Mathematics, M.Sc.
Mathematics
Head: Shaun Lui
Grad Chair: Adam Clay
Campus Address/General Office: 420A Machray Hall
Telephone: 204-474-9693
Email Address: mathdept@umanitoba.ca
Website: umanitoba.ca/science/mathematics
Academic Staff: Please refer to the Mathematics website for current staff listing.
Mathematics Program Information
The department offers programs leading to Master of Science and Doctor of Philosophy degrees.
Admission Information
Admission to the Faculty of Graduate Studies
Application and Admission Procedures are found in the Academic Guide.
Admission requirements for Master’s students are found in the Master’s Degrees General Regulations section of the Guide.
Mathematics M.Sc. Admission Requirements
Students should generally have a strong background in Mathematics with courses leading to an Honours or four-year Major in Mathematics in a B.Sc., B.A., or equivalent degree. The department’s Graduate Studies Committee will evaluate the student's background. Admission to the program will be based on this evaluation.
Students with other degrees or backgrounds may be eligible for admission to a pre-Master’s program to the satisfaction of the department. Courses will be prescribed on an individual basis to help the student qualify for graduate work in Mathematics.
Pre-Master's Option
This unit offers a Pre-Master’s program of study. The Pre-Master’s program of study is intended to bring a student’s background up to the equivalent of the required 4-year degree in the major department/unit, and to provide the student with any necessary prerequisites for courses to be taken in the Master’s program. Completing the Pre-Master’s program does not guarantee acceptance to the Master’s program.
Application Information
Students should complete and submit their online application with supporting documentation by the date indicated on the Mathematics M.Sc. program of study page.
Degree Requirements
Thesis Route: Students are required to complete at least 15 credit hours of course work, of which at least 9 credit hours must be from courses designated MATH 7000 or above and at least 6 credit hours in an area of mathematical sciences clearly different from the area of specialization of the thesis (as approved by the Department Head or designate). Each student in the thesis-based M.Sc. program must write a thesis.
Coursework Route: Students are required to complete at least 24 credit hours of course work at the 3000/7000/8000 level. At most 6 credit hours can be at the 3000 level. 4000 level courses do not count toward the degree requirement. Courses outside the Department of Mathematics (at most 9 credit hours) are also possible, subject to approval by the Department Head or designate. At least 6 credit hours must be in an area of mathematical sciences clearly different from the area of specialization of the report (see below). The minimum GPA of all courses must be at least 3.25.
Certain programs of study within mathematics may require courses outside the Department of Mathematics. A student may take at most two 3 credit hour reading courses from any one instructor for credit in this degree program.
Every M.Sc. student must make one 50-min presentation in any of the seminar series approved by the Department.
Expected Time to Graduate: 2 years
Progression Chart
THESIS PROGRAM
| Year 1 | Hours | |
|---|---|---|
| GRAD 7300 | Research Integrity Tutorial | 0 |
| GRAD 7500 | Academic Integrity Tutorial | 0 |
| MATH 7XXX | Courses designated MATH 7000 or above | 9 |
| Select two courses in an area of mathematical sciences | 6 | |
| Hours | 15 | |
| Year 2 | ||
| GRAD 7000 | Master's Thesis 1,2 | 0 |
| Hours | 0 | |
| Total Hours | 15 | |
| 1 | Students must demonstrate their mastery of the field and that they are fully conversant with the relevant literature through their thesis/practicum. |
| 2 | The M.Sc. thesis proposal must include a literature review, description of the proposed work, and a schedule for completion. The proposal should normally be completed within 10 months following the start of the program and must be approved by the student’s advisor. |
Coursework Program
| Years 1-2 | Hours | |
|---|---|---|
| GRAD 7500 | Academic Integrity Tutorial | 0 |
| GRAD 7300 | Research Integrity Tutorial | 0 |
| MATH XXXX | Courses designated MATH 3000/4000/7000 or above 1 | 12 |
| Select two courses in the area of mathematical sciences | 6 | |
| MATH 8996 or MATH 8998 |
MSc project 1 (A project, or work done in industry, together with a report OR report on teaching an undergraduate course.) or MSc project 2 |
6 |
| Hours | 24 | |
| Total Hours | 24 | |
| 1 | At most 6 credit hours can be at the 3000 level. 4000 level courses do not count toward the degree requirement. Courses outside the Department of Mathematics (at most 9 credit hours) are also possible, subject to approval. |
Notes:
- Certain programs of study within mathematics may require courses outside the Department of Mathematics.
- A student may take at most two 3 credit hour reading courses from any one instructor for credit in this degree program.
Registration Information
Students should familiarize themselves with the Faculty of Graduate Studies ‘GRAD’ courses applicable to their program. If you have questions about which GRAD course(s) to register in, please consult your home department/unit.
All new and returning students are required to consult with a department advisor prior to registration.
Regulations
Students must meet the requirements as outlined in both Supplementary Regulation and BFAR documents as approved by Senate.
Supplementary Regulations
Individual units may require specific requirements above and beyond those of the Faculty of Graduate Studies, and students should consult unit supplementary regulations for these specific regulations.
Bona Fide Academic Requirements (BFAR)
Bona Fide Academic Requirements (BFAR) represent the core academic requirements a graduate student must acquire in order to gain, and demonstrate acquisition of, essential knowledge and skills.
All students must successfully complete:
- GRAD 7300 prior to applying to any ethics boards which are appropriate to the student’s research or within the student’s first year, whichever comes first; and
- GRAD 7500 within the first term of registration;
unless these courses have been completed previously, as per Mandatory Academic Integrity Course and Mandatory Research Integrity Online Course.
Students must also meet additional BFAR requirements that may be specified for their program.
General Regulations
All students must:
- maintain a minimum degree grade point average of 3.0 with no grade below C+,
- meet the minimum and not exceed the maximum course requirements, and
- meet the minimum and not exceed the maximum time requirements (in terms of time in program and lapse or expiration of credit of courses).
Courses
Mathematics
Representation theory of finite groups, presentations of finite and infinite groups, or other topics. May not be held with MATH 4240.
PR/CR: A minimum grade of C is required unless otherwise indicated.
Prerequisite: permission of department.
Equiv To: MATH 4240
Lebesgue and abstract measures, measurable functions, convergence theorems, absolutely continuous functions, measure spaces, the Radon-Nikodym theorem, Fubini's and Tonnelli's theorems. May not be held with MATH 4260 and the former MATH 4750.
PR/CR: A minimum grade of C is required unless otherwise indicated.
Prerequisite: Permission of department.
Equiv To: MATH 4260, MATH 4750
This course will serve as an introduction to elements of homotopy or homology theory. May not be held with MATH 4270 and the former MATH 4230.
PR/CR: A minimum grade of C is required unless otherwise indicated.
Prerequisite: Permission of department.
Equiv To: MATH 4230, MATH 4270
Banach spaces, Hahn-Banach, open mapping and closed graph theorems, linear operators and functionals, dual space, Hilbert spaces and compact operators. May not be held with MATH 4280 and the former MATH 4750.
PR/CR: A minimum grade of C is required unless otherwise indicated.
Prerequisite: Permission of department.
Equiv To: MATH 4280, MATH 4750
Conformal mappings, normal families, harmonic and subharmonic functions, Perron's family, Dirichlet problem and Green's function. May not be held with MATH 4290 and the former MATH 4710.
PR/CR: A minimum grade of C is required unless otherwise indicated.
Prerequisite: Permission of department.
Equiv To: MATH 4290, MATH 4710
Topics in combinatorial geometry, including arrangements of convex bodies, introduction to polytopes, problems in discrete geometry, repeated distances, and geometric graphs. May not be held with MATH 4300.
PR/CR: A minimum grade of C is required unless otherwise indicated.
Prerequisite: Permission of department.
Equiv To: MATH 4300
Techniques for the qualitative analysis of nonlinear systems of ordinary differential equations and discrete-time systems. May not be held with MATH 4320 and the former MATH 4800.
PR/CR: A minimum grade of C is required unless otherwise indicated.
Prerequisite: Permission of department.
Equiv To: MATH 4320, MATH 4800
Theoretical aspects of approximation theory: density, existence, uniqueness; direct and inverse theorems for polynomial approximation. May not be held with MATH 4330.
PR/CR: A minimum grade of C is required unless otherwise indicated.
Prerequisite: Permission of department.
Equiv To: MATH 4330
This course will introduce students to the basics of affine and projective varieties through a combination of basic theoretical tools and elementary examples. May not be held with MATH 4340.
PR/CR: A minimum grade of C is required unless otherwise indicated.
Prerequisite: Permission of department.
Equiv To: MATH 4340
Manifolds and submanifolds. One of: exterior calculus and Stokes' theorem, Riemannian or symplectic geometry, and Hamiltonian mechanics. May not be held with MATH 4360 and the former MATH 4730.
PR/CR: A minimum grade of C is required unless otherwise indicated.
Prerequisite: Permission of department.
Equiv To: MATH 4360, MATH 4730
Norms, matrix factorizations, eigenvalues/eigenvectors, theory of non-negative matrices. Applications to differential equations, math biology, numerical analysis, graph theory, etc. May not be held with MATH 4370 and the former MATH 4310.
PR/CR: A minimum grade of C is required unless otherwise indicated.
Prerequisite: Permission of department.
Equiv To: MATH 4310, MATH 4370
Formulation, analysis and simulation of models in math biology. Applications will be chosen from population dynamics, epidemiology, ecology, immunology and cellular dynamics. May not be held with MATH 4380 and the former MATH 3530.
PR/CR: A minimum grade of C is required unless otherwise indicated.
Prerequisite: Permission of department.
Equiv To: MATH 3530, MATH 4380
Computational aspects of approximation by interpolatory polynomials, convolutions, artificial neural networks, splines and wavelets. May not be held with MATH 4390.
PR/CR: A minimum grade of C is required unless otherwise indicated.
Prerequisite: Permission of the department.
Equiv To: MATH 4390
Finite difference method, theory of Elliptic PDEs, finite element method, iterative solution of linear systems. Emphasis will be on the error analysis. May not be held with MATH 4440 and the former MATH 8150.
PR/CR: A minimum grade of C is required unless otherwise indicated.
Prerequisite: Permission of department.
Equiv To: MATH 4440, MATH 8150
Algebraic number theory, arithmetic geometry and analytic number theory, Diophantine equations, examples such as arithmetic of elliptic curves and Dirichlet L- functions. May not be held with MATH 4450 and the former MATH 3450.
PR/CR: A minimum grade of C is required unless otherwise indicated.
Prerequisite: Permission of department.
Equiv To: MATH 3450, MATH 4450
Green's function, Poisson, heat, Schrodinger and wave equations, Fourier and Laplace transforms, introduction to functional analytic techniques. May not be held with MATH 4460 and the former MATH 4810.
PR/CR: A minimum grade of C is required unless otherwise indicated.
Prerequisite: Permission of department.
Equiv To: MATH 4460, MATH 4810
The general theory of (non-commutative) rings, modules and algebras. May not be held with MATH 4470.
PR/CR: A minimum grade of C is required unless otherwise indicated.
Prerequisite: Permission of department.
Equiv To: MATH 4470
This course, cross-listed with MATH 4490, introduces the theory and practice of optimization. Topics include unconstrained optimization (quasi-Newton's, BFGS, nonlinear conjugate gradient methods), linear programming (Simplex method, duality), nonlinear constrained optimization (optimality conditions, duality, saddle point theory, barrier and penalty methods, Slater's condition) and integer programming (branch- and-bound, cutting plane and branch-and-cut methods). Applications to calculus of variations, statistics, data science, optimal control, signal processing and neural networks are given. Some computer programming will be required. This course is especially useful for students studying Data Science. Students cannot obtain credit for both MATH 4490 and MATH 7490.
PR/CR: A minimum grade of C is required unless otherwise indicated.
Prerequisite: permission of instructor.
Matrix computation, decomposition of matrices, iterative methods, sparse matrices, eigenvalue problems.
PR/CR: A minimum grade of C is required unless otherwise indicated.
Prerequisites: linear algebra, computing, numerical analysis, and consent of instructor.
Theory and practice of the finite element method of the solution of partial differential equations and its application to engineering and scientific problems. It includes the h, p and h-p versions, a priori and a posteriori error estimates, adaptability and the structure of finite element software.
PR/CR: A minimum grade of C is required unless otherwise indicated.
Prerequisite: numerical analysis and partial differential equations or consent of the instructor.
Continuation of MATH 4440/7440. Topics include spectral methods, time dependent equations, multigrid, domain decomposition methods, problems on infinite domains, methods for boundary integral equations, Riemann-Hilbert problems and integrable systems.
PR/CR: A minimum grade of C is required unless otherwise indicated.
Prerequisite: Permission of the department.
Topics will be chosen from the areas of algebraic combinatorics, coding theory, design theory, enumerative combinatorics, graph theory,
PR/CR: A minimum grade of C is required unless otherwise indicated.
Prerequisite: approval of department.
Continuation of MATH 4460/7460. Topics include functional analytic techniques for linear and nonlinear partial differential equations, conservation laws, KdV equation, singular perturbation, viscosity solutions.
PR/CR: A minimum grade of C is required unless otherwise indicated.
Prerequisites: Permission of the department.
Designed to accommodate special topics in applied or computational areas of mathematics not included in other course offerings. Students are advised to consult the department as to availability.
Designed to accommodate special topics in applied or computational areas of mathematics not included in other course offerings. Students are advised to consult the department as to availability.
Designed to accommodate special topics not included in topics courses.
PR/CR: A minimum grade of C is required unless otherwise indicated.
Prerequisite: approval of department.
Designed to accommodate special topics not included in topics courses.
PR/CR: A minimum grade of C is required unless otherwise indicated.
Prerequisite: approval of department.
Designed to accommodate special topics not included in topics courses.
PR/CR: A minimum grade of C is required unless otherwise indicated.
Prerequisite: approval of department.
Topics will be chosen from the areas of associative and non-associative algebras, Boolean algebra and lattice theory, category theory, group theory, ring theory and universal algebra.
PR/CR: A minimum grade of C is required unless otherwise indicated.
Prerequisite: approval of department.
Topics will be chosen from the areas of asymptotics, functional analysis, operator theory, real and complex variables, summability theory, topological vector spaces.
PR/CR: A minimum grade of C is required unless otherwise indicated.
Prerequisite: approval of department.
Topics will be chosen from the areas of asymptotics, functional analysis, operator theory, real and complex variables, summability theory, topological vector spaces.
PR/CR: A minimum grade of C is required unless otherwise indicated.
Prerequisite: approval of department.
Topics will be chosen from the areas of logic, model theory, recursive functions, set theory.
PR/CR: A minimum grade of C is required unless otherwise indicated.
Prerequisite: approval by department
Topics will be chosen from the areas of algebraic curves, combinatorial geometry, Euclidean geometry, fractal geometry, groups and geometrics, projective geometry.
PR/CR: A minimum grade of C is required unless otherwise indicated.
Prerequisite: approval of department.
Topics will be chosen from the areas of compactifications and related extensions, covering properties, rings of continuous functions, set-theoretic topology, topological groups, uniformities and related structures.
PR/CR: A minimum grade of C is required unless otherwise indicated.
Prerequisite: approval of department.
This is a project course exclusively for students enrolled in the Course-based MSc program. Students must submit a written report, on the order of 40 to 60 pages, which can be a survey of a topic in mathematics, for instance. This course is taken under the supervision of a faculty member. Course graded pass/fail.
This is a project course exclusively for students enrolled in the teaching track of the Course-based MSc program. Students must submit a written report, on the order of 20-30 pages, which can be a survey of a topic in mathematics, for instance. In addition, students are required to teach one undergraduate course. This course is taken under the supervision of a faculty member. Course graded pass/fail.