Norms of ideals in direct sums of number fields and applications to the circulants problems of Olga Taussky-Todd.

This thesis, `Norms of Ideals in direct sums of number fields and applications to the circulants problem of Olga Taussky-Todd', presents wide-ranging material in the Mathematical areas of Algebraic and Analytic Number Theory. The work, which is substantially original, is set out in three chapters which are supported by appendices. As the title suggests, the main aim is to tackle a problem which was originally posed by Olga Taussky-Todd who asked what values can be taken by the determinant of a certain type of n x n matrix with integer entries - the circulant (see [15]).