The mathematics I do – Dr Andy Verity-Harrison
I am Dr Andy Verity-Harrison, Principal Consultant in the Highways Asset Management Group at Atkins.
The mathematics I use at work includes:
- simple spreadsheet arithmetic to summarise and report financial information
- whole life cost calculations that incorporate quantified risk and Monte Carlo sampling to support long-term (30-year) investment planning, and
- discrete optimisation that can be used to schedule satellites, route gritter lorries in the winter or freight lorries – to reduce the number of miles driven empty – or place labels on a map so as to minimise overlap.
The mathematics I’ve used in the last week included stochastic programming (a form of optimisation that incorporates uncertainty) to account for the impact of changing weather patterns due to climate change on long-term asset investment planning. The more extreme summers and winters that are predicted as a consequence of climate change will accelerate the deterioration of highway assets, such as the carriageway, bridges, drainage and embankments, and make the likelihood of catastrophic failures due to extreme weather outside their design specification more likely. At times of severe fiscal constraints, the answer is not simply to invest more in maintenance of the road network to meet the worst case scenario. Stochastic programming allows investment decisions to be made that simultaneously account for several potential scenarios and their probability. This provides an invest plan that makes more cost-effective use of available finances rather than merely planning against the average case.
Mathematics which has amazed and/or surprised me is probability theory, although it would be more correct to say that its counter-intuitive results continue to frustrate me. One day I will understand the Monty Hall Problem!
The part of mathematics I like best is that moment when a complicated and messy real problem has been converted into an elegant mathematical form that captures all the key factors and inter-dependencies, and knowing that this will help clients make better decisions.
The part of mathematics I like least is the moment when after a great of effort and checking someone provides a simple counter-example that undermines all the work I’ve just done, or worse, when I’ve proved something that I know can’t be true but I can’t work out where I went wrong.
A maths teacher I remember is Professor Christopher Zeeman who taught Foundations in Mathematics in the first term of my mathematics degree at Warwick University. I remember him because of his enthusiasm for mathematics and his ability to explain why mathematics was important and how it linked to the real world, rather than presenting it as a list of facts to be learnt.
And another teacher I remember is my A-level chemistry teacher (Mr Winn) who was able to make the subject exciting and fun. I only wish that health and safety in the 1980s would’ve allowed him to still do some of the experiments (mainly involving blowing things up in ingenious ways) that he had been able to do earlier in his career.
Other people/events that have influenced my attitude to mathematics include...
Ian Stewart through all of his wonderful books and Vic Rayward-Smith who introduced me to computational complexity and optimisation when he was supervising me for my MSc.