HDTenEightyP/NetNews huggingface dataset:
From: ara@zurich.ai.mit.edu (Allan Adler)
Newsgroups: sci.math,misc.books.technical
Subject: Re: High Prices of Math Books. I am pissed.
Date: 6 Jan 93 05:53:04 GMT
	<1993Jan5.173010.19718@Princeton.EDU>
	<1993Jan5.183953.9606@monu6.cc.monash.edu.au>
Organization: M.I.T. Artificial Intelligence Lab.


I agree that text books are too expensive. So are other
technical books that are not necessarily text books.

I would like to see volunteers get together and do for the publication of
text books what the Free Software Foundation has done for software.
I propose that volunteers write books in TeX and leave them in archives
where anyone can download them and print them out for free. 
copyleft. Let the group call itself The Free Textbook Foundation or
something like that. People who don't want to or can't print out the
TeX files can also order the books from the Free Textbook Foundation
and obtain them for a certain distribution fee. The books can be copyleft
just as Free Software Foundation software is.

If the book is to be used for a large course where it would not be practical
to print out dozens or hundreds of copies on a laser printer, a single
copy can be printed out and the local xerox place can print out as many
copies as one needs and give them cheap binders, or the students can
print out their own. Copies can also be previewed using a TeX previewer
on a PC, which is even cheaper, and the class can just purchase
diskettes containing the dvi files and do what they want with them.

I for one would be glad to cooperate with such an effort.

Allan Adler
ara@altdorf.ai.mit.edu
Newsgroups: sci.math,sci.astro
From: aberman@cs.washington.edu (Andrew Berman)
Subject: Algorithms for determining dimension of a set of points
Organization: Computer Science & Engineering, U. of Washington, Seattle
Date: Fri, 8 Jan 93 02:25:45 GMT

I'm looking for info on algorithms to solve the following problem:

Given a set of points in 3 space, what is the "dimension" of the shape
represented by the points?

Obviously, one could draw a squiggly line through all the points, or
a bunch of planes, or put the whole thing in a cube, thus yielding 1,2
or 3 dimensional answers.  I'm looking for an algorithm which gives the
most "reasonable" answer, i.e., if all the points lie on a line, I'd like
the algorithm to pop out a "1".

The set of points might be considered a random sampling from some manifold,
for example.

PLEASE E-MAIL, since I do not normally read either of these newsgroups.

Thanks in advance,

Andrew P. Berman

-- 
Andrew P. Berman           |  "I have no idea what White House statement was
Dept. of Computer Science  |  was issued, but I stand by it 100 percent"
University of Washington   |    -- Richard Darman
aberman@cs.washington.edu  |
From: kraai4712@iscsvax.uni.edu
Newsgroups: sci.math
Subject: Re: Closed forms for sums
Date: 11 Jan 93 10:26:44 -0600
Distribution: world
Organization: University of Northern Iowa

In article <964.165.uupcb@hal9k.ann-arbor.mi.us>, james.jones@hal9k.ann-arbor.mi.us (James Jones)  writes:
> OB>Subject: sum(i=1 to n, i^3) = ??   URGENT !!
> 
> While we're on the subject, I was killing some time with Derive, a
> Mathematical Assistant one day waiting form my Finite class to begin
> and found the closed form for
> 
>         ---
>         \     j
>          >   i
>         /
>         ---
>         i=1
> 
> where j went from 1 to about 12 or 13.  Can't remember exactly where I
> stopped at.
[stuff deleted]
> 
> Any explanation or references (explanation preferred) would be
> appreciated.

Isn't this all explained in the Chemical Rubber Company's (a.k.a. the "Rubber
Book" or C.R.C. Manual) in the a-### section?

As I recall, they gave explicit closed-form sums for the first six values of j,
and then proceeded to give the general formula.

Of course, this is just off the top of my head.

--jim
Newsgroups: sci.math
From: dy@shire.math.columbia.edu (Deane Yang)
Subject: Re: proof wanted 2
Organization: Mathematics Department, Columbia University
Date: Mon, 11 Jan 1993 22:23:38 GMT
X-Posted-From: shire.math.columbia.edu
NNTP-Posting-Host: sol.ctr.columbia.edu

In article <1993Jan11.210012.18587@Princeton.EDU> tao@fine.princeton.edu (Terry Tao) writes:
>>>In article <ARA.93Jan10172314@camelot.ai.mit.edu> ara@zurich.ai.mit.edu (Allan Adler) writes:
>>>>
>>>>
>>>>True or false: A metric space (X,d) is locally compact if and only if
>>>>for every point p of X and every closed subset Y of X, there is a
>>>>point q of Y such that d(p,q) = inf {d(p,r) | r in Y}.
>>>>
>>>
>
>False.  A friend suggested the following counter example:
>
>Let X be the space of infinitely many copies of {0} union {1/n: n = 1, 2,
>...} with all the 0's glued together.  the metric is the natural one
>between two points on the same copy, or through 0 on different copies.  The
>space is not locally compact at 0, yet every closed set and every point has
>a point of closest approach.  Basically the reason for this is that the
>only problematic point is 0, and the fact that Y is closed then guarantees
>that 0 is in Y.
>
>Terry
> 
>

The point here is that, except for 0, X is a discrete and therefore 
locally compact space. The conjecture needs a further assumption,
something that makes the space everywhere nondiscrete.

If I'm not mistaken, a reasonable assumption is that X is a length space.
This means that the distance between two points in X is equal to the infimum
of the lengths of continuous curves joining the two points. In particular,
this means that given two points that are a finite distance apart,
then you can always move one point a little bit and make the distance a little
smaller.

Now suppose X is not locally compact. Then we can find a bounded sequence
that has no convergent subsequence. In particular, this is a closed set.
Pick a point outside the sequence that is a finite distance from the sequence.
By nudging the points in the sequence, you should be able to obtain a closed
set and a point such that the distance between the two is not realized by
the distance between the given point and a point in the closed set.



Newsgroups: sci.math,alt.books.technical
From: ilan@leland.Stanford.EDU (ilan vardi)
Subject: Re: High Prices of Math Books. I am pissed.
Organization: DSG, Stanford University, CA 94305, USA
Date: Wed, 6 Jan 93 12:01:23 GMT

In article <1993Jan5.173010.19718@Princeton.EDU> bathurst@phoenix.Princeton.EDU (Bruce Bathurst) writes:
>
>Generations of Americans educated their children for a better life.
>The fact that the educated go without luxuries, or sometimes food, is
>not a fact that Americans will soon believe.
>

I think this is related to ethnic backround. I don't know about
Princeton but at state schools a sizeable percentage of the students
have to support themselves due to having been totally written off by
their families. As a matter of fact, I have known a number of students
from upper middle class families who have had to get legal documents
stating that their families refuses to give any money so that they
could be eligible for student loans.

Newsgroups: sci.math
From: gardner_c@apollo.hp.com (Cal Gardner)
Subject: Re: Value of the US Dollar
Date: Tue, 12 Jan 1993 16:42:34 GMT
Organization: Hewlett-Packard Corporation, Chelmsford, MA

In article <C0po8L.JFr@comp.vuw.ac.nz> harper@kauri.vuw.ac.nz (John Harper) writes:
>In article <1993Jan11.180318.6541@cs.unca.edu> snodgras@cs.unca.edu (Ryan Snodgrass) writes:
>>How do I compute the value of the US dollar? 
>>
>See C V Durell & A Robson "Advanced Trigonometry" (Bell, London, 1930) 
>Exercise XV no 6 is "Is it true to say that i^i pounds is 1 dollar ?"
>[Sometime in 1929 or 1930 was the exchange rate near exp(-pi/2) ?]
>
>John Harper Mathematics Dept. Victoria University Wellington New Zealand

Well before the Brits went off the gold standard in (I think) 1931
and FDR devalued the US Dollar, the fixed exchange rate was
 
             1 pound Sterling = $4.85

If you calculate golcd at US$20.00 and check the gold weight of a
sovereign you should get the above exchange rate unless I should
have used a value of $20.87 to cover Uncle Sam's vigorish.

Cal gardner_c@apollo.hp.com

Newsgroups: sci.math,alt.philosophy.objectivism
From: auerbach@ncsu.edu (David D Auerbach)
Subject: Re: godel theorem and godel theorem ....(Re: Where's
Organization: North Carolina State University
Date: Tue, 12 Jan 1993 04:13:52 GMT

An incredibly nice book on the Godel theorems, very very clean has just
come out--Smullyan: Godel's Incompleteness Theorems.  It is very uptodate
in using "technology" that avoids doing extra mathematics and in giving
abstract (i.e. operator, i.e. we don't need your stinking quantifiers)
versions of various flavors of the proof.  Very elegant and some nice
connections with the truth results that I hadn't known about (perhaps not
a remarkable claim), namely Askanas' Theorem.  
Bonuses are an accurate treatment of the Second Theorem and of the Rosser
systems. 
Smullyans 135 pages should erase some of the confusions evident in some of
this thread.  

Newsgroups: sci.math,news.answers
From: dzk@cs.brown.edu (Danny Keren)
Subject: Re: What is the 'sinc' function?
Keywords: sinc
Organization: Brown University Department of Computer Science
Date: Tue, 12 Jan 1993 04:46:01 GMT

hougen@focus.csl.uiuc.edu (Darrell Roy Hougen) writes:

# I came accross it in a paper about the scattering of electromagnetic
# radiation. 

As far as I know it is the common name for the Fourier transform
of the "rect" function (rect is constant on some interval and
zero outside). "sinc" turns out to be sin(x)/x (defined to be
1 at x=0).

-Danny Keren.
 


Xref: sparky sci.math:17689 sci.physics:22112
From: jgk@osc.COM (Joe Keane)
Newsgroups: sci.math,sci.physics
Subject: Re: Bayes' theorem and QM
Summary: Banach-Tarski has no relation to reality.
Keywords: infinite
Date: 5 Jan 93 06:55:14 GMT
Followup-To: sci.math
Organization: Versant Object Technology

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.

Banach-Tarski is a good demonstration of the tricks you can play if you have
axioms which claim the existence of objects with infinite information, or
however you want to interpret the non-constructible things that you can get
only with the Axiom of Choice.  But does anyone think this has any relation to
reality?

If you think so, please show me some pieces that you could make out of
something real like wood, such that that they almost fit together into either
one sphere or two.  Also please show me a computer chip that can store an
infinite amount of information.  In fact i'll be generous, you only have to
store an arbitrarily large amount of information.

Don't get me wrong, i'm quite interested in math logic.  I like considering
strange axioms that let you enumerate the reals or decide whether Turing
machines will halt.  (No, these are not contradictory, as long as you
understand that such an axiom applies only to things you can make without
using the axiom.)  But i'm worried if people think we can do new things in the
real world by inventing new axioms about infinite sets.

A mostly unrelated observation is that if you mix 1 liter of water and 1 liter
of alcohol, you get about 1.8 liters of something like vodka.

--
Joe Keane, amateur mathematician
jgk@osc.com (uunet!amdcad!osc!jgk)
From: andrew@rentec.com (Andrew Mullhaupt)
Newsgroups: sci.math
Subject: Re: bitonic sorting networks
Date: 11 Jan 93 03:30:47 GMT
Organization: Renaissance Technologies Corp., Setauket, NY.

In article <C0MwMv.Bz0@world.std.com> rsilver@world.std.com (Richard Silver) writes:
>
>Would someone define a bitonic sorting network and
>tell me where I might obtain some info? I believe
>they are used in signal processing. 

Ken Batcher invented the bitonic sorting networks (so far as I know).
As in all such matters, Knuth's _Art of Computer Programming_ is the
first place to look.

Later,
Andrew Mullhaupt
Newsgroups: sci.math
From: wjcastre@magnus.acs.ohio-state.edu (W.Jose Castrellon G.)
Subject: Re: combinatorial? problem
Organization: The Ohio State University,Math.Dept.(studnt)
Date: Sun, 10 Jan 1993 19:55:37 GMT

In article <1993Jan10.031604.25753@cbnewsm.cb.att.com> thf@cbnewsm.cb.att.com 
(thomas.h.foregger) writes:

>
>In article <Dec.23.18.15.49.1992.22657@pepper.rutgers.edu>, gore@pepper.rutgers.edu (Bittu) writes:
[...]

>> given m,n nonnegative integers, the quantity
>> 
>>      (2m)! (2n)!
>>     -------------      is an integer.
>>      m! n! (m+n)!
>> 
>> 
>> Note that this is very easy to show by the standard argument where for
>> every prime p, you find the highest power of p (say p^k) that divides
>> the denominator and then show that p^k divides the numerator as well.
>> 
>> I want a combinatorial proof of this. I have tried rewriting the above
>> as C(2m,m)*C(2n,n)/C(m+n,m) where C(a,b) is "a choose b" and also in
>> other ways, but I still haven't come up with a combinatorial proof.
>> 
>> --Bittu
>
>
>This problem is harder than I thought. I have now run 
>across a generalization of the problem in the American Math. Monthly,
>for Dec.  1976, p. 817, Problem 6121, which is solved in
>AMM for Aug-Sept, 1978, p. 602. 
>The method is to look at the number of times a prime p divides
>the numerator and denominator. 
>It is stated: "It would be interesting to have a combinatorial proof." 

I believe Ira Gessel has generalizations with combinatorial proofs,
[it might not yet be in press, I learned about that 6 months ago]. Also,
you might want to try the Annual-Key index of Math Reviews under _ballot 
numbers_ .

>
>tom foregger

Newsgroups: sci.math
From: yeomans@austin.onu.edu (Charles Yeomans)
Subject: Re: High Prices of Math Books. I am pissed.
Date: Wed, 6 Jan 1993 18:11:31 GMT
Organization: Ohio Northern University

In article <1icl8cINN983@roundup.crhc.uiuc.edu>, hougen@focus.csl.uiuc.edu (Darrell Roy Hougen) writes:
> 
> bathurst@phoenix.Princeton.EDU (Bruce Bathurst) writes:
> 
> % Because of this (I suspect) there is no mechanism, as there is in
> % medicine, for the cost of expensive necessities to be shared by the
> % rest of society.
> 
> Do we need this socialist drivel on sci.math?  Look at the state of
> medicine in America and tell me whether you think it has benefitted
> from massive government intervention.  
> 
> %  Many students can't buy even basic texts, others
> % sell them back.  Students, as a consequence, are not only less
> % educated, but have not learned how to teach themselves, through
> % reading.  Those who choose to devote their lives to advancing
> % knowledge in basic fields face the choice of purchasing books or food.
> 
> Have they suddenly lost the ability to use the libraries?
> 
> % Generations of Americans educated their children for a better life.
> % The fact that the educated go without luxuries, or sometimes food, is
> % not a fact that Americans will soon believe.
> 
> The fact that undergrad and grad students can't afford luxuries is
> well known.  The idea that some are going without food is ridiculous.
> Undergrad students, grad students and professors are already reaping
> the benefits of massive state and federal government subsidies of
> their education.  Would you like to further increase the burden on the
> less well educated to pay for the life styles of the educated?  That
> hardly seems fair.  As a grad student myself, I have no sympathy for
> other grad students or undergrad students that whine about their
> living conditions.  At least college students have a chance to make
> their lives better doing something they want to do.  If the result is
> not improved living conditions, then some people should consider
> changing careers.
> 
I sometimes went without food as an undergraduate.  I don't find it 
so ridiculous.  I couldn't buy books for most of my days as an
undergraduate.  I went to the library, but they didn't always have the
books for the courses I took. Thank goodness for Texas-style
courses.  Indeed, my graduate school stipend enabled me to enjoy a higher
standard of living than ever before.

But I didn't feel that I was owed anything because of any talent I 
had or because I wanted to learn. It is certainly the case that many
intellectuals feel they are owed a living by society - it's a bit like 
being pissed off at someone because you love them and they don't love you
back.

As much as it sometimes annoys me, I wonder if the general trend of anti-
intellectualism in American history hasn't been a big benefit to the
development of this country.

Charles Yeomans
Newsgroups: sci.math
Subject: Re: Value of the US Dollar
From: harper@kauri.vuw.ac.nz (John Harper)
Date: Mon, 11 Jan 1993 22:38:44 GMT
Organization: Victoria University of Wellington

In article <1993Jan11.180318.6541@cs.unca.edu> snodgras@cs.unca.edu (Ryan Snodgrass) writes:
>How do I compute the value of the US dollar? 
>
See C V Durell & A Robson "Advanced Trigonometry" (Bell, London, 1930) 
Exercise XV no 6 is "Is it true to say that i^i pounds is 1 dollar ?"
[Sometime in 1929 or 1930 was the exchange rate near exp(-pi/2) ?]

John Harper Mathematics Dept. Victoria University Wellington New Zealand
Newsgroups: sci.math
From: ara@zurich.ai.mit.edu (Allan Adler)
Subject: Job Application Skills
Organization: M.I.T. Artificial Intelligence Lab.
Distribution: sci
Date: Sat, 9 Jan 1993 18:38:43 GMT


After several years of refusing to apply for jobs, I decided a few days
ago to start applying again. I don't feel any differently about the 
complaints I have had about the profession, but I am not prepared to
take it to the point of sleeping in the streets. The decision to apply again
brings up a number of issues that were unresolved when I stopped and which, 
after a period of years show some signs of preservation as well as decay.

My question, first of all, is whether the process of selecting candidates
evaluates them on their mathematical abilities, other things being equal, 
or whether it evaluates them on their skills in writing resumes, cover letters,
research proposals and other official documents. In other words, is it 
primarily a  matter of bureaucrats selecting one of the own and 
secondarily a matter of mathematical ability?


Here is another point of some concern to me:
Many places say that they encourage people with disabilities to apply.
However, who has the right to define what is a disability? I would say
that any condition that makes it more difficult to perform or obtain a
job is a disability, but this definition does not have the force of law.
Accordingly, I would be inclined to list among my disabilities:
(1) inability to write an appropriate resume, cover letter, research proposal,
    and here the emphasis is on "appropriate behavior", understood by one and
    all except myself to be appropriate.
(2) inability to find suitable housing on my own, which has left me living
    in the most incredible dumps at times and at other times homeless
(3) idealistic attitudes about education and employment
(4) inability to confine my creative tendencies to areas where I am 
    specifically paid to be creative
(5) unconventional lifestyle and career history


I am however dimly aware that I am not supposed to list these on my resume.
May I interpret this as follows: any disability that does not have the
force of law is severely punished?

One last thing: if anyone wants to look at the present stage of my resume
and offer criticism, they will be welcome. Some people are already doing this.

Allan Adler
ara@altdorf.ai.mit.edu
From: dubhashi@mpii01044.NoSubdomain.NoDomain (Devdatt Dubhashi)
Newsgroups: sci.math
Subject: Euclidean domains
Keywords: valuation euclidean
Date: 9 Jan 93 13:04:57 GMT
Organization: Max-Planck-Institut f"ur Informatik

>> |>Why there are not other candidates for the Euclidean function?

I'm not sure what the original question was, but hopefully the following
is not altogether irrelevant!

A Euclidean domain is a ring equipped with a special kind of a valuation -- an
euclidean valuation, essentially one that makes it amenable to carry out the
Euclidean algorithm. As usual, one can get a norm out of this by taking a negative
exponential. Ostrowski's classic theorem asserts that the only possible norms on
the rationals are the absolute value and the p-adic norms obtained from p-adic
valuations. I am unaware of of similar general normal form results about 
euclidean valuations on various classes of rings. Perhaps a book on Valuation
Theory (such as Endler's, which unfortunately is inaccessible to me at present)
might shed some light on this.
Newsgroups: sci.math
From: bs@gauss.mitre.org (Robert D. Silverman)
Subject: Re: factorization in commutative rings
Organization: Research Computer Facility, MITRE Corporation, Bedford, MA
Distribution: sci.math
Date: Tue, 5 Jan 1993 14:26:30 GMT

In article <Jan.3.02.05.44.1993.24643@spade.rutgers.edu> cadet@spade.rutgers.edu (Uniquely TiJean) writes:
 
stuff deleted....

:I am looking for counterexamples 
:B) D= princ. idl. domain doesn't imply D= euclidean domain.
:
:   Well, I found in Hungerford ( Algebra ) 
:
:   the following  Z( (1+sqrt(-19)) / 2 )
:
:Question: How come? I have no cue as to why the above domain isn't euclidean.
:
 
A good reference for this is the chapter(s) in Hardy and Wright's Number Theory
book that covers quadratic fields. They completely enumerate ALL of the
imaginary quad. fields that are Euclidean. 
They have discriminant:  -1, -2, -3, -7, -11.

They also enumerate all of the real Euclidean quad. fields as well.

--
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"
From: fc03@ns1.cc.lehigh.edu (Frederick W. Chapman)
Newsgroups: sci.math
Subject: Re: Job Application Skills
Date: 12 Jan 93 14:26:59 GMT
Organization: Lehigh University

In article <93011.175039U53644@uicvm.uic.edu>, U53644@uicvm.uic.edu writes:
>Uhhhhhh...........Well, at the risk of repeating some bad history.......
>
>         Yes, recent graduates in Mathematics HAVE been having a rough time
>getting work, as almost everyone acknowledges right now (kind of like
>admitting that the weather has been getting cold). However, while I might
>respect the determination of someone who is about to renew his abandoned job
>hunt, I can't respect his judgement. After a while, one has to face
>the reality that a certain avenue of attack is futile, and try
>something else.

This kind of "one size fits all" vocational advice really irritates
the hell out of me.  It makes scores of unwarranted assumptions
(especially in this case), the most objectionable of which is that it
fails to take into account the ability of specific individuals to
compete successfully in a difficult job market.  It assumes that the
recipient of the advice is essentially "average".  You need to face
the reality that in every field there are people at the top of that
field, and they will make their own success.

-- 

o ------------------------------------------------------------------------- o
|  Frederick W. Chapman, User Services, Computing Center, Lehigh University |
|    Campus Phone:  8-3218     Preferred E-mail Address:  fc03@Lehigh.Edu   | 
o ------------------------------------------------------------------------- o
|             Ecstasy is transitory, but a theorem is forever!              |
o ------------------------------------------------------------------------- o
Newsgroups: sci.math