1/z_{n+1}, so y_n is decreasing.  QED



--
			Victor S. Miller
			Vnet and Bitnet:  VICTOR at WATSON
			Internet: victor@watson.ibm.com
			IBM, TJ Watson Research Center
Xref: sparky sci.math:17343 sci.math.stat:2667
Newsgroups: sci.math,sci.math.stat
Subject: FK Hwang's Email Address Wanted  
From: geoff@tahi.isor.vuw.ac.nz (Geoffrey Grimwood)
Date: Wed, 23 Dec 1992 02:27:00 GMT
Organization: Institute of Statistics and Operations Research, VUW, Wellington, NZ


I am after the email address of FK Hwang of AT&T Bell Laboratories, Murray Hill,
New Jersey, USA. This address is given in a reference in a recent paper in
the European Journal of Operational Research 58 (1992) 293-300. The article was
on Stiener problems.

Regards

Geoff Grimwood
Institute of Statistics and Operations Research
Wellington
NEW ZEALAND

geoff@isor.vuw.ac.nz
Xref: sparky sci.math:17604 sci.philosophy.tech:4674