Headstart courses are residential summer schools for 17 year olds who want to find out more about studying Science, Technology, Engineering and Mathematics (STEM) subjects at university. They typically last between three and four days and involve direct engagement with university-level topics. Headstart courses are led by academics at the host institutions and are coordinated nationally by the Engineering Development Trust (EDT).

In Lancaster, we run the only Headstart course focused on Pure Mathematics. Our course is entitled "Exploring Shape and Space" and includes topics such as

• Combinatorial geometry: e.g. the construction of the five Platonic solids (and why there can only be five!)
• Topology: how might we formally capture the idea that two different sized squares are "the same shape"? We need to ignore lengths and focus on how shapes are joined together - this is what topology does
• Discrete geometry: if we connect some rods together by some joints, when is the result rigid or flexible? This is an interesting pure mathematical problem with some very applicable answers from small scales (understanding atomic lattices and crystals) to the large ones (construction of bridges)
• Fractal geometry: fractals arise when simple geometric patterns are repeated to infinity but surprisingly also occur in nature. Fractals can have dimensions that are not whole numbers!

This is done through short lectures introducing problems and techniques, mini-projects based on the lectures, a major group project, extending the mini-projects and presentation of the project results to the other participants. Attendees also get to experience university academic and social life in lecture rooms, computer labs and halls, interacting with our student ambassadors and finding out first hand about what it is like to study Mathematics and related subjects at university.

This year, we hosted the fifth Headstart summer school with 36 secondary school students from across the UK. Over the course of four days students heard short lectures by Dr Jan Grabowski, Dr Bernd Schulze, Dr James Groves and Dr Derek Kitson. Lancaster graduate Steven White returned to tell students how studying mathematics has helped throughout his career while Saif Saahil (EDT) described his experiences in the EDT Year in Industry (YINI) program.

The attendees also learned about student life from current Lancaster mathematics students Helen Coombes, Roland Kanda, Megan Winter, Glen Hopkins, Jamie Ayres and Leila Green. Judges James Whittle (EDT) and Dr Niels Laustsen crowned the winning team for their project on the rigidity and flexibility properties of two dimensional grids. The local organisers were Dr James Groves, Dr Derek Kitson and Mr Joe Allen.

For further information and photos, please see our Headstart webpages or contact Dr Derek Kitson at d.kitson@lancaster.co.uk.