Problems in Mathematics

• Credit value: 30 credits at Level 6
• Convenor: Professor Maura Paterson
• Assessment: two collections of short problems (15% each), an essay preparation task (20%) and a 10-page mathematical essay (50%)

In this module you will engage with two of the important problems which have shaped mathematics. Problems will be put in their historical context and will be used to illustrate the development of different areas of mathematics. You will have the opportunity to tackle more open-ended work, make links between the many branches of mathematics that have been studied on the degree programme, and plan and produce an extended piece of written work. The topics taught will change from year-to-year.

Indicative syllabus

• Writing mathematics, how to synthesise sources and describe formal mathematics
• Planning and writing a mathematical essay, including synthesising sources, providing examples and referencing

Topics may include:

• Cycloids, the brachistochrone problem and calculus of variations
• Computability
• Graph colouring
• Newton and polynomial interpolation
• Fermat’s last theorem
• Problems involving sharing

By the end of this module, you will be able to:

• understand a range of results in mathematics and/or statistics
• appreciate the need for proof in mathematics
• follow and construct mathematical arguments, in particular, the way mathematics is done by working mathematicians
• appreciate the power of generalisation and abstraction in the development of mathematical theories
• demonstrate a deeper knowledge of particular areas of mathematics and/or statistics.