Applied and Computational Mathematics
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.
Core Course Requirements
Normally courses that are cross-listed as undergraduate courses cannot be used to satisfy graduate course requirements.
Beyond all the courses the student completed for the bachelor's degree, the candidate will complete 24 units that consist of 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 above course lists that has not already been completed
and an additional eight graduate units.
In addition to the core course requirements, the student should complete a satisfactory thesis normally involving a significant computational component, which is submitted and defended at an oral examination.
In addition to the core course requirements, the student completes a further 4 units of graduate coursework. The student should also complete a project that normally involves a significant computational component, and requires a project report and a final presentation. The project component should normally be completed within one term, during which the student should register in MATH 880-6.
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.