

Public and other lectures using Maple
A note of late March 2017.
You may encounter a problem opening my Maple worksheets (as indeed I do myself) here at my web site  it would appear to depend on the internet
browser being used.
Thus, if I attempt to open one of my worksheets using Interner Explorer there is never a problem, whereas if I use Firefox (or Google Chrome) then all
that one sees  this is just an example  is something like this:
{VERSION 3 0 "IBM INTEL NT" "3.0" } {USTYLETAB {CSTYLE "Maple Input" 1 0 "Courier" 0 0 128 0 128 1 0 1 0 0 1 0 0 0 0 }{CSTYLE "2D Math" 1 2
"Times" 0 1 0 0 0 0 0 0 2 0 0 0 0 0 0 }{CSTYLE "2D Comment" 2 18 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 } {CSTYLE "2D Output" 2 20 "" 0 0 0 128 0 1 0 1 0 0
0 0 0 0 0 }{CSTYLE " " 1 256 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" 1 257 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" 1 258 "" 0 1 0 0 0 0
1 0 0 0 0 0 0 0 0 }{CSTYLE "" 1 259 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE ""
and so on (almost at infinitum)...
I asked Maplesoft for advice on this and they recommended doing the following (and I found it worked):
 Don't attempt directly to open the worksheet (by clicking on my link), instead right click and save the worksheet to (say) the download folder.
 Now that the worksheet is in the download folder (cut it out if you wish and put into whatever folder you wish) you may open the worksheet
in the usual way (I should add that while I see this 'works', I have absolutely no idea as to why it does... ) [END OF NOTE].
A note of 28th March 2017. On Wed 8th of this month I gave a talk (one which I dedicated to the memory of Jon Borwein (19512016)) to the student Mathematics society at Trinity College Dublin. Some weeks beforehand I had provided the following description to give a flavour of my intentions for my talk:
Title. The (remarkable and beautiful) binomial coefficient theorem of Gauss, and more besides.
Abstract. One of Gauss's most memorable and beautiful discoveries (with an extremely difficult proof) is his socalled 'binomial coefficient congruence' (it's a mod p congruence, prime p = 1 mod 4). One might think he had discovered it by doing ... , but a reading of his original Latin paper (1828, when he was 51) one sees he discovered it by a quite different approach. In any event, his original mod p theorem seemed a dead end until Karl Dilcher and I discovered the most general extended version of it (i.e., mod p^alpha, again for prime p = 1 mod 4, and all alpha = 2, 3, 4, ... ). What I would like to attempt is not just to state what this general extension, but rather show *how* this extension first occured to us, before we eventually made a proof of it. Not even the mod p^2 extension had ever been guessed. All of this can be described in quite simple language. " [END]
A html version may be accessed
here.
During the academic year 199596 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 (I was very naive... ) ...
(In January 2004, Fred Piper gave the annual Turing Lecture at the invitation of the
British Computer Society.
On May 6^{th} 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 may need to allow some time
for downloading (at least years ago you did, but now  2017  perhaps not).
 In November 1996 I gave a
public lecture Prime Numbers and Publickey
Cryptography (56 KB). I gave a better (I think!) and more expanded version of this lecture in
September 1998 (the ClintonAhern lecture below), and so I don't give a html version
here.

 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 ecommerce'
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
(OctNov 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 ClintonAhern lecture, may be viewed here.
Early in 1999 Wiland
Schmale of Oldenburg University (Germany)
asked me if he could use my ClintonAhern lecture as the basis for a public lecture by
himself (as one of a series to be given in Oldenberg, marking the 25^{th}
anniversary of its university), and I was happy to do so. His lecture, in html format  in
German  may be accessed here.

 In August
1999 I gave two talks (using Maple) in Plymouth, England, at the ICTMT4 (the
4^{th}
International Conference on the use of Technology in Mathematics Teaching):
1. Using Maple to investigate L and Rapproximations to quadratic
irrationalities (mws
format (34KB), and in html
format (38KB, with an images folder))
2. The mathematical context of the recent (25^{th}July
1999) discovery of the largest known composite Fermat number (mws
format (60KB). A html version is available here
(70KB)

 On Thursday 28^{th}
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
here)
The mws file may be downloaded here (134
KB), and
a html format version may be downloaded here.

 On Thursday 23^{rd}
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 fortyfive 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
bytes), UCC_20001.html
(106KB) or UCC_2000TOC.html
(267 bytes).

 In August
2001 I gave a talk (using Maple), in Klagenfurt, Austria, at the ICTMT5 (the
4^{th}
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
Klagenfurt; rather,
at Klagenfurt, I introduced my massive Maple worksheet on that
celebrated topic.

 In Chicago,
OctoberNovember 2003, at the 16^{th}
International Conference on the use of Technology in Collegiate Mathematics
(ICTCM16) I gave a Bill Clinton, Bertie Ahern, and digital signatures
(96
KB in size) talk. A
html version is available here.


On Thursday
19^{th}
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.
Gauss4 primes (a beautiful new sequence of primes)
University College Dublin, Wed 26th March 2008. Extensions of the GaussWilson theorem
Rutgers university colloquium, Thurs. 10th April 2008. Extensions of the GaussWilson 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 GaussWilson 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. GaussJacobi advances.
University College Cork colloquium, Fri. 19th Feb. 2010. GaussJacobi advances.
NUI Galway. Thurs. 25th Feb. 2010. GaussJacobi 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?

 
