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Department of Mathematics
K10512 Shrum Science Centre, 778.782.3059 Tel, 778.782.4947 Fax,
Chair
T. Archibald BMath (Wat), MA (York), MA, PhD (Tor)
Graduate Program Chairs
N. Bruin PhD (Leiden)
S. Ruuth BMath (Wat), MSc, PhD (Br Col)
Faculty and Areas of Research
See “Department of Mathematics” on page 196 for a complete list of faculty.
B.R. Alspach* – graph theory, discrete mathematics
T. Archibald – history of mathematics
J. Bell – algebra, analytic number theory, combinatorics, asymptotic enumeration
J.L. Berggren* – history of mathematics, algebra
P.B. Borwein – analysis, computation, number theory
T.C. Brown* – algebra, combinatorics
N. Bruin – arithmetic geometry, number theory
C. Chauve – bioinformatics, algorithmics, combinatorics
I. Chen – number theory, arithmetic geometry
K-K.S. Choi – number theory, algebra
R. Choksi – calculus of variations, partial differential equations, and applications to material science
A. Das* – variational techniques; interior solutions in general relativity
M. DeVos – structural graph theory, combinatorial number theory
R. Fetecau – numerical methods, mathematical modelling, analysis for multi-scale phenomena; geometric mechanics and its relation to numerical algorithms for mechanical systems, symplectic integration, variational methods for collisions
L. Goddyn – combinatorics
J. Jedwab – discrete mathematics, exploratory computation, digital communication
M.C.A. Kropinski – numerical solutions of nonlinear differential equations; fluid dynamics
A.H. Lachlan* – mathematical logic
P. Lisonek – combinatorics, coding theory
Z. Lu – algorithm design and analysis for large-scale continuous discrete optimization and stochastic programming, application of operations research in bioinformatics, data mining, finance, logistics and supply chain, manufacturing and structural design
M. Mishna – combinatorial functional equations, algorithmic and algebraic combinatorics, computer algebra
B. Mohar – topological graph theory, graph colouring, algebraic graph theory, graphs and matrices, infinite graphs
M.B. Monagan – algebra, computer algebra
D. Muraki – asymptotic analysis and modelling for the physical sciences, nonlinear waves and dynamics, atmospheric fluid dynamics
N. Nigam – PDE and numerical analysis, with applications in computational electromagnetics and micromagnetics
A.M. Oberman – nonlinear partial differential equations, numerical analysis, math finance
A. Punnen – discrete/combinatorial organization and applications
N.R. Reilly*– algebra
R.D. Russell – numerical analysis; numerical solution of differential equations, dynamical systems
S. Ruuth – scientific computing, differential equations, dynamics of interfaces
C.Y. Shen* – electromagnetic scattering; large scale scientific computing
L. Stacho – graph theory, discrete mathematics
T. Stephen – combinatorial optimization, approximation algorithms, complexity and combinatorics
J. Stockie – fluid dynamics, scientific computing, industrial mathematics
B.S. Thomson* – analysis
M.R. Trummer – numerical analysis; differential equations, integral equations
P. Tupper – molecular dynamics, phase field models, phylogenetics, statistical mechanics, stochastic differential equations
J.F. Williams – asymptotic analysis for nonlinear PDEs, adaptive numerical metholds and industrial mathematical modeli
R. Wittenberg – nonlinear dynamics, differential equations
K. Yeats – comfinatorics and quantum field theory
*emeritus
See “1.1 Degrees Offered” on page 219 for admission requirements. Applicants normally submit aptitude section scores and an appropriate advanced section of the Educational Testing Service’s graduate record exams. Applicants whose first language is not English will be asked to submit TOEFL results.
The department has introduced co-op education into its graduate program to allow students to gain work experience outside the academic sphere. Students who are currently enrolled in the MSc or PhD programs may apply.
Applied and Computational Mathematics
Admission Requirements
See “Graduate General Regulations” on page 219 for admission requirements. Applicants normally submit scores in the aptitude section and an appropriate advanced section of the Educational Testing Service’s graduate record examinations. Applicants with backgrounds in areas other than mathematics (for example, a bachelor’s degree or its equivalent in engineering or physics) may be considered suitably prepared for these programs.
An MSc candidate will normally obtain 26 units beyond courses completed for the bachelor’s degree. These 26 will consist of at least four courses chosen from the core courses list below, with at least one from each of the pairs APMA 900, 901; APMA 920, 922; APMA 930, 935; a further seven graduate units; and a further three units which may be graduate or 400 undergraduate division. Normally courses that are cross-listed as undergraduate courses cannot be used to satisfy graduate course requirements. The six core courses are as follows.
APMA 900-4 Advanced Mathematical Methods I
APMA 901-4 Advanced Mathematical Methods II
APMA 920-4 Numerical Linear Algebra
APMA 922-4 Numerical Solution of Partial Differential Equations
APMA 930-4 Fluid Dynamics
APMA 935-4 Analysis and Computation of Models
In addition to this requirement (normally completed in five terms), the student completes a project involving a significant computational component and submits and successfully defends a project report. This project should be completed within about one term.
PhD candidates must obtain a further eight graduate units beyond the MSc requirements. Candidates who are admitted to the PhD without an MSc must obtain credit or transfer credit for an amount of course work equivalent to that obtained by students with a MSc.
Candidates pass an oral candidacy exam given by the supervisory committee before the end of the fourth full time term. The exam consists of a proposed thesis topic defence and supervisory committee questions about related proposed research topics. The exam follows submission of a written PhD research proposal and is graded pass/fail. Those with a fail complete a second exam within six months. A student failing twice will normally withdraw.
A PhD candidate must submit and defend a thesis based on his/her original work that embodies a significant contribution to mathematical knowledge.
Courses
See page 312 for APMA course descriptions. The APMA courses replace courses formerly labelled MATH. For MATH 800-899 descriptions, see page 417. Course descriptions for STAT 801-890 are on page 446. Except for selected topics courses, students with credit for a MATH labelled course may not complete the corresponding APMA course for further credit.
Mathematics
Thesis Option
MSc candidates normally complete at least 18 graduate units beyond courses completed for the bachelor’s degree. Of these, at least 12 should be numbered 800 or above. The course work should involve at least two different mathematics areas subject to supervisory committee and department graduate studies committee approval. The candidate also submits a satisfactory thesis and defends it at an oral exam based on the thesis and related topics (MATH 898). See “Graduate General Regulations” on page 219 for regulations.
Project Course Option
An MSc candidate is normally required to complete at least 30 graduate units beyond courses completed for the applicant’s bachelor’s degree. Of these, at least 18 units should be from courses numbered 800 or above. The course work should normally involve at least three different mathematics areas subject to the approval of the student’s supervisory committee and the department’s graduate studies committee.
The candidate is required to complete and pass the project course MATH 880 and the examination course MATH 882. At most, one unsuccessful attempt each at MATH 880 and at MATH 882 is allowed.
See “Graduate General Regulations” on page 219 for further information and regulations.
A PhD candidate is normally required to complete the MSc requirements (either option) and at least 12 further graduate units. Of these, at least eight units should be from courses numbered 800 or above. Subject to the approval of the department’s graduate studies committee, a PhD candidate with a MSc is deemed to have completed the MSc requirements for the purpose of the PhD program requirements. The graduate course work should normally involve at least four different areas of mathematics subject to the approval of the student’s supervisory committee and the department’s graduate studies committee.
Candidates normally pass a two stage general exam. The first stage consists of successful completion of a comprehensive exam (MATH 878). In the second, students present to their supervisory committee a written thesis proposal and then defend it at an open oral defence (MATH 879). The supervisory committee evaluates the thesis proposal and defence, and passes or fails the student. A candidate cannot complete either general exam stage more than twice. Both stages must be completed within six full-time terms of initial enrolment in the program.
Students must submit and successfully defend a thesis which embodies a significant contribution to mathematical knowledge (MATH 899).
See “Graduate General Regulations” on page 219 for further information and regulations.
Courses
Seven hundred division courses may be offered in conjunction with a 400 division course. Students may not complete a 700 division course if it is offered in conjunction with a 400 division course which they have completed previously.
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