# Graduate Admission and Degree Requirements

UNB offers programs at both the MSc and PhD level in Mathematics and Statistics. This page covers details of degree requirements. For information on possible research topics please refer to the main Research Areas of the department and individual Faculty pages.

Interested persons should also read the **Graduate Calendar** for detailed regulations and application instructions.

## Masters of Science (MSc)

Candidates for an MSc in Pure or Applied Mathematics should hold a Bachelor's degree with first or second class honours in mathematics or a related field from a recognized university. The normal time required for completion of the requirements for the MSc is at least one year. Students with high standings in a Majors program may be admitted to a two-year MSc program.

Candidates for an MSc in Statistics should hold a Bachelor's degree with first or second class honours in mathematics or statistics or equivalent from a recognized university. A candidate with a sufficient background in both mathematics and statistics can complete the MSc in Statistics in one year.

Students who have difficulty with spoken English may have to defer MATH/STAT 6392, and the program will then take at least 16 months.

A student's progress is monitored by a three-member Committee, including the student's supervisor and two other members of the Graduate Academic Unit. Choice of courses, of seminar, report and thesis topics, and of comprehensive examination topics is subject to the Committee's approval.

Candidates for the MSc in Mathematics or Statistics may, with the consent of the Committee, choose one of two options for the degree program, viz., the report or the thesis option. For either option, candidates may be required to take any undergraduate courses deemed necessary to make up for deficiencies in the candidate's background. Further requirements:

#### Report Option:

- Seven graduate courses, including at least three from Group A and the remainder from Group B.
- A written report on an assigned topic and a passing grade in an oral examination on the report.

#### Thesis Option:

- Five graduate courses, including at least two from Group A and the remainder from Group B.
- A written thesis, which must contain original work embodying the results of the candidate's research on an approved topic, and a passing grade in an oral examination on the thesis.

##### Rules for selection of courses are as follows:

For an MSc in Statistics, students must take STAT 6392, STAT 6211 and at least two more courses from the Statistics listings.

With Committee approval, the candidate for an MSc may replace at most two Group B courses by one-term graduate courses listed elsewhere in the calendar.

**Doctor of Philosophy (PhD)**

Candidates for a PhD should hold a Masters degree from a recognized university. Promising students may transfer from the MSc program to the PhD program.

The requirements for the PhD:

- Any undergraduate or graduate courses required to make up deficiencies in the candidate's background.
- Four graduate courses, at least three from Group A and the remainder from Group B.
- A passing grade on each of three comprehensive examinations, to be completed within 18 months of starting the program.
- A thesis and passing grade on an oral examination on the thesis.

Rules for selection of Group A courses are the same as for the MSc programs, with MATH/STAT 6392 replaced by MATH/STAT 6492. A candidate for PhD, holding an MSc from this Graduate Academic Unit, is not exempt from MATH/STAT 6492.

Each comprehensive examination is a three hour written paper. One examination must be in the candidate's field of specialization. The other two must be chosen from these fields: algebra, analysis, combined algebra and analysis, applied mathematics, topology, differential geometry, combined topology and differential geometry, statistics. The combined algebra and analysis examination is intended for students specializing in applied mathematics or statistics.

Choice of examinations must be approved by the student's Committee. Reading lists for comprehensive examinations are updated periodically, and are available to registered students upon request.

## Program in Applied Mathematics and Theoretical Physics

Applicants who have a suitable background in Applied Mathematics and Theoretical Physics, may be admitted to an MSc program in these areas which is offered jointly by the GAU of Mathematics and Statistics and the GAU of Physics.

In order to enter the program, prospective students will require the approval of both Departments. Students will be attached to one of the Departments, but their course of studies will require the approval of both Departments. Completion of this program will be officially noted on the student's transcript.

- A minimum of nine one-term graduate courses selected from appropriate courses offered by both GAUs. A maximum of four of these courses may be replaced by undergraduate 4000 level courses selected from the GAU other than the one in which the student is registered. A student may replace two of these 4000 level courses from a GAU other than Mathematics and Statistics or Physics. All course selections require the approval of both the GAU of Mathematics and Statistics and the GAU of Physics.
- A report on an assigned topic.
- Any undergraduate courses required to make up deficiencies in the candidate's background (apart from those mentioned in 1 above).

The examining committee for the report shall normally consist of at least three faculty members drawn from the two GAUs, one of whom is the supervisor and the majority of whom are members of the Department in which the candidate is registered.