EDT Headstart: Exploring Shape and Space

Mon 29 July - Thu 01 August 2013
Charles Carter Building A19

Geometry has been a major part of mathematics since the days of the Ancient Greeks. This residential summer school will explore some of the different questions arising from geometrical problems from 2000 years ago to the present day. Participants will meet concepts from university-level mathematics and experience what it is like to study mathematics though formulating problems precisely, looking at examples, generalising and applying logical argument and proof.

Organisation

This Summer School is part of the Engineering Development Trust (EDT) Headstart scheme and applications are administered by the EDT. All places on this course for 2013 have now been filled.

What is it all about?

We will explore topics including:

  • Combinatorial geometry: e.g. the construction of the five Platonic solids (and why there can only be five!)
  • Differential geometry: how calculus can help us solve problems about curves and surfaces, in particular relating to minimization problems - why is a soap bubble a sphere, for example?
  • 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!

What will we be doing?

  • Short lectures introducing problems and techniques
  • Mini-projects based on the lectures
  • A major group project, extending the mini-projects
  • Presentation of project results to the other participants
  • Experiencing university academic and social life in lecture rooms, computer labs and halls