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 Degree Requirements

Index

  1. Prerequisites
  2. Master's Degree Requirements
  3. Doctoral Degree Requirements
  4. The Qualifying Exam
  5. The Candidacy Exam

Prerequisites

In order to obtain a graduate degree in Mathematics, a student must have completed courses in the following topics at the senior undergraduate level or above:

  1. Real Analysis (including metric spaces, Lebesgue measure and Integration)
      Examples at UBC:
    • Real Analysis (Math 420 and 421, or Math 507 and 510)
  2. Complex Analysis
      Examples at UBC:
    • Complex Analysis (Math 440 or 508)
  3. Abstract Algebra
      Examples at UBC:
    • Abstract Algebra (Math 422 and 423, or Math 501 and 502)
  4. A mathematical topic different from those above
      Examples at UBC:
    • Applied Analysis (Math 400 and 401)
    • Probability and Stochastic Processes (Math 418 and 419)
    • Theory of Differential Equations (Math 416 and 417)
    • Differential Geometry (Math 424 and 425)
    • Algebraic Topology (Math 426 and 427)
    • Calculations of Variations and Optimal Control (Math 402 and 403)

Most students will have completed these four requirements before starting their graduate programs. Students admitted in spite of a gap in their background will be required to address it during the first year of the program.

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Master's Degree Requirements

To complete the Master's (M.A. or M.Sc.) program, a student must . . .

  1. Satisfy the prerequisites described above.
  2. Earn at least 30 credits in one of this two ways:
    Option One —
    1. earn 27 or more credits from MATH courses numbered 400 or higher, at most 6 credits of which can come from MATH courses numbered 400-499;
    2. earn 3 credits for MATH 589 (M.Sc. Major Essay);
    3. pass the qualifying examination described below.
    Option Two —
    1. earn 24 or more credits from MATH courses numbered 400 or higher, at most 6 credits of which can come from MATH courses numbered 400-499;
    2. earn 6 credits for MATH 549 (Thesis for Master's Degree).

Mathematics students pursuing a Master's degree through the Institute of Applied Mathematics face slightly different requirements: details are provided on the IAM web page.

Credit may be given for equivalent courses taken before the student started a graduate degree program at UBC, provided those courses were not counted toward another degree.

Students may also request that credit be given for appropriate courses in departments at UBC other than Mathematics.

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Doctoral Degree Requirements

To complete the PhD program, a student must . . .

  1. Satisfy the prerequisites described above.
  2. Complete 30 credits of approved graduate coursework. (Credits from an M.Sc. program, either UBC or equivalent, are included. Mathematics courses numbered 399 and below are not eligible.)
  3. Pass the qualifying exam within two years of starting the program. (See below.)
  4. Pass a candidacy examination in the student's field of specialization. The examination syllabus is to be determined by the student's Ph.D. committee with the approval of the Graduate Affairs Committee. Passing this examination gains a student admission to candidacy.
  5. Write a thesis and defend it in a public oral examination administered by the Faculty of Graduate Studies.

Registration requirements:

A full-time Ph.D. student must register in at least 12 credits of course work in the first year of their graduate program at UBC if they have not completed a M.Sc. degree or if they were admitted directly to Ph.D. after completion of B.Sc. degree.   After being admitted to candidacy, a student working on a thesis may register for Math 649 with the approval of the thesis supervisor.

All PhD students are expected to take at least four graduate-level courses, totaling at least twelve credits, at UBC as part of their program. Courses counted towards the 30 credits of approved coursework (#2 above) can also be counted towards this requirement, if taken at UBC as a PhD student. These courses cannot be reading courses; however, seminar courses with credit will be considered separately as they become available, to determine whether they can be counted in the requirement.

Every doctoral student at UBC must have a supervisory committee of at least three members: the research supervisor and two others, typically UBC faculty with a rank of Assistant Professor, Associate Professor, or Professor. The committee should be identified as soon as possible. Students in Mathematics are expected to have a committee in place no more than two years after being admitted to a doctoral program at UBC. The Graduate Advisor should be notified (through the Graduate Program Coordinator) as soon as the committee is formed. The committee is responsible for guiding the student's course selection and research program, and for administering the candidacy examination and the final doctoral examination. Details are provided by the Faculty of Graduate Studies [link] .

IAM Students: Mathematics students pursuing a doctorate through the Institute of Applied Mathematics face slightly different requirements. Details are provided on the IAM web page.

Students are expected to attend the weekly mathematics colloquium. Mathematics students registered with the IAM are expected to attend the Applied Mathematics colloquia.

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The Qualifying Examination

The qualifying examination is a written test on undergraduate material. It is offered twice a year: once in late August or early September, and once in early January. The syllabus is posted below. All Ph.D. students in the Mathematics Department, including those in the IAM, must pass this examination by the end of their second year (For example, for a PhD Student who started in September 2010, their last chance to write the exam will be January 2012). Doctoral students are strongly encouraged to attempt the examination immediately upon their arrival at UBC. Those who do not are required to participate in the next scheduled sitting.

The exam is designed to . . .

  • help students integrate their knowledge of advanced undergraduate mathematics,
  • give students and supervisors an early baseline indication of preparedness,
  • guide students' course selections in cases where a weakness is identified,
  • allow well prepared students to move into research more rapidly,
  • allay potential concerns regarding TA assignments,
  • define initial standards clearly and uniformly for prospective and new students.

Students may attempt the examination any number of times, but they must pass it by the end of their second year.

The exam is available in two versions: pure mathematics and applied mathematics. It suffices to pass either one of these. Each student is free to choose which exam to write, and to make a different choice at every scheduled sitting of the examination. The pure and applied exams will have significant number of problems in common.

Precise dates and times for examination sessions are posted well in advance. Students must inform the Graduate Program Coordinator ahead of time which version of the test they plan to attempt.

The only two possible marks are "pass" and "fail". The committee will make an effort to notify the students of the results within two weeks of writing the exam.  Appeals regarding marking and questions should be made in writing to the Graduate Affairs Chair. Exams can be reviewed in the graduate office. Exams are destroyed after 3 years.

The total exam time is six hours, divided into two three-hour sessions on the same day, typically 9:00–12:00 and 13:00–16:00. The exam has a total of 12 questions, giving approximately equal value to each of the four fields detailed in the syllabus. Students who demonstrate competence in each subfield and earn a sufficiently high overall score will receive a passing grade.

Here are some resources that will help students prepare for the Qualifying Examination.

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The Candidacy Examination

The Candidacy Examination is a mandatory formal event to assess the student's readiness to undertake research at the doctoral level. It probes the student's knowledge, problem-solving, and communication skills through mathematical writing, oral presentation, and interactive discussion.

The candidacy examination is normally held less than 24 months after a student enters a doctoral program at UBC.

For mathematics students in a program sponsored by the Institute of Applied Mathematics (IAM) [link] , the IAM's Thesis Proposal Examination replaces this requirement.

More information is available here.

 
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