PhD Programme

The PhD in Mathematical Sciences programme is a four-year programme that provides graduate students with a stimulating environment for conducting original research in the mathematical sciences. Graduate students take advanced courses focusing on active research topics, and perform research under the supervision of a faculty member. Our students receive intensive support in their theoretical work, as well as in practical and computational aspects (where appropriate), including access to state-of-the-art computational resources. The programme culminates in writing and defending a doctoral research thesis before a panel of experts.

The PhD programme has a minimum candidature period of 2 years, and a maximum of 5 years. Most students complete the programme in 4 years.

Applicants must satisfy the following criteria:

  • BSc in Mathematics, Mathematical Sciences, or a very closely related discipline (for those with degrees in other fields, see below). If the university has an honours system, at least second-upper class honours, or the equivalent, is required.
  • For the PhD programme, applicants may optionally have a MSc degree in Mathematics or a related discipline, but this is not mandatory. If the university has an honours system, at least second-upper class honours in the MSc degree, or the equivalent, is required.
  • Demonstrating strong quantitative, verbal, or analytical skills through the submission of GRE/GATE test scores will greatly enhance your chances of admission. Submitting these test scores is strongly encouraged. 
  • International applicants who are not native English speakers must have TOEFL scores or IETLS scores.

There are two application periods each year: October to January (for admission in August), and June to July (for admission in January). Most students are admitted during the first period.

For more information about admission procedures (including the list of required supporting documents and application fees), please visit NTU Graduate Admissions page.

Applicants with Bachelor Degrees in Other Fields

Applicants without a Bachelor degree in Mathematics may be considered for admission if they have a Bachelor degree (or equivalent) in a related area, such as Computer Engineering or Natural Sciences, and have sufficient mathematical background. In addition to the other requirements, such students must submit the following documents together with their application:

  1. A complete list of courses taken in Mathematics and related areas, with detailed description of the course contents.
  2. A list of any further material relevant for the mathematical background, e.g. an annotated list of mathematics textbooks used for self-study.
  3. An informal essay describing their motivation to enter graduate studies in the Mathematical Sciences.

Students must complete a total of 16 Academic Units (AU) of graduate-level coursework, consisting of:

  • At least two MH70XX modules, 4 AU each
  • One MH70XX (Graduate Seminar) module, 4 AU
  • One additional MH70XX module (apart from Graduate Seminar modules), 4 AU
    Alternatively, the student may take one or two courses offered by other Schools/Divisions, counting for at least 4 AU, subject to approval from the Division and the other Schools/Divisions.

Please take note of the above coursework requirements by the MAS Division.

Students are expected to maintain a minimum CGPA of 3.5. We recommend finishing the coursework by the end of the first year, in order to sit for the Qualifying Examinations on time.

Communication Courses

Students are also required to complete the following courses on communication and related topics. These courses do not carry any AU.

  • College of Science (CoS) Transferable Skills Programme:
    • CoS Research Integrity Workshop
    • Career Preparation Workshop (for students admitted from Academic Year 2022/2023 and before)
    • Any 3 elective modules (for students admitted from Academic Year 2022/2023 and before)
  • ERWA01 - Epigeum Research Integrity Course (during first semester)
  • SLKC01 - Anti-Harassment at our Workplace (during first semester)
  • GP8000 - Artificial Intelligence Literacy (for August 2024 intake onwards, during first semester)
  • Seminar attendance of at least 5 seminars per semester.
  • Completion of Graduate Assistantship Programme (GAP), if applicable
  • Annual meeting with Thesis Advisory Committee (TAC) members
  • Submission of regular progress reports, including list of publications, TAC reports, and degree audit

The Qualifying Examinations (QEs) test a PhD student's mastery of mathematical fundamentals, research progress, and ability to answer technical questions from other mathematicians. Unless special permission is granted by School, the QEs must be completed within 18 months from enrolment in the PhD programme.

Before being allowed to take the QEs, PhD students must have completed the required MH70XX courses with a CGPA of at least 3.5, and must have completed the communication courses HWG703 and HWG702.

The QE consists of two components:

QE Report

In general, the report must address the following:

  • The research topic must be clearly defined
  • An appropriate research methodology must be shown
  • Clear presentation of data to support the research investigations
  • Relevant literature review and references made to the literature

Oral QE

The Oral QE has a duration of 40 minutes, consisting of:

  • A 30-minute presentation about the student's research progress, covering the same materials as your QE report.
  • A 10-minute Q&A session.

The oral QE is assessed by three faculty examiners.

 

Each PhD student must write a research thesis. Once the student and supervisor have agreed that the thesis is ready, it should be submitted online (via GSLink → Academic → Thesis → Thesis Submission). After being endorsed by the supervisor, the thesis is sent to three independent examiners for evaluation. After this evaluation, the student must defend the thesis in an oral examination scheduled by the school.

Completed theses must be posted to the NTU Digital Repository.