isquared Volume 1 Number 4 Editorial Finance and the economy are topics that are currently on the minds of many people in Britain, with consumers feeling the effects of the credit crunch, the present high rate of inflation and rising fuel prices. Among those with an intimate involvement in the world’s financial markets are ‘quants’ – mathematicians whose models are increasingly relied upon by banks and other investors. Iain Clark is one such financial mathematician. In our interview (see page 26) he discusses how maths is used to devise minimum-risk investments and what it is like to work on the trading floor. Economists are concerned more with the underlying theories than with the practical applications of financial mathematics, although they can nonetheless also influence the world markets through their role in advising policy makers. A mathematical tool which has long been applied to economic analysis is game theory. Indeed, the mathematician John Forbes Nash, whose life was dramatised in the Hollywood film A Beautiful Mind, won the Nobel Prize in Economics for his contributions to game theory. One branch of game theory involves the study of cooperative games – that is, games in which players are able to form coalitions, making cooperative contracts that are enforced by an outside party. Chris Gaffney explores the subject of cooperative game theory in his article on page 18. The other articles in this issue span the scales of natural phenomena, from the microscopic scale of bacteria (“Chemotaxis: the way bacteria move”, page 8) up to the much larger magnitude of moving mountains (“Rheology: the science of deformation and flow”, page 30). Mathematical tools can be applied with equal success to both these small and large scale behaviours, highlighting the unparalleled ubiquity and adaptability of mathematics. 8 30 Sarah Shepherd Cover image by Maikloff iSquared magazine, published quarterly. Volume 1 Number 4 (ISSN 1755-7275). Printed by MIXAM UK LIMITED. Editor: Sarah Shepherd Editorial advisors: Professor Christopher J. Budd, Dr Mary Lunn, Professor Michael C. Mackey, Professor Brian D. Sleeman iSquared would like to thank the Institute of Mathematics and its Applications (IMA) and the London Mathematical Society (LMS) for supporting the magazine through their small grant schemes. Postal address: iSquared magazine, 1 Pound Cottages, Shillinglee, Godalming, Surrey, GU8 4SZ. 2 iSquared magazine Summer 2008 Email: email@example.com. Website: www.isquaredmagazine.co.uk.
contents summer 2008 FEATURES Chemotaxis: how bacteria move 8 By Nikita Vladimirov Why mathematical modelling is useful for understanding chemotaxis, a mechanism used by bacteria to enable them to travel up chemical gradients towards nutrient-rich regions. Cover Story: We’re not all prisoners in here 18 By Chris Gaffney How players can benefit from forming coalitions in Cooperative Game Theory. Rheology: The science of deformation and flow 30 By Tim Reis The mathematics behind some of the strangest phenomena in materials science, including the “miracle” of walking on custard. REGULARS News 4 Mathematical greats 14 The life and tragic early death of Alan Turing, who is famous for founding the field of computer science and for his contributions to British cryptanalysis during World War II. Book review 24 The Music of Pythagoras, by Kitty Ferguson. Interview 26 Quantitative analyst Iain Clark explains how maths is used in the world of finance. Puzzles 36 Endnotes 39 www.isquaredmagazine.co.uk iSquared magazine 3