A doctorate in mathematics is awarded for a solid body of original research. Typically this is on a relatively narrow question in a particular subdiscipline, which is studied in depth and for which novel results are found. Moreover, the dissertation you write should be fully at the level of publishable research as regards the maturity of insight into the important issues in the field and the quality of the presentation.
The actual content of a PhD thesis cannot be fully specified at the start. Instead, you embark on a research project with your supervisor, and as the results unfold they set the direction in which you continue. At the end of this process, you should arrive at research independence, which means you can formulate and successfully pursue your own research projects.
The Department offers two PhD degrees, both by dissertation only:
· PhD in Mathematics (MAM6000W).
· PhD in Applied Mathematics (MAM6001W)
The requirement for entry into PhD study is an Masters degree with suitable mathematical content, as agreed on by you and your supervisor (see below).
The process of application for PhD study in the department is as for MSc: the student applies to and corresponds with a potential supervisor. If this goes well, they will agree on a thesis topic, a plan of work, and a plan of funding (typically, several sources of funding need to be found, and the degree of support supervisors can give varies widely). Once this agreement is reached, the department issues a formal invitation to register for the degree, and the Faculty of Science then handles the actual registration.