BioEd 2009

So what is a mathematics teacher doing at a Biology education conference? Like Sting's 'Englishman in New York', I was somewhat of an odd man out.

BioEd 2009, held in Christchurch in the middle of February was one of a worldwide series of events to mark the 200th anniversary of the birth of Charles Darwin (and 150th anniversary of the publication of 'The Origin of Species'). The major sponsors of BioEd were the Allan Wilson Centre and IUBS (International Commission of Biological Sciences). I was interested to note listed among the sponsors (along with the Royal Society and the MacDiarmid Institute among others) the Society for Mathematical Biology, an international society which exists to promote and foster interactions between the mathematical and biological sciences communities. And it was the fact that there were to be sessions dealing with the role of mathematics in biology (and biology education) that gave me the incentive to attend the conference.

A very interesting talk on ‘The Evolution of Medieval Manuscripts’ was given by Christopher Howe from Cambridge University, UK. He described how techniques that have been developed to reconstruct the evolutionary relationships from DNA sequence data have been applied to medieval manuscripts to get relationships between different versions of a text and reconstruct their copying history. The added complication of a scribe using more than one copy in copying a text has parallels to lateral gene transfer. The conclusions reached from the computer programs seem to agree with those from conventional analysis.

There were three speakers from USA who are involved in the use of mathematics and computer science in biology education, Holly Gaff, John Jungck and Tony Weisstein.

Holly Gaff, in her talk ‘Teaching the Biology and Ecology of Infectious Diseases through Mathematics’ pointed out the value of mathematical modelling to assess the potential spread of disease (without running actual trials!) and trying to predict the best practices for prevention and control. She illustrated the modelling of vector-borne diseases (e.g. via the mosquito) and the problem of genetic modification of pathogens.
Holly is involved in a project developing a high school (secondary) maths-biology curriculum. http://dimacs.rutgers.edu/BMC/


John Jungck’s talk in the ‘Towards Biology 2020’ theme of BioEd concerned the importance for students to be involved in conducting investigations and the increasing need for quantitative analysis – he listed calculus, discrete mathematics and statistics as the key areas of maths. Important applications mentioned included those from medicine, agriculture and environmentalism.

In 1997, John published a paper entitled ‘Ten Equations that Changed Biology: Mathematics in Problem-Solving Biology Curricula’ in which he argues the importance of mathematics in undergraduate biology education and draws attention to a variety of mathematical models that have been intrinsic to many of the significant discoveries in biology in the 20th century. These encompass evolution, genetics, developmental biology, biochemistry, cellular and molecular biophysics, and population biology.
Ten Equations that Changed Biology: Mathematics in Problem-Solving Biology Curricula

Tony Weisstein introduced Excel-based simulations of population genetics which he (along with John Jungck and others) has been involved in developing to support a multi-disciplinary approach to learning (mathematics, biology and computer science).
Their downloadable ESTEEM modules can be found at
http://bioquest.org/esteem

Two of the presenters were from Canterbury University’s Biomathematics Research Centre:

Charles Semple presented some of the mathematical difficulties involved in trying to reconstruct evolutionary trees and the search for methods that can reduce computer time. He gave an introduction to some notable problems in the area: the unrooted supertree problem, the maximum parsimony problem and the reconciling gene trees problem.

Mike Steel outlined the importance of phylogenetics (e.g. understanding evolutionary processes, biodiversity conservation and epidemiology) and the need for mathematics.
He suggested the type of mathematical skills that are likely to be most useful for future students wishing to work in this area, namely:
· Discrete maths (graph theory, algorithms, etc.),
· Probability (discrete markov chains, branching processes, etc.)
· Algebra and calculus (linear algebra, discrete Fourier analysis, modelling with DE’s).
At the end of his talk, Mike made reference to an essay written by Joel E. Cohen, Professor of Population at Rockefeller and Columbia Universities, New York, discussing ways each field can benefit from the other. It makes for very interesting reading:

Mathematics Is Biology's Next Microscope, Only Better; Biology Is Mathematics' Next Physics, Only Better

Susan Worner, from the Bio-Protection Research Centre at Lincoln University, gave a presentation on how evolutionary computing is helping in the battle to protect New Zealand from alien invasive species, such as the painted apple moth. Over 3000 insect pest invaders potentially could establish in NZ. Evolutionary computation used in phylogenetic studies can help identify which species are most threatening, where in the world they might come from and where they could establish a viable population. Computers can then be used to run various models of spread and control that can help scientists and authorities be better prepared.

There were many other interesting presentations at the conference and the website is still up if you'd like to check out the list of speakers:

http://awcmee.massey.ac.nz/IUBS_BioEd_2009/index.htm

I have become aware that there are a number of mathematicians working on biological problems in New Zealand, notably at the Allan Wilson Centre for Molecular Ecology and Evolution in Palmerston North, at Canterbury University, Auckland University and Massey University in Auckland, and I hope to have the opportunity to see what some of these mathematicians are doing later in the year.

More on Maths in Industry Study Groups

A summary of projects from MISG 2005 and 2006 (held in Auckland) can be found at

www.mathsinindustry.co.nz/massey/depart/sciences/centre/centre-for-mathematics-in-industry/case-studies.cfm

A summary of projects from MISG 2007 and 2008 (held in Wollongong) can be found by following links at

www.uow.edu.au/informatics/maths/research/misg/index.html

2008 Royal Society Teacher Fellow

During 2008, Peter Jaques from Takapuna Grammar was hosted by the Centre for Mathematics in Industry at Massey University, Albany, for his project ‘What is going on in Industrial Maths?’ and he produced a set of Powerpoint presentations (suitable for year 13 students), which can be found at

www.thinking-outside-the-box.co.nz/indmaths.html

Reporting back from the group looking at the network problem at MISG 2009
A Wollongong Honours student in the Coil Slumping group debates a point with Dr Bob Anderssen of CSIRO (Aust)
VUW's Mark McGuiness recording some of the initial thoughts from the Coil Slumping group

MISG 2009

My fellowship year began by attending the Mathematics in Industry Study Group (MISG) at Wollongong University in the last week of January.  These combined Australia-NZ study groups have been occurring annually since 1985.  A number of problems are presented by representatives from various industries (commercial or government) and these problems are workshopped by groups of applied mathematicians over three or four days. Ongoing research and work with industry often follows the study groups.

Five problems were presented at MISG 2009:

1. Coating deformation in the jet stripping process (an industrial process problem – when steel strip is coated with a layer of alloy, a pair of air knives is used to wipe the excess molten metal coating off to achieve the desired coating thickness, but surface quality problems arise in trying to get thin coats with high air-knife pressure – presented by Bluescope Steel Research.)
   
2. Analysis of coil slump (another problem presented by Bluescope, concerning the sagging/ slumping that can occur after thin steel sheets are coiled up under tension into large cylindrical coils)
   
3. Provenance of sedimentary rocks (a statistics problem arising from trying to analyse rock samples to ascertain geological history, presented by Geoscience Australia)
   
4. Quantifying and modelling ‘Value-at-Risk’ metric for electricity derivatives (a financial mathematics problem faced by electricity retailers when they sell to consumers at a fixed price but purchase wholesale electricity in a volatile market, presented by Integral Energy)
   
5.  Multipoint-to-multipoint communication for dissemination in multi-user virtual environments (an operations research problem involving networks presented by ICT Research Institute)
   

So, what did I observe?

• These real world industrial problems are complex!
• A search of recent literature related to a particular problem is an important first step.
• Animated discussion and debate occurs when a group of mathematicians look at a problem, just as it does with secondary students.
•  There are a variety of different approaches to a problem.
• Mathematicians are prepared to follow an idea through, even while acknowledging at the outset that they may be on the wrong track.
• Computers are an important tool in testing mathematical models.
• Differential equations, of one form or another, are everywhere! In the summary reports presented at the end of the week, DE’s featured in all but the statistics problem (problem 3 above) and were a key part of the models in problems 1, 2 and 4.

After the first day, when projects were presented and initial project meetings took place, I joined the group looking at the coil slump problem, staying with that group for the duration, so that I could observe the progression of ideas. It was soon obvious to me that while the problem was an easy one to understand in basic terms, I had to get familiar with various engineering terms (such as stress, strain, Young’s modulus, Poisson’s ratio) and their symbols if I was to follow discussions and read papers related to the problem.

Two kiwi mathematicians were in the Coil Slump group, Mark McGuiness of Victoria University and Robert McKibbin of Massey University (Albany) and their company and support was very much appreciated.

My thanks to the encouragement of Peter Donelan of Victoria University and Graeme Wake of Massey University’s Centre for Mathematics in Industry, Albany, for their encouragement to attend MISG 2009.