Scientific Computation and Mathematics
(it goes without saying that this page is under constant development and is almost always out of date, but only a little - we hope)

John Belward is a Professional Mathematician, an expert in Scientific Computation and an outstanding teacher.
He retired in 2003 as Associate Professor from the Mathematics Department at the University of Queensland . 
He remains associated with the university in an honorary capacity as Honorary Reader with research projects in the Institute for Molecular Biosciences (concluded) and the Centre for Nutrition and Food Sciences (ongoing).
John is also an Adjunct Professor at Queensland University of Technology co supervising Ph.D. students and as a Chief Investigator on the ARC funded Linkage grant Modelling interactions of spray droplets with plants.

Scientific Computation

A computer can be used to compute the outcomes of events which might otherwise have  taken place in a laboratory.  In short the computer simulates a real event or set of events .  The use of the computer as a scientific instrument is known by many of its practitioners as Scientific Computation. Examples of Scientific Computation include the activities of several groups at UQ.  The ACMC, the CPAI and the IMB for example

Mathematical Software

Here we are using the term software as a name for a suite of programs set up to do particular tasks.  Mathematical Software is the phrase used when the service intended for the software is the execution of some particular mathematical task . Well-known examples are the packages Matlab, Maple, Mathematica, and MathCAD.  We also apply this to algorithms coded in lower level languages, Fortran, C, etc.etc. and available from software houses such as NA Software Ltd and NAG

Real world Mathematics, Undergraduate Mathematics, High School Mathematics

These links attached to the title should give the best indication of what is meant by these rather arbitrary terms.

Members of QCSCM

This is, presently, an example of a set with one member!

Scientific Computation

In the Advanced Computional Modelling Centre (ACMC) issues of high performance computing are addressed.  Almost 10 years ago the University of Queensland  and The Queensland Department of Primary Industries decided to purchase supercomputers.  The decisions were the oucomes of the percieved need for fast computation of pasture maps.  It was thought that these which be used as elements in information systems for planning in primary industries

Mathematical Software

In order to use a computer efficiently it is necessary to have soundly based well written algorithms.  This will underpin Scientific Computation and the use of mathematics in real world applications.  To avoid unneccesary duplication of effort it is expedient to use a math software package.  The following packages are good examples of well written user friendly packages.  Matlab, Maple, Mathematica, Derive.  MathCAD also has widespread support.  There are Mathematics facilites provided in Excel and many other spread sheets, slide presentation and word processing programs.  While these offer a broad range of methods they do not have the flexibility of a software library.  Here the user has access to alibrary of porcedures and writes programs to call these procedures. Thus greater acess is availaable to the parameters which govern the behaviour of the algorithms and the communications interface is to a large extent in the hands of the user.  Examples are NAG, NAS Math Encyclopaedia and Netlib. Texts also contain listings of software.  Numerical Recipes has been immensely successful.

Real world Mathematics

Mathematics is applied constantly in situations which impinge directly on the daily lives of most members of society.  Here are some examples.

Undergraduate Mathematics

The teaching of undergraduate mathematics needs to address the needs of career mathematicians and potential users of Mathematics.  Presently many university courses are anchored in the mathematics of the eighteenth and nineteeth centuries.  Current first year undergraduate courses need to give some indication to the students where mathematics may be used and what is important in Mathematics today.  This is because with current structures students may only do one year of Mathematics and for those who might enrol for a second year the material needs to be stimulating.
 

High School Mathematics

The balance between depth and breadth of content,  the wide spectrum of abilities of students and relevance to real world applications all make the creation of a syllabus for all students in the final years in high school an almost unsolvable problem.  The texts which I have coauthored with Kiddy Bolger, Rex Boggs and Rhonda Faragher address the fundamentals of the subject while providing many examples of applications.  It reflects the latest revisions in the Queensland Board of Secondary School Studies (now the Queensland Studies Authority) Mathematics B syllabus, and is we believe the best account of the subject as set out in that syllabus. for information on the texts either send an e-mail to john.belward@qcscm.com or go to the web page at  www.mathematics-for-queensland.com
 
 
 
 
 
 

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