| Major Code: 9073 |
Degree Awarded: Doctor of Philosophy |
| Delivery Mode(s): Classroom |
Admission Status: Graduate |
| Admission Materials: letters of recommendation, résumé/CV, statement of objectives, transcripts |
Location(s): Main Campus - Melbourne |
The doctoral program in mathematics is designed for students interested in pursuing research at the cutting edge of the discipline. Students conduct in-depth research in a field of mathematics that complements their academic interests and career goals. Current areas of research by faculty include differential equations, partial differential equations, optimization, control theory, numerical analysis, scientific computing, mathematical biology, mathematical physics and stochastic analysis.
The core curriculum is designed to help students develop and advance their mathematical rigor and understanding of the applications of mathematics to engineering, science and nontechnical disciplines. The aim of the program is to prepare students at the highest academic level for a career in academia, research institutions and industry.
Admission Requirements
Applicants for the doctoral program in mathematics usually have a bachelor’s or master’s degree in mathematics or a related discipline. For admission, a student should have a superior academic record demonstrating sufficient mathematics background. An application packet must include official transcripts, a statement of objectives, two letters of recommendation, résumé, and other relevant documents supporting the applicant’s academic preparation for a Ph.D. program in applied mathematics. Applicants may contact faculty in the department to identify a prospective advisor.
General admission requirements and the process for applying are presented under Graduate Academic Information . Applications for fall semester enrollment must be submitted by June 8 and for spring semester enrollment by October 14.
Degree Requirements
The degree of doctor of philosophy (Ph.D.) in applied mathematics is conferred primarily in recognition of the breadth of scientific accomplishment and the ability 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 the 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 of mathematics.
Curriculum
The doctoral program in applied mathematics requires a minimum of 72 semester credit hours after the bachelor’s degree or 42 semester credit hours after the master’s degree.
Each doctoral student must:
- complete an approved program of study,
- pass a comprehensive examination,
- successfully defend a research proposal and file a petition for admission to candidacy,
- complete a program of significant original research and present it at the graduate seminar and/or at a professional conference,
- submit at least one manuscript to peer-reviewed journals, and
- prepare and successfully defend a dissertation.
Required Coursework
Core courses:
Students entering the program with a bachelor’s degree are required to successfully complete a minimum of 48 semester credit hours of coursework equivalent to sixteen 5000 or higher-level courses, six of which must include the core courses required for the master’s degree in applied mathematics.
Students entering the program with a master’s degree are required to successfully complete a minimum of 18 semester credit hours of coursework equivalent to six 5000 or higher-level mathematics courses on-site at the Melbourne campus.
Additional coursework in mathematics or a related field might be recommended in order to ensure the student has satisfactory knowledge for research. The academic advisor assists the student in any program plan revisions, which also require department head approval.
Comprehensive Examination
A comprehensive examination committee is appointed by the student’s doctoral advisor with the approval of the department head. The committee must include at least four graduate faculty members: at least three faculty members from the Department of Mathematics and Systems Engineering including the student’s doctoral advisor and one graduate faculty member from another academic unit.
The student must pass a comprehensive examination after the successful completion of all coursework required for the comprehensive examination. The examination is written, comprising three parts: analysis, differential equations and computational mathematics. The subject areas must be approved by the student’s advisor and the examination committee.
A passing score on the comprehensive examination is 80 percent. A student who scores between 70-79 percent on anyone part is given a follow-up oral examination on the respective subject area conducted by the committee. A written re-test for any subject area is given for a score of less than 70 percent.
Once the comprehensive examination is successfully passed, the comprehensive examination committee is dissolved, and the dissertation committee is formed.
Proposal Defense and Candidacy
The dissertation committee may be different from the comprehensive examination committee with the exception of the student’s doctoral advisor and is based on Graduate Policy2.3.2 Changes in Committee. A dissertation committee must include at least four graduate faculty members: at least three faculty members from the Department of Mathematics and Systems Engineering including the student’s doctoral advisor and one graduate faculty member from another academic unit.
Each doctoral student must prepare a research proposal. The proposal represents the research plan that the student will pursue for the dissertation. Dissertation proposal should be written under the close supervision of the advisor and must be submitted to the dissertation committee at least one week before the oral proposal defense. Dissertation proposal must have the approval of the dissertation committee. A student who passes the proposal defense is admitted to candidacy.
Dissertation Research
The dissertation committee may be different from the comprehensive examination committee with the exception of the student’s advisor and is based on Graduate Policy 2.3.2 Changes in Committee.
The doctoral program requires the completion of a minimum of 24 semester credit hours of research under the supervision of the student’s advisor. At least 15 semester credit hours of dissertation research are required beginning with the term the student is admitted to candidacy.
The graduate policies pertaining to the requirements for the dissertation defense are available on the Dissertation Requirements webpage. Before graduation, the student must present their dissertation research at the Graduate Student Seminar hosted by the Department of Mathematics and Systems Engineering, or at a professional conference. Before the dissertation defense, each candidate is required to have one manuscript submitted to refereed journals. It is expected that the dissertation work should produce at least one peer-reviewed research publication.
General degree requirements are presented under Graduate Academic Information .
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