HDTenEightyP/NetNews huggingface dataset:
From: wrightd@math.okstate.edu (David J. Wright)
Newsgroups: sci.math
Subject: Question on Putnam B6
Summary: Trying to prove a stronger statement.
Keywords: Putnam Exam, Problems
Date: 23 Dec 92 21:26:32 GMT
Organization: Oklahoma State University, Math Department



Well, I've been thinking about B6 now, and can't figure out
the truth of the matter. So I might as well ask. Of course,
I understand the solution to the stated problem, but it's the
unstated problems that are bugging me.

I can prove that if n is odd, then |M| must be 1. This is a
consequence of each A^2 = +- I and the stated hypotheses.

Also, if M is a valid set of matrices of degree n, then

	 M' = { ( +- A   0         (  0   +- A
				0    A )  and     A     0  ) ,  A \in M }

is a valid set of matrices of degree 2n. Note that 
		 Card( M' ) = 4 Card( M )

Moreover, if n = 2m is even, then after conjugation 
M must contain    ( 0  -I
					I   0 )
again using m x m block notation.

If I could just show that after another conjugation M also
contains ( -I  0
			0  I )
then I would be done because that would imply that M arises 
from a valid set of matrices of degree m by the above construction.

However, I'm not sure that that last statement is true. Still I 
would believe the maximal cardinality in degree n is 
2^2k where 2^k exactly divides n.

Anyway, it was an interesting problem.
Xref: sparky sci.math:17518 sci.physics:21900
From: bhoughto@sedona.intel.com (Blair P. Houghton)
Newsgroups: sci.math,sci.physics
Subject: Re: Bayes' theorem and QM
Date: 30 Dec 1992 20:37:47 GMT
Organization: Intel Corp., Chandler, Arizona
NNTP-Posting-Host: stealth.intel.com

In article <1992Dec24.101452.16194@oracorp.com> daryl@oracorp.com (Daryl McCullough) writes:
>It would be nice if the volume of a region of space were always
>well-defined, but it is not. A demonstration due to Banach and Tarski
>showed that it is possible (mathematically, rather than physically
>possible) to decompose a sphere into a finite number of pieces and
>then recombine them by rotations and translations to get two complete
>spheres. It is easy to see that these pieces cannot possibly have
>volumes, since that would lead to the conclusion that the volume of
>two spheres equals the volume of one sphere.
>
>So one cannot always assume that *every* set has a measure (or volume,
>or probability).

I'll buy the explanation (conditioned on the conjecture
that such a situation might exist, which as yet isn't
anything more than conjecture), but not the example.

The two spheres thus formed do indeed have the same volume
sum as the original sphere, but each has less volume than
the original, or else they weren't composed of a finite
number of pieces[*], or else when constructed they contained
gaps, internally.

That, or their "volume" is fractal, being the effective
volume of a convoluted surface, and therefore isn't
actually of order 3 but of some order less than 3 and
greater than 2.  This way you get a finite number of pieces
but some pieces are composed of an infinite number of
infinitesimal objects connected by infinitesimal objects,
e.g. concentric spheres of rational diameters connected
by a single diameter, leaving concentric spheres of
irrational diameters connected by a single chord displaced
from the diameter by an irrational, infinitesimal amount (i.e.,
tangent to the smallest spherical shell of irrational diameter).

And it might even be "possible" physically; imagine a large
crystal of NaCl carved to be spherical.  Now separate
disintegrate it so that you have two spheres, one only of
Na+ ions and one only of Cl- ions, with each ion in its
original position wrt the center of mass of its own kind.
Their masses are each now less than the original, but their
"volumes" are each at least as large (likely larger and
expanding at a fantastic rate, unless you do something
interesting like containing them inside inert, solid shells
for the purpose of argument).

But that's beside the point.

Are there any constraints on the mathematics of "quantum
probabilities" that are similar to Sigma algebras for
"classical probabilities?"

				--Blair
				  "Beside the point is of
				   course another point."
Newsgroups: sci.math
From: pkeller@sam.math.ethz.ch (Philipp Keller)
Subject: Self-Avoiding Random Walks
Organization: Seminar for Applied Mathematics, ETH Zurich.
Date: Wed, 23 Dec 1992 11:23:17 GMT

I was playing around with my computer and tried to program
a self avoiding random walk in 2 dimensions. 
The 'particle' can move in any direction (k*pi/2) except to
those places which it has already before occupied.
The steplength is constant 1 unit.
After some time this particle is trapped because it can't 
turn in any direction anymore:

 for example       ______
                   |   _ |
              start   |__|

It seems to be that the average length of a path is
about 116 units.
I was wondering if there is any proof of this or if
this a yet unsolved problem and if there is some good
literature about this.

pkeller@sam.math.ethz.ch

                       
Newsgroups: sci.math
From: rjk@world.std.com (robert j kolker)
Subject: Help with a category th. problem (not homework)
Keywords: Category Theory, CLosed Cartesion Categories
Organization: The World Public Access UNIX, Brookline, MA
Date: Fri, 25 Dec 1992 16:18:51 GMT

I need an example of a small category which has products and a
terminal element, but is not a closed cartesian category. Any
help will be gratefuly received. Pls post to me by e-mail. If
anything really unusual comes my way I will post to the group.

Thanks in advance. Merry winter solstice.

Bob Kolker


-- 
"If you can't love the Constitution, then at least hate the Government"
From: sitarama@cps.msu.edu (Kocherlakota Sitarama)
Newsgroups: sci.math
Subject: Re: Two problems
Date: 31 Dec 1992 05:47:42 GMT
Organization: Dept. of Computer Science, Michigan State University
Reply-To: sitarama@cps.msu.edu (Kocherlakota Sitarama)
NNTP-Posting-Host: indian.cps.msu.edu
Originator: sitarama@indian.cps.msu.edu

The second problem is a famous problem called 
Problem Des' Menages

You can count the number of ways that we can arrange the couple
with man not sitting next to his wife. Actually this problem is 
a combinatorial problem and can be formulated as placing rooks
on a chess board. And from the calculating the probability is easy.

If there are n couples the number of such seatings is given as 

    n 
--------
\        2n                              k
 \     --------* C(2n-k,k) * (n-k) * (-1)
 /      2n - k 
/
---------
  k = 0 


I have a two page proof of that. But u can find, I think, find
the proof any good book on comibinatorics. Such as Richard Stanlesy
"Enumertive Combinatorics"


Let me know if you need more help on this.

Swamy
=======================================
Sita Rama Swamy Kocherlakota
Michagan State University, East Lansing
=======================================

Newsgroups: sci.math
From: schimmel@gandalf.ca (Fred Schimmel)
Subject: Re: The golden number
Organization: Gandalf Data Ltd.
Distribution: na
Date: Wed, 23 Dec 1992 04:10:40 GMT

In <BzF76u.B7x@unccsun.uncc.edu> sbardhan@uncc.edu (Soumendu Bardhan) writes:

>Will someone start discussing about it. I'm not sure  about its properties.

A good book with lots of discussions regarding the golden number is:

The Divine Proportion, A Study in Mathematical Beauty

by H. E. Huntley

published in 1970

ISBN 0-486-22254-3 (Dover paperback)
From: rouben@math9.math.umbc.edu (Rouben Rostamian)
Newsgroups: sci.math
Subject: Re: need help in calculus problem.
Date: 3 Jan 1993 15:28:25 GMT
Organization: University of Maryland Baltimore Campus
NNTP-Posting-Host: math9.math.umbc.edu

In article <1i688pINNls9@usenet.INS.CWRU.Edu> cd187@cleveland.Freenet.Edu (Aye Naing) writes:
>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.

Differentiate each equation wrt t, via the chain rule:
F_x x' + F_y y' + F_t = 0,
G_x x' + G_z y' + G_t = 0,
H_y y' + H_z z' + H_t = 0,
where F_x indicates the derivative of F wrt the x variable, etc.  (I know,
it's a bad notation, but you know what I mean.)
Solve this linear system of three equations for the three unknowns x', y', z'.
The vector (x',y',z') is the desired tangent vector.

To alleviate the concerns of another reader regarding the implicit
form of these derivatives,  let's note that no differential
equations are involved anywhere.  The solution vector is of the form:

(x'(t), y'(t), z'(t) ) = an an explicit function of x(t), y(t), z(t).  (*)

Each value of t corresponds to a point (x(t), y(t), z(t)) on the curve,
and a tangent vector, given by (*), at that point.

Of course if you are only given a specific point (x0, y0, z0) on the curve,
you first need to determine the correspoinding t value.  This amounts
to solving any one of the three original equations describing the curve.
For instance, one may solve
F(x0, y0, t0) = 0,
to compute t0 in terms of x0 and y0, and then proceed as before.  No
differential equations arise.

--
Rouben Rostamian
Newsgroups: sci.math
From: yeomans@austin.onu.edu (Charles Yeomans)
Subject: Re: What waves in light waves? (was Re: TIME HAS INERTIA)
Date: Mon, 21 Dec 1992 16:50:06 GMT
Organization: Ohio Northern University

In article <DREIER.92Dec18100700@durban.berkeley.edu>, dreier@durban.berkeley.edu (Roland Dreier) writes:
> 
> Even more troubling for me, as a student of modern algebraic geometry,
> is the concept of schemes.  How can one have a "scheme" in the absence
> of someone scheming?
> --
The schemimg was done by Grothdieck and Dieudonne, who sat around thinking
of a way to stick it to those preservering individuals who had plowed through
and mastered Weil's "Foundations".  You see, the whole EGA development
was nothing more than a big practical joke.  THus the name "schema"!

Charles Yeomans

P.S. This isn't historically accurate, as far as I know.
From: amirishs@acf9.nyu.edu (shaahin amiri sharifi)
Newsgroups: sci.math
Subject: complemented subspaces!
Summary: complemented subspaces!
Date: 30 Dec 92 16:50:27 GMT
Organization: New York University

Is that true, every closed subspace of C[0,1], with sup-norm topology,
has a closed complement?
Newsgroups: sci.math
From: schavema@fwi.uva.nl (John Schavemaker)
Subject: Help wanted with equation !
Organization: FWI, University of Amsterdam
Date: Mon, 21 Dec 1992 15:56:33 GMT

	Hi,

	Does anyone know how to solve the following equation:

		7 * y + 3 = x * x

	Both the variables y and x are integers. Otherwise stated:
	Can a square be the addition of a multiple of seven and
	three ? Any help appreciated, e-mail prefered.


				John Schavemaker

---
John Schavemaker
schavema@fwi.uva.nl
-- 
John Schavemaker
schavema@fwi.uva.nl
Newsgroups: sci.math
From: michaelg@Xenon.Stanford.EDU (Michael Greenwald)
Subject: Re: Rounding Rules
Organization: CS Department, Stanford University, California, USA
Date: 21 Dec 92 22:45:21 GMT

news@massey.ac.nz (USENET News System) writes:

>In article <LOTTO.92Dec21062820@math.math.berkeley.edu>, lotto@math.berkeley.edu (Ben Lotto) writes:
>> 
>> I was told way back in my undergraduate days that one should generally
>> "round to evens."  Someone recently explained the rationale for this
>> as follows.  Suppose we start with 1.49 and round in the traditional
>> manner twice.  First we would round to 1.5 and then to 2.  On the
>> other hand, if we round just once we get 1.  Rounding to evens
>> prevents us from getting different answers.

I missed the beginning of this thread, so pardon my asking a question
that might have been answered already.  Why is there a value in having
two rounding operations producing the identical result as one
(coarser?)  rounding operation?  Surely, since each application of
ROUND loses some information, it is unreasonable to expect identical
results?
Newsgroups: sci.math
From: atbat.Princeton.EDU!johnmpaz (John Manuel Paz)
Subject: nearby points
Originator: news@nimaster
Keywords: number theory
Organization: Princeton University
Date: Wed, 30 Dec 1992 03:36:48 GMT

hi,
	In "Number Theory" Hardy shows that the difference between an
irrational number and a rational approximation is:

	| r - p/q | <= 1/q^2,	0<p<=q, r irrational, p and q integers.

Another interpretation of this is to consider this as the nearest point
of an approximating grid to a line of irrational slope.  I was wondering
if anyone could tell me where to find any results for curves with non-zero
curvature.  Thanks in advance.
From: ramachandran@amreto.enet.dec.com
Newsgroups: sci.math
Subject: Used Math Book/C Book wanted
Date: 30 Dec 92 19:51:39 GMT
Reply-To: ramachandran@amreto.enet.dec.com ()
Organization: Digital Equipment Corporation

Ii am looking for these used books,  to be used for a course on DISCRETE MATH, 
and  C programming, anyone wanna sell ? Please reply directly, appreciate it.

1. DISCRETE MATHEMATICS WITH COMPUTER SCIENCE APPLICATIONS
by KVARCIUS R, ROBINSON W   
PUBLISHED BY BENJAMIN CUMMING PUBLICATION


2. C - BY DISCOVERY, FOSTER, SCOTT
PUBLISHED BY JONES INC.

ram
Xref: sparky sci.math:17356 comp.edu:2243 misc.education:5518
From: haddadi@sipi.usc.edu (Navid Haddadi)
Newsgroups: sci.math,comp.edu,misc.education
Subject: Re: Integration  Was: Re: Student attitudes
Date: 23 Dec 1992 04:51:10 -0800
Organization: University of Southern California, Los Angeles, CA
NNTP-Posting-Host: sipi.usc.edu

In article <1992Dec18.182743.15553@galois.mit.edu> jbaez@riesz.mit.edu (John C. Baez) writes:
>> Integration is a purely formal exercise in which a formula is
>> transformed into another formula, using particularly odd rules.
>
>Actually, this sounds like a nonmathematician's definition of
>"mathematics"!  :-)

Actually, how does a mathematician define math? If we take math to be
an exercise in logic, then rules of logic that we use to make trivial
an otherwise nontrivial matter (i.e. give a proof down to AC or ZL) are
only a set of transformations operating on some language.
Navid
Newsgroups: sci.math
From: hammond@csc.albany.edu (William F. Hammond)
Subject: Re: Need: prpndcular dist from pt to line
Organization: Dept of Math & Stat, SUNYA, Albany, NY
	<kedlaya.725687324@husc.harvard.edu>
Date: 30 Dec 92 11:15:54

In article <kedlaya.725687324@husc.harvard.edu> kedlaya@husc8.harvard.edu
(Kiran Kedlaya) writes:

> ...
> More generally, in n-space the distance from the point
> (z_1, ..., z_n) to the line a_1x_1 + ... + a_nx_n + c = 0
> is just |a_1z_1 + ... + a_nz_n + c| divided by the square
> root of a_1^2 + ... + a_n^2.
> ...

When  n  is 3 (or more) this is a formula for distance from the
point  z  to the PLANE (or hyperplane) given by the single linear
equation.  An explanation of this formula can be found in most
current third semester calculus books.

That posting was in response to:

> From: ilan@seas.gwu.edu (Ilan Berkner)
> Newsgroups: sci.math
> Subject: Need: prpndcular dist from pt to line
> Date: 29 Dec 92 21:05:54 GMT
> Organization: George Washington University
> 
> Given a line, or line segment (I can do both), I need to find the 
> distance from a point (that may or may not be on the line) to that line.
> If the point is on the line, then the distance is zero, obviously.
> ...

                                         P
                                        .


                 _________________________________________
                A                                         B

In the picture above, which is a SCHEMATIC picture that could represent
any situation involving three points  A, B, and  P  in  n-dimensional
real Euclidean space, the simplest general way to find the distance
from  P  to the line  AB  is to take the LENGTH of the vector that
is the "perpendicular projection" of the vector  AP  [ = P - A ]
on the vector  AB = [ B - A ].

The "perpendicular projection" is the difference vector

                         AP - proj(AP, AB) ,

where  proj(AP, AB)  is the "(parallel) projection" of  AP  on  AB .
For "proj" one has the formula

                      proj(V,W) = (V.W/W.W) W ,

where "." is the scalar product (or "dot" product) of two vectors.
[Note that replacing  W  by  rW  for a positive scalar  r  does not
change proj(V,W);  that is, proj(V,W) depends on  W  only for its
"direction".]  More details are available in most current third
semester calculus books.

All of this is very easy to "code".  It involves only rational
arithmetic (quotients of integers) but for the extraction of a single
square root at the final stage in computing the length.

----------------------------------------------------------------------
William F. Hammond                   Dept. of Mathematics & Statistics
518-442-4625                         SUNYA, Albany, NY 12222 (U.S.A.)
hammond@csc.albany.edu               FAX: 518-442-4731
----------------------------------------------------------------------
Newsgroups: sci.math,sci.physics,sci.astro,sci.bio,sci.chem,misc.education
From: pg@sanitas.stortek.com (Paul Gilmartin)
Subject: Re: Is Math Hard?
Followup-To: sci.math,sci.physics,sci.astro,sci.bio,sci.chem,misc.education
Organization: Storage Technology Corp.
X-Newsreader: TIN [version 1.1 PL7]
Date: Thu, 24 Dec 1992 21:26:29 GMT

This thread began as commentary on the Talking Barbie doll that says, "Math
class is hard!"  Mattel discontinued that variant and agreed to replace
any doll whose repertoire contained the offending sentence.

NBC broadcast a followup a few days ago.  Mattel reports that five dolls
have been returned for replacement.  It's a much better deal to contact
a collector, who may offer as much as $150.  And the mother who started
the protest has not exchanged a doll.  Her daughter is attached to it,
and won't consider a replacement.
Newsgroups: sci.math
From: a722756@roper.mc.ti.com (W. Donald Rolph)
Subject: Re: TO ALL !!! -- End of Discussion, I hope
Originator: a722756@roper.mc.ti.com
Organization: Texas Instruments / Attleboro Mass / USA
Date: Mon, 21 Dec 1992 20:39:46 GMT


In a sense of fairness to0 all of us, may we all wish all of us a good seasons 
holidays!
-- 

Regards.
 
Don Rolph  a722756@pan.mc.ti.com WD3 MS10-13 (508)-699-1263
From: glenne@csd4.csd.uwm.edu (Neuromancer )
Newsgroups: sci.math
Subject: math dictionary
Date: 1 Jan 1993 17:22:41 GMT
Organization: Computing Services Division, University of Wisconsin - Milwaukee
Distribution: world
NNTP-Posting-Host: 129.89.7.4
Originator: glenne@csd4.csd.uwm.edu

Hi,
 
I bought _The Penguin DICTIONARY OF MATHEMATICS_.  Many times
I find the definitions either too cryptic or lacking enough
explanation.  Does anyone know of a matematical dictionary
for idiots that still contains useful and comprehensive
information?
 
Thanks in advance,
 
Glenn                  glenne@csd4.csd.uwm.edu
From: dont@execu.execu.com (Don Thompson)
Newsgroups: sci.math
Subject: Re: Math ( and other ) education.
Summary: No disrespect intended.
Date: 1 Jan 93 16:30:17 GMT
Distribution: na
Organization: Austin Dev. Center, Comshare Inc.


	Everyone please know that I meant no disrespect what-so-ever
towards the fine community college system in Austin, Texas, nor the persons
teaching therein.
-- 
________________________________________________________________________________
Don "Syco" Thompson                 |   I may be opinionated, but at least
Comshare Inc. dont@execu.execu.com  |   my opinions are my own.
--------------------------------------------------------------------------------
    "There's no kill like a guns kill".  Lt Commander Joe "Hoser" Satrapa, USN
--------------------------------------------------------------------------------
From: bryan@kolsky.tamu.edu (Bryan Milligan)
Newsgroups: sci.math.symbolic
Subject: Re: Maple V Release 2 (was Re: Derive)
Keywords: world
Date: 22 Dec 92 17:06:59 GMT
Organization: Texas A&M University, College Station, TX
NNTP-Posting-Host: kolsky.tamu.edu

In article <1992Dec21.143617.28533@math.toronto.edu>  
madore@math.toronto.edu (Blair F. Madore) writes:
> MathCAD is a great product that was primarily numerical at first.
> Now it has some good symbolics. If you're primarily interested in
> symbolics
> of course it's not the package for you. But many average users
> with minimal symbolic requirements will find MathCAD the tool of choice.

	I found it to be too slow on user input.  (Type, type,type,
wait for the characters to appear on the screen. Repeat.)  I also found
their upgrade policies a little expensive.  If you have minimal
symbolic requirments, use Derive.

--

Bryan Milligan
Department of Aerospace Engineering
Texas A&M University
bryan@kolsky.tamu.edu  (NeXT Mail accepted)
From: halldor@groebner.me.washington.edu (Halldor Magnusson)
Newsgroups: sci.math.symbolic
Subject: Mathematica  <-> Lisp
Date: 28 Dec 92 22:39:31 GMT
Article-I.D.: shelley.1hnvn3INNj85
Organization: University of Washington
NNTP-Posting-Host: groebner.me.washington.edu

Does anyone know of a code to translate Mathematica 
functions to Lisp functions, similar to CForm
in Mathematica.

Thanks
-Halldor
From: mstankus@oba.ucsd.edu (Mark Stankus)
Newsgroups: sci.math.symbolic
Subject: Bug: Mma thinks Sqrt[3] is rational
Date: 3 Jan 93 07:40:47 GMT
Distribution: usa
Organization: Mathematics @ UCSD

Check out this seession. Sometimes gives a decimal approximation
to Sqrt[3] instead of just Sqrt[3].

In[126]:= xx = Sqrt[1-r^2]

DialogIndent[0]Out[126]= (1 - r^2)^(1/2)

In[127]:= xx//.r->0.5

DialogIndent[0]Out[127]= 0.866025403784439

In[128]:= (* Now  -- the same thing happens *)

In[129]:= 1-r^2 /.r->0.5

DialogIndent[0]Out[129]= 0.75

In[130]:= Sqrt[%]

DialogIndent[0]Out[130]= 0.866025403784439

In[131]:= (* Now 0.75 = 3/4 *)

In[132]:= Sqrt[3/4]

DialogIndent[0]Out[132]= 3^(1/2)/2

In[133]:= (* Sqrt[3] is not rational *)

-- 
mstankus
mstankus@oba 
Newsgroups: sci.math.symbolic
From: jaffer@zurich.ai.mit.edu (Aubrey Jaffer)
Subject: Book "Algorithms for Computer Algebra" Authors
Organization: M.I.T. Artificial Intelligence Lab.
Date: Mon, 4 Jan 1993 03:36:34 GMT

I have found some minor errors in "Algorithms for Computer Algebra".
What are the email adresses of the authors (Keith O. Geddes, Stephen
R. Czapor, and George Labahn)?
Newsgroups: sci.math.symbolic
From: katherle@daisy.uwaterloo.ca (Kate Atherley)
Subject: Re: Maple V graphics on PC
Organization: University of Waterloo
Date: Thu, 31 Dec 1992 15:05:27 GMT

In article <15275.2b41c8fc@ohstpy.mps.ohio-state.edu> klinich@ohstpy.mps.ohio-state.edu writes:
>Help!!
>  I am running Maple V on a '386 PC and cannot figure out how to print true
>graphics other other than just character graphics.  The version I have is A
>site-licensed version from the university, and I'm sure that it is  a
>full-blown version.  How do I do it? 

All that you need to do is set the interface variable plotdevice
appropriately.  For vga graphics, the command would be
interface(plotdevice=vga);

For more information,  please contact Maple Technical Support
at support@maplesoft.on.ca.

Kate
Waterloo Maple Software Technical Support

 (please do not reply to the address from which I am posting;
 all replies should go to support@maplesoft.on.ca)
Newsgroups: sci.math.symbolic
From: madore@math.toronto.edu (Blair F. Madore)
Subject: Re: Help with user defined functions in Maple.
Organization: Department of Mathematics, University of Toronto
Date: Mon, 21 Dec 92 14:46:00 GMT

In article <1992Dec17.060755.53708@ns1.cc.lehigh.edu> jmp1@ns1.cc.lehigh.edu (JEFFREY MICHAEL PARSONS) writes:
>I tried defining a function in Maple V r1.1 like this:
>
>f := proc(x)  if x<0 then -1 else 1 fi;  end;
>
>I could then type f(3) or f(-100) and get the correct result.  The problem is
>that I can't integrate it, etc.  I always get:
>
>Error, (in f) cannot evaluate boolean.
>
>Is there a better way to be doing this kind of thing?

What you may want to look at is somehting called algorithmic differentiation.
It's in the Maple Share library. It allows you to differentiate procedures
like the one you've defined.

Off the top of my head I can't remember the ftp address for the share library,
but I'm sure info@maplesoft.ont.ca would help you.

Blair