The Doctor of Philosophy (PhD) is the highest degree offered by the University of Otago. It is awarded on the submission of a thesis which must meet rigorous standards. It requires highly developed academic ability, independence and perseverance. Most students take between 3-4 years of full-time study to complete their PhD. Nature of the Degree Candidates for the degree of the Doctor of Philosophy are required to pursue an approved programme of advanced study and research under supervision as enrolled students of the University. The degree of Doctor of Philosophy is awarded on the basis of the submission of a thesis. The thesis, which may include a nominated creative component, should give evidence of the candidate’s ability to carry out research, that the candidate has shown originality and independence, and that the candidate has made a significant contribution to the advancement of their particular field. The research should be of a kind which a diligent and competent student might reasonably be expected to complete within three years of full-time study. Mathematics Mathematics is valuable at all levels, either as a tool to allow physical systems to be modelled in a quantitative way, or as a logical framework that underpins and describes processes, objects or structures. Significant research is being carried out in the Department in these areas of Mathematics: Graph theory and combinatorics Mathematical and computational relativity Mathematics of evolutionary biology Numerical analysis and uncertainty quantification Point patterns and processes Quantitative Genetics Semiclassical and harmonic analysis Stochastic integro-differential equations and their applications Waves Duration of the Programme A candidate shall pursue a programme of study and research under supervision for a period normally equivalent to 3 full-time years. The minimum period of study shall be equivalent to 3 full-time years and the maximum period shall be equivalent to 4 full-time years. Exceptions shall be permitted only with approval of the Senate. No programme shall exceed the equivalent of six years of full-time study from the date of first admission. A candidate shall be enrolled continuously for the entire period of the candidacy, up to the submission of the thesis, except that a candidate may apply to the Senate for permission to withdraw temporarily from study. Location of Study and Research Candidates are normally expected to be resident and studying in New Zealand while enrolled for the degree. Exceptions shall be permitted only with approval of the Senate. Candidates proposing to study overseas may be approved to do so on a case-by-case basis by the Senate. Normally such study must be deemed necessary for the candidate's research. While overseas, the candidate must continue to be enrolled at the University.