Pablo Picasso, " Child with a Dove", 1901. Collection: The National Gallery, London. "These pictures belong to the public and entrance to see them is free". The Fourier transform, finite differences and
differential
operators
Carathéodory's definition of
measurable sets
Applications of school mathematics to
social policy
The factorization of differential
and difference operators (in preparation)
Extreme points and Banach limits
Basic sequences and moment problems
in Banach spaces (in preparation )
Chaos and dynamical systems (in preparation)
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Given a regular pentagon, the five diagonals of the pentagon intersect in
a regular pentagon contained within the original one. This process can be
repeated on the regular pentagon so obtained, a procedure that can be
repeated yet again, and carried out indefinitely. The fact that the
procedure can be carried out indefinitely leads to the conclusion that the
square root of 5 is irrational. Read
more about this....
Universities, education and societyCultural change in universities Submission to the Government's "crossroads" enquiry in 2002 Applications of school mathematics to
social policy
Government funding of state
and private schools
"A heavy warning used to be given that pictures are not rigourous; this has
never had its bluff called and has permanently frightened its victims into playing
for safety. "
J. E. Littlewood (1885 - 1977)
"Mr. Locke, I think, recommends the study of geometry even to those who
have no design of being geometricians: and he gives a reason for it ...... Such
persons may forget every problem that has been proposed, and every solution
that they or others have given; but the habit of pursuing long trains of ideas will
remain with them, and they will pierce through the mazes of sophism, and
discover a latent truth, where persons who have not this habit will never find
it."
Henry St. John, Lord Bolingbroke (1678 - 1751)
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In Australia, the Commonwealth Government subsidizes pupils who attend
independent schools. This saves taxpayer funds, because the subsidy per pupil
is less than the cost of funding that pupil to go to a state school. In 2005 the
then Minister for Education, Brendan Nelson (now Leader of the Opposition),
released figures that showed the subsidy per independent pupil is 67% of the
cost of funding a state school pupil. This raises the question: could
there be greater tax payer savings by having a different level of subsidy?
Assuming a linear model for demand, with a different subsidy the
Government could save at least $500 million more than under the
policies described by former Minister Nelson. In fact, under the model, if we
were to assume for example that 10% of pupils will go to independent schools
even if there were no subsidy, the Government could save $1,252 million more.
The issue of funding independent schools continues to be controversial -- the
Sydney MorningHerald , of February 10th 2008, has some details of
an internal report commissioned by the Howard Government on the funding of
independent schools. The report apparently calls for a fairer system for
distributing funds to independent schools, but at the time of writing the report
has not been publicly released by the Rudd government.
Read more about this...
Download a list of formulas for Pi and a list of list of mathematical quotations prepared for Mathematics Teachers' Day at the University of Wollongong, June 2007. |