His 2023 teaching in Trimester A consisted of the second half of ENGEN301-23A (HAM) Engineering Mathematics and Modelling 3 as well as all of
MATHS165-23A (HAM) General Mathematics and
MATHS166-23A (HAM) Management Mathematics. MATHS165 and MATHS166 are taught together.
His Trimester B teaching consists of
COMPX367-23B (HAM)Computational Mathematics
and
COMPX567-23B (HAM)Advanced Computational Mathematics. COMPX367 and COMPX567 share some common classes.
Research
Current research is on lattice methods for the numerical evaluation of
integrals in many variables. He has also recently supervised two PhD students on
statistical modelling.
He has been working on projects to do with the apparent success
of quasi-Monte Carlo methods when applied to high-dimensional integrals
arising in applications such as mathematical finance. Though the standard theory
of complexity indicates that such problems are `intractable', there is
no doubt that such integrals are being evaluated successfully with only
hundreds or thousands of function evaluations required.
One way of explaining
this success is to make use of weighted function spaces in which the variables
are of differing importance. Earlier joint work with his
(former) Ph.D. student, Professor Frances Kuo and Professor Ian Sloan of the University
of New South Wales has shown that
there do exist lattice rules which are `good'
in this situation. Moreover, their generating vectors may be obtained by
using a component-by-component construction.
Work on topics related to the construction of lattice rules is continuing. In
particular, the results above are based on a L2
version of a weighted discrepancy. These results have been extended by him
and a (former) PhD student, Vasile Sinescu,
to a L∞ version of a weighted discrepancy, sometimes
referred to as a weighted star discrepancy.
He
is also working on the structure of lattice rules.
Besides lattice rules, he and Frances Kuo have also done some work on
Sobol' points, which are another type of quasi-Monte Carlo method. More details about this project are available at
this link.
Born and bred in Palmerston North, it was natural that Stephen should
attend the university there. At Massey University he did a BSc(Hons)
degree in statistics followed by a MSc in mathematics. While a student at
Massey he developed an interest in numerical analysis. This interest
led him to obtain a Commonwealth Scholarship which enabled him to do a PhD at the University of New South Wales (UNSW)
in Sydney. His PhD research topic was on the numerical solution of integral
equations (these are equations in which the unknown function occurs as
part of an integral).
After completing his Ph.D., he worked at UNSW
for five years (as a lecturer and as a postdoctoral research fellow)
before taking up a lectureship at the University of Waikato in 1992.
He was promoted to Senior Lecturer in 1995 and to Associate Professor in 2005. He was Associate Dean in
the School of Computing and Mathematical Sciences from mid-2003 until the end
of 2004. He was Chairperson of the Department of Mathematics for a three
year term which ended at the end of 2007. He was then the Acting Dean in the School of Computing and Mathematical Sciences from 1 February to 30 September 2008.
After that, he was the Deputy Dean of the Faculty of Computing and Mathematical Sciences from 1 October 2008 to 31 January 2019. He was the Acting
Head of the School of Computing and Mathematical Sciences until 31 January
2020.
In 2011, he was a recipient of an award for Administrative Excellence and also received the 2011 Vice-Chancellor's Medal for Staff Excellence.
His interest in numerical analysis continues to this day. As mentioned above,
his current
research is on lattice methods for the numerical evaluation of integrals in
many variables.
Though numerical analysis may be considered part of applied mathematics,
it is an area of research which makes extensive use of pure mathematics
as well as computers. For instance, his research on lattice methods
has made use of number theory and group theory and has involved the
development of algorithms and computer programs to test the theory and
implementation of the methods.