moved to wordpress

I'm in the process of moving this blog to wordpress, which has much better LaTex support. The new URL is wdjoyner.wordpress.com.

latex on blogger test

This is a test following http://wolverinex02.googlepages.com/emoticonsforblogger2.

The latex code

should display some latex code for pi/4. Cool! (Don't forget to use the compose window, not the "Edit Html" window.) Seems to only work for displayed equations.

Here is another test:


sage: x = var("x")
sage: integral(1/(1+x^2),x,0,1)
pi/4
sage: plot(1/(1+x^2),x,0,1)

The plot is below.



The (Hamming) weight enumerator polynomial $A_C$ is defined by

where


denotes the number of codewords of weight $i$.
The support of $C$ is the set

open source firmware for some canon digital cameras

I just found out that there is an open source firmware for certain Canon cameras http://chdk.wikia.com/wiki/CHDK. Will one for Nikon be created?

J. G. Thompson and J. Tits share 2008 Abels prize

http://www.reuters.com/article/scienceNews/idUSL2768807220080328

John Griggs Thompson of the United States and Jacques Tits of France were awarded the Abels prize (sharing $1.2 million) on 3-27-2008 for their work in algebra and group theory.

Copyright law as it pertains to mathematics

This is a brief survey on copyright law, as it pertains to mathematicians. It does not cover other aspects of intellectual property law, such as laws governing patents, trade secrets, and so on (see for example, [K]). The basic reference is the excellent book by Leaffer [L].

I am not a lawyer and this is not meant as legal advice. However, I think everyone would benefit from more information and discussion of copyright law, so please leave comments if you have something to add.

U.S. copyright law applies to writings, or "physical renderings", produced by an author. For this article, we assume the author is a U. S. citizen and the work was produced on U. S. soil. However, a "writing" is not assumed to be human-readable, so, for example, a software program in executable binary form, or "object code", is included [L], section 3.06. The owner of the copyright of a work has the exclusive right for

* reproduce or copy the work,
* prepare derivative works,
* distribute the work,
* perform the work publically,
* display the work publically.

Before explaining these terms, exceptions to these rights, and how these rights relate especially to mathematical works, we discuss works for which copyright law cannot be applied. The law is designed to protect creative written works.

1. 
   Ideas which are only communicated oraly are generally not subject to copyright, as they have not been "physically rendered." If you tell a friend your unwritten idea of how to solve the Riemann hypothesis, who proceeds to write up the idea and publish it, feel flattered because copyright law won't help you.
   
2. 
   An unoriginal work, or a work "mechanically produced", say by a computer program whose use requires no originality, are not copyrightable (more precisely, are not subject to a separate copyright - the program could, for example, output copyrighted elements). For example, the output of an automatic theorem proving program is not copyrightable. On the other hand, the output of
   an image processing program which takes an image and applies a de-noising algorithm is a "mechanical" derivation of the original image, so the copyright is the same as that of the original.
   
3. 
   Data is not copyrightable. It doesn't matter how much money or man power it took to discover, collect, or obtain it. (However, there are various laws which can be used to protect such intellectual property, such as trade secret laws.) In some cases, a creative arrangement of the data itself is copyrightable, even if the data itself is not.
   
4. 
   Works in the public domain (in particular most "official" works by the U. S. government), are not copyrightable. All written works eventually pass into the public domain. Due to the variety of copyright laws which have been passed in the United States over the years, the duration of copyright depends on when the work was written, if it is a joint work (or a "work for hire") or not, and various other factors. However, life plus 50 years is a minimum, according to the Berne convention, so that will apply in most cases.
   

For the owner of a creative mathematical work, whether it is an article or a piece of software, we explain next what these rights mean.

Reproduction: A reproduction is to fix a copy in a tangible and relatively permanent form, such as a xerox copy or a file on a computer (though a copy stored in your cache is exempted). Aside from non-profit, educational, government, or "fair use", the copyright holder have the sole right to make unlimited copies of your work. For example, if you publish a paper or book, you often sign over your copyright to a publisher. If anyone could make a copy of your article freely, the commercial interest of the publisher would disappear. Similarly, if you wrote a mathematical software program which you wanted to market, you would want to restrict the copies of the program to those who paid for it. A research paper downloaded from the internet and then emailed to a colleague is an example of a reproduction.

However, there is a fair use exception to copyright law regarding copying for personal use if you are a scholar (at a non-profit institute) or the educational use of your students if you are a teacher (at a non-profit institute). These do not apply to commercial think-tanks or to commercial training centers. The guidelines are different for research than for educational use, but the basic idea is to copy no more than is necessary. The guidelines for education are more strict. Generally, 1000 words or 10\% of the material (the minimum of the two) are recommended limits [L], section 10.12.

Derivative works: Only the copyright holder can create a new work which is adapted from the original but which contains copyrightable modifications. For example, if you wrote a mathematical textbook and you retained its copyrights, then only you have the right to create a translation into another language or a second edition. Conversely, if you wrote a mathematical software program which you wanted to give away for free but subject to the open source General Public License (GPL), then you want to restrict the modifications or derivations of your program to those who publically redistribute the modified program under the same open source terms. This is what the carefully crafted legal language of the GPL does for you [F], [W]. (An example of such a project is the SAGE software program [S].)

Distribution: A work is distributed if it is made available to the "public" in some form. For example, a copy in a public library or a file posted on a world-accessible internet site are publically distributed. However, defining the term "public" precisely in this context is a technical legal matter, for which we refer to [L], section 8.13.

Performance and display rights generally refer to works of drama or art, and probably less useful to a mathematician. For these rights, we only mention that a talk on a scholarly paper could be a performance. Legally, such a performance does not constitute a "public distribution" or "reproduction" of the paper itself.

References:
[F] Free Software Foundation, http://www.fsf.org

[K] B. Klemens, Math you can't use,
Brooksings Institute Press, Washington DC, 2006.

[L] M. Leaffer, Understanding copyright law, 4th edition, LexisNexis, 2005.

[S] Sage mathematical software, http://www.sagemath.org

[W] M. Webblink, Understanding Open Source Software,
http://www.nswscl.org.au/journal/51/Mark_H_Webbink.html

East Coast Computer Algebra Day, ECCAD 2008

ECCAD 2008 homepage

INVITED SPEAKERS

* John F. Nash, Jr.
Department of Mathematics
Princeton University

* Emmanuel N. Barron
Department of Mathematics and Statistics
Loyola University Chicago

* Erich Kaltofen
Department of Mathematics
North Carolina State University

* Y. V. Ramana Reddy
Department of ComputerScience and Electrical Engineering
West Virginia University

* Paul Wang
ICM/Kent
Kent State University

some favorite quotes

Truth, like gold, is to be obtained not by its growth, but by washing away from it
all that is not gold. Leo Tolstoy

The best thing for being sad is to learn something. That is the
only thing that never fails. You may grow old and trembling in your
anatomies, you may lie awake at night listening to the disorder of
your veins, you may miss your only love, you may see the world about
you devastated by evil lunatics, or know your honor trampled in the
sewers of baser minds. There is only one thing for it then to learn.
Learn why the world wags and what wags it. That is the only thing
which the mind can never exhaust, never alienate, never be tortured
by, never fear or distrust, and never dream of regretting.
T. H. White, in The Once and Future King

Education is what survives when what has been learnt has been forgotten.
B. F. Skinner

The advantage is that mathematics is a field in which one's
blunders tend to show very clearly and can be corrected or
erased with a stroke of the pencil. It is a field which has
often been compared with chess, but differs from the latter
in that it is only one's best moments that count and not
one's worst. A single inattention may lose a chess game,
whereas a single successful approach to a problem, among
many which have been relegated to the wastebasket, will
make a mathematician's reputation.
Norbert Wiener, in Ex-Prodigy: My Childhood and Youth

Wir müussen wissen.
Wir werden wissen.
David Hilbert
[Engraved on his tombstone in Göttingen]

What we hope ever to do with ease we may learn first to do with diligence.
Samuel Johnson

Rigor is to the mathematician what morality is to men.
Andre Weil

Science is a differential equation. Religion is a boundary condition.
Alan Turing

Find out just what any people will quietly
submit to and you have found out the exact measure of injustice
and wrong which will be imposed upon them.
Frederick Douglass

Where the mind is without fear and the head is held high
Where knowledge is free
Where the world has not been broken up into fragments
By narrow domestic walls
Where the words come out
From the depth of truth
Where the tireless striving stretches its arms towards perfection
Where the clear stream of reason has not lost its way into the dreary desert sand of dead habit
Where the mind is led forward by thee
In ever widening thought and action
Into that heaven of freedom, my father
Let my country awake.
Rabindranath Tagore
(from his book Gitanjali)

Everything is vague to a degree you do not realize till you
have tried to make it precise.
Bertrand Russell

For every complicated problem there is a solution that is simple,
direct, understandable, and wrong.
H. L. Mencken

If people do not believe that mathematics is simple,
it is only because they do not realize how complicated life is.
John Louis von Neumann

In mathematics we do not appeal to authority, but rather you are
responsible for what you believe.
Richard Hamming, Americ an Math Monthly, vol 105 no 7.

There are some things which cannot be learned quickly,
and time, which is all we have,
must be paid heavily for their acquiring.
They are the very simplest things,
and because it takes a man's life to know them
the little new that each man gets from life
is very costly and the only heritage he has to leave.
Ernest Hemingway
(From A. E. Hotchner, Papa Hemingway, Random House, NY, 1966)

The scientist does not study nature because it is useful;
he studies it because he delights in it,
and he delights in it because it is beautiful.
If nature were not beautiful,
it would not be worth knowing,
and if nature were not worth knowing,
life would not be worth living.
Henri Poincaré

Believe that none of the effort you put into coming closer to God is ever
wasted -- even if in the end you don't achieve what you are striving for.
Rebbe Nachman of Breslov

Marriage is an alliance entered into by a man who can't
sleep with the window shut and a woman who can't sleep
with the window open.
George Bernard Shaw

If you think education is expensive, try ignorance.
Derek Bok

Whatever you can do, or dream you can do, begin it.
Boldness has genius and power and magic in it.
Johann Goethe
(John Anster's translation of Faust}

Every society honors its live conformists and its dead troublemakers.
Mignon McLaughlin

Praise and blame, gain and loss, pleasure and sorrow come and
go like the wind. To be happy, rest like a giant tree in the
midst of them all.
Buddha

If a dog barks his head off in the forest and no human hears
him, is he still a bad dog?
Anonymous

I believe that a scientist looking at nonscientific problems is
just as dumb as the next guy.
Richard Feynman

To be what we are, and to become what we are capable of becoming,
is the only end in life.
Baruch Spinoza

Watch your thoughts; they become words.
Watch your words; they become actions.
Watch your actions, they become habits.
Watch your habits, they become character.
Watch your character; it becomes your destiny.
Frank Outlaw

Creativity is God's gift to you. What you do with it is your gift to God.
Bob Moawad

Maturity is the ability to do a job whether or not you are supervised,
to carry money without spending it, and to bear an injustice
without wanting to get even.
Ann Landers

If you do not change direction, you may end up where you are heading.
Lao Tzu

I love you when you bow in your mosque, kneel in your temple, pray in
your church. For you and I are sons of one religion, and it is the
spirit.
Kahlil Gibran

The earth is but one country, and mankind its citizens.
Baha'u'llah

new Rubik's cube face turn record

Tom Rokicki has announced that 25 moves suffice to solve the Rubik's cube. (The previous record was 26, by Gene Cooperman and Dan Kunkle.) His paper is at http://tomas.rokicki.com/rubik25.pdf

Hadamard matrices links

Here are some interesting links for Hadamard matrices:

* for general info
http://en.wikipedia.org/wiki/Hadamard_matrix

* for tables
http://research.att.com/~njas/hadamard/

* online database
http://www.iasri.res.in/webhadamard/

* some conjectures:
http://www.uow.edu.au/~jennie/hadamard.html

new SAGE email list: sage-edu

Group specifics:
* Group name: sage-edu
* Group home page: http://groups.google.com/group/sage-edu
* Group email address sage-edu@googlegroups.com
Please join if you are interested in SAGE and education in a high school
or a university.

protest of microsoft offer for yahoo+flickr

protest of microsoft offer for yahoo+flickr, originally uploaded by David Joyner.

I will quit Flickr if the MS purchase of Yahoo goes through.

SAGE and differential calculus

I've finished a book on SAGE and differential calculus. The idea was to simply take the old book Granville's Elements of Calculus, which is public domain now, and slightly modernize and "SAGE-ify" it. The source code, with the pdf form (and the pdf scan of the original book of Granville) can be found at
http://www.opensourcemath.org/books/granville-calculus/ or
http://sage.math.washington.edu/home/wdj/teaching/.
It is open-source and about 230+ pages printed. Hope it is useful for some people.
It is not quite in it's final form, so if you find typos, of have comments, please feel free to email me.

first aliquot factor found by SAGE ECM interface

Paul Zimmermann (http://www.loria.fr/~zimmerma/records/aliquot.html) reports:

The SAGE ECM interface found a first factor of the aliquot sequence starting
from 552:

remains 23648161798622140141259448258749760352819524456141488104537419990481892694930432002158957619604181055633215274583954462907657503167424176909 (140 digits)
found factor by ecm: 58417195751812372006463994075468288063413 with parameters {'poly': 'Dickson(6)', 'sigma': '300411371', 'B1': '3990569', 'B2': '8561602150'}
Other nice factors will surely follow.

An aliquot sequence is simply the iteration of the function n -> sigma(n)-n,
where sigma(n) is the "sum of divisors" function. One open question from
Catalan is whether this sequence always converges to 1 (or to a cycle). The
first to perform extensive computations on aliquot sequences was Lehmer, who
found that all sequences starting from n <= 1000 converge, except perhaps
n=276, 552, 564, 660 and 966. These are the "Lehmer five" sequences. Since
several years, together with other people, I try to extend these Lehmer five
sequences. The main difficulty is that to compute sigma(n), you have to
factor n. For the current large numbers we encounter (150-160 digits) we use
a combination of different algorithms (ECM, QS, NFS). I have now converted
to SAGE the script that (tries to) extend aliquot sequences. The above
factorization is a first success of the new script.