HDTenEightyP/NetNews huggingface dataset:
From: tenny@euclid.uucp (Nathan Tenny)
Newsgroups: sci.math
Subject: Re: a first year grad student freaks out.
Date: 12 Nov 92 05:32:55 GMT
Article-I.D.: nntp.1992Nov12.053255.23048
Organization: Department of Mathematics, University of Oregon

In article <BxKu9s.BAw@news.udel.edu> cornwall@bach.udel.edu (Ray J Cornwall) writes:
>For those of us who wish to do research (cause we'll get our names in
>really cool journals! :) can you give us some pointers on how to come
>up with such topics?

I'm no authority---I'm just starting to stumble into topics that look like
workable ground---but I'm finding that it sort of sneaks up on me.  Based on
a talk at a conference, I decided that this business of non-Haken 3-manifolds
looked kind of interesting; looked at a paper or two and put it in the mental
"interesting stuff" file.  Read a paper by my advisor; hmm, this is sort of
interesting, but I don't see the 3-manifold topology in it; stumbled suddenly
onto a paper about deciding whether 3-manifolds are Haken, looked at it, and,
gee, this is just like that last paper I read...and now, all of a sudden,
I'm not doing groundbreaking research or anything, but whatever it is I am
doing is more like research than coursework.

'Course, we'll see if it pans out over the next couple of years...

Do those who have done research-ish work for more than a month or so have
similar experiences?  Until quite recently, I sort of assumed research must
be done through divine revelation...

	NT
Newsgroups: sci.math
From: pratt@Sunburn.Stanford.EDU (Vaughan R. Pratt)
Subject: Re: Boolean Algebras
Organization: Computer Science Department,  Stanford University.
Date: Thu, 12 Nov 1992 05:29:59 GMT

In article <42536@gremlin.nrtc.northrop.com> jbarnett@nrtc.northrop.com (Jeff Barnett) writes:
>
>Is there a free boolean algebra such that the cardinality of
>the algebra (not the cardinality of its generators) is that
>of the continuum?
>
>Jeff Barnett

The cardinality of any infinite free Boolean algebra is that of its set
of generators.  (Visualize it as equivalence classes of Boolean
formulas, interpreting generators as variables.)  So yes, the free
Boolean algebra on the continuum, and no others.

Infinite free *complete* Boolean algebras on the other hand are so much
larger than their generator sets that they cannot exist!  This was
shown in 1964 by Gaifman and Hales, independently.
-- 
Vaughan Pratt				Formal logic and casual fallacy
Newsgroups: sci.math,misc.education
From: lady@uhunix.uhcc.Hawaii.Edu (Lee Lady)
Subject: Re: Is Math Hard?
Followup-To: sci.math,misc.education
Summary: Card games
Organization: University of Hawaii (Mathematics Dept)
Date: Tue, 10 Nov 1992 08:37:05 GMT


In article <1992Nov10.004159.29572@news.Hawaii.Edu> I write:
>
>Finally, I would like to say that if I were in Eric Green's situation (in
>which I would be much less successful than he is) I would start having my
>students measure things.  I suspect that they would learn more
>mathematics in wood shop than in arithmetic class.  

I think that card games are also very useful in teaching young children
mathematics.  Some of them, such as blackjack, require a certain amount
of arithmetic and a lot, like canasta, involve keeping score.  But I
think that almost any card game does some good by focusing a child's
attention on numbers as something worth paying attention to. 

--
It is a poor sort of skepticism which merely delights in challenging
those claims which conflict with one's own belief system.  
                                                          --Bogus quote 
lady@uhunix.uhcc.hawaii.edu         lady@uhunix.bitnet
Xref: sparky sci.math:14837 sci.physics:18758
From: mueller@schaefer.math.wisc.edu (Carl Douglas Mueller)
Newsgroups: sci.math,sci.physics
Subject: Re: Three-sided coin (ANSWER)
Date: 12 Nov 92 13:41:11 GMT
Reply-To: mueller@schaefer.UUCP (Carl Douglas Mueller)
Organization: Univ. of Wisconsin Dept. of Mathematics

In the DOVER book "Fifty Challenging Problems in Probability with Solutions,"
the 38th problem is called "The Thick Coin."  It is:  "How thick should a coin
be to have a 1/3 chance of landing on edge."  In the solution it is claimed
that John von Neumann solved it (to three decimal places) in his head in 
20 seconds.  THe solution goes on to note that there is no definite solution 
without some simplifying.  They essentially use the "drop through honey" 
idea expressed here earlier.  Consider the coin as being carved out of a sphere
(the edges of the top and bottom of the coin are on the surface of the sphere
and stuff is carved away to leave the coin (two chunks of sphere removed by
slicing along the faces of the coin -- and a sort of belt which is then 
removed by slicing along the outer edge of the coin).  The answer is given
by finding the thickness that makes the surface areas (ON THE SPHERE) of these
three chunks of sphere equal.  The answer is:

The thickness should be the diameter divided by the square root of 8.
(That is, the thickness is to be about 35.4% of the diameter.)

                                      Carl Mueller (mueller@math.wisc.edu)
Newsgroups: sci.math
From: pratt@Sunburn.Stanford.EDU (Vaughan R. Pratt)
Subject: Re: Games with Nonmeasurable Sets
Organization: Computer Science Department,  Stanford University.
Date: Sat, 7 Nov 1992 05:27:10 GMT

In article <1992Nov5.045644.21270@oracorp.com> daryl@oracorp.com (Daryl McCullough) writes:
>Vaughan, I think you have completely missed the point of the original
>posting.

Indeed I did, and recanted last Tuesday.  Maybe the systems hackers at
Odyssey can speed up the connection.
-- 
Vaughan Pratt				There's no truth in logic, son.
From: israel@unixg.ubc.ca (Robert B. Israel)
Newsgroups: sci.math
Subject: Electoral college (was Re: Bill Clinton and Complex Analysis : -))
Date: 5 Nov 92 19:23:47 GMT
Organization: The University of British Columbia
NNTP-Posting-Host: unixg.ubc.ca

In <1992Nov4.054813.20137@CSD-NewsHost.Stanford.EDU> rivin@SAIL.Stanford.EDU (Igor Rivin) writes:

>Does the electoral college actually help in fairness? I was under the
>impression that it was a purely political compromise to augment
>states' rights, so it would interesting if it actually serves an a
>posteriori purpose...

Fairness is a very subjective term, but it may be of interest to note
that Perot received enough votes to give him an absolute majority of
the electoral college.  You just have to rearrange the existing voters
(keeping national totals for each candidate fixed as well as total votes
in each state) so that he gets just over 1/3 the votes in each of a 
set of states having just over half the electoral votes, and Bush and
Clinton each get just under 1/3 in those states.  In the other states, he
needs no votes.  In a system with electoral votes proportional to 
voters, you thus need only about 1/6 of the total votes to get a
majority this way.  Where it's not perfectly proportional, you can
get by with less if you pick the "over-represented" states.  Exercise:
using the actual data, find the actual minimum number of votes needed.

To get a plurality, rather than a majority, in the electoral college,
you just need about 1/9, rather than 1/6. 

This is not entirely a fanciful exercise. It could quite easily happen
that a candidate with fairly strong appeal in one half of the country and
little in the other would be elected despite finishing a poor third in
popular vote. 

-- 
Robert Israel                            israel@math.ubc.ca
Department of Mathematics             or israel@unixg.ubc.ca
University of British Columbia
Vancouver, BC, Canada V6T 1Y4
Newsgroups: sci.math
From: brennan@tfs.com (Brennan Hildebrand)
Subject: Looking for a linear programming package
Organization: TRW Financial Systems
Date: Fri, 6 Nov 1992 07:47:40 GMT

I'm looking for a package to solve linear programming problems from
simple to complex problems.  This would preferably be written in c,
although c++, f77, or pascal would suffice.  I would rather get source
if possible.  Also, it would be nice if it was available via anonymous ftp.

Also, I'm running on a fairly standard bsd4.3 system, if that matters.

In any case, if you know of any, please reply to

brennan@tfs.com

Thanks
-brennan
-- 
+------------------------------------------------------------------------------+
| Brennan Hildebrand                                              oo           |
| brennan@tfs.com                                            o oooooooo        |
|                                                   oooo  ooooooooooooooooo    |
Newsgroups: sci.math,sci.edu,sci.engr,sci.misc,sci.physics,sci.med
From: corbier@edmund.cs.andrews.edu (Daniel Corbier)
Subject: the Ultimate Calculator
Followup-To: sci.math
Organization: Andrews University
Date: Fri, 13 Nov 1992 07:38:30 GMT

===============================================================

     T H E      U L T I M A T E     C A L C U L A T O R

===============================================================

I am now releasing a scientific calculator which supports many
built-in functions, operators, numerical notations, and modes.
This expression evaluator has the following features:

* High precision: 18 significant digits. Range: 3.4E-4932 to 1.2E+4932
* Trig, hyperbolic, and many other common functions
* Summations, numerical integration, equation solving
* Radian, Degree, and Gradient modes for trig functions
* User defined functions and variables
* Flexible notations:  ** or ^, SQR or SQRT, MOD or % etc...
* Decimal, Hexadecimal, Binary and Octal notations
* Arithmetic, bitwise, and relational operators
* Line editor with expression recall
* Expressions can also be entered at the DOS command line
* Adjustable FIX notation
* Online help

Ucalc can be used for anything from quick arithmetic, to
advanced financial & scientific calculations alike.

File Description
----------------

It runs on IBM PC compatibles.

Name:  UCALC12.ZIP
Size:  53K bytes
Where: FTP  garbo.uwasa.fi, under pc/math
-- 
--------------------------------------------------------------------
Daniel Corbier            |   Can you rub your tummy and press
corbier@andrews.edu       |   <ctrl> <alt> <F6> at the same time?
--------------------------------------------------------------------
From: proberts@informix.com (Paul Roberts)
Newsgroups: sci.math
Subject: Re: a first year grad student freaks out.
Date: 12 Nov 92 21:28:52 GMT
Organization: Informix Software, Inc.

In article <92314.170255RVESTERM@vma.cc.nd.edu> RVESTERM@vma.cc.nd.edu writes:
>i'm a first year grad student.  i can do most of the homework assigned
>to me.  i can pass tests i have to take.  i can usually understand
>proofs of theorems that we're studying, given some thought.  i think
>that with a lot of work, i can pass my orals.
>
>however, what's the deal with this thesis thing? what happens if you
>simply cannot prove whatever your advisor assigned?
>
>bob vesterman.

Oh, you just hang about for ever and ever and eventually you walk into
your advisors office and kill him with a hammer. They put you away for
seven years or so (after all, it is *almost* justifiable homocide), you
eventually get released, still muttering darkly about "other scores
you still have to settle at Stanfo ...", ooops, at your ex-University.

No big deal. This is a true story.
Newsgroups: sci.math,sci.physics,sci.astro,sci.bio,sci.chem,misc.education
Newsgroups: sci.math
Subject: Re: Apology about f'(g(x))
From: <CHM103@psuvm.psu.edu>
Date: Fri, 6 Nov 1992 01:14:10 EST
Organization: Penn State University

In article <1992Nov2.115020.11332@linus.mitre.org>,
  bs@gauss.mitre.org (Robert D. Silverman) says:
>
>In article <1992Nov2.035511.826@massey.ac.nz> news@massey.ac.nz (USENET News
>System) writes:
>:
>:Please don't look to Bob for support - he's usually right but
>:I think he's about to recant this time!
>
>
>I am NOT.
>

"You can lead a horse's ass to knowledge, but you can't make him admit it!"
Xref: sparky sci.math:14890 sci.physics:18803 sci.astro:11948 sci.bio:4121 sci.chem:4556 misc.education:4278
From: mccolm@darwin.math.usf.edu. (Gregory McColm)
Newsgroups: sci.math
Subject: Re: Well-known people who majored in math (other than mathematicians)
Date: 28 Oct 92 18:32:22 GMT
Organization: Univ. of South Florida, Math Department

In article <1992Oct20.090735.11632@infodev.cam.ac.uk> rgep@emu.pmms.cam.ac.uk (Richard Pinch) writes:
>In article <81909@ut-emx.uucp> tim@ccwf.cc.utexas.edu writes:
>>
>>Hmm, Mr. Khayyam died in 1123 AD, several years before the first university
>>was founded at Oxford.  I wonder where one could major in math back in those
>>times, particularly in Persia.
>>
>Oh dear.  The University of Oxford was not even the first university
>in Europe, let alone in the world.  The Islamic countries had a much
>higher standard of learning than Europe in the 12th century: they had
>[...]


I was under the impression that the oldest university-like 
institution was Plato's Academy, which was similar to that, 
er, cult that Pythagoras had set up in South Italy.  The 
oldest university---according to some undergrad texts---was 
the Museum at Alexandria.

But were there universities in Medieval Islam?  I thought 
that it was like pre-Academy Greece, with various "enlightened 
monarchs" setting up large courts inhabited by painters, 
writers, astrologers, theologians, and the like.  Certainly, 
that was the environment that Khayyam lived in----a world 
closer politically to Mozart's than to Newton's.

-----Greg McColm
Newsgroups: sci.math
From: wjcastre@magnus.acs.ohio-state.edu (W.Jose Castrellon G.)
Subject: Re: Axioms of set theory, infinity and R. Rucker
Organization: The Ohio State University,Math.Dept.(studnt)
Date: Sun, 8 Nov 1992 02:38:39 GMT

In article <1992Nov7.001459.7644@magnus.acs.ohio-state.edu> I write:

[...]
>Actually without using the Axiom of Choice, it is possible to prove the exis-
>tence of the set of natural numbers, from the other axioms of set theory with
>"There is an infinite set" in place of the Axiom of Infinity.
>

Herman Rubin has posted a proof of this, involving Hartog's function.

I have received a few requests to clarify what definition of _infinite_
I had in mind for the statement "There is an infinite set". Well, one
can think of Dedekind's: A set is infinite if there is a function from
it into itself that is injective but not onto; however it turns out 
that all definitions of _infinite_ will work as well, if one makes a
small assumption on the property of being _infinite_.

[some blank lines, in case you want to think about it]





















A reasonable request is that if  X is _infinite_ then it remains so when we
remove one of its elements.  [and that the empty set not be infinite...]
So let  I(X)  _X is infinite_  a formula that satisfies:
For all X and all y in X,  I(X) --> I (X\{y})
Then one would like to show that the existence of a set satisfying I(X),
implies the existence of the set of natural numbers (set of all the 
ordinals strictly smaller than any non-zero limit ordinal, or equivalently 
the smallest set containing 0 and the succesor of each of its elements).
For this, take the range of the Hartogs function, restricted to the
ordinals smaller than all limits (intuitively this is the set of finite 
ordinals that can be mapped injectively into X), and claim that this set H
is the set of natural numbers (and some more to help in the proof).
Claim: If  t  is an ordinal strictly smaller than all limits then  t  
       belongs to  S  (i.e. there is an injective  f: t --> X), and 
       I(X\f(t))  (i.e. the complement of the range of  f  is _infinite_) 
Suppose not, then take the least  r  for which it is false. Then since  r
is not a limit, the claim is true for  the ordinal  r-1:
so there is an injective  g: r-1 --> X  and  I(X\g(r-1)). By the property
of the formula  I, one can remove an element  z  of  X\g(r-1) and still have
I( (X\g(r-1)) \ z ). This is enough to get a contradiction, since one can
extend  g  to  an  f: r --> X  by sending the new element to  z, and have
that the claim in fact did hold for  r , contrary to the assumption that
r  was a counterexample.

By the way, I think the proposer's original problem is very interesting, and
giving a correct solution is not simple at all.
From: sdunbar@nde.unl.edu (steven dunbar)
Newsgroups: sci.math
Subject: Re: group theory for HS students
Date: 11 Nov 92 02:29:30 GMT
Distribution: sci
Organization: University of Nebraska--Lincoln
NNTP-Posting-Host: nde.unl.edu

sdunbar@nde.unl.edu (steven dunbar) writes:


>Here's a data point.  My daughter is in the eighth week of 7th grade.  She 
>is in an "honors" math class of about 30 kids.  They all know the basic 
>concepts of operation, inverse, and identity in general and with specific 
>application to the cyclic groups and at least the permutation group on 3 
>elements, along with a couple of other examples.  They have not yet called 
>these a group or in the case of two operation on Z mod n, a ring, but they 
>do recognize when they have what the book calls a uni-fold system ( a 
>group) and a bi-fold system, ( a ring).  I am waiting for the introduction 
>of these names.  Right now, the book they are in is explicitly titled 
>"Intuitive Ideas".  It's part of a comprehensive series designed for grades
>7-10.  I don't have the series title or the authors handy, but it was 
>developed at Southern Illinois University, at least in part.

>- Steve Dunbar

I have had a couple of requests for the textbook mentioned above, so here's
the detailed information:
Comprehensive School Mathematics Program: Elements of Mathematics
There is a team of authors.  Some are bona fide mathematicians.
The publisher's address and phone:
Comprehensive School Mathematics Program
12500 E. Iliff Ave. Suite 201
Aurora, Colorado 80014
(303) 337-0990

In Volume 0, Intutive Background, are the Chapters
1. Operational Systems, 2. The Integers, 3. Sets, Subsets, Operations with 
Sets, 4. Ordered n-tuples, 5. Mappings, 6. The Rational Numbers, 7. 
Decimals and an Application of the Rational Numbers. 8. Introduction to 
Probability, 9. Introduction to Number Theory, 10. Algebra in Operational 
Systems, 11, Algebra of Real Functions, 12, Geometry, Incidence and 
Isometries, 13, Geometry, Similitudes, Coordinates and Trigonometry, 14, 
Topics in Probability and Statistics, 15, Topics in Number Theory, 16, 
Introduction to Computer Programming.

The 7th grade will cover Chapters, 1,2,3,4,7,8,9,13,14.
Newsgroups: sci.math
From: ledwards@leland.Stanford.EDU (Laurence James Edwards)
Subject: Re: definition of topological space
Keywords: Topology; Open sets; Continuity
Organization: DSG, Stanford University, CA 94305, USA
Date: Fri, 6 Nov 92 09:12:00 GMT

In article <1992Nov5.165530.21866@CSD-NewsHost.Stanford.EDU>, pratt@Sunburn.Stanford.EDU (Vaughan R. Pratt) writes:
|> In article <1992Nov5.094404.15550@infodev.cam.ac.uk> rgep@emu.pmms.cam.ac.uk (Richard Pinch) writes:
|> >Incidentally, {1,2,3} {} {1} is a perfectly good family of open sets
|> >for a topology on {1,2,3}: but it has nothing to do with epsilons and
|> >deltas.
|> 
|> Well, not nothing at all.  Any topology determines the nearness
|> relation:  point x is NEAR set Y when x does not belong to Y but does
|> belong to every closed set containing Y (i.e. to the CLOSURE of Y).
|> 
|> (The points near the INTERIOR of X (= complement of closure of
|> complement of X) constitute the FRONTIER of X.  The BOUNDARY of X is
|> the portion of its frontier lying within X, equivalently those points
|> near the complement of X.  So the frontier of X is the boundary of X
|> plus all points near X.)
|> 
|> Applying this to the example, 1 is a hermit (is near no set) while 2 is
|> near {1}, {3}, and {1,3}, and 3 is near {1}, {2}, and {1,2}.  (So x
|> being near singleton {y} need not imply that y is near singleton {x}.)
|> 
|> This is the topologically abstract expression of the general idea of
|> epsilon-delta.

Ok, this was one of the things that was confusing me with regard to finite
sets. To me it seemed that determining the closure requires the definition
of neighborhood and that neighborhood depends on the definition of near,
but in the above near depends on the definition of closure. I'm having a
hard time figuring out why this isn't a circular chain of definitions.
To my untrained eye it would seem that a set in the absence of any
ordering or distance relationships cannot be categorized as open or
closed.

Larry Edwards
Newsgroups: sci.math
From: daryl@oracorp.com (Daryl McCullough)
Subject: Re: Games with Nonmeasurable Sets
Organization: ORA Corporation
Date: Thu, 5 Nov 1992 04:56:44 GMT

pratt@Sunburn.Stanford.EDU (Vaughan R. Pratt) writes:

>Now where did this depend on the cardinality of the well-ordered deck?
>The *only* relevant fact, an elementary measure theoretic one, is that
>only countably many cards can be assigned a nonzero probability.
>(Proof:  every such card is in the finite set of cards assigned
>probability at least 1/n for some postive integer n, and there are only
>countably many such sets.)

Vaughan, I think you have completely missed the point of the original
posting. Let me repeat the key points:

    1. There is one card for every real between 0 and 1.
    2. Cards are dealt randomly according to the usual Lebesgue
       measure on reals.

So the probability of being dealt any particular card is precisely 0.
However, for any particular real r, the probability of being dealt
a card greater than r in the ordering LT is the Lebesgue measure of
the set

    { r' | LT(r,r') }

Since this is the complement of a countable set, it has Lebesgue measure
1.

>The resolution of the paradox is that whatever the distribution of a
>player's cards, once her opponent knows it, her estimated likelihood of
>winning becomes realistic.  This is true not just for the countable
>deck, as you imply, but for all decks, including Daryl's.

In the case of the uncountable game, the distribution is known ahead
of time. The paradox *follows* from facts about the Lebesgue measure.

>The one thing I will concede is that the paradox is harder to see
>through when you state it for a higher cardinal.

>But this was my point in the beginning.  The right approach is to ask
>why there is no paradox at lower cardinals (answer: look at the
>probability distribution), and then increase the size of the deck to
>see if anything changes: no it doesn't.  The measure disappeared back
>when the set was well-ordered, so continuing to refer to it is merely
>a red herring (again, my point).

A completely mistaken point, I'm afraid.

>I don't think this contradicts anything anyone else has said; in
>particular I think it is completely consistent with Herman Rubin's
>answer, even if it looks superficially different.  It merely proposes a
>different line of attack on the paradox: ask what role the large
>cardinal is playing, and attack that question by asking for the
>smallest cardinal for which the paradox works.

It works for uncountable cardinals, but not countable ones. I think
the reason is that measures are countably additive, so there is no way
to give probabilities on the naturals so that for all n, the measure
of the set of m such that m < n is always 0.

Daryl McCullough
ORA Corp.
Ithaca, NY
 

Xref: sparky sci.math:14855 sci.physics:18775 sci.astro:11930 sci.bio:4113 sci.chem:4542 misc.education:4267