Successful applicants typically have a bachelor's degree and master's in mathematics. They should have completed courses at the senior undergraduate level or above, in order to pass two of the courses from List A, which is required by the program. Doctoratal students also need to pass three written preliminary exams based on material from List A and List B courses (including at least two from List A), no later than 18 months into the program.
 Alexandru Badescu: Mathematical finance, actuarial science
 Larry Bates: Analysis and differential geometry, applications of modern analysis to questions in Hamiltonian mechanics and differential geometry, reduction theory
 Kristine Bauer: Algebraic topology and homotopic theory, calculus of factors, homological algebra
 Mark Bauer: Number theory and cryptography
 Karoly Bezdek: Combinatorics, geometry and logic, geometric analysis and rigidity, computational discrete geometry
 Elena Braverman: Delay differential equations, delay equations of population dynamics, logistic equations, impulsive equations, equations with distributed delay
 Berndt Brenken: Operator algebras, Ktheory, analysis, mathematical physics
 Alex Brudnyi: Fundamental groups of compact Kahler manifolds, limit cycles and the distribution of zeros of families of analytic functions, etc.
 Clifton Cunningham: Number theory, topology and algebraic geometry
 Gilad Gour: Quantum information science, foundations of quantum mechanics
 Matthew Greenberg: Algebraic Geometry, Cryptography, and Number Theory, Algebra and Topology
 Claude Laflamme: Set theory, theory of homogeneous structures, elearning systems, graph theory
 Michael Lamoureux: Mathematics of wave propagation and seismic imaging, numerical methods and applications to geophysics, etc.
 Wenyuan Liao: Seismic inversion and applications, mathematical modelling and the application of mathematics, especially perturbation and numerical methods, to industrial problems, numerical methods and applications to geophysics
 Dang Khoa Nguyen: algebraic dynamics, diophantine geometry, and related problems
 Jinniao Qiu: Analysis, mathematical finance, quasilinear and fully nonlinear partial differential equations, stochastic calculus, operations research
 Cristian Rios: Analysis and partial differential equations, quasilinear and fully nonlinear partial differential equations, degenerate elliptic equations, etc.
 Renate Scheidler: Number theory, mathematical cryptography
 Karen Seyffarth: Graph theory
 Deniz Sezer: Credit risk and finance, superprocesses, Markov chain Monte Carlo methods
 Anatoliy Swishchuk: Financial mathematics, biomathematics, stochastic delay differential equations, insurance mathematics, stochastic models in economics, applications of random evolution, etc.
 Antony Ware: Numerical analysis, biomedical applications of mathematics, wavelets, numerical solution of unsteady convectiondiffusion problems, computational finance
 Robert Woodrow: Theory of relations (a branch of model theory in mathematical logic, and its applications to combinatorics), homogeneous structures and their applications to infinite group actions, etc.
 Yuriy Zinchenko: Applications to medicine and healthcare, optimal radiation therapy design; operations research, optimization algorithms and software; scientific parallel computing and highperformance linear algebra; mathematical programming with applications to computational geometry
The course requirements for a doctorate are determined on an individual basis and must include eight half courses in the student’s combined master's and PhD program in addition to MATH 600A and MATH 600B seminar course which must be taken in the first or second year of the program.
Performance level: Should maintain a minimum cumulative GPA of 3.00 calculated on a fourpoint scale at the end of each registration year and attain at least a B on each course taken for credit.
Course selections
 MATH 600 Research Seminar (this course is not one of the eight required courses).
 Two courses from List A courses
 At least three courses at List A or List B

List A courses
MATH 601 Measure and Integration
MATH 603 Analysis III
MATH 605 Differential Equations III
MATH 607 Algebra III 
List B courses
MATH 617 Functional Analysis
MATH 621 Complex Analysis
MATH 625 Introduction to Algebraic Topology
MATH 627 Algebraic Geometry
MATH 631 Discrete Mathematics
MATH 641 Number Theory
MATH 661 Scientific Modelling and Computation I
MATH 681 Stochastic Calculus for Finance
MATH 685 Stochastic Processes
STAT 701 Probability Theory
The PhD is a fulltime degree with an expected completion time of four years. The maximum time allowed is six years.
 Supervisors will decide with their students on what courses the students have to take, and what preliminary exams the students have to write.
 A supervisory committee must be established within three months after the program starts. The supervisory committee includes a supervisor (and a cosupervisor if there is one), and two supervisory committee members.
 The supervisory committee should meet with the student regularly to provide guidance through the program.
Written preliminary exams
Students must pass three written preliminary examinations on material from List A and List B courses (including at least two from List A), no later than 18 months into the program.
Presentations
All mathematics PhD students are required to give three invited or contributed presentations during their doctoral degree, not including presentations that are required as part of a graduate course or the 600 seminar course.
Written candidacy proposal and oral candidacy exam
 Program course work and examination requirements completed (prior to candidacy oral examination)
 Written proposal submitted to supervisory committee (recommended six months, minimum four months in advance of expected oral examination date)
 Reading list approved by the graduate program director (at least three months prior to scheduling oral examination)
 Written research proposal approved (at least two months prior to scheduling oral examination)
 The oral candidacy examination must be taken no later than 28 months from the start of the doctoral program. Prior to the oral examination, the student must have completed all the course work and the written preliminary examinations
 The oral candidacy exam must be scheduled at least four weeks before the intended date.
 The exam committee contains a supervisor, a cosupervisor (if it is applicable), supervisory committee members (usually two), and two examiners (outside of student’s program, within the department or within the university)
More information can be found under the following links:
Faculty of Graduate Studies candidacy regulations
Departmental guidelines for candidacy examinations
Thesis and thesis oral examination
The student must complete a thesis on a topic to be agreed to by the student and their supervisor.
 After completion of the thesis, the student must pass a thesis oral examination
 A thesis oral exam committee contains a supervisor, a cosupervisor (if applicable), supervisory committee members (usually two), an examiner (outside of student’s program, within the department or within the university) and an external examiner (from outside of the university)
 The external examiner must be applied for approval from Faculty of Graduate Studies six weeks prior the intended examination date
 The exam must be scheduled at least four weeks prior to date of oral exam
 Examiners must have a copy of the thesis at least three weeks prior to the date of oral exam
 Final thesis oral examinations are open
More information can be found on the Faculty of Graduate Studies website under examinations.