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Applied and Computational Mathematics
The Master of Science (MSc) in Applied and Computational Mathematics offers advanced education and research training in applied analysis, computation and mathematical modelling. Students admitted to the program will complete one of two program options.
間眅埶AV Requirements
Applicants must satisfy the University admission requirements as stated in Graduate General Regulations 1.3 in the 間眅埶AV Calendar. Applicants normally submit scores in the aptitude section and the appropriate advanced section of the Educational Testing Service's graduate record examinations (GRE). Applicants with backgrounds in areas other than mathematics (e.g. a bachelor's degree, or its equivalent, in engineering or physics) may be considered suitably prepared for these programs.
Program Requirements
This program consists of required courses, elective courses, and a thesis for a minimum of 36 units.
Students must complete one of
Analysis and computation of classical problems from applied mathematics such as eigenfunction expansions, integral transforms, and stability and bifurcation analyses. Methods include perturbation, boundary layer and multiple-scale analyses, averaging and homogenization, integral asymptotics and complex variable methods as applied to differential equations.
First order non-linear partial differential equations (PDEs) and the method of characteristics. Hamilton-Jacobi equation and hyperbolic conservation laws; weak solutions. Second-order linear PDEs (Laplace, heat and wave equations); Green's functions. Sobolev spaces. Second-order elliptic PDEs; Lax-Milgram theorem.
and one of
Conditioning and stability of numerical methods for the solution of linear systems, direct factorization and iterative methods, least squares, and eigenvalue problems. Applications and mathematical software.
Analysis and application of numerical methods for solving partial differential equations. Potential topics include finite difference methods, spectral methods, finite element methods, and multi-level/multi-grid methods.
and one of
Basic equations governing compressible and incompressible fluid mechanics. Finite difference and finite volume schemes for hyperbolic, elliptic, and parabolic partial differential equations. Practical applications in low Reynolds number flow, high-speed gas dynamics, and porous media flow. Software design and use of public-domain codes. Students with credit for MATH 930 may not complete this course for further credit.
Analysis of models from the natural and applied sciences via analytical, asymptotic and numerical studies of ordinary and partial differential equations.
and at least one other course from the courses listed above that has not already been completed
and an additional eight graduate units
and either the thesis or project option
Thesis Option
and a thesis
Project Option
and an additional 4 graduate units
and a project
A project leading to research in mathematics completed under the supervision of a faculty member. The project will consist of a written report and a public presentation. This course can only be used for credit towards the MSc project course option. Graded on a satisfactory/unsatisfactory basis.
| Section | Instructor | Day/Time | Location |
|---|---|---|---|
| TBD | |||
| TBD |
NOTE: 間眅埶AV students enrolled in the Accelerated master's degree program within the Department of Mathematics may apply a maximum of 10 graduate course units, taken while completing the bachelor’s degree, towards the upper division undergraduate electives of the bachelor’s program and the requirements of the master’s degree. For more information go to: .
Program Length
Students are expected to complete the program requirements in six terms.
Other Information
Cross-listed Courses
Normally courses that are cross-listed as undergraduate courses cannot be used to satisfy the graduate course requirements.
Thesis
The thesis normally involves a significant computational component which is submitted and defended at an oral examination.
Project
The project normally involves a significant computational component and requires a project report and a final presentation. The project component is normally completed within one term.
Academic Requirements within the Graduate General Regulations
All graduate students must satisfy the academic requirements that are specified in the Graduate General Regulations, as well as the specific requirements for the program in which they are enrolled.