HDTenEightyP/NetNews huggingface dataset:
From: andrew@rentec.com (Andrew Mullhaupt)
Newsgroups: sci.math
Subject: Re: Course on stochastic models of derivative securities
Date: 22 Dec 92 16:38:39 GMT
Distribution: ny
Organization: Renaissance Technologies Corp., Setauket, NY.

In article <1992Dec18.200305.15884@sol.ctr.columbia.edu> dy@shire.math.columbia.edu (Deane Yang) writes:
>The mathematics department at Polytechnic University in Brooklyn
>is considering offering a course on mathematical models of derivative
>securities. The prerequisites for the course would consist only of
>2 years of calculus and basic probability. No knowledge of economics
>or finance is being assumed. The purpose of the course is to develop
> the mathematical methods necessary for understanding
> financial models, such as the Black-Scholes equation.

This should be do-able. 
>1) Are there people on Wall Street who would want to take this course?

Pretty much anyone who needs this kind of course on the street has had 
more than one graduate level course in stochastic processes. I think
a plurality of the Ph. D.'s on the street do some form of derivative
pricing or other.

>Obviously, people who are already doing this sort of stuff don't need
>this course. However, would it be useful to have someone who is not
>a "quant" take a course like this? If so, who?

Possibly young programmers who want to understand what their programming,
etc. However you should expect CS graduates to be ill-prepared on the
mathematics side.

>2) If such people exist, what would be the best way to advertise the
>course?

The course should not be isolated, but part of some sensible program,
because if you just explain Black-Scholes you're not doing anything
which can't be found in any decent finance course. People who will
really need to use this information will need to understand other
important facts, either mathematical or financial, so it makes sense
for this course to be one in a broader program.

>3) Other suggestions or questions are welcome.

You might get more takers if you put a program in mathematical finance
together with a cooperating finance/economics/business department. This
would be a master's program including probability, statistics with data
analysis, linear algebra, numerical analysis, optimization, partial
differential equations, time series and stochastic processes, and on the
finance side, at least courses in macro/micro economics investments,
portfolios, markets, and derivative pricing.

If you can compress this into a master's program with any room to spare,
or you turn some of these courses into pre-requisites, you could have
electives in information theory, specific instruments (stocks, bonds,
CMO's), and practical aspects of scientific, real-time and network computing.

Later,
Andrew Mullhaupt
Newsgroups: sci.math
From: jbaez@riesz.mit.edu (John C. Baez)
Subject: Re: Rounding Rules
Organization: MIT Department of Mathematics, Cambridge, MA
Date: Sun, 20 Dec 92 18:51:26 GMT

In article <1992Dec20.003018.14325@sol.ctr.columbia.edu> shaw@toadflax.UCDavis.EDU (Rob Shaw) writes:
>
>What is the rationale behind the following rounding rule?
>
>when dealing with 5's followed by all zero's, check the
>next digit to the left. If it's even, round down; odd,
>round up.
>
>For example both 1.13500 and 1.14500 are 1.14 to 3 places.
>What is the advantage of having the interval closed at both
>ends around even digits, and open at both ends around odds?
>
>Why the asymmetry?

I can't see any real "reason" for this rule except the following: about
half the time you will round down, and about half the time you will
round up, so if you are (say) adding up a bunch of numbers the expected
error of the sum will be about zero.  

Newsgroups: sci.math,rec.puzzles
From: zellner@stsci.edu
Subject: Re: Marilyn Vos Savant's error?
Organization: Space Telescope Science Institute
Distribution: na
Date: Fri, 1 Jan 1993 01:39:34 GMT

>   1) You meet a man on the street and ask him how many children he has.
>      He replies "two, and one is a boy."  What is the probability that
>      his other child is also a boy?
>
>   2) You meet a man on the street and ask him how many children he has.
>      He replies "two, and the older one is a boy."  What is the
>      probability that his other child is also a boy?
>
>The answer to problem 1 is 1/3, while the answer to problem 2 is 1/2.

> The answer to both is 1/2.  One child whose gender is not known, and 
> two choices for that gender.  It's a 50-50 proposition.

Nope.  Let's re-phrase it a bit.  Suppose the man says 
  
  A.  "I have two children, and one of them is right over there."  
or
  B.  "I have two children, and the older one is right over there."

You look and see a boy.  What's the chances that they are both boys?
Enumerate the cases:

   Boy - Boy
   Boy - Girl
   Girl- Boy
   Girl- Girl

Each of those cases is assumed to have exactly the same frequency
in the total of all two-children families.

In case B you can rule out the latter two combinations, and you are 
left with probability 1/2.  But in case A you can only rule out the 
fourth combination, and the probability is 1/3. 

Or toss two coins, a penny and a nickel.  You look at the nickel 
only, and see a head.  What's the probability that they are both
heads?  One half, of course.  Likewise if you look at only the 
penny.  

But suppose someone else looks, and says "at least one of them 
is a head."  Then the probability that BOTH are heads is 1/3.
If you don't believe it, try a few hundred tosses.

Cheers, Ben
From: arodgers@dcs.qmw.ac.uk (Angus H Rodgers)
Newsgroups: sci.math
Subject: Re: TO ALL !!! -- End of Discussion, I hope
Date: 21 Dec 92 18:21:18 GMT
Organization: Computer Science Dept, QMW, University of London

In <BzM0y5.Iru@watdragon.uwaterloo.ca>
deghare@daisy.uwaterloo.ca (Dave Hare) writes:

>Season's greetings.

>(And, in case I forget, Happy Groundhog Day, too.)

When was Beethoven's birthday?
--
Gus Rodgers,  Dept. of Computer Science, |  [Profound thought for 1993]
Queen Mary & Westfield College, Mile End |     "Philishave is about
Road, London, England.   +44 71 975 5241 |      personal choice" 
E-mail (JANET):   arodgers@dcs.qmw.ac.uk |             -- TV advert
From: cadet@spade.rutgers.edu (Uniquely TiJean)
Newsgroups: sci.math
Subject: factorization in commutative rings
Date: 3 Jan 93 07:05:44 GMT
Distribution: sci.math
Organization: Rutgers Univ., New Brunswick, N.J.

Well, Given D an integral domain 

Then D = euclidean domain ==> D = principal ideal domain ==> D = factorial 
                                                                 domain.

I am looking for counterexamples 

A) D= factorial domain doesn't imply D= princ. idl. domain

   Standard example   Z[x] or F[x,y] where F=field

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.

Any suggestion is appreciated. 

Happy New Year!

JC

PS. I am preparing for my quals so that's why I asked.
From: dbh@doc.ic.ac.uk (Denis Howe)
Newsgroups: sci.math
Subject: Re: Game of pentominos
Followup-To: sci.math
Date: 21 Dec 92 15:23:55
Organization: Computing Department, Imperial College, London, UK
Distribution: world
	<pete.03it@bignode.equinox.gen.nz>
	<rcbaaw.724692264@rw6.urc.tue.nl>
NNTP-Posting-Host: wombat.doc.ic.ac.uk
In-reply-to: rcbaaw@rw6.urc.tue.nl's message of 18 Dec 92 15:24:24

In article <rcbaaw.724692264@rw6.urc.tue.nl> rcbaaw@rw6.urc.tue.nl
(Angelo Wentzler) wrote:

>has anybody ever tried to write a program to compute all
>(N+1)-ominoes from the set of N-ominoes?  It's not difficult: Just
>take one N-omino at a time and fit an extra square onto it.  This
>produces one extra (N+1)-omino.  Fit a square on all possible
>positions, (just "roll" it along the edge) then proceed with the next
>N-omino.

This is precisely how a very old Basic program of mine works.  You
start off with one square (the set of 1-ominoes), add another to the
right then roll it round the outside to generate all 2-ominoes etc..
You then apply the eight reflections and rotations, shift each shape
generated so that its minimum x and y coords are both 0 and compare it
with all previously found n-ominoes.  It's this last step that is the
boring bit.  Anyone come up with any good hashing functions for
ominoes?  Centre of gravity?  Moment of inertia?

Mail me if you want the program.  It's in Acorn Basic and runs on the
Archimedes.
--
Denis Howe <dbh@doc.ic.ac.uk>
So Biggs, you're the idiot who bought all these IBM PCs.  You're fired!
Newsgroups: sci.math,comp.edu,misc.education
From: freier@mail.physics.utah.edu (rodney james freier)
Subject: Re: Education crisis (was RE: how much math...)
Organization: University of Utah - Physics Department
Date: Thu, 31 Dec 92 02:40:15 GMT

In article <1hr5fjINN972@mirror.digex.com>, kfl@access.digex.com (Keith F. Lynch) writes:
|> In article <PRENER.92Dec12015805@prener.watson.ibm.com> prener@watson.ibm.com (Dan Prener) writes:
|> > Little kids learn much faster. ...
|> > But the fact that little kids' learning capacity is so much greater
|> > than that of older people ...
|> 
|> Is there any evidence for this?  It goes against my experience.
|> 
|> Keith Lynch, kfl@access.digex.com

  Well, I remember reading something.  At about the third grade level,
A child's brain goes thru and amazing growth spurt, and it literally doubles
its number of neural connections.  It seems there's evidence that if these
new connections are not put to use (what that was supposed to mean, I don't know)
soon after the growth stage, they probably will never be used.

   Just a bunch of heresay, really.

Rod
 
Newsgroups: sci.math,rec.puzzles
From: stephen@mont.cs.missouri.edu (Stephen Montgomery-Smith)
Subject: Re: Integral Puzzle (Cute, not Evil)
Organization: University of Missouri
Date: 22 Dec 92 23:52:22 GMT

In <isopi.724948656@acf9> isopi@acf9.nyu.edu (Marco Isopi) writes:

>edgar@function.mps.ohio-state.edu (Gerald Edgar) writes:


>>In more flowery language: given the L_infinity and L_1 norms of f, estimate
>>the L_2 norm of f.

>And then Riesz-Thorin theorem shold bring you home.
>Or there are other and better ways?

>>  Gerald A. Edgar                Internet:  edgar@mps.ohio-state.edu

>Marco Isopi

If you use the real interpolation method instead, you get a stronger result:

  || f ||_{2,1}  <=  c sqrt( ||f||_1 ||f||_infty ).

Here ||f||_{2,1} is a so called Lorentz space.  It is defined:

  ||f||_{2,1}  =  int_0^infty  sqrt(measure(|f|>t)) dt .

One can give a direct proof of the above inequality to get c = 1:

  ||f||_{2,1}  =  int_0^||f||_infty  sqrt(measure(|f|>t)) dt
               <= (int_0^||f||_infty 1 dt)^(1/2)  
                                    (int_0^||f||_infty measure(|f|>t) dt)^(1/2)
               =  sqrt( ||f||_1 ||f||_infty ) .

The quantity ||f||_{2,1} is always larger than or equal to ||f||_2, and
usually is not equal (equal only when |f| takes two values one of which is 0).

If you are interested in finding out more about Lorentz spaces, here are
some references.

C.~Bennett and R.~Sharpley,\sl\ Interpolation of Operators,\rm\
Academic Press 1988.\cr
J.~Bergh and J. L\"ofstr\"om,\sl\ Interpolation Spaces,\rm\
Springer-Verlag 1976.\cr
R.A.~Hunt,\rm\ On $L(p,q)$\ spaces,\sl\ L'Enseignement Math.\ (2)
{\bf 12} (1966), 249--275.\cr

Stephen

Newsgroups: sci.math
From: ted@nmsu.edu (Ted Dunning)
Subject: Re: High Prices of Math Books. I am pissed.
Reply-To: ted@nmsu.edu
Organization: Computing Research Lab
Date: Sun, 27 Dec 1992 23:36:52 GMT


In article <3800@tansei1.tansei.cc.u-tokyo.ac.jp> mhiroshi@tansei.cc.u-tokyo.ac.jp (H. Murakami) writes:


   | If they can sell paperback versions in the international
   | market why can't it be done within the US, one might ask.
   | That is a different issue altogether...
   | 

	   The practice of selling something in high price domestically, 
   and in cheap at foreign should be called "dumping", and may be 
   called as an unfair trading.

i am sure that the japanese can teach us all a lesson about this
practice.

but note that the original talked about selling the hardcover edition
in the US, and the paperback edition abroad.  this is hardly dumping
since the two editions different products.  the practice stems from
the fact that expensive paperbacks sell in europe, while in this
country, people buying expensive books want a hardback.  note that the
hardback books in question generally sell for higher prices abroad,
not lower.  i don't really know why book prices in general are so
exorbitant in europe, certainly the size of the tariffs is not
sufficient to explain the difference.

	   The Western book publisher in recent years establish their
   branch in Japan, and distribution of the books are dominated through
   their channel. We usually find they use the currency conversion rate
   around 200yens/dollar or more (the true rate is 125yen/dollars). 

true rate?

currency conversion is a marketplace.  if you want to do the
conversion, then get whatever price you can.  if you want them to do
the conversion, then they can charge whatever price they like.

   Even we try to order to the US book publisher directly expecting
   to get the 125yen/dollar rating of the prices, what those publisher
   will do to us is just ignore the order or circulate the order to
   those Japanese branch which we would not want to.

this is actually typical of most companies that maintain sales
territories. 

   The only way to escape these dirty practice is order the books
   not the the publisher directly but order a book seller in USA
   who is not controlled by the publishing jiants.

this sounds like a fine way around the problem.



btw.... you shouldn't get me started on the practices of *japanese*
publishing companies regarding foreign orders.  they make US and
european companies look like pussy cats.
Newsgroups: sci.math
From: hdev@dutiai.tudelft.nl (Hans de Vreught)
Subject: Re: Xmas and netiquette (was: TO ALL !!!)
Organization: Delft University of Technology
Date: Mon, 21 Dec 1992 08:41:41 GMT

ak005@cleveland.Freenet.Edu (Yona Webb) writes:
>I made  *ONE*  card to reflect this excitement and to greet all my friends,
>Christian and Jewish.  At one moment I thought of Sci.Math. as a single
>entity because of the help I received from so many people there and ... hop,
>the card was uploaded in a public msg TO ALL!!! Good intentions, wrong move!

Good intentions taken. I think the majority don't mind receiving your good
intentions. Don't be overwhelmed by an angry minority ("He who shout loudest,
has the floor.").

Receiving tens of cards, well, that's something different. Sci.math is not
intended for that stuff. If you (and other people as well) want to express
your intentions the next time, answer or comment somebody's article, and give
a small note with your intentions before you sign.

Personally, I am much more displeased by people that don't take the courtesy
to trim previous articles. About half of the time I read news by modem (2400
baud). Reading two pages of old stuff (your card + comment of the minority)
and then seeing somebody stating "I agree with you." definitely pisses me off.

Best wishes for xmas (hm, I'm not even religious) and 1993.
--
Hans de Vreught                          | John von Neumann:
hdev@dutiba.twi.tudelft.nl               | Young man, in mathematics
Delft University of Technology (TWI-ThI) | you don't understand things,
The Netherlands                          | you just get used to them.
Xref: sparky sci.math:17428 sci.physics:21780
From: edgar@function.mps.ohio-state.edu (Gerald Edgar)
Newsgroups: sci.math,sci.physics
Subject: Re: More on Huygens' principle
Date: 26 Dec 1992 13:51:55 -0500
Organization: The Ohio State University, Dept. of Math.
NNTP-Posting-Host: function.mps.ohio-state.edu

In article <1992Dec24.073852.20633@nuscc.nus.sg> tim@iss.nus.sg (Tim Poston) writes:
>Could some synth sound wizard out there make a recording of what
>2D or 4D piano music would sound like?

Such a recording was included in the mathematics journal
called "The Mathematical Intelligencer",  Volume 11, number 3.  The
record in entitled "Sphere and Torus Music".  It has music computed
based on spheres of dimensions
1, 2, 3, 6, and 12; it also has music based on
two-dimensional tori with sides in various ratios.
-- 
  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)
Newsgroups: sci.math
From: Greg_Tjosvold@mindlink.bc.ca (Greg Tjosvold)
Subject: Naming numbers
Organization: MIND LINK! - British Columbia, Canada
Date: Tue, 22 Dec 1992 16:35:34 GMT

Hi all,
I am trying to track down as many number "names" as possible. So far I have
only been able to find a name for numbers up to 10^33. Is there a name for
10^36? How about something like 10^1983? Thanks to all in advance.
'Til later,
Greg "Nanook" Tjosvold
The One-Off CD Shop (Vancouver)
From: saouter@irisa.fr (Saouter Yannick)
Newsgroups: sci.math
Subject: Square roots and continued fractions
Date: 21 Dec 92 11:07:41 GMT
Organization: IRISA, Rennes (Fr)



I consider the following algorithm to evaluate the square root of M:

x_0=1

x_{n+1}=\frac{x_n}{2}+\frac{M}{2 . x_n}

coming from Newton method.

In my previous courses one of my math teacher says that this algorithm is very fast and is
even a sub-series of the series of continued fraction for M integers.

It seems to be true for M=2 and 3 and is likely to be easily demonstrable. But for higher
number, this basic algorithm seems not to behave in this way.

If we initially take x_0=int(\sqrt{x}) where int denotes the integer part, it seems again
to give a sub-series of continued fraction.


Is there any pointers or bibliography to this kind of problems ?

Yannick Saouter - saouter@geocub.greco-prog.fr
Xref: sparky sci.math:17392 sci.physics:21736 sci.astro:13408 sci.bio:4674 sci.chem:5553 misc.education:5547
From: marder@agri.huji.ac.il
Newsgroups: sci.math,sci.physics,sci.astro,sci.bio,sci.chem,misc.education
Subject: Re: Is Math Hard?
Date: 24 Dec 92 18:17:41 GMT
 <00721013472@elgamy.uucp.taronga.com> <BxB3B6.417@mentor.cc.purdue.edu> <1992Nov7.184203.1496@allegra.att.com>
Organization: The Hebrew University of Jerusalem - Faculty of Agriculture

In article <1992Nov7.184203.1496@allegra.att.com>, rfc@allegra.att.com (Robert F. Casey) writes:
[ . . . ]

> One time I visited a friend who had a young kid, about 4 to 5 years old,
> and the kid was learning to count and such.  My friend asked questions
> like "How many hands do you have? feet? noses?  Could be memorized responses
> for answers, so I asked "How many tails do you have?"  kid:"Ahhh...
> none! zero!"  He had to think a little for that one, probably noone ever
> asked that question before.  Then "How many fingers?  Thumbs?"  "OK,
> how many fingers do you have that are not thumbs?"  kid: "Ahh.. 10?"
> looks at hands "no, ahhh.. 1,2,3,4,5,6,7,8 eight."  Another wierd
> question!
That reminds me the time that I asked my 3-year-old daughter how many legs
we have in our family.  She couldn't answer until my wife came out of the
shower! (3 years later this is still a family joke).  Actually, I am
constantly surprised about my daughter's (now 6) capacity for abstraction.
The other day while I was lying down, she wanted to play noughts and
crosses (tic-tac-toe).  Instead of opening my eyes, I suggested we play by
grid references (A1, B2, C3 etc.).  She has learned the concept of grid
references before, but what really surprised me was that she was clearly
quite able to play the game without any visual aid!
  Unfortunately, I am not a math teacher, but this incident taught me an
excellent way to test kids for their grasp of grid co-ordinates!

--
                                 '      Jonathan B. Marder
Internet: MARDER@AGRI.HUJI.AC.IL |      Department of Agricultural Botany
Bitnet:   MARDER@HUJIAGRI        | /\/  The Hebrew University of Jerusalem
Phone:    (08 or +9728) 481918   |/  \  Faculty of Agriculture
Fax:      (08 or +9728) 467763   /      P.O.Box 12, Rehovot 76100, ISRAEL
Newsgroups: sci.math
From: dwsmith@bilbo.encore.com (Dwight Smith)
Subject: WANTED: MATH PROBLEM SOLVING PROGRAM AND/OR MATH TUTORIAL PROGRAMS
Organization: Encore Computer Corp.
Date: Thu, 31 Dec 1992 17:36:51 GMT
Keywords: Mathematica, Calculus, Algebra, tutor

For those 3 or 4 guys-that-always-sat-on-the-front-row-in-math-class-and-were-
the-only-ones-the-professor-paid-any-attention-to...you can probably skip this
mail article.

I am looking for some math software that either resolves (step-by-step) Algebra
and Calculus problems, or tutors you through resolving them. I will run the
package on a MAC or a PC, doesn't matter much to me. I even have access to a
unix box (3b2). I am interested in SHAREWARE too, if it does the above. These
are the kinds of math programs I'm looking for ($cheap):

	- Mathematica
	- Calculators!
	- Power Math
	- The Evaluator
	- MathCAD
	- MathParser Extender
	- MathType
	- Calculus (Broderbund SW)
	- The Kemeny/Kurtz Math Series
	- Mastering Calculus Series
	- Math Teachers Workstation
	- Studyware (Calculus)

Enough? If you've got it - or something close (or better), let me know.

Thanks,
D. Smith

Newsgroups: sci.math
From: hrubin@pop.stat.purdue.edu (Herman Rubin)
Subject: Topology of the long integers and the long line
Organization: Purdue University Statistics Department
Date: Mon, 21 Dec 1992 14:21:36 GMT

In article <1992Dec21.103233.723@black.ox.ac.uk> mbeattie@black.ox.ac.uk (Malcolm Beattie) writes:

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

>As John points out, the `more than this' is that the map has to
>be eventually constant. Somebody sketched the proof for me once,
>but I can't remember how it goes. Anyone?

The "easy" way to see this is to start with the fact that the intersection
of any sequence of unbounded closed subsets of either must contain an 
unbounded closed subset even of the long integers.  This can be done
since any non-empty (closed) subset of I (L) has a smallest element.
So one can construct a double sequence x_ij such that x_ij >= a is an
element of S_i, x_i(j+1) >= x_ij +1, and x_(i+1)1 > x_ij for all j. 
The common limit on j of the x_ij is the  desired point.

The eventual constancy of continuous functions follows from this by
the usual proof by contradiction.
-- 
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)
Newsgroups: sci.math
From: dbradley@symcom.math.uiuc.edu (David Bradley)
Subject: Re: G=Ab Gp. H<G => G/H embedds in G, don't use Hom(G,Q/Z)
Organization: Math Dept., University of Illinois at Urbana/Champaign
Date: Tue, 22 Dec 1992 02:48:58 GMT

In article <Bzn3GF.Gt@news.cso.uiuc.edu> dbradley@symcom.math.uiuc.edu (David Bradley) writes:
>Let G be an abelian group and H a subgroup.  Then G has a subgroup
>isomorphic to G/H.  I managed to prove this using the character group

Of course, that should read "Let G be a _finite_ abelian group...

-D.M.Bradley
Xref: sparky sci.math:17284 sci.physics:21557
Newsgroups: sci.math,sci.physics
Subject: Re: Help me deal w/ infinity
From: news@massey.ac.nz (USENET News System)
Date: Tue, 22 Dec 92 00:45:22 GMT
Organization: Massey University

In article <1992Dec21.180815.16110@novell.com>, dseeman@novell.com (Daniel Seeman) writes:
> >
> >I appeal to any math gurus out there to comment on the validity of .9(r)
> >equals one [...]

Just a brief reminder that this is in the FAQ which has just been posted.