HOT TOPIC: Which AFL teams should REALLY make the
This segment is a follow-up to my talks at the University's Open Days in
Burnie and Launceston. The talks dealt with the lack of balance in the
Premiership rounds of the AFL football competition--each team plays 7 other
teams twice and the remaining 8 teams just once. I proposed a scoring method
which takes into account the different strengths of the teams played (which
make some wins more meritorious than others). Here this is called the "power
Exactly the same mathematical technique involved is also
extremely useful and important in many applications-- there are examples
in production scheduling, logistics management, fisheries stock research,
structural engineering and lots of other areas too. Good reasons
to stick with Maths through your school career!
Explore the website
for the sorts of great careers maths can lead to.
At the end of the 2001 home-and-away games, we'd have to agree the
right teams are playing in the finals, despite the lack of balance in the
rounds. And now to the final series: may the best team win!
Table 1. The number of wins and the "power score" for each
team after round 22.
||No. of wins
Inverse semigroups. Applied statistics.
BSc(Hons) (Qld), PhD (Monash), Dip Ed (Hawthorn), Grad Dip App Stat (IoS),
Handling & Statistics
in Life Sciences 1
IV (Introductory Applied Statistics)
students said about these units...
Representations of inverse monoids by partial automorphisms, Semigroup
Forum 61 (2000) 357—362. Abstract
The ubiquity of power functions, Biometrical Journal 41 (1999)
Green's relations in some categories of strong graph homomorphisms,
Forum 58 (1999) 445—451. Abstract
Dual symmetric inverse monoids and representation theory, Journal of
the Australian Mathematical Society (Series A) 64 (1998) 345—367
(with J E Leech). Abstract
Development staff characteristics and service stability in leading Australian-owned
Information Technology firms, in Purvis, M., ed., Software Engineering:
Education and Practice, IEEE Computer Society Press, Los Alamitos,
1998, 96—103 (with G R Lowry and G W Morgan).
Identifying excellence in leading Australian - owned Information Technology
firms: five emerging themes, in Seventh Australasian Conference on Information
Systems, Australian Computer Society / ACIS, Hobart, Australia, 1996,
419-429 (with G R Lowry and G W Morgan).
Normal bands and their inverse semigroups of bicongruences, Journal
of Algebra 185 (1996) 502-526. Abstract
Organisational characteristics, cultural qualities and excellence in leading
Australian-owned Information Technology firms, in 1996 Information Systems
Conference of New Zealand, Palmerston North, New Zealand, IEEE Computer
Society Press, Los Alamitos, 1996, 72-84 (with G R Lowry and G W Morgan).
Inverse semigroups of bicongruences on algebras, particularly semilattices,
in Almeida, J. et alii, eds., Lattices, Semigroups and Universal Algebra,
Plenum Press, 1990, 59-66.
Scheduling sports competitions with a given distribution of times, Discrete
Applied Mathematics 22 (1988/89) 9-19 (with D C Blest).
Computing the maximum generalized inverse of a Boolean matrix, Linear
Algebra and its Applications 16 (1977) 203-207.
Divisibility in categories of a class which includes the category of binary
relations, Glasgow Mathematical Journal 17 (1976) 22-30.
On inverses of products of idempotents in regular semigroups, Journal
of the Australian Mathematical Society 13 (1972) 335 - 337.
Divisibility of binary relations, Bulletin of the Australian Mathematical
Society 5 (1971) 75 - 86 (with G B Preston).
I have latterly branched out into applied statistics, with a particular
current interest in ambient air quality (a problem in winter in Launceston).
There are plenty of research topics here, combining data analysis with
methodological and modelling issues (as well as environmental protection
and public health). I am happy to share these topics with anyone interested.
A continuing thread in my work is the interplay between the properties
of semigroups and of categories with which they are related. The unifying
idea here is the search for ‘algebraic invariants’ of objects, which may
express the symmetries of the object (perhaps, for example, a fractal),
or how it is related to other objects. In particular, I am interested in
the ways inverse semigroups of partial symmetries carry information
about the associated object. There are as many research projects in this
area as there are different kinds of objects!
For recreation, I enjoy coffee and cake; balancing the conflicting demands
of home and work, career and family, teaching and research; bicycling when
the weather is fine; and playing (bass clarinet) in the University's Community
Music Programme. My Erdös number is 3.
Dr Des FitzGerald
School of Mathematics and Physics, University of Tasmania
Locked Bag 1-360, Launceston, Australia, 7250
PHONE: (03) 6324 3486
FAX: (03) 6324 3414