HDTenEightyP/NetNews huggingface dataset:
From: asimov@wk223.nas.nasa.gov (Daniel A. Asimov)
Subject: Re: another trivial homology question
Organization: NAS, NASA Ames Research Center, Moffett Field, California
Date: Tue, 24 Nov 92 02:45:51 GMT

>In article <1992Nov23.150344.2734@crl.dec.com>, herlihy@crl.dec.com (Maurice
>Herlihy) writes: 
>Let D be an n-dimensional simplicial complex that is connected with trivial
>homology groups above dimension 0.  Is D necessarily homeomorphic to an n-disk?
>
J.H.C. Whitehead constructed a contractible open set in R^3 which is not 
homeomorphic to R^3.  This would have not only trivial homology groups, 
but also trivial homotopy groups as well, of course.

This can be represented by a 3-dimensional simplicial complex, but not a finite one.  

Dan Asimov
Mail Stop T045-1
NASA Ames Research Center
Moffett Field, CA 94035-1000

asimov@nas.nasa.gov
(415) 604-4799
Newsgroups: sci.math
From: frank@Cookie.secapl.com (Frank Adams)
Subject: Re: Most important event in the history of mathematics
Date: Tue, 17 Nov 1992 21:46:24 GMT
Organization: Security APL, Inc.

Here's a summary of the nominations I received, both by mail and on the net.
Since most respondents made no effort to choose just one, I am counting
nominations, not votes.

Essentially, only 3 items got more than one nomination apiece.  Clearly,
there is no consensus here.

4 The discovery of irrationals

3 The invention/discovery of the calculus.

1 The discovery that an axiomatic approach could have lots of consequences
1 Birth of the idea of proof from axioms ("Elements" or soon before)
1 The discovery by the Greeks that: (1) simple (obvious) geometric facts
  require proof; and (2) it is possible to provide proofs for them.
1 The decision that theorems need proofs
1 The publication of The Elements (Stoicheia) of Euclid.

1 Russell's paradox.

1 The Pythagorian theorem.

1 The solution of higher degree equations;

1 Diophantus' discovery of the idea of using symbols for quantities

1 Discovery of coordinate geometry

1 Realisation that issues of convergence etc. are harder than they look,
  leading to rigorisation of analysis

1 Riemann's paper on prime numbers and the zeta-function

1 Cantor's proof that 2^x>x

1 Discovery of the Lebesgue integral and measure

1 Discovery of generating functions

1 The first and second incompleteness theorems.

1 The discovery of zero

1 The discovery of the paradoxes of the infinite.

1 Counting on one's fingers.

1 The development of the decimal system.

1 The discovery of nonEuclidean geometry

1 The discovery that ordinal and cardinal finite numbers coincide.

1 The discovery that the numbers go on forever

1 The discovery of idealizable shapes---circles, triangles, etc

1 Number as the first foundation of mathematics.

1 Geometry as the second foundation of mathematics.

1 The use of idealized forms to represent scientific problems

1 The notion that theories merely describe, but do not explain or provide The
  Truth.


Newsgroups: sci.math
From: gm115@emu.pmms.cam.ac.uk (Gabor Megyesi)
Subject: Re:    1+1/2+1/3+1/4+...+1/n
Organization: DPMMS University of Cambridge
Date: Thu, 19 Nov 1992 14:45:22 GMT


sum 1+1/2+1/3+1/4+...+1/n is approximately log n+gamma, where gamma~0.577
is Euler's constant, so the smallest n for which the sum exceeds 100 is in
the range of e^100.

Gbor Megyesi
G.Megyesi@pmms.cam.ac.uk
Newsgroups: sci.math
From: bs@gauss.mitre.org (Robert D. Silverman)
Subject: Re: Prime test algorithm
Organization: Research Computer Facility, MITRE Corporation, Bedford, MA
Date: Thu, 19 Nov 1992 17:02:17 GMT

In article <BxuIp4.3ss@iat.holonet.net> rkinder@iat.holonet.net (Robert J. Kinder) writes:
:blom@husc15.harvard.edu writes:
:: Does anyone have C source code for an algorithm to determine whether an
:: enormous number (over 1000 decimal digits) is prime or composite?  I have
:: Derive and Mathematica for my 486, but they run slowly on some of my large
:: prime-test problems (546!-1) and I would like to be able to use my VAXstation
:: 4000-90.  I think I may also be able to compile Fortran, and maybe Pascal.  I
:: have the best luck with C programs because they are so portable.
:: 
:: Thanks in advance.
:: --Eric Blom
::   Harvard
:
:The best package seems to be Arjen Lenstra's arbitrary precision
:arithmethic package written in C, based on what I've read.
:
 
Actually, no. Arjen's package (unless he has improved it) works in 15
bit arithmetic as the RADIX. There are faster packages. PARI, Dik Winter's
package, mine, Peter Montgomery's are all faster than the version I have
of Arjen's code. (But they are less portable, having assembler code)
 
This is NOT to denigrate Arjen's code. It was written with portability, not 
speed, in mind.


:BigNum directory.  The file should be about 91KB in size.  This package
:has -, +, *, /, mod, primality testing, and exponentiation plus other
		      ^^^^^^^^^^^^^^^^^^  

You mean "probable prime testing". The code doesn't actually do primality
PROOFS. 
 
If you really want proofs, it is best to write to Francois Morain, or
Wieb Bosma and ask them for their code.
 
I will send my MPP code to anyone who writes *personally* and asks for it.
--
Bob Silverman
These are my opinions and not MITRE's.
Mitre Corporation, Bedford, MA 01730
"You can lead a horse's ass to knowledge, but you can't make him think"
Newsgroups: sci.math,sci.physics,sci.astro,sci.bio,sci.chem,misc.education
From: scottj@magic.dml.georgetown.edu (John L. Scott)
Subject: Re: What can we have for an educational system?
Followup-To: misc.education
Organization: J. Random Misconfigured Site
Date: Fri, 20 Nov 1992 17:11:24 GMT
X-Posted-From: iamac-1.dml.georgetown.edu
NNTP-Posting-Host: sol.ctr.columbia.edu


[NB: Follow-ups directed to misc.education]

In article <1992Nov19.004734.20143@linus.mitre.org>, bs@gauss.mitre.org
(Robert D. Silverman) wrote:
> Actually, at least in my experience, the conditions that would make 
> most PhD's happy are essentially impossible to obtain. Nothing the
> schools or school systems could do would provide what they want.
> 
> What they want of course is motivated students and students who
> are *interested* in learning. This is the responsibility of parents.
> Currently, cultural conditions in the U.S. are such that most people
> do not place a high value on education. The result? Students who
> don't give a shit.

I must disagree.  You are right, of course--without a proper parental
attitude a child is going to be hard to interest in learning; however, even
with proper parental attitude, the hours spent in the stupifying atmosphere
of today's schools can destroy a child's natural interest in learning.  The
"students who don't give a shit" you speak of may actually have been
created by the school system.  On this point, I highly recommend John
Holt's "How Children Fail" (and by all means, get the 2nd edition), among
many other books.  Parents are important, but so are the schools.

--John L. Scott
Newsgroups: sci.math
From: rlm7638@tamsun.tamu.edu (Jack McKinney)
Subject: Looking for name of group of order 12...
Organization: Texas A&M University, College Station
Date: Wed, 18 Nov 1992 19:44:40 GMT


     Here I go, with yet another group theory question. This one is of
etymology. There are five groups of order 12: The cyclic group of order
12 (Z_12), the direct product of the cyclic groups of orders 2 and 6
(Z_2 x Z_6), The alternating group on 4 objects (A_4), the dihedral
group of a 6-sided object (D_6), and then one more. This last one
I have always seen written as just 'T'. Can anyone tell me where this
name comes from?

           T={<a,b>: a^6=e, a^3=b^2, ba=a^5 b}

+---------------------------------------------------+------------------------+
| "I'll never be creul to electrons in a particle   | Jack McKinney          |
|  accelerator again."                              | jmckinney@tamu.edu     |
|      -the Fourth Doctor, "The Pirate Planet",     +------------------------+
|           Dr. Who                                 | R[x] / <x^2+1> = C!!!! |
+---------------------------------------------------+------------------------+
Newsgroups: sci.math
From: dzk@cs.brown.edu (Danny Keren)
Subject: Re: compactness ?
Organization: Brown University Department of Computer Science
Date: Sat, 21 Nov 1992 01:36:05 GMT

franz@ccrl.nj.nec.com (test user for max) writes:

#? It seems to me that (0,1) is contained in the collection of
#open sets { (0,0.6) (0.5,1) (0,1) } and this has finite subsets that 
#contain (0,1), so (0,1) should be compact.  Does the definition mean that
#S must be contained in any possible collection, as opposed
#to just one possible collection being sufficient?  

Yep - *every* open cover must have a finite sub-cover (by "open cover"
I mean a collection of open sets that contain the space).

#If so, then 
#I would intuitively think that a (1/n,..) type construction
#would prevent any open set from being compact.  

Not true for any topological space, but true for some classes - for
instance, in Euclidean space a subset is compact iff it is bounded
and closed.

#Any insight on understanding the definition (and its relevance)
#would be appreciated.  

Compact spaces have many nice properties. For instance, every
real valued function on them is bounded (one of the simplest
properties). That is the reason they were studied so extensively.

-Danny Keren.


Newsgroups: sci.math
From: rgep@emu.pmms.cam.ac.uk (Richard Pinch)
Subject: Re: Geometrical parking problem.
Organization: Department of Pure Mathematics, University of Cambridge
Date: Wed, 18 Nov 1992 10:11:07 GMT

In article <1992Nov17.225821.6579@augean.eleceng.adelaide.edu.AU> 
dabbott@augean.eleceng.adelaide.edu.AU (Derek Abbott) writes:
>
>A car of length L reverses into a parking space without touching the kerb.
>Has anyone calculated the minimum theoretical length of the parking space?

Yes, it's the length of the car.  The commutator of two rotations is
a translation, so you can drive sideways by making very small moves of
the form LRLR.

Richard Pinch

Newsgroups: sci.math
From: gay@selkirk.sfu.ca (Ian D. Gay)
Subject: Re: 1+1/2+1/3+1/4+...+1/n
Organization: Simon Fraser University, Burnaby, B.C., Canada
Date: Thu, 19 Nov 1992 18:12:43 GMT

Mutter Christoph Johannes <K3032E2@ALIJKU11.BITNET> writes:

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

>Chris. ------------

Everybody's computer is too slow!

1 = 1
1/2 + 1/3 < 1
1/4 + 1/5 + 1/6 + 1/7 < 1
etc.
You will need to sum at least 100 such lines, and the 100th line
has 2^99 terms!

So the problem has to be solved by mathematics, not by computation.






Newsgroups: sci.math
From: asp+@cs.cmu.edu (James Aspnes)
Subject: Re: ok, i'll bite.
Organization: School of Computer Science, Carnegie Mellon
Date: Mon, 16 Nov 1992 21:22:23 GMT

In article <92320.214859RVESTERM@vma.cc.nd.edu> RVESTERM@vma.cc.nd.edu writes:
>i understand "cryptography".  i understand "np".  someone please
>explain the connection.

If you can solve any problem in NP, and you have a polynomial-time test for
whether a string could be a message, you can decrypt messages encrypted with
any efficient (small keys, small description of algorithm, algorithm is fast)
algorithm as follows:

 1. Guess the key and the algorithm (this is where non-determinism comes in).
 2. Decrypt the message according to the key/algorithm you have guessed.
 3. Test to see if the result is a plausible message.

The only tricky part is the test for plausibility, since you don't want it to
answer yes too often.  For public-key systems the test is straightforward; you
encrypt the alleged decryption using the public key and see if it matches.
For private-key systems you have to know something about the space of possible
messages (e.g. that they are ASCII English-language text followed by a 64-bit
CRC checksum :-]), but in practice this shouldn't be much of a problem.
Newsgroups: sci.math
From: pratt@Sunburn.Stanford.EDU (Vaughan R. Pratt)
Subject: Re: exp(pi*sqrt(x))
Organization: Computer Science Department,  Stanford University.
Date: Mon, 23 Nov 1992 00:12:03 GMT

In article <1992Nov22.124131.17689@husc15.harvard.edu> blom@husc15.harvard.edu writes:
>Aitken once remarked that exp(pi*sqrt(163)) differs from an integer by
>less than 10^-12.  Why and when does exp(pi*sqrt(x)) approximate an integer?

Q(sqrt(-163)) (the field of rationals extended to complex quadratic
field with sqrt(-163)) is a unique factorization domain ("class number
1").  The 9 numbers that work here are 1 2 3 7 11 19 43 67 163, the
larger ones work much better for getting good integer approximations
this way.

Though these 9 were part of a case of a conjecture due to Gauss, it was
discovered only in 1933 that there were no others in the range -164 to
-5e9.  In 1934 it was shown that there was no 11th number---at most one
remained to be discovered.  By 1966 the -5e9 bound had been improved to
-1e(9e6) (10 to the 9 million), i.e. if there was a tenth it was below
that limit.  In 1966 H. Stark and A. Baker independently ruled out the
possibility of a tenth altogether.  [Source: Harold Stark's "Intro to
Number Theory", p.295]


Problem: characterize those powers of exp(pi*sqrt(163)/3) that
approximate an integer (to better than .1% say).  Why is it about half
of the first 24, and seemingly none of the rest (except for the
necessary one in a thousand due to the .1% tolerance)?

If you want a very convenient way to play around with these numbers
interactively, and have a Sun-4, a binary of Hans Boehm's
infinite-precision calculator can be found on boole.stanford.edu as
/pub/calc.  To get the base power, start it and type 163rp*3/x to get
640320.00000000060486373504901603947174181881853947577148576036659181946522182
-- 
Vaughan Pratt	  		A fallacy is worth a thousand steps.
From: marcos@iota.Berkeley.EDU (Marcos Valerio)
Newsgroups: sci.math
Subject: latin square-like problem
Keywords: magic squares, latin squares
Date: 16 Nov 92 19:38:44 GMT
Article-I.D.: ucsbcsl.6722
Reply-To: marcos@iota.Berkeley.EDU (Marcos Valerio)

I have a nice little problem for you.

I need an algorithm to build n*n latin squares with two extra properties:

P1: All the elements in the main diagonal are different and equal to the row
    (or column) which they belong.

P2: If for each row we select the element equals to row-1, they will all be in
    different columns.

For example: 

 n=3: 
 ----

  0 2 1
  2 1 0
  1 0 2 

 n=5:
 ----

  0  2  4  1  3
  4  1  3  0  2
  3  0  2  4  1
  2  4  1  3  0
  1  3  0  2  4

Please observe that in both cases the elements in the main diagonal are:
0, 1, 2, ..., n-1 and also if we select the Aii-1 elements from each row,
they are in different columns.

There is no solution for n=4.

In my solution there is a separate algorithm for odd and even numbers, but
I don't think it is the best one. That's why I'm posting the problem to you.

I came across this problem when trying to simulate broadcast in a ring
based network. Details can be given upon request.

Thanks,

-- 
Marcos de Macedo Valerio
Center for Distributed Systems
Department of Computer Engineering
University of California, Santa Barbara
Phone : (805) 893-4461 office
        (805) 685-9677 home
email address : marcos@nu.ece.ucsb.edu
From: borchers@nmt.edu (Brian Borchers)
Newsgroups: sci.math
Subject: Mixed Integer Linear Programming: sample problems
Date: 15 Nov 92 01:50:48 GMT
Article-I.D.: nmt.1992Nov15.015048.1742
Organization: New Mexico Tech

It's been a couple of years since I first made this request, so I thought
a repost might be helpful.  
 
I'm looking for large zero-one mixed integer linear programming problems.  
By large, I mean that the problem should have thousands of variables
and at least a few hundred constraints.  I'm interested in problems
with up to about 100 integer variables.  I'm also interested in applications
of these problems.  So far, the problems that I have seen are mostly 
facility location/fixed charged network design problems.  
 
Yes, I'm familiar with the MIPLIB collection.  MIPLIB contains a number
of interesting problems, including mod011, rentacar, modglob, and khb05250.
Some of these problems are extremely hard to solve.  Unforutnately, most 
of the rest of the problems in MIPLIB are pure zero-one problems which 
aren't of much interest to me.  
 
Why am I looking for these problems?  I'm doing research into branch
and bound algorithms that use LP relaxations to obtain bounds.  For 
pure IP's, there are a number of better techniques (take a look into
implicit enumeration, problem reformulation, cutting planes, and
rounding heuristics.)  For large mixed problems, branch and bound
with LP relaxations still seems to be the way to go.  

---------------------------------------------------------------------------
Brian Borchers                                             borchers@nmt.edu
Department Of Mathematics                 New Mexico, home of the green 
New Mexico Tech                           chile cheeseburger.
Socorro, NM 87801
 
Newsgroups: sci.math,sci.math.stat
From: edgar@function.mps.ohio-state.edu (Gerald Edgar)
Newsgroups: sci.math
Subject: Re: closed forms
Date: 23 Nov 1992 10:39:23 -0500
Organization: The Ohio State University, Dept. of Math.
NNTP-Posting-Host: function.mps.ohio-state.edu


>Note.  Derivation of the fact that integral exp(-x^2) dx = exp(-x^2) w + C
>for rational function w is impossible:  First, w must satisfy the
>differential equation  w' - 2x = 1.  Deduce that w has no (finite) poles, so
                        ^^^^^^^^^^^
               should be w' - 2xw = 1

>w is a polynomial.  Obtain a contradiction by comparing the degrees of
>polynomials.


-- 
  Gerald A. Edgar                Internet:  edgar@mps.ohio-state.edu
  Department of Mathematics      Bitnet:    EDGAR@OHSTPY
  The Ohio State University      telephone: 614-292-0395 (Office)
  Columbus, OH 43210             -292-4975 (Math. Dept.) -292-1479 (Dept. Fax)
From: ramsay@math.ubc.ca (Keith Ramsay)
Newsgroups: sci.math
Subject: Re: Bozos Synonymous
Date: 19 Nov 1992 01:47:57 GMT
Organization: University of British Columbia, Vancouver, B.C., Canada
NNTP-Posting-Host: gauss.math.ubc.ca

In article <burt.722061313@aupair.cs.athabascau.ca> 
burt@aupair.cs.athabascau.ca (Burt Voorhees) writes:

>Mathematicians tend to be rather sexist.

My experience has not suggested this. I hear scarcely any sexist
comments from fellow mathematicians. I haven't witnessed any
discriminatory action lately either. If anything, it seems as though
academics in general, and academic mathematicians included, are
typically less sexist than the non-academics I've encountered, and are
interested in women participating in mathematics as equals. I'd *like*
to think this is true. Of course, this is only loose anecdotal
evidence, so I could be wrong. On what is your opinion based?

Keith Ramsay
ramsay@unixg.ubc.ca
Newsgroups: sci.math
From: frisch1@athena.mit.edu (Jonathan Katz)
Subject: ODE problem...
Organization: Massachusetts Institute of Technology
Date: Fri, 20 Nov 1992 18:41:02 GMT

>The following ODE problem came up recently.
>I know how to solve it by the power series method, but was wondering
>if anyone could figure out an easier way of solving it (maybe a nice
>substitution?).
>(x and y are functions of t, a is a constant)
>x'=(a)(x)cost+(a)(y)sint
>y'=(a)(x)sint-(a)(y)cost.

Hi, I was the one to originally pose this problem, and I'm glad to see the
interest it has sparked.
Thanks to all those who sent email.

However, while playing with this system, I came upon a neat 'trick' which no one
has yet pointed out.

multiply the first equation by y and the second by x.  Then add the two equations
together, getting:
yx'+xy'= xy(acos(t)+asin(t))
letting f=xy, note that this simplifies to:
f'=f(acos(t)+asin(t)) which is easily solvable.

Now subtract the two equations, and divide the resulting equation by y^2.  Then
let g=x/y, and the equation becomes:
g'=some function of g  (sorry I don't have my work in front of me, but it's
simple enough to carry out)

Now we have xy=some function of t   and
x/y=some other function of t.

x and y can then be solved for easily.
From: amirishs@acf9.nyu.edu (shaahin amiri sharifi)
Newsgroups: sci.math
Subject: A Question About Fundamental Group
Date: 18 Nov 92 04:06:28 GMT
Organization: New York University

Consider a bunch of infinitely many (countable) circles with a
point in common. The radii of these circles make a sequence like
{1/n}. What is the fundamental group of this space? Any comments
or referenc would be so helpful!
Newsgroups: sci.math
From: hrubin@pop.stat.purdue.edu (Herman Rubin)
Subject: Trivial is not the same as obvious; good research makes things obvious
Organization: Purdue University Statistics Department
Distribution: sci.math
Date: Sun, 15 Nov 1992 15:50:12 GMT

In article <1992Nov13.090126.7142@jarvis.csri.toronto.edu> leemike@eecg.toronto.edu (Michael Lee) writes:
>re: zelany's reponse to zach@csdec1.tuwien.ac.at:

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

>>From the mathematician's
>>viewpoint, the proof is trivial: A simple
>>diagonalization argument (in Kreisel's words).

It would be better to state that the proof is obvious, once stated.  In 
Landau's book, this occurs after a theorem, and loses nothing in translation:

Remark:  Not trivial.

Proof:	Obvious.

Research is no more significant if the proofs are obscure and difficult to 
follow.
-- 
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)
Xref: sparky sci.math:15358 comp.edu:1924 misc.education:4450 sci.edu:1186
From: rusin@mp.cs.niu.edu (David Rusin)
Subject: another sphere decomposition
Organization: Northern Illinois University
Date: Mon, 23 Nov 1992 20:46:15 GMT

Prove or disprove (for a colleague's student): If the 2-sphere is
written as the union of two compact pieces K and L having finitely
many components, then (K intersect L) has finitely many components.

Easily the answer is no if the union need not be all of the sphere,
and it's yes if 'compact' is replaced with 'open'. If the sphere is
replaced by a torus, say, then the number of components may be
greater (e.g. K and L can be connected but not their intersection)
but undoubtedly it's finite in the torus case if it must be so 
in the sphere case.

dave rusin@math.niu.edu 
Newsgroups: sci.math,comp.edu