other lectures, using Maple
During the academic year
1995-96 I conceived the idea of having an annual sponsored public mathematics in
my College, and I wrote innumerable letters to various companies seeking sponsorship.
Since I had already lined up the eminent mathematician and cryptographer, Professor Fred Piper, as our first
speaker, I expected that my only problem would be that two sponsors would materialise at
the same time, and that I would have to disappoint one of them ...
2004, Fred Piper gave the annual Turing Lecture at the invitation of the British
Computer Society. On May 6th
2004 I gave a talk
on transcendental numbers, which I dedicated to Fred Piper - who taught me when I was an undergraduate at Royal
Holloway College - marking his retirement.)In September 1996 an event
occurred which made me take the plunge and
offer a public lecture myself: the announcement by Cray supercomputers of
a new world record (which was broken shortly afterwards by
George Woltman's GIMPS). While I was at it I also
decided to offer a public lecture linking prime numbers with cryptography. Those two lectures, and some
others, are available below.
In those far off
days my college didn't have email or web facilities, but I did at home. It was
from my home that I notified the Maple Users Group (which no longer exists) of
my two initial lectures, and I offered the files to anyone who contacted me. I
saved the early requests, and here
they are (a pdf file).
Important note with regard to html versions of my lectures below.
Maple, in converting active worksheets into html code, turns outputs (calculations, etc)
into gif files, and so you must allow some time (not too much, but...) for downloading.
In November 1996 I gave a
public lecture Prime Numbers and Public-key
Cryptography (56 KB). I gave a better (I think!) and more expanded version of this lecture in
September 1998 (the Clinton-Ahern lecture below), and so I don't give a html version
In September 1998 the U.S.
President, Bill Clinton, during a visit to Ireland, together with the Irish Prime
Minister, Bertie Ahern, engaged in an 'historic, first digital signing of a treaty on e-commerce'
between the U.S. and Irish governments. In November 1998 I gave a public lecture called Bill Clinton, Bertie Ahern, and digital signatures (128
KB in size). A
html version is available here
(subsequently, having been invited to give that same talk in Chicago
(Oct-Nov 2003), I made some improving alterations, and that altered version
is available below).
An article by me in the Irish Times of Mon. 16th.
Nov. 1998, about the Clinton-Ahern lecture, may be viewed here.
Early in 1999 Wiland
Schmale of Oldenburg University (Germany)
asked me if he could use my Clinton-Ahern lecture as the basis for a public lecture by
himself (as one of a series to be given in Oldenberg, marking the 25th
anniversary of its university), and I was happy to do so. His lecture, in html format - in
German - may be accessed here.
1999 I gave two talks (using Maple) in Plymouth, England, at the ICTMT4 (the
International Conference on the use of Technology in Mathematics Teaching):
1. Using Maple to investigate L- and R-approximations to quadratic
format (34KB), and in html
format (38KB, with an images folder))
2. The mathematical context of the recent (25thJuly
1999) discovery of the largest known composite Fermat number (mws
format (60KB). A html version is available here
On Thursday 28th
October 1999, I offered a public lecture entitled The history of Fermat numbers from
August 1640. The background to that lecture was my discovery,
with Yves Gallot, in July 1999 of the [then] largest known
composite Fermat number. That record has now (February 2003, and - to
everyone's surprise - October 2002) been surpassed
by Yves Gallot, George Woltman, Paul Jobling and myself (see
The mws file may be downloaded here (134
a html format version may be downloaded here.
On Thursday 23rd
March 2000 I gave a talk - A Prime For The Millennium - to the student mathematics society at University College Cork. In my talk (whose title is taken
directly from my recently published
booklet) I attempted to sketch what one might call classical primality testing, with
particular emphasis on ideas of Henry Cabourn Pocklington. Because of generous sponsorship
from Turlough Crowe of Allied Irish Banks, Elaine
Bragg of Adept Scientific, Charlie Hipwell of
Pfizer, and Gerry McGovern of Irish Internet
consulting and development company Nua, I was able to
present every student present with a copy of my booklet. Many thanks to these companies (I
wrote to forty-five altogether) for their enlightened support.
The Maple mws file (176KB) of my talk may be accessed here,
and various html
files of it may be accessed here: UCC_2000.html (453
(106KB) or UCC_2000TOC.html
2001 I gave a talk (using Maple), in Klagenfurt, Austria, at the ICTMT5 (the
International Conference on the use of Technology in Mathematics Teaching): Fermat's
'little' theorem. It would not be accurate to say I gave the talk at
at Klagenfurt, I introduced my massive Maple worksheet on that
October-November 2003, at the 16th
International Conference on the use of Technology in Collegiate Mathematics
(ICTCM16) I gave a Bill Clinton, Bertie Ahern, and digital signatures
KB in size) talk. A
html version is available here.
October 2006 I offered - as my contribution to the first ever Maths Week (Ireland) - a Number Theory and Cryptography
(161KB) talk to some secondary
(high) school students and the general public. A html version is available here.
My talk was a much modified version of my Chicago talk (above), and
contained a much improved version of the Maple code for the technical to_number
and from_number procedures.
Note of February 2011. Seminar talks (based on research work with Karl Dilcher) given since 2007:
Dalhousie university colloquium, Mon. May 14th 2007. Gauss-4 primes (a beautiful new sequence of primes)
University College Dublin, Wed 26th March 2008. Extensions of the Gauss-Wilson theorem
Rutgers university colloquium, Thurs. 10th April 2008. Extensions of the Gauss-Wilson theorem (link to prepared Maple worksheet of talk)
City University of New York (CUNY), Fri. 11th April 2008. Repeat of previous day's Rutgers talk.
Brigham Young University, Mon. and Wed. 2nd and 4th Feb. 2009. Two classic theorems of Gauss (the Gauss-Wilson theorem, and Gauss's binomial coefficient congruence) - Then and Now".
(While visiting BYU I also gave my Bill Clinton, Bertie Ahern, and digital signatures talk, on Tues. 3rd Feb. 2009).
Bogazici university (Istanbul, Turkey) colloquium, Wed. 7th Oct. 2009. The (new) world of Gauss factorials.
St Patrick's College (Drumcondra), Tues. 16th Feb. 2010. Gauss-Jacobi advances.
University College Cork colloquium, Fri. 19th Feb. 2010. Gauss-Jacobi advances.
NUI Galway. Thurs. 25th Feb. 2010. Gauss-Jacobi advances.
Manchester university colloquium, Wed. 13th Oct. 2010. What is a Gauss factorial?
Dalhousie university colloquium, Mon. 8th Nov. 2010. What is a Gauss factorial?