Talented Youth



My paper - An Introduction to Number Theory with Talented Youth - was accepted for publication in a special edition of the School Science and Mathematics Journal (U.S.A.) on gifted and talented mathematics and science students. The paper was published in the Volume 99, Number 6, October 1999, edition of School Science and Mathematics (pages 348-353).

That paper was a much abbreviated version of a substantial document (54 pages) with the same title, which describes some of the work that I did with a group of sixteen students in July 1993 in the Irish Centre for Talented Youth at Dublin City University in its first year of operation.

My entire emphasis was on trying to get students to think about serious mathematical questions. I believe I succeeded ... . See for yourself, and let me know what you think (Over the years I have heard from only one person: Dr. Charalampos Toumasis, Director of the Patras State Department of Education (Greece); as Gauss said in another context: few, but great).

The entire test of the original 54-page document (which has my now out-of-date email address, and old web site address) is now available here in pfd format. Anyone who wishes to write to me about this document should use my email address at the foot of this page.

I greatly value Paul Halmos' opinion of the above document.

The following year I was invited to teach for a second time on the programme, and I happily accepted. On that occasion, having just decided to teach a new course (Number Theory and Cryptography) to my undergraduate students, I thought it an ideal opportunity to test out the basic ideas of my course with my young students... A bit of a risk, yes, but it worked. They learned a lot of new Number Theory, quite different from what they had encountered the previous year (several came for a second time).

When I was about mid-way through what I intended doing I was approached by the (then) head of the Mathematics Department Alistair Wood (oh dear, not much there...) who asked if I would mind if some invited observers from the USA could sit in on one of my sessions with my stars. Yes, of course, any time. I told my young students to expect a visit sometime, to simply ignore them, that they wouldn't have a clue what we were doing. Eventually a large group entered, sat at the back, looked suitably bemused, and left after a full hour. Later Alistair Wood - with some visiting observer from London - informed me excitedly that some of the U.S.A. observers had pledged (on the basis of what they had seen me do with my stars) half-a-million dollars to D.C.U. Wasn't that great? Well, yes, it was...

Besides myself teaching one group, there was a wonderful high-school teacher (Martin Hilliard) taking a second group; Martin and I got on wonderfully well (and we still do!) and we had many a happy mathematical discussion at lunch times.

Coming to the end of the three weeks we heard that the big-wigs were taking themselves off to a dinner in some fancy restaurant, but that none of us (the worker bees) were being asked to join them. I hope they left a big tip out of the half million dollars... That ended my days at D.C.U.


Contact details. jbcosgrave at gmail.com