One of my major interests is in supporting gifted and talented
students, a group I feel has been fairly neglected until
recently. For this reason, I wrote one of my PGCE assignments
on the issue, and you can discover what I learnt here.
As I am training, I am collecting together and making available
the reusable teaching resources that I am making; see here for more information on that.
Well, with a doctorate in the subject and beginning a career in
teaching it, it's hopefully clear that I enjoy it! Here are
the things that I worked on during my Ph.D. which were actually
published.
Parking functions: I have co-authored a paper on a
bijection between parking functions and priority queues
together with Louis Kalikow. The paper appeared as: Julian
D. Gilbey and Louis H. Kalikow, Parking functions, valet
functions and priority queues, Discrete Mathematics
197/198 (1999) 351-373. You can download an edited, corrected
version in PDF format. (It has an
image in, so plain DVI won't suffice.)
Permutation group algebras: I managed to make progress
on an old conjecture of Cameron concerning an algebra
connected to permutation groups. My paper on the subject
appeared as Julian D. Gilbey, Permutation Groups, a Related
Algebra and a Conjecture of Cameron, Journal of Algebraic
Combinatorics, 19 (2004) 25-45. You can download a
slightly older version in DVI or PDF format (with hyperlinks). If you want
to read the DVI file, though, you will need the following
METAFONT source files (in addition to the standard Computer
Modern source files); these are in the public domain and may
be freely redistributed: shuffle10.mf, shuffle7.mf and shuffle.mf, which contain the code to
create the shuffle product symbols used within this paper. A
version of this paper is also available from the ArXiv
preprint server at http://www.arXiv.org/abs/math.CO/0112173.
My thesis: My Ph.D. thesis is essentially a
compilation of the above two papers. If you really want to
download it (one-and-a-half spaced), you can do so from here.
There's no hyperlinking in this version, though. The final
version (including corrections) is available as PDF (800 kB).
Now... As I am a first year teacher teacher, my time
is severely limited. (And add on to that all the other stuff
below, and I wonder how I have time to do anything!) I'm
enjoying reading about algebraic number theory (although I'm
unlikely to progress that far with my limited time),
combinatorics, and dabbling in other bits and pieces (I've
recently read R. G. Bartle's book A Modern Theory of
Integration, which blew me away!). For those who have
never come across the p-adic numbers before, Gouvêa has
a wonderful book, p-adic Numbers, which I'm currently
reading. Also, there's a lovely book on elementary partition
theory called Integer Partitions, by George E. Andrews
and Kimmo Eriksson which is well worth a look.
Most summers since 2000, I have been a Mentor at the Canada/USA Mathcamp, a
five-week summer programme in North America for mathematically
gifted high school students, teaching and mentoring these
students, as well as having a whole lot of fun. In 2001, I
co-taught an introductory ring theory course following the
"Moore Method": we gave the students the theorems, and they had
to provide the proofs! You can download the material we
designed and used, either as PDFLaTeX
source or as a formatted PDF
version. Note that you will need certain other files to format
the source: you will need to run makeindex, and you will need
the patched files efcode.tex, protcode.tex and abbr.tex. (Alternatively, you could just
remove the PDFLaTeX stuff from the beginning of the LaTeX file.
Also, I have also not tested it with the latest versions of
PDFLaTeX, so it may no longer quite work as it once did.)
Dave Savitt, who was Mathcamp's Academic Coordinator, asked
which Springer GTM book I would be. Here's what I found out....
If I were a Springer-Verlag Graduate Text in
Mathematics, I would be Lawrence C. Washington's
Introduction to Cyclotomic Fields.
I am a carefully written exposition of a central area of
number theory that can be used as a second course in
algebraic number theory. Starting at an elementary level,
I cover p-adic L-functions, class numbers,
cyclotomic units, Fermat's Last Theorem, and Iwasawa's
theory of Zp-extensions, leading the
reader to an understanding of modern research
literature. Many exercises are included.
Limmud is a sizeable Jewish
organisation running a number of interesting activities
throughout the year, including an annual winter conference,
which attracts around 2000 participants for five days of
learning, sharing, singing, talking, eating, sleeping and then
some! What makes Limmud so amazing is that it is run almost
entirely by volunteers! My role for Conference 2004 was to
co-chair the Shabbat team, organising a pre-Conference weekend
for about 350 people. My current role is as Chavruta Liaison,
overseeing the ongoing development of the Chavruta Project
within Limmud. It is a truly remarkable experience.
I have been studying a course in interpersonal and personal
skills with John
Seymour Associates, entitled "Neurolinguistic Programming"
(NLP for short). I have now received both Master Practitioner
and Trainer certification from JSA, and continue to use the
skills I learnt there on a daily basis. As one part of the
course, I modelled a friend to figure out how he was able to
bounce out of bed in the mornings. You may be interested to
find out what I discovered here
(PDF).
That led me on to explore further the art and science of
hypnosis and hypnotherapy. I have been training in that skill
with The London School of
Clinical Hypnosis, and I will be fully qualified once I have
had an opportunity to take my Diploma Exam. See their site for
more information on what hypnosis is and how it can help you. I
have not been seeing many clients recently, as teaching has
taken up most of my time. If you want to visit a
hypnotherapist, the British
Society for Clinical Hypnosis has a directory of qualified
hypnotherapists.
I sing in Kol Rina, a
wonderful Jewish a cappella group. We write and perform
our own music, and our next concert is coming up quite soon!
Please see the Kol Rina
website for more information and to hear clips from our CD.
I have been programming computers as a hobby for over 20 years,
and really enjoy the algorithmic side of things. I mainly
program in Perl at the moment, although I am quite comfortable
in C and various other languages. Recently, for my school
classes, I have been writing material in Excel (see the resources section), even though I would
far prefer to be using free software. In some of my remaining
spare time, I volunteer as a developer for the Debian project and I also have
a simple homepage
there.
