HDTenEightyP/NetNews huggingface dataset:
From: weemba@sagi.wistar.upenn.edu (Matthew P Wiener)
Newsgroups: sci.math
Subject: Re: What a weird group!!!
Date: 15 Oct 92 15:04:00 GMT
Reply-To: weemba@sagi.wistar.upenn.edu (Matthew P Wiener)
Organization: The Wistar Institute of Anatomy and Biology
In-reply-to: edgar@function.mps.ohio-state.edu (Gerald Edgar)

In article <1bjnc4INN7hp@function.mps.ohio-state.edu>, edgar@function (Gerald Edgar) writes:
>The construction uses the Axiom of Choice, so no one knows...

>Or, before you tackle visualizing that, how about visualizing the
>Stone-Cech compactification of the integers?

As a doable warm up, given a function f, you can indeed visual a
compactification that f extends to.  Consider, for example, the
function f:x|->=sin(1/x) on the open interval X=(0,1).  X is
homeomorphic to G, the graph of f.  Consider G', the closure of
G.  It's G along with the interval [-1,1] on the y-axis.  On G',
f has an obvious continuous extension: the identity map.  Now
visual a compactification for two functions, and pretty soon the
role of choice is reduced to the comforting belief that you can
now just dotdotdot your way to Stone-Cech visual bliss.
-- 
-Matthew P Wiener (weemba@sagi.wistar.upenn.edu)
Xref: sparky sci.math:13354 sci.math.num-analysis:3036 sci.math.stat:2157 sci.math.symbolic:2749
From: jerry@cs.mcgill.ca (Gerald (Jerry) KUCH)
Newsgroups: sci.math,sci.math.num-analysis,sci.math.stat,sci.math.symbolic
Subject: Re: Richard Fateman's e-mail address
Keywords: finger command, unix
Date: 17 Oct 92 03:27:03 GMT
Organization: SOCS - McGill University, Montreal, Canada

In article <1992Oct16.193731.15674@samba.oit.unc.edu> Herman.Woltring@bbs.oit.unc.edu (Herman Woltring) writes:
>In article <92285.111410C44590@TRMETU.BITNET> <C44590@TRMETU.BITNET> writes:
>>Hi,
>>i am looking for e-mail adresses of either Prof.Kathy Yeklick or Mr.
>>Richard Fateman of the department of Mathematics,Berkeley University.
>>
>>any help is highly appreciated.
>>
>>regards.
>>reza
>>METU; Ankara_ TUrkey
> 
>If you have access to a Unix machine, you can issue the command
> 
>   finger yeklick@stanford.edu
>   finger fateman@stanford.edu
> 
>upon which the true email address, *if* published, is returned, together
>with help information.  I've tried it, and scored negative on both counts.
>From a BITNET machine like yours, you might send a query for help to
>POSTMAST@STANFORD.BITNET.  For more specifics about STANFORD, send the
>command SEND NODENTRY STANFORD to NETSERV@TREARN.BITNET.

When did Richard Fateman move from UC Berkeley to Stanford???

>Good luck -- Herman J. Woltring <woltring@hnykun53.bitnet>
>--
>   The opinions expressed are not necessarily those of the University of
>     North Carolina at Chapel Hill, the Campus Office for Information
>        Technology, or the Experimental Bulletin Board Service.
>           internet:  bbs.oit.unc.edu or 152.2.22.80


-- 
 Jerry Kuch (jerry@cs.mcgill.ca) ----- SOMETHING NEAT SHOULD GO HERE.
 "I was wrong to play God.  Life is precious, not a thing to be toyed with.
  Now take out that brain and flush it down the toilet."
                  --- M. Burns  "Treehouse of Horror II"
From: robin@ruchem.ru.ac.za
Newsgroups: sci.math
Subject: Turbo C matrix routines
Date: 14 Oct 92 16:01:59 GMT
Article-I.D.: hippo.1992Oct14.160008.8136
Reply-To: robin@ruchem.ru.ac.za
Organization: Rhodes University, Grahamstown, SA

Anyone got or know of Turbo C matrix routines (diagonalization,
eigenvalues, eigenvectors) which I can ftp?
Thanks in advance
Robin
Newsgroups: sci.math
From: urjlew@ecsvax.uncecs.edu (Rostyk Lewyckyj)
Subject: Re: Mattel says "Math is tough."
Summary: How about "One plus one is three" :-)
Organization: UNC Educational Computing Service
Date: Sun, 11 Oct 1992 01:38:13 GMT



Well how about it?
From: litow@csd4.csd.uwm.edu (bruce e litow)
Newsgroups: sci.math
Subject: real exponential sums
Date: 13 Oct 1992 13:11:49 GMT
Organization: Computing Services Division, University of Wisconsin - Milwaukee
Distribution: world
NNTP-Posting-Host: 129.89.7.41
Originator: litow@proclus.csd.uwm.edu

Let a_k = exp(k/N) where 0 <= k < N and let S1 and S2 be two sums
over two disjoint subsets of the a_k. By Lindemann's Thm, 
S1 - S2 can never vanish but is there a decent lower bound on
|S1 - S2| ? In particular, 1/N^O(1) ?

Please send email to


Bruce Litow
Computing Services Division
P.O. Box 413
Univ. Wisconsin-Milwaukee, Milwaukee, WI, 53201
litow@proclus.csd.uwm.edu
Newsgroups: sci.math
From: tordm@vana (Tord G.M. Malmgren)
Subject: Re: Calculating pi: help!
Reply-To: TordM@VanA.PhySto.SE
Organization: Department of Physics, University of Stockholm -- Sweden
Date: Thu, 15 Oct 1992 10:38:12 GMT

In article <7567@charon.cwi.nl>, dik@cwi.nl (Dik T. Winter) writes:

>Compiler bug?  Try main(){printf("%.4d\n",0);} if this program does not
>print 0000 your compiling system has a bug.

 compiler bug indeed; yet another reason not to use "c" :-)




---------------+--------------------------------
 Tord Malmgren | InterNet: TordM@VanA.PhySto.SE | These opinions are my OWN,
               | BITNet  : TordM@SESUF51        | and NOT of this department!
---------------+--------------------------------
 Department of Physics, University of Stockholm
From: hrubin@mentor.cc.purdue.edu (Herman Rubin)
Newsgroups: sci.math
Subject: Re: Mattel says "Math is tough."
Summary: Math is not the only thing taught badly
Date: 8 Oct 92 00:27:55 GMT
Organization: Purdue University Statistics Department

In article <1992Oct7.150850.23195@murdoch.acc.Virginia.EDU> crb7q@kelvin.seas.Virginia.EDU (Cameron Randale Bass) writes:
>In article <Bvr62B.2BA@mentor.cc.purdue.edu> hrubin@mentor.cc.purdue.edu (Herman Rubin) writes:

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

>>Properly explained, and this is almost never done, the concepts are not
>>all that difficult, although practice and application are necessary to
>>really understand them.  The notion of variable, possibly the most important
>>in mathematics, is essentially the notion of pronoun.  The notions of 
>>theorem and proof are extremely important, and not well taught; knowing
>>these does not make one adept at producing them.  It does not make one
>>adept at using them, either, but that is of comparable difficulty to
>>writing sentences and paragraphs, and is even similar to that.

>     Try teaching sentence and paragraph writing to a young child.

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

The level got changed in the discussion.  I would teach the notion of
variable to a young child and even expect to get it across.  Theorem
and proof would have to await a better understanding of language, and
except for a really bright child, probably not before 9 or 10.

But understanding the concepts corresponds to being able to RECOGNIZE
a sentence or paragraph, not to produce them.  A young child can 
certainly be taught to recognize a properly formed sentence; paragraphs
are more vague.  Teaching someone to produce a good sentence or 
paragraph or proof is teaching someone to be an artist; it cannot
really be taught, just evoked.  However, do not believe that the
teachers teaching young children English know English grammar any
more than those teaching young children mathematics know mathematical
structure.

-- 
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
Subject: Re: Looking for a slick proof
From: news@massey.ac.nz (USENET News System)
Date: Wed, 7 Oct 92 19:52:33 GMT
Organization: Massey University

In article <Bvr85r.26E@watdragon.uwaterloo.ca>, deghare@daisy.uwaterloo.ca (Dave Hare) writes:
> 
> In article <hunt.718423655@shy.umd.edu> hunt@shy.umd.edu (Brian Hunt) writes:
> >bubai@matt.ksu.ksu.edu (P.Chatterjee) writes:
> >>How does one prove that 2^n divides n*(n+1)*(n+2)*......*(2n) without     
> >>having to resort to the 'odd' and 'even' induction? Any ideas?
> >
> >In fact 2^n divides (n+1)(n+2)...(2n), and it's the largest power of 2
> >to do so.

This can be done by an ordinary induction. I'll prove more, that for
prime p, p^n | f(n) = (n+1)(n+2)...(pn) and is the largest power of p
to do so.

Clearly true for n=0.
Now f(n+1) = f(n)(pn+1)(pn+2)...(pn+p)/(n+1) = pf(n)(pn+1)(pn+2)...(pn+p-1)
and p divides none of the factors after f(n).

Exercise, what happens if p is not prime?
Clearly, divisibility by p^n still holds, but
what is the highest power of p which works?

Terry Moore
From: bumby@no.rutgers.edu (Richard Bumby)
Newsgroups: sci.math
Subject: Re: Another GRE question for you folks
Date: 12 Oct 92 15:25:41 GMT
Organization: Rutgers Univ., New Brunswick, N.J.

nin15b66@merrimack.edu writes:
>...
>This one came from a sample GRE test.
>...HOWEVER, I was taught (* perhaps incorrectly *)
>that the square root of any number is + or -  ie, the square root of 9 is
>+ or - three.  ...

I think that current usage is to demand that square root be a function
(so you can make it a button on your calculator).  This demands that a
single answer be agreed upon, and the positive square root is the
natural choice for being THE square root.  This allows "absolute
value" to be defined as "the square root of the square".  None of
these arbitrary choices can change the fact that the equation x^2=9
has two solutions.  Furthermore, if you are looking for square roots
in a p-adic field instead of the real numbers, there is not always a
way to prefer one of the square roots to the other.  However, for
primes which are congruent to 3 modulo 4, the same reason that selects
positive real numbers should select those which are products of powers
of p (assumed >0) and units which are quadratic residues modulo p.  In
particular, in the 7-adic numbers, THE square root of 9 is -3.
-- 
R. T. Bumby **  Rutgers Math ||   Amer. Math. Monthly Problems Editor
bumby@math.rutgers.edu       || P.O. Box 10971 New Brunswick, NJ08906-0971
bumby@dimacs.rutgers.edu     || Phone: [USA] 908 932 0277 * FAX 908 932 5530
Newsgroups: sci.math
From: wjh@cbnewsl.cb.att.com (william.j.hery)
Subject: Finite field software?
Organization: AT&T Bell Laboratories
Distribution: na
Date: Mon, 12 Oct 1992 20:38:06 GMT

Does anyone know of software (C or C++ routines would be fine) for
doing calculations in finite fields. Particularly needed are routines
for polynomials (manipulation, finding irreducibles, finding primitve
roots, etc.) over fintite fields, including "polynomials of polinomials"
i. e.,  polynomials over an extention field which is itself a field of
polynomials modulo an irreducible polynomial over the prime field.

Public domain software preferred, but not required.

Bill Hery
AT&T Bell Labs
201-386-2362
hery@att.COM
Newsgroups: sci.math
From: kavuri@lips.ecn.purdue.edu (Surya N Kavuri )
Subject: The problem of Irish men
Organization: Purdue University Engineering Computer Network
Date: Thu, 15 Oct 1992 06:37:57 GMT

  Prove that there are at least two Irish men who shook 
  hands the same number of times with other Irish men.



  Surya Kavuri


Xref: sparky sci.math:13005 sci.math.symbolic:2682 sci.math.num-analysis:2979
From: huang@deakin.OZ.AU (Weiguang Huang)
Newsgroups: sci.math,sci.math.symbolic,sci.math.num-analysis
Subject: RE: Where to get math symbolic shareware
Date: 10 Oct 1992 23:09:24 +1000
Organization: Deakin University, Victoria, Australia
Distribution: world
NNTP-Posting-Host: sol.deakin.oz.au
Expire: 2 month

	I suggest you consider SymbMath.
	It has three versions: Shareware, Student, and Advanced. The 
shareware version is available from SIMTEL20 archives on anonymous FTP sites 
(wsmr-simtel20.army.mil as /calculator/sm211a.zip, rana.cc.deakin.oz.au as 
/huang/sm211a.zip, etc) or by e-mail from listserv@ndsuvm1.bitnet.
From: multimus@aud2.aud.auc.dk
Newsgroups: sci.math
Subject: NON-LIN-DIFF-SIM
Date: 16 Oct 92 17:02:35 GMT
Organization: Aalborg University Center, Denmark


Does anyone have, or know of, C libraries for simulation of 
NONlinear differential equations, by  using Runge Kutta or
simular methods?

Please reply to s7hbj92@control.auc.dk

Thanks in advance 
Helgi

(My News didn`t work so I borrowed a friends username.)
From: hougen@vision.csl.uiuc.edu (Darrell Roy Hougen)
Newsgroups: sci.math
Subject: Re: Mattel says "Math is tough."
Date: 15 Oct 92 15:59:13 GMT
Organization: Center for Reliable and High-Performance Computing, University of Illinois at Urbana-Champaign
NNTP-Posting-Host: vision.csl.uiuc.edu

mbk@jacobi.ucsd.edu (Matt Kennel) writes:

*>Perhaps then, a good solutions, would be for teachers and TA's to specifically
*>organize problem sessions and encourage full participation by all students,
*>especially those who seem to be out of the social mainstream in the
*>class.

I am of the opinion that people that do the problems by themselves
learn the subject better and learn how to think more clearly too.  Of
course, there is a point of diminishing return for any problem at
which time a person should admit that s/he needs help or at least a
different perspective.  However, it helps to be stubborn :-)

Darrell
From: artl@hpcvnb.CV.HP.COM (Art_Lee)
Date: Tue, 13 Oct 92 14:07:00 PDT
Subject: Correspondence courses
Organization: Hewlett-Packard Co., Corvallis, Oregon
Newsgroups: sci.math

I am looking for information about mathematics correspondence courses.
I would like stories of good and bad experience people have had with
them. What they liked or disliked.  What level of material was in the
course? Who offered it? What did it cost? 


Newsgroups: sci.math
From: jamie@hal.gnu.ai.mit.edu (Andrew John Radcliffe)
Subject: Re: Combinatorics Problem (probably easy)
Summary: It's Sperner's lemma
Organization: /etc/organization
Date: Fri, 16 Oct 1992 18:58:41 GMT

In article <1992Oct15.232815.26763@u.washington.edu> cxu@milton.u.washington.edu (Chongguang Xu) writes:
>
>I have a conjecture about a combinatorics question which I have been 
>unable to prove.  I'm hoping someone on the net knows the answer or
>can give me a reference.
>
>Given a set S of k elements, let A be the largest family of subsets of S
>such that for every two elements a and b of A, b is not a substet of a.  
>My conjecture is that the cardinality of A is C(k, [k/2]), where C(p,q)
>is the binomial coefficient, and [c] is the floor of c.  I can prove that 
>the cardinality of A is at least that big, but I can't prove it can't 
>be bigger.
>

Your conjecture is true, and the result is known as Sperner's lemma.
(Somewhat unfairly Sperner has >two< lemmas to his name.) There
are several lovely proofs, none really short enough to give here.
A good book that talks about Sperner's lemma, among other things, is
B. Bollobas, Combinatorics, Cambridge University Press. I'll email
you several proofs if you want.

Jamie Radcliffe



Xref: sparky sci.math:13170 sci.physics:16486 sci.astro:10737 sci.bio:3561 sci.chem:3932 soc.men:17720 soc.women:17714
From: mapsj@gdr.bath.ac.uk (Simon Juden)
Newsgroups: sci.math,sci.physics,sci.astro,sci.bio,sci.chem,soc.men,soc.women
Subject: Re: Is Math Hard?
Date: 14 Oct 92 18:06:57 GMT
Organization: School of Mathematics, University of Bath, UK

In the referenced article, frisinv@alleg.edu writes:
>That seems to be the big question these days. Is it hard for girls, boys,  
>adults, toy companies, mathematicians, college students, or anyone else?  
>I've spoken with many people -including a math professor- who swear math  
>is the hardest thing on the face of this earth. I know others who laugh  
>insanely and say math is child's play. I want to take a little poll:
>  
> How hard do you find mathematics? Were you one of those people who  
>dreaded cracking a book or one of those people who did calculus in junior  
>high school for fun? 
>
>Send replies to frisinv@alleg.edu. I'll post the results. 
>--
I think it is easy to make a mistake and use 'hard' in a pejorative sense; my
own view is that one cannot expect to get something worthwhile out without
putting a lot of effort in: you don't get something for nothing. I enjoy maths
(obviously!) and have generally found the stuff which interests me most is the
stuff which takes most effort to get to grips with. Don't be afraid of making
it hard, just be sure to make it interesting!

My 200 pounds worth (ie 2 pence a couple of weeks ago)

Simon
Newsgroups: sci.math
From: tao@ginger.princeton.edu (Terry Tao)
Subject: Re: Zeno
Originator: news@nimaster
Organization: Princeton University
Date: Thu, 8 Oct 1992 14:03:27 GMT

The question was: if you take steps closer and closer to B, starting at A, with
each step halving the distance between you and B, and the time taken per step
halving as well, starting at 1/2 a minute, will you ever get to B?

well, after 1/2 a minute, you are halfway to B.
after 3/4 a minute, you are 3/4 way to B.
after 7/8 a minute, you are 7/8 way to B.
.
.
.

well, it can be seen that nowhere in this sequence do you actually GET to B, 
although you get arbitarily close.  However, in none of the above statements
has a minute actually elapsed.  If you plot a distance versus time graph, and
use one of the axioms of physics: continuity of motion, then you can deduce
that at after exactly one minute, he is exactly on point B.  This happens
"after" all the steps taken to halve the distance to B.

Terry
Newsgroups: sci.math
From: dagjo@ifi.uio.no (Dag Espolin Johnson)
Subject: Re: 'Perfect' numbers SUMMARY
Organization: Dept. of Informatics, University of Oslo, Norway
Date: Tue, 13 Oct 1992 12:51:24 GMT
Originator: dagjo@munken.ifi.uio.no


Thanks to all of you that responded to my question about perfect numbers.

First, from Martin Gemmel <mgemmel@cs.vu.nl> i got this list:

 1. 6
 2. 28
 3. 496
 4. 8128
 5. 33550336
 6. 8589869056
 7. 137438691328
 8. 2305843008139952128
 9. 2658455991569831744654692615953842176
10. 191561942608236107294793378084303638130997321548169216
11. 13164036458569648337239753460458722910223472318386943117783728128
12. 14474011154664524427946373126085988481573677491474835889066354349
    131199152128 (77 digits)
13. 23562723457267347065789548996709904988477547858392600710143027597
    50633728317862223973036553960260056136025556646250327017505289257
    80432155433824984287771524270103944969186640286445341280338314397
    90236838624033171435922356643219703101720713163527487298747400647
    801939587165936401087419375649057918549492160555646976 (314 digits)

Several of you told me that:

An even number is perfect if and only if it can be written in the form
2^(n-1)*(2^n-1), where (2^n-1) is a prime. It is not found any odd perfect
numbers, but it is NOT prooved that all perfevt numbers are even.

        2^(n-1) 2^n-1   product
-------------------------------
n=1     1       1               1 is not a prime
n=2     2       3       6
n=3     4       7       28
n=4     8       15              15 is not a prime
n=5     16      31      496
n=6     32      63              63 is not a prime
n=7     64      127     8128
:       :       :       :

It is also true that (2^n-1) is NOT a prime if n is NOT a prime. But, if n IS
a prime, you are NOT SURE that (2^n-1) is a prime.

Also, from David G Radcliffe <radcliff@csd4.csd.uwm.edu> i got this list of
n's where (2^n-1) is a known prime:

2, 3, 5, 7, 13, 17, 19, 31, 61, 89, 107, 127, 521, 607, 1279, 2203, 2281,
3217, 4253, 4423, 9689, 9941, 11213, 19937, 21701, 23209, 44497, 86243,
110503, 132049, 216091, 756839.      

And, finaly I looked in Guinness Book of Records, and it says that it is 35
known perfect numbers.

If some of you have any more information on perfect numbers, or find any
incorrects in this document, please tell me.

Dag Espolin Johnson  -  dagjo@ifi.uio.no
From: lawton%ecfa@jesnic.jsc.nasa.gov (Eric G. Lawton)
Newsgroups: sci.math
Subject: Re: Well-known people who majored in math (other than mathematicians)
Date: 13 Oct 92 20:25:53 GMT
Organization: Lockheed Engineering and Sciences Co.

In article <1992Oct8.191230.16442@lehi3b15.CSEE.Lehigh.EDU> 
buyskes@lafcol.lafayette.edu (Steve Buyske) writes:
>         So the question is, do you know of any well-known people who 
> majored in math but aren't known as mathematicians?

I believe Phillip Glass (the American Composer) has a background in 
mathematics.  Can someone verify this?

Eric G. Lawton
lawton%ecfa@jesnic.jsc.nasa.gov

My opinions and views are not necessarily those of my employer.
Xref: sparky sci.math:12837 sci.physics:16097
From: pcl@oxford.ac.uk (Paul Leyland)
Newsgroups: sci.math,sci.physics
Subject: Re: How do you draw a straight line?
Date: 7 Oct 92 08:04:15 GMT
	<1ass0lINNhc2@agate.berkeley.edu>
	<1992Oct6.232636.20173@linus.mitre.org>
Organization: Oxford University Computing Service, 13 Banbury Rd, Oxford, OX2
	6NN
In-reply-to: bs@gauss.mitre.org's message of 6 Oct 92 23:26:36 GMT

In article <1992Oct6.232636.20173@linus.mitre.org> bs@gauss.mitre.org (Robert D. Silverman) writes:
   In article <1ass0lINNhc2@agate.berkeley.edu> chrisman@wheatena.berkeley.edu (chrisman) writes:
   stuff deleted....
   >a straight line, how about a laser?  For the physicist (not the
   >mathematician), I suppose that the path followed by a beam o
   >light is the closest thing to a definition of a straight line.
   >
   It still bends under gravity, unless you assume the Earth is a perfect
   sphere and point it in a direction normal to the surface. Even then,
   there is the Sun's gravity...........

I've known people who *define* "straight line" to be equivalent to
"geodesic", on the grounds that "a straight line is the shortest
distance between two points".

Paul


--
Paul Leyland <pcl@oxford.ac.uk>          | Hanging on in quiet desperation is
Oxford University Computing Service      |     the English way.
13 Banbury Road, Oxford, OX2 6NN, UK     | The time is come, the song is over.
Tel: +44-865-273200  Fax: +44-865-273275 | Thought I'd something more to say.
From: cxm7@po.CWRU.Edu (Colin Mclarty)
Newsgroups: sci.math
Subject: Re: help with recursive functions
Date: 12 Oct 1992 14:47:26 GMT
Organization: Case Western Reserve University, Cleveland, OH (USA)
Reply-To: cxm7@po.CWRU.Edu (Colin Mclarty)
NNTP-Posting-Host: slc5.ins.cwru.edu


In a previous article, cxm7@po.CWRU.Edu (Colin Mclarty) says:

>
>	I'd like some help with partial recursive functions which
>do not extend to (total) recursive ones.  I can prove there is no
>effective routine for extending all partials to total recursive
>functions, but I do not see how to prove there are particular
>partial recursive functions that do not extend to recursive.  Are
>there typical methods from proving this in particular cases?
>
>Colin McLarty
>
	Thanks to the people who pointed out the easy example.  
But are there more general ways of finding partials that do not 
extend to total recursive functions?

	More generally, for subsets A and B of the naturals, with
A containing B, what is known about extending partial recursive 
functions defined on A to ones defined on B?  And what if the 
extension is required to take values in the image of the original
p.r. function?
From: andrew@rentec.com (Andrew Mullhaupt)
Newsgroups: sci.math
Subject: Re: Question on numerical integration
Date: 12 Oct 92 14:50:29 GMT
Organization: Renaissance Technologies Corp., Setauket, NY.

In article <1992Oct8.131346.16921@cs.mun.ca> cory@riemann.math.mun.ca (Cory C. Pye) writes:
>In article <1992Oct7.113401.1322@rz.uni-karlsruhe.de> vhansen@ipfs.bau-verm.uni-karlsruhe.de (Wolfgang von Hansen) writes:
>>How can one calculate things like
>>
>> a                oo
>>Int f(x) dx  or  Int f(x) dx
>>-oo               a
>>
>>numerically. I know how to do such things with finite limits,
>>but I've got no idea how to deal with infinite limits.
>>
>>Thanks in advance, Wolfgang
>
> Try re-expressing the integrand using a substitution which transforms
>the infinite limit to a finite number and leaves the finite number
>finite. This will obviously depend on the integrand.


This can be OK, but there are significant other approaches which are
appropriate in different situations. In particular the Gauss-Laguerre
quadrature rules are good for single-tailed integrals. (Gauss-Hermite
is good for double sided).

The book by Rabinowitz on numerical integration is full a fine advice on
this subject.


Later,
Andrew Mullhaupt