Applied Maths Summer School

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By Dr Peter H. Charlton and Dr Jordi Alastruey

In our day-to-day research we dedicate much of our creative thinking to meeting the needs of patients and clinicians. It is unusual that we are given time to reflect on how best to inspire the next generation of engineers. A range of questions spring to mind upon doing so. How do you foster engineering mindsets capable of developing ingenious solutions to sometimes overwhelming problems? Which are the most important engineering tools to equip future engineers with? What is the best way to become fluent with these tools? Try coming up with insightful answers whilst juggling your daily work.

The Applied Maths Summer School was different.

A group of highly talented students travelled to London from across the globe, eager to apply their skills to challenging real-world problems. A syllabus was prepared covering the fundamentals of engineering – all the bricks required to lay a solid foundation. Our task was to instil in students the excitement of becoming inventors. We were to provide them with the necessary tools, and create an environment in which they could find the creativity within themselves to develop as applied mathematicians and engineers.

How do you foster engineering mindsets? Introduce students to the fore-fathers of modern engineering through a research assignment. Summer school students had the opportunity to study the great thinkers of the previous millennium, whose work will continue to form the basis of engineering solutions deep into this millennium. Ever wondered how you supply water to remote mountainous areas at times of drought? You’ll need to apply your knowledge of calculus, developed by Isaac Newton and Gottfried Leibniz in the 17th century.

Which engineering tools are most important? Perhaps differentiation, which can be used by policy makers to decide how best to allocate taxpayers’ money. Perhaps integration, which is used to design cargo vessels which transport goods around the world. Maybe vector algebra, suitable for generating 3D virtual reality to enable robot-assisted surgery? On each day of the course the students were given a lecture on one of the fundamental mathematical tools, equipping them with a toolbox for solving engineering problems.

What is the best way for students to become fluent in these tools? Each lecture was followed by a problem class, in which a range of engineering problems and solutions were presented to students. They quickly became familiar with the pattern of using mathematical tools to develop innovative solutions to complex problems. Each day finished with a group activity, in which students were challenged to apply the tools in new settings. During the course each student used differentiation to develop methods for heart rate monitoring, creating valuable tools for clinicians and fitness trackers alike. Students also applied integration to the problem of monitoring the delivery of oxygen to bodily organs – vital for life.

So, how can we best inspire the next generation of engineers? A summer school seems like a great starting point.