This is a higher research degree suitable for candidates with a very strong academic record. The DPhil requires a significant and substantial contribution to knowledge. Subject areas cover the entire spectrum of mathematics and the department's research is conducted in many fields. The DPhil is a research-based degree, with subject areas including: algebra (primarily group theory and representation theory); number theory; algebraic geometry; differential geometry; topology; complex manifolds; global analysis; functional analysis; stochastic analysis; dynamical systems; mathematical logic; optimisation; combinatorial theory; quantum theory; string theory; relativity; mathematical biology and ecology; mathematical modelling; fluid and continuum mechanics; numerical analysis; history of mathematics; mathematics applied to problems in earth sciences, materials science and finance. You are normally admitted to a research group suitable to your research interests and allocated a supervisor before arrival. You are admitted initially to a probationary status and approved for transfer to DPhil only when the Mathematical Institute is satisfied of your ability to attempt such a contribution; this transfer involves the submission of written work and oral examination. You normally undergo a confirmation of status in the third year of your DPhil. Similarly to transfer this involves the submission of written work and oral examination. The purpose of the confirmation of status is to enable you to receive an assessment of your work by one or more assessors. It is intended to provide an important indication that if work on the thesis continues to develop satisfactorily then it would be reasonable for you to consider submitting your thesis within three terms. Undertaking the course is regarded as equivalent to working full-time hours and may also sometimes require some additional hours. The minimum period of registration for the DPhil is six terms but in practice you may need nine terms at least.