PhD in Mathematics (PhD-MTH)
The Doctor of Philosophy in Mathematics (PhD-MTH) degree program, offered by the Department of Mathematics and Statistics, draws on the expertise of faculty in a wide range of areas in pure and applied mathematics. The PhD-MTH offers advanced education and research opportunities at the frontier of mathematics and mathematical innovation.
Our program emphasizes the application of cutting-edge mathematical methodologies to tackle intricate challenges, preparing graduates for impactful careers in academia, government or industry. Through rigorous training and mentorship in advanced research and teaching, we aim to empower our students to make significant contributions to the advancement of mathematical knowledge and its practical applications.
The program admits both part-time and full-time students. Competitive assistantships are available for qualified full-time students. Find out more about our assistantship opportunities here.
Admission
In addition to meeting the university's general requirements for admission to PhD degree programs, applicants to the PhD-MTH degree program are required to have completed a Master of Science in Mathematics or Applied Mathematics from an independently accredited university recognized by the UAE Ministry of Education's Higher Education Affairs Division and by AUS.
Applicants must submit three reference letters using the AUS online template (available through apply.aus.edu). At least two of the letters must be from an academic advisor/faculty member who is familiar with the applicant’s background.
Mission Statement
The mission of the PhD-MTH program is to train mathematicians and equip them with advanced knowledge and skills to conduct original and quality research at the frontiers of mathematics, apply contemporary mathematical tools to solve complex problems, and poise them to have successful careers in academia, government or industry.
Program Goals and Learning Outcomes
The program seeks to accomplish the following:
- develop the student’s competencies to become an effective and independent research scholar capable of expanding mathematical knowledge by conducting quality research and producing and communicating original results
- provide, in an inquiry-based environment and through a comprehensive curriculum, advanced mathematical knowledge and skills that can be utilized to solve complex problems and benefit the society
- prepare students for careers that require advanced mathematics such as research and teaching at the university level or research and development in industry and government
Upon completion of the program, graduates will be able to:
- demonstrate mastery of comprehensive, deep and overarching knowledge of at least two main areas of mathematics such as algebra, analysis, dynamical systems and statistics
- apply advanced mathematical skills to solve problems and communicate solutions in precise mathematical language
- design, conduct and defend independent and original research in a specialized area of mathematics
- effectively disseminate and communicate research outcomes to relevant audiences in both written and oral formats
- uphold standards of ethical academic and professional conduct
To view the brochure, please click here.
Contact
For more information about the program, please contact:
Department of Mathematics and Statistics
+971 6 515 2163
[email protected]
To qualify for graduation with the PhD-MTH degree, students must successfully complete all the requirements of the program, which consist of a minimum of 54 credit hours with a minimum cumulative GPA of 3.00 as follows:
- a minimum of 24 credit hours of coursework (8 courses)
- doctoral seminar (0 credit hours)
- qualifying examination
- a minimum of 30 credit hours of research work
The expected minimum duration for completion of the PhD-MTH degree program is four years. All graduation requirements must be completed within 10 years of admission to AUS as a doctoral student, inclusive of any leave. Graduation residence requirements must be met.
Required Core Courses
Students must successfully complete the following core courses (12 credit hours), which cover advanced topics in fundamental areas of mathematics and expand on their mathematical knowledge.
- MTH 705 Theory of Ordinary Differential Equations (3-0-3)
- MTH 710 Functional Analysis (3-0-3)
- MTH 711 Measure Theory (3-0-3)
- MTH 733 Commutative Algebra (3-0-3)
- MTH 795 Doctoral Seminar (1-0-0)
Elective Courses
Students must successfully complete a minimum of four courses (for a minimum of 12 credit hours) selected from the following list and subject to the approval of the program coordinator.
- MTH 701 Advanced Probability Theory (3-0-3)
- MTH 706 Analysis of Partial Differential Equations (3-0-3)
- MTH 707 Extreme Values and Financial Risk (3-0-3)
- MTH 715 Operator Theory (3-0-3)
- MTH 735 Nonlinear Algebra (3-0-3)
- MTH 736 Multiplicative Ideal Theory (3-0-3)
- MTH 741 Dynamical Systems and Chaos (3-0-3)
- MTH 751 Algebraic Coding Theory (3-0-3)
- MTH 761 Algebraic Topology (3-0-3)
- MTH 762 Applied Topology (3-0-3)
- MTH 775 Computational Differential Equations (3-0-3)
- MTH 794 Special Topics in Mathematics (3-0-3)
With the approval of the program coordinator and the student’s advisor, a student may choose to take up to two elective courses in addition to the required 12 credit hours that are to be chosen from the program’s list of elective courses. The courses must provide knowledge and skills that contribute to the program learning outcomes. The request must be approved by CAS Associate Dean for Graduate Affairs, who will inform the Office of the Registrar before course registration.
Qualifying Examination
To be considered as a candidate for the PhD-MTH degree, the student must pass a written qualifying examination (MTH 790). The student may choose to do the examination in two of the following areas: analysis, algebra, numerical analysis, differential equations, and topology. The Program Coordinator has a detailed list of the topics covered in each area, and this list is also available in the syllabus of MTH 790. Full-time students should successfully complete the examination in the first two years.
Registration for the qualifying examination is conditional upon meeting the following requirements:
- The student must be in good academic standing.
- The student must have successfully completed a minimum of 12 credit hours of coursework.
The qualifying examination may result in a pass or a fail grade. A student who fails the qualifying examination is academically dismissed from the university. A student who was academically dismissed as a result of failing the qualifying examination may petition for reinstatement and a repeat of the failed qualifying examination to the Program Coordinator, one month ahead of the registration of the semester immediately following academic dismissal. The student petition form is available at www.aus.edu/registration/forms. The petition will be reviewed by the Program Coordinator, who will make a written recommendation to the Associate Dean for Graduate Affairs. The associate dean will then provide a recommendation to the Vice Provost for Research and Graduate Studies. Decisions regarding reinstatement and repeat of the qualifying examination will be made by the Vice Provost for Research and Graduate Studies. A student who failed the qualifying examination may be allowed to repeat the qualifying examination only once.
Students need to seek guidance from the Program Coordinator regarding the qualifying examination requirements and deadlines. Further details on the qualifying examination are provided in the Graduate Studies Policies and Procedures document available on iLearn and accessible by students and faculty.
PhD Dissertation (minimum of 30 credits)
The PhD dissertation (MTH 799) includes the preparation of a research proposal, presentation and defense of the research proposal, write-up of the dissertation, and presentation and defense of the dissertation. The expected research outcomes of the dissertation work should be sufficiently significant and contribute to creating new knowledge in the field.
A PhD-MTH candidate develops a dissertation research proposal and completes the dissertation under the direct supervision and guidance of a principal advisor. The principal advisor serves as the chair of the student’s Dissertation Advisory Committee (DAC). The DAC also includes at least two additional faculty members. The student may request the appointment of an external committee member.
A PhD-MTH candidate is eligible to defend the dissertation research proposal only after all coursework is successfully completed. The research proposal defense includes a comprehensive examination of all coursework completed. PhD candidates are expected to successfully complete the dissertation proposal within three semesters of dissertation first registration. Failure to complete the dissertation proposal within the specified time frame or failure to demonstrate progress after the proposal defense may result in assigning an NP grade, resulting in withdrawal of candidacy from the PhD degree program.
The dissertation must be publicly defended to the satisfaction of the Final Oral Defense Committee (FODC). The FODC is formed by the Program Coordinator in consultation with the DAC chair; it is approved by the Associate Dean for Graduate Affairs and appointed by the Vice Provost for Research and Graduate Studies.
A complete guide for forming the DAC and the FODC, and preparing the dissertation, including the dissertation research proposal, the dissertation defense schedule and deadlines, is given in the Graduate Studies Policies and Procedures document available on iLearn and accessible using the following path: iLearn-CommunityGraduate Studies-Graduate Studies Policies and Procedures.
