HDTenEightyP/NetNews huggingface dataset:
From: mccolm@darwin.math.usf.edu. (Gregory McColm)
Newsgroups: sci.math
Subject: Re: Most important event in the history of mat
Date: 12 Oct 92 17:05:15 GMT
Organization: Univ. of South Florida, Math Department


The most important mathematical accomplishment ... ?
I haven't seen the following nominated by anyone yet:

The discovery that ordinal and cardinal finite numbers 
coincide;  the discovery that the numbers go on forever
(prehistoric?).

The discovery of idealizable shapes---circles, triangles, 
etc (nearly prehistoric?).

The decision that theorems need proofs, either for 
practical reasons (Thales) or religious reasons 
(Pythagoras).

Number as the first foundation of mathematics (Pythagoras).

Geometry as the second foundation of mathematics (Plato et 
al).

The destruction of Logic/Set Theory as the third foundation 
(stay tuned).

The use of idealized forms to represent scientific problems 
(Galileo), and the notion that theories merely describe, 
but do not explain (Newton) much less provide The Truth 
(Kant).

-----Greg McColm

Devil's advocate:  The launching of Crelle's journal.
From: adumi-v@acsu.buffalo.edu (virgil adumitroaie)
Newsgroups: sci.math
Subject: Hint?
Date: 9 Oct 92 00:29:34 GMT
Organization: UB
Originator: adumi-v@cfd11.eng.buffalo.edu





	I wonder if somebody could give me a hand in solving
an easy problem, which I did it once some time ago, but it
seems that it doesn't work anymore (and I threw away the
scratch notes).

The problem is to demonstrate the tensorial relation

  E   E   = d  d  - d  d
   ijk pqk   ip jq   iq jp

where E is the alternating tensor and d the Kronecker tensor.

The way I did it once was using the representation of 

		      | d    d    d  |
          ^   ^   ^   |  ii   ij   ik|
E as E   =e .(e x e )=| d    d    d  |
      ijk  i   j   k  |  ji   jj   jk|
                      | d    d    d  |
                      |  ki   kj   kk|
      ^
where e  are the orthogonal unit vectors. The same thing for
       i 

E   , and then multiplying the two matrices I got the desired 
 pqk

relation, but now I get a mess. If you have seen this idea of

demonstration anywhere else, or you can solve in this way, please

give me a hint.


Thanks,
 
Virgil
Newsgroups: sci.math
From: jbaez@riesz.mit.edu (John C. Baez)
Subject: Re: Mattel says "Math is tough."
Organization: MIT Department of Mathematics, Cambridge, MA
Date: Thu, 15 Oct 92 03:04:32 GMT

In article <9247@amsaa-cleo.brl.mil> matt@amsaa-cleo.brl.mil (Matt Rosenblatt) writes:

>According to this, fair competition in the "marketplace of ideas"
>between the doll's message that "math is hard" and the educator's
>message that "math is not hard" is not good enough.  The doll's
>message must be suppressed, so that *no one* -- not even a mother
>who believes that math *really is* hard -- will be able to buy
>this particular talking doll for her daughter.

Suppressed???  We're not talking about passing a law here or even suing
Mattel.  It doesn't count as "suppressing" the doll's message if you
call Mattel's 800 number and tell them you think the doll sucks.
Presumably they don't mind some feedback or they wouldn't have a toll-free
number.  Marketplace principles do not require us to nod and smile
whenever a company releases a product.  Griping is allowed.
From: fenthe@drycas.club.cc.cmu.edu
Newsgroups: sci.math
Subject: P=NP?
Date: 16 Oct 92 13:13:37 GMT
Article-I.D.: drycas.1992Oct16.181337.2291
Organization: Carnegie Mellon Computer Club


 Now, I guess I would have heard something about this if it had been resolved,
but -- has anyone yet (dis)proved P=NP?

 Email answers, please -- sorry to waste this much bandwith. I'll summarise if
there's interest.

 (oh, and ideally answers of the level of 'yes', or 'no' -- I suspect anything
much beyond that'll go straight over my head.. <grin> Pointers to literature
would be nice. )

 Thanks.
-- 
Daniel Mitchell = Fenthe Marten = fenthe@drycas.club.cc.cmu.edu =
m91djm@ecs.ox.ac.uk = dmitchell@cix.compulink.co.uk = bi furry juggler
Snailmail: 18, High St // Earls Colne // Essex CO6 2PA // ENGLAND
Newsgroups: sci.math
From: seal@leonardo.Jpl.Nasa.Gov (David Seal)
Subject: math programs with configurable or arbitrary floating point accuracy
Organization: Jet Propulsion Laboratory
Date: Wed, 14 Oct 1992 17:49:48 GMT

Having been duly inspired by an episode of northern exposure i tried
fiddling with ramanujan's and borwein and borwein's formulas for
computing pi on my mac.  however, the floating point accuracy
for MATLAB (which i was using) isn't settable and i can't get past
the sixteenth decimal place or so.  other mac programs or ways of computing
pi?  thanks.

ds

--
-----------------------------------------------------------------------------
David Seal                 |  Jet Propulsion Laboratory  |     sunset: 7:54pm
seal@leonardo.Jpl.Nasa.Gov |       Mission Design        |   temp: 82 degrees
Newsgroups: sci.math
From: alvisd@bronze.ucs.indiana.edu (dean alvis)
Subject: number theory question
Organization: Indiana University
Date: Wed, 14 Oct 1992 19:17:08 GMT

Let $p$ be an odd prime, and assume $\beta$ is an algebraic
integer of the form $$\beta = \sum_\omega \mu_\omega (1-\omega),$$
where the coefficients $\mu_\omega$ are nonnegative rational
integers and $\omega$ ranges over the primitive complex $p$-th
roots of unity.  Assume further that $\beta$ is irrational,
so the coefficients don't assume a constant value, that the
coefficients of $\beta$ are relatively prime, and that
the product of the algebraic conjugates of $\beta$ is a power
of $p$ (so the norm of $\beta$, in the field-theoretic sense,
is a power of $p$).  Does it necessarily follow that $\beta$
has the form $1-\omega$ or $2 Re(1-\omega)$?

Any information on this problem would be helpful. 
Please respond via e-mail to alvisd@natasha.iusb.indiana.edu

Xref: sparky sci.math:13186 rec.music.classical:14264
From: jaeger@buphy.bu.edu (Gregg Jaeger)
Newsgroups: sci.math,rec.music.classical
Subject: Degrees and Departments (Re: Glass and math)
Date: 14 Oct 92 19:28:39 GMT
Followup-To: sci.math
Organization: Boston University Physics Department

In article <1bhqnnINN77v@calvin.usc.edu> alves@calvin.usc.edu (William Alves) writes:
>In article <1992Oct13.223043.16366@husc3.harvard.edu> elkies@ramanujan.harvard.edu (Noam Elkies) writes:
>>In article <1992Oct13.202553.7542@aio.jsc.nasa.gov>
>>>I believe Phillip Glass (the American Composer) has a background in 
>>>mathematics.  Can someone verify this?

>I don't think Glass ever majored in math. However, Steve Reich's undergrad
>degree is in Philosophy.

>Milton Babbitt finally received his doctorate in math from Princeton -
>several decades late. They had originally rejected his dissertation,
>which I believe concerned serial theory in music. The Princeton pundits
>now say that the dissertation was too far ahead of its time to have
>been appreciated when he wrote it.

This is no doubt, not an isolated incident.

It reminds me of the story of the positivist philosopher Rudolf
Carnap, who wanted to do a logical analysis of Einstein's theory
of relativity for his physics thesis; the physics department told
him to go to the philosophy department! Now `axiomatic' approaches
to physical theories abound.


Gregg


-- 
Gregg Jaeger    (jaeger@buphy.bu.edu)          VOTE PEROT  VOTE PEROT       
If you think the Republicans screwed up the country, can you afford to
see what the Democrats will do?!   ->BEWARE OF SLICK-WILLY CLINTON!!<-
Newsgroups: sci.math
From: kwright@hoss.unl.edu (Kevin Wright)
Subject: Why is slope denoted by m?
Organization: University of Nebraska - Lincoln
Date: Wed, 7 Oct 1992 18:14:05 GMT

We use Z for the integers because of the German 'Zahlen' and we have
F for a closed set because of the French 'Ferme' and we have R for rings 
because of the English word 'ring.'  

What is the origin of m for denoting the slope of a line?

--
Kevin Wright, Univ of Nebraska - Lincoln.  E-mail: kwright@hoss.unl.edu
From: cxm7@po.CWRU.Edu (Colin Mclarty)
Newsgroups: sci.math
Subject: help with recursive functions
Date: 8 Oct 1992 02:41:16 GMT
Organization: Case Western Reserve University, Cleveland, OH (USA)
Reply-To: cxm7@po.CWRU.Edu (Colin Mclarty)
NNTP-Posting-Host: slc5.ins.cwru.edu


	I'd like some help with partial recursive functions which
do not extend to (total) recursive ones.  I can prove there is no
effective routine for extending all partials to total recursive
functions, but I do not see how to prove there are particular
partial recursive functions that do not extend to recursive.  Are
there typical methods from proving this in particular cases?

Colin McLarty
From: falatic@mentor.cc.purdue.edu (MacGyver)
Newsgroups: sci.math
Subject: Calculating pi: help!
Date: 13 Oct 92 22:36:13 GMT
Organization: Purdue University Computing Center


	Just a quick query: I need a program, in either Unix C or Borland/
Turbo C, that will calculate Pi as far as I want... I can get it to 17 
digits, but I want to get it to an UNLIMITED number of digits (I know, it'd
be slow, but I just want to do it.
	Also, if anyone has the value of Pi in a file, to say 30 or more 
digits, I'd like that also (to doublecheck...)

Please reply via >E-Mail<, since I don't read news very much.... (address
is in the .sig below)
******************************************************************************
    This .sig may not be reproduced, in whole or in part, by any means, 
                           including but not limited to:   
   Mechanical reprints, electronic storage or scanning, theatrical release, 
   musical ballads, word of mouth, sign language, braille, pantomime, hetero- 
   or asexual reproduction, genetic engineering, or inclusion in other .sigs. 
	 .SIG  (c) 1992  Martin F. Falatic, All rights Reserved
			falatic@mentor.cc.purdue.edu
     "What? ME?!? No way!!!" - MacGyver, the birthday reunion episode
******************************************************************************
Newsgroups: sci.math
From: ilan@leland.Stanford.EDU (ilan vardi)
Subject: Re: FAREY
Organization: DSG, Stanford University, CA 94305, USA
Date: Fri, 16 Oct 92 21:21:06 GMT

In article <1992Oct16.170803.14345@nntp.uoregon.edu> scavo@cie.uoregon.edu (Tom Scavo) writes:
>In article <168827A63.DUENTSCH@dosuni1.rz.uni-osnabrueck.de> DUENTSCH@dosuni1.rz.uni-osnabrueck.de writes:
>>In article <98687@bu.edu> rehman@math.bu.edu (Naved Rehman) writes:

>Ian Stewart also mentions the Farey sequence in his _Does God Play Dice?_
>(Basil-Blackwell, 1989?).

On the other hand, I would not trust Ian Stewart about such things.
In one of his books he states that the Riemann hypothesis is
equivalent to

  pi(x) = x/log(x) + O(sqrt(x) log^2(x))

so he is clearly writing about something that he has no clue about.
In fact, de la Valle Poussin showed that 

  pi(x) = li(x) + O(x exp(-c sqrt(log(x))))

where 

  li(x) = int_2^x 1/log(x) dx 

and integration by parts gives

  li(x) = x/log(x) +  x/log^2(x) + ...  
           
          + (k-1)! x/log^k(x) + O(x/log^{k+1}(x))

so 

  pi(x) = x/log(x) + x/log^2(x) + O(x/log^3 (x)).

The point is that a popular account of something as well understood
and easy to look up as this should be extremely accurate.

Moreover, I find the way he writes his column in Scientific American
to be totally insulting. If the material were at all interesting then
there would be no reason to dress it up as some fable.

-ilan
From: gjm11@cus.cam.ac.uk (G.J. McCaughan)
Newsgroups: sci.math
Subject: Re: Do you know ?
Date: 16 Oct 92 16:40:29 GMT
Organization: U of Cambridge, England

In article <1992Oct16.050019.25103@noose.ecn.purdue.edu> kavuri@lips.ecn.purdue.edu (Surya N Kavuri ) writes:

>  Can you give me a function on an interval [a b] which is
>  not differentiable anywhere on that interval ?

I presume you want it to be continuous too.

For k=1,2,3,... let f_k be the function whiose graph starts at (a,0) and
then zig-zags up and down with slope alternately +1 and -1, changing direction
every 2^(-k).(a-b). So the graph of f_k has 2^(k-1) pointy tops, and its
maximum value is 2(-k).

Let f be the sum over all k of f_k. Then it's very easy to show that f is
continuous; but also f is not differentiable anywhere; to show f is not
differentiable at x, take successively nearer and nearer points of the form
a+t(a-b)/2^k (there are points of this form arbitrarily near x) and look at
the gradients of the chords joining x to them, which go haywire.

-- 
Gareth McCaughan     Dept. of Pure Mathematics & Mathematical Statistics,
gjm11@cus.cam.ac.uk  Cambridge University, England.    [Research student]
Newsgroups: sci.math
From: crb7q@kelvin.seas.Virginia.EDU (Cameron Randale Bass)
Subject: Re: Mattel says "Math is tough."
Organization: University of Virginia
Date: Wed, 7 Oct 1992 15:08:50 GMT

In article <Bvr62B.2BA@mentor.cc.purdue.edu> hrubin@mentor.cc.purdue.edu (Herman Rubin) writes:
>In article <1992Oct7.005439.193@murdoch.acc.Virginia.EDU> crb7q@kelvin.seas.Virginia.EDU (Cameron Randale Bass) writes:
>>In article <1at131INNc50@roundup.crhc.uiuc.edu> hougen@vision.csl.uiuc.edu (Darrell Roy Hougen) writes:
>
>>>In summary, I don't believe that math is hard.  Thinking is hard, but
>>>who would want to discourage that?
>
>>     Try teaching multiplication to a seven-year-old.  That way, 
>>     you get to see how 'hard' it is from both sides.
>
>The way it is usually taught, it is almost meaningless, which helps to
>make it hard.  Young children can be easily taught the structure of the
>number system; with this, the notion of multiplication becomes easy.
>
>This does not make it much easier to learn how to carry out multiplication,
>but it may motivate it.
>
>Properly explained, and this is almost never done, the concepts are not
>all that difficult, although practice and application are necessary to
>really understand them.  The notion of variable, possibly the most important
>in mathematics, is essentially the notion of pronoun.  The notions of 
>theorem and proof are extremely important, and not well taught; knowing
>these does not make one adept at producing them.  It does not make one
>adept at using them, either, but that is of comparable difficulty to
>writing sentences and paragraphs, and is even similar to that.

     Try teaching sentence and paragraph writing to a young child.

     Judging by the results of former students, they often are not 
     taught well either.

                                 dale bass
-- 
C. R. Bass                                           crb7q@virginia.edu
Department of Mechanical and Aerospace Engineering
University of Virginia
Charlottesville, Virginia                            (804) 924-7926
Newsgroups: sci.math
From: vhansen@ipfs.bau-verm.uni-karlsruhe.de (Wolfgang von Hansen)
Subject: Question on numerical integration
Organization: IPF, University of Karlsruhe
Date: Wed, 7 Oct 1992 11:34:01 GMT

How can one calculate things like

 a                oo
Int f(x) dx  or  Int f(x) dx
-oo               a

numerically. I know how to do such things with finite limits,
but I've got no idea how to deal with infinite limits.

Thanks in advance, Wolfgang
From: conrad@germain.harvard.edu (Keith Conrad)
Newsgroups: sci.math
Subject: p-adic gamma again-sorry
Date: 15 Oct 92 03:57:30 GMT
Article-I.D.: husc3.1992Oct14.235731.16404
Distribution: world
Organization: Dept. of Math, Harvard Univ.

I apologize for my last message, whose first half didn't appear.  I'll mail
it correctly at a later time.

Keith Conrad
Date: Monday, 12 Oct 1992 19:52:23 EST
From: <RVESTERM@vma.cc.nd.edu>
Newsgroups: sci.math
Subject: Re: Another GRE question for you folks
Distribution: world
 <1bcao2INN8c8@fido.asd.sgi.com>

i took the gre's about one year ago.  the problem that i couldn't decide
upon an answer for was part of the general math, not the math subject.
it was a "a if the first thing is greater, b if the second is greater,
c if it can't be determined, and d if they're equal" type.  there was
a picture of a circle, and four points on it (A, B, C and D).  there was
a line segment AB, and a line segment BD.  they wanted to know which, if
either, was longer.

the correct answer, of course, is that it can't be determined; they never
said that the line segments intersect in the center of the circle or not.
this is the answer i put down.  however, the picture that they gave with
the problem sure looked like the line segments intersected damn close to
the center; this led me to believe that they wanted the answer "the two
segments are equal".

to this day, i don't know whether i was credited with a correct answer
or not.
From: masfeb@gdr.bath.ac.uk (F E Burstall)
Newsgroups: sci.math
Subject: Re: Spectum of a Lie group ...
Date: 14 Oct 92 19:31:48 GMT
Organization: School of Mathematics, University of Bath, UK

In the referenced article, kwhyte@dent.uchicago.edu (Kevin Whyte) writes:
>
>
>  Let G be a compact semi-simple Lie group.  The killing
>form gives a canonical Riemannian metric, and hence a 
>laplacian acting on smooth functions.  What are the eigen-values
>of this laplacian?
>
>  L (the laplacian) is a G invariant elliptic operator, on, say
>L2(G).  Hence the eigenspaces  are finite dimensional and G invariant.
>Peter-Weyl then tells us that each one of these is just some sum
>of irreduciple reps. of G (each of which occurs as many times as
>its weight).  Thus, given an irreducible rep. of G, it occurs in at
>most n such eigenspaces (if G is an n dimensional rep.), so it
>should have n positive real numbers associated to it. What are they?
>
>-Kevin
>kwhyte@math.uchicago.edu


These questions are essentially algebraic: the action of the Laplacian on
smooth functions is just that of the Casimir element in the universal
envelopping algebra.  Now on an irred subrep, the eigenvalue of the Casimir is
determined entirely by the highest weight of the subrep via a simple formula
which is something like

evalue=(l,l+2r)

where l is the highest wt and r is half the sum of the positive roots (I cannot
remember the exact formula right now...).  This answers yr questions:

1) The evals of the Laplacian are the numbers (l,l+2r) (or whatever) as l
ranges over all dominant weights (all irred reps appear in the regular rep).

2) A given irred only appears in ONE eigenspace of the Laplacian.

Hope this helps--Fran
Date: Tuesday, 13 Oct 1992 15:59:11 EST
From: <RVESTERM@vma.cc.nd.edu>
Newsgroups: sci.math
Subject: Re: Another GRE question for you folks
 <1bcao2INN8c8@fido.asd.sgi.com> <92286.195223RVESTERM@vma.cc.nd.edu>
 <1992Oct13.192415.8003@math.utexas.edu>

at the beginning of the section, it said things like, "what looks like
a circle is a circle.  what looks like a square is a square."  but no
"what looks like a point exactly in the center of a circle is a point
exactly in the center of a circle."
From: shaw@toadflax.UCDavis.EDU (Rob Shaw)
Newsgroups: sci.math
Subject: Penrose Tiles / Beatty Seq's.
Date: 10 Oct 92 03:45:28 GMT
Reply-To: shaw@toadflax.UCDavis.EDU (Rob Shaw)
Followup-To: comp.theory,rec.puzzles
Organization: UC Davis, EECS Division of Computer Science


A while ago I was reading a Gardner-ish rec math book, and
it contained an update about Penrose tilings. I would 
appreciate anyone giving me pointers to the material below,
since I have completely forgotten where I read this.

The are only a handful of Penrose (kite+dart) tilings as
shown by taking infinite strips across the tiling. These
strips come in a sequence containing "thin" and "thick"
strips. The sequence is a Beatty sequence.

Something like 

10010101001010010010010...

Could be a Beatty sequence, since one of the two elements
always appears alone, and the other appears alone or in
pairs.

This book also described how successive powers of the 
golden ratio, rounded up and down form complementary
Beatty sequences, and moreover, that one of these
sequences is something that was previously thought
to only be computable by some recursive method that 
required calculating all the terms preceding the 
desired one.

This is all from memory, so I may have gotten a few things
confused...

Please, anyone who can give me pointers to books/articles
about this material, please post or email.

Thanx!

Rob
Newsgroups: sci.math
From: guckes@math.fu-berlin.de (Sven Guckes)
Subject: Re: Mattel says "Math is tough."
Originator: guckes@medusa
Organization: Free University of Berlin, Germany
Date: Mon, 12 Oct 1992 02:49:55 GMT

fsmgs@camelot.acf-lab.alaska.edu (Michael Schmahl [Black-Robe Mage]) writes:

>As a person who once was seven years old, I would like to say that I never  
>found multiplication hard, except for seven times six and seven times eight.   
>I could multiply and do long division since I was five.

The four random talks of the "Schmal" barbie:

"Math is easy! Multiplying is easy!"
"Seven times six is fourty-two. Seven times eight is fifty-six."
"I can multiply and do long division since I was five."
"Michael is bright!"

Back to math, folks. ;)
Newsgroups: sci.math
From: benjamin@athena.mit.edu (Benjamin J Renaud)
Subject: Order of stuff in prime field
Organization: Massachusetts Institute of Technology
Date: Wed, 14 Oct 1992 03:27:23 GMT

This editor is screwed up, so sorry for any weird layout..s a ut....

What is the order of Fn, the space of n dimensional row vectors, for F=Fp, that is F is a prime field? I am especially interested in a method that does not rely on the computation of the order of GLn(F) GLn for F=Fp


Benjamin
benjamin@athena.mit.edu  -- benjamin@ai.mit.edu (please reply theplease reply @ai if possibl

GOD this is so screwed up.. i have no idea what it will look like...
Newsgroups: sci.math
From: tusk@daimi.aau.dk (Martin M|ller Pedersen)
Subject: Magic Squares Orden 4 solved
Organization: DAIMI: Computer Science Department, Aarhus University, Denmark
Date: Thu, 15 Oct 92 07:35:15 GMT

It took 17 minute on my 486 to find all 880 two times and
about 15 minute to submite these which were equals.
If you are interest in the TP6.0 source please mail me.

There are two parts:

part 1: encode 
part 2: not encode

tusk@daimi.aau.dk
From: dik@cwi.nl (Dik T. Winter)
Newsgroups: sci.math
Subject: Re: Calculating pi: help!
Date: 15 Oct 92 02:09:57 GMT
Organization: CWI, Amsterdam

In article <stephen.719088307@mont> stephen@mont.cs.missouri.edu (Stephen Montgomery-Smith) writes:
 > In <7557@charon.cwi.nl> dik@cwi.nl (Dik T. Winter) writes:
The pi program I wrote with help of Jurjen Bos (who no longer works here).
 > 
 > I would be very interested to know how this program works.
 > 
I have gotten quite a few request about the program.  It is a bit
convoluted indeed (I ought to have submitted it to the obfuscated
C contest).  There are a few levels of obfuscation.  I will give
a some hints, and when time comes I might even reveal the innards.
(And to those who asked whether it is easy to get more digits by
changing some constants, the answer is no.  Quite a bit of error
analysis is needed.)
So, some hints:
1.  Standard C obfuscation.  Mostly C beautifiers help, but here:
2.  After beautifying you still see nothing, except a loop with as
    a body a loop with an empty body.  You have to move manually
    from the for statement to the bodies of the loops to see some
    structure, but:
3.  Some expressions are split over statements.  Strange enough the
    main reason was not so much to obfuscate, but to get the program
    as short as possible!  So look what those statements are doing
    and rearrange as you would write the expressions, but:
4.  We are finally there.  What are all those calculations doing?
    What is the relation between successive iterations?  And
    finally:
5.  Think about the cheapest way to calculate the digits of 'e',
    take some reference book (Abramovitz and Stegun is good enough),
    and you are done.
-- 
dik t. winter, cwi, kruislaan 413, 1098 sj  amsterdam, nederland
home: bovenover 215, 1025 jn  amsterdam, nederland; e-mail: dik@cwi.nl