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School of Physical, Environmental and Mathematical Sciences |
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A Little Personal History
I was born in Great Gonerby, a little village just outside the town of Grantham in Lincolnshire, England. My father was a dairy farmer and I grew up interested in the countryside and farming (but there was already an older brother to take over the farming business!). At age 11 I started at the King's School in Grantham following in the footsteps of Sir Isaac Newton, who was born (rather earlier) in the village of Woolsthorpe, also just outside Grantham.
I had developed a great interest in natural history and especially ornithology, an interest that remains strong today, and probably should have had a career in biology. However, little biology, especially at the higher levels, was done at the King's School presumably because it was a boys school! On the other hand the grammar school for girls had more biology and less physics. (That school too has had its notable pupils: Margaret Thatcher and more importantly Johanna, who became my wife.)
So my final years at school were devoted to studying Pure Mathematics, Applied Mathematics and Physics, plus German and other odd bits and pieces. Then it was off to the University of London where I entered Queen Mary College's physics program with an emphasis on theoretical physics and mathematics.
I then decided to come to Australia! People at Queen Mary College said I was insane - nobody goes to Australia. However, they relented when I told them I was coming to work with Professor John M. Blatt. (His 1952 book with Victor Weisskopf, "Theoretical Nuclear Physics" was the bible in that subject and was even reprinted in 1979, and he was also famous for work on superconductivity.) So it was that Johanna and I sailed for Australia late in 1964.
I gained my PhD from the University of New South Wales and after a brief time at Duke University I became a lecturer in the Department of Applied Mathematics at UNSW. Some of my first lectures were in numerical analysis, classical dynamics and fortran programming. We loved the life in Sydney and our children Melanie and Daniel were born there.
In 1971 I took up a Queen Elizabeth Fellowship in the just established Department of Applied Mathematics in the Research School of Physical Sciences at ANU. I stayed on there in the Institute of Advanced Studies as a Fellow and progressed to Senior Fellow in 1978. My research interests developed in optics and vision, especially in waveguide theory and fibre optics, with various offshoots into coherence theory and things like numerical analysis and nonlinear classical dynamics. The whole family enjoyed a stay in Germany while I was on leave to work on insect vision at the Max Planck Institute in Tubingen.
Also during that time the family completed undergraduate degrees: Johanna - honours in prehistory and geography, Melanie - Education, primary school teaching, Daniel - Communications-Journalism. I got to proof-read a lot of very interesting essays!
In 1986 I became Professor and Head of the Department of Mathematics (later the School of Mathematics and Statistics) in University College, that part of the University of New South Wales in the Australian Defence Force Academy in Canberra. So once again I work for UNSW and get to interact with undergraduate students, which I greatly enjoy after spending so (too?) long in a purely research environment. In 2000 I became Presiding Member of the University College Academic Board. I have also done a stint as Deputy Rector.
I gave up being Head of School after 12 years so now I can concentrate more on some things Professors like to do -
research, teach and write. Who knows, I may even get to play more croquet, a game Johanna and I took up a few years ago (and which
involves lots of challenging classical dynamics!). Also a few years ago we moved from our family home in Canberra to build a smaller house
on the edge of the bush adjoining Queanbeyan so once again I can enjoy natural surroundings every day. Daniel lives in Canberra. Melanie,
husband Peter and daughters Aysha and Mia live in Sydney. We share our house with two spaniels and our bushland with a little mob of
kangaroos, a wombat or two, several possums, many kinds of birds, numerous lizards and the occasional brown snake.
Teaching
In recent years my main interest has been in developing an algebra course for first year students based around linear algebra and the move into nonlinearity, with the study of polynomial equations and complex numbers as a first step. I have produced a set of notes with the material building up in the way I personally believe it should be taught.
I also have a strong interest in the teaching of wave theory and have taught the third year course called Waves. Again I have my own views on how the material should be motivated and ordered.
Another of my major teaching interests centres on the Calculus of Variations and sometimes I present a third year course on that topic. In 1999 I introduced the topic as part of the second year Differential Equations course.
I am interested in the way mathematics and its applications can be described and presented to "non-mathematical" audiences. This has lead me to teach General Education courses for BA students. (One called The World of Mathematics was given in semester two of 2000.) It has also lead me to an examination of the popular writing about mathematics and an analysis of that is now almost a research interest for me.
I have also developed the second year course, Networks and Patterns, (introduced in 2001) which is a little graph theory and things like that. The idea is to introduce a little more on the non-calculus side in our School offerings. I have also developed a new Linear Systems course which builds on first year material and shows students just how important the concept of linearity is in mathematics and science. In 2007 I will develop a third year course based on a study of Newton's "Principia".
For 2007:
| First Year | Maths 1A (Algebra) |
| Second Year | Linear Systems |
| Third Year | Introduction to Newton's Principia |
Current Research and Research Interests
Vision - The waveguiding properties of retinal receptors and their effect on the visual process (e.g. the Stiles-Crawford Effect) and measurement methods.
The analysis of popular writing about Mathematics
The nature of the role played by Mathematics in applications and in Science. Visual Thinking in Mathematics and Science.
Mathematical Understanding and Education and a book at the "popular level". This is now my main area of work and the first draft on a book almost complete.
Previous Research
I have published over 140 papers in international journals. In addition I have presented conference papers at a variety of meetings and many have been published in conference proceedings. I have also published lecture notes and book reviews in various journals.
HERE ARE SOME OF THE AREAS I HAVE WORKED IN:
- Theoretical nuclear physics - especially the effects, derivation and mathematical forms of three-body potentials
- Waveguide theory and the design of optical fibres
- Methods for characterising optical fibres and their measurement
- Geometric optics and the concept of leaky rays
- Coherence theory and representations of optical fields
- Coherence effects in fibre optics, diffraction theory, image formation, inverse source problems and measurement methods in vision science
- Chaos in ray theory and optical circuits
- Potential shapes and properties, regular and irregular motion in classical dynamics
- Images and super-resolution
- Insect photoreceptors and their waveguide properties
- Tapering dielectric waveguides and their applications in fibre optics and to insect lens systems
- Inverse problems and methods for measuring preforms and biological lens properties
- Human vision - photoreceptor properties and their influence on the visual process and on measurement techniques
- Nonlinear optics - waveguide mode mixing, frequency mixing and generation, the spectral theory on pulses, momentum in nonlinear optics
Recent Publications
In Nonlinear Optics:
"Energy balance in linear and nonlinear optical waves" (with N. Ansari) JOSA B (2000) 36.
"Momentum in nonlinear optics" (with A. Ansari and D. Rowland) Jnl of Mod. Optics, 7 (2000) 993.
"Constant of motion for modal interactions in nonlinear dielectric waveguides" (with D. Rowland and W. Samir) JOSA B, 15 (1998) 1871.
In Classical Dynamics:
"The missing wave momentum mystery" (with D. Rowland) Am. Jnl of Physics, 67 (1999) 378.
In Vision:
"Optical properties of retinal photoreceptors and the Campbell Effect" (with A. Stacey) Vision Research 38 (1998) 953.
"Spatial frequency response of a photoreceptor and its wavelength dependence II Partially coherent sources" (with A. Stacey) JOSA A, 14 (1997) 2893.
In Mathematical Education:
"The Monkey and the Coconuts Puzzle: Exploring mathematical approaches" IMA Teaching Maths and its Applications 17 (1998) 123.
"Discussing a puzzle as an introduction to ideas in mathematics and its applications" AMS Gazette (2000) 27 (2000) 96.
"Answering junior ant's why for Pythagoras' Theorem" Int. Jnl. of Math. Educ. in Science and Tech. (2002).
In History and Philosophy of Science:
"Mathematics and the Science of Analogies: Amer. Jnl. of Physics (2002).