Maths at Lancaster University 

Exploring Shape and Space

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

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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!). 

• 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). 

• 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. 

• 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 
        you will find out what this means! 

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What will I be doing? 

• Short lectures introducing problems and techniques 

• Mini-projects based on the lectures 

• A major group project, extending the mini-projects 

• A presentation of your project results to the other participants 

• Experiencing university academic and social life in lecture rooms, computer labs and halls 

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Will this course suit me? 

If you think you would like to study mathematics at university, then yes!  You will need to be studying A Level Mathematics or an equivalent course, such as International Baccalaureate Mathematics HL.  Exposure to Further Mathematics is advantageous but not required.  If you are interested in problem-solving and exploring new ideas through logical thinking, this course will suit you.  It will contain both pure and applied aspects of mathematics and show how these interact with each other. 

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Who will be on this course?

This will be a mixed course with 36 student places available.

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Dates of course?

29th July – 1st August 2024 (3 nights residential)

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Price of course?

£440 (Bursaries are also available)

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