Programme Structure

You can choose from four topics:

• History of modern geometry

This topic covers the history of geometry in the nineteenth century. It follows the history of projective geometry and the discovery of non-Euclidean geometry from the 1820s and 1830s. 

• Advances in approximation theory

This topic extends the material in Approximation theory  to the study of splines and piecewise polynomials, and their possible application to the approximate solution of differential equations. 

• Variational methods applied to eigenvalue problems

This topic extends the theory developed in Calculus of variations and advanced calculus to deal with some types of linear partial differential equations. 

• Algebraic graph theory

Algebraic graph theory is a branch of mathematics that studies graphs and other models of discrete structures by a combined power of spectral methods of linear algebra; group theory (covered in part in Further pure mathematics; and algebra over finite fields.