Doctor of Philosophy
Main Campus - Melbourne

Doctor of Philosophy in Applied Mathematics

The doctoral program in mathematics is designed to produce a mathematician with a broad background in analysis and a strong field of specialization in applied analysis, modeling or numerical analysis and scientific computing. This combination of training will prepare the student for a career in a variety of areas, such as government or industrial research, or academic research and teaching. Doctoral graduates have the necessary experience in areas of application to be able to work successfully with other members of multidisciplinary research teams. Graduates also have the critical ability to think independently and analytically. They are able to make significant contributions to knowledge in their chosen fields of inquiry.

A preliminary program of study should be prepared by the student and advisor during the first semester of graduate studies. The final doctoral program of study must be approved by the student's advisory committee and program chair.

Admission Requirements

Applicants for the doctoral program in mathematics usually have a bachelor's or master's degree in mathematics. However, applications are also invited from graduates in physical and engineering sciences. In these cases, necessary undergraduate courses have to be taken to remove deficiencies before the student enters the doctoral program. In evaluating international applicants, due consideration is given to academic standards in the country in which the graduate studies were performed. Graduate teaching assistants carry on a variety of teaching assignments and in view of this, evidence of good English-speaking skills is an important criterion in processing the applications. For admission, a student should have a superior academic record and letters of recommendation. Preference will be given to applicants who have good scores on the GRE.

General admission requirements and the process for applying are presented in the Academic Overview section of the university catalog.

Degree Requirements

The degree of doctor of philosophy (Ph.D.) is conferred primarily in recognition of the breadth of scientific accomplishment and the power to investigate scientific problems independently, rather than for the completion of a definite course of studies. Although demanding a strong mathematical orientation, the doctoral program in mathematics does not fall within the traditional boundaries of a single academic unit and the scope is quite broad. Consequently, every course in a student's program of study is evaluated not only as to content, but also as to the way in which it complements other courses and furnishes breadth and depth to the program. The work should consist of advanced studies and scientific research that lead to a significant contribution and knowledge of a particular area.

Each student must pass a preliminary examination covering the core courses, complete an approved program of studies, pass the comprehensive examination (usually oral), complete a program of significant original research work and defend a dissertation concerning the research work completed.

General degree requirements are presented in the Academic Overview section of the university catalog.


After a bachelor's degree in mathematical sciences, a minimum of 75 credit hours is required for the doctoral program, including the courses listed below:  

Core Areas (30 credit hours)
Linear Algebra 3
Real and Complex Variables, Functional Analysis 9
Numerical and Computational Mathematics 6
Probability and Statistics 6
Differential Equations 6

Areas of Specialization (21–27 credit hours)
Areas of specialization include nonlinear analysis; stochastic analysis; optimization; numerical analysis and scientific computing; modeling, computational number theory, probability theory and statistics.

Considerable flexibility is allowed in the selection of courses in core areas and areas of specialization. Selected course offerings from the mathematics department and other areas of science and engineering may be taken to fulfill the requirements.

Doctoral Dissertation

The dissertation consists of 24–30 credit hours of work and is expected to be completed within two years. The doctoral dissertation is expected to represent original research in mathematics. It may present new theoretical developments or new areas of application or both. The dissertation should contain results that constitute a significant contribution to the literature of the field of investigation. These results should be worthy of publication in an established technical journal.