Public and other lectures
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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):

  1. 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.

  2. 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 (1951-2016)) 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 so-called '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 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 (I was very naive... ) ...  

    (In January 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 may need to allow some time for downloading (at least years ago you did, but now - 2017 - perhaps not). 

In October 1996 I gave a public lecture The [then] recently discovered world record prime number. A html version may be accessed here.

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 here.

In May 1998 I gave a three and a half hour talk (with a short coffee break!) to Mathematics and Computer staff in the Cork Institute of Technology. The title of my talk was On the use of MAPLE in the St. Patrick's College, Drumcondra (43 KB).  A html version may be accessed 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 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.

In August 1999 I gave two talks (using Maple) in Plymouth, England, at the ICTMT4 (the 4th International Conference on the use of Technology in Mathematics Teaching):

1. Using Maple to investigate L- and R-approximations to quadratic irrationalities (mws 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 (70KB)

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 here)

The mws file may be downloaded here (134 KB), and 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 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 4th 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, 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 (96 KB in size) talk. A html version is available here.

On Thursday 19th 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?



Contact details. jbcosgrave at