Program Requirements
Thesis Courses (24 credits)
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MATH 600 Master's Thesis Research 1 (6 credits)
Overview
Mathematics & Statistics (Sci) : Thesis research under supervision.
Terms: Fall 2015, Winter 2016, Summer 2016
Instructors: There are no professors associated with this course for the 2015-2016 academic year.
Restriction: Not open to students who have taken or are taking MATH 640
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MATH 601 Master's Thesis Research 2 (6 credits)
Overview
Mathematics & Statistics (Sci) : Thesis research under supervision.
Terms: Fall 2015, Winter 2016, Summer 2016
Instructors: There are no professors associated with this course for the 2015-2016 academic year.
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MATH 604 Master's Thesis Research 3 (6 credits)
Overview
Mathematics & Statistics (Sci) : Thesis research under supervision.
Terms: Fall 2015, Winter 2016, Summer 2016
Instructors: There are no professors associated with this course for the 2015-2016 academic year.
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MATH 605 Master's Thesis Research 4 (6 credits)
Overview
Mathematics & Statistics (Sci) : Thesis research under supervision.
Terms: Fall 2015, Winter 2016, Summer 2016
Instructors: There are no professors associated with this course for the 2015-2016 academic year.
Required Course
(1 credit)
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MATH 669D1 CSE Seminar (0.5 credits)
Overview
Mathematics & Statistics (Sci) : Techniques and applications in computational science and engineering.
Terms: This course is not scheduled for the 2015-2016 academic year.
Instructors: There are no professors associated with this course for the 2015-2016 academic year.
Restriction: This seminar course is open only to students who were admitted to the CSE Program Option.
No credit will be given for this course unless both MATH 669D1 and MATH 669D2 are successfully completed in consecutive terms
Students must register for both MATH 669D1 and MATH 669D2
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MATH 669D2 CSE Seminar (0.5 credits)
Overview
Mathematics & Statistics (Sci) : See MATH 669D1 for course description.
Terms: This course is not scheduled for the 2015-2016 academic year.
Instructors: There are no professors associated with this course for the 2015-2016 academic year.
Prerequisite: MATH 669D1
No credit will be given for this course unless both MATH 669D1 and MATH 669D2 are successfully completed in consecutive terms
Complementary Courses (22 credits)
(minimum 22 credits)
Two courses from List A, two courses from List B, and the remaining credits to be chosen from graduate (500- or 600-level) courses in the Department of Mathematics and Statistics. Two complementary courses must be taken outside the Department of Mathematics and Statistics.
List A - Scientific Computing Courses:
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CIVE 602 Finite Element Analysis (4 credits)
Overview
Civil Engineering : Development of displacement based simple and high order, one, two and three dimensional elements for linear elastic stress analysis. Variational and other methods for element formulation. Plate bending and shell elements. Finite element programming. Use of package programs in static analysis of structures.
Terms: This course is not scheduled for the 2015-2016 academic year.
Instructors: There are no professors associated with this course for the 2015-2016 academic year.
(3-0-9)
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COMP 522 Modelling and Simulation (4 credits)
Overview
Computer Science (Sci) : Simulation and modelling processes, state automata, Petri Nets, state charts, discrete event systems, continuous-time models, hybrid models, system dynamics and object-oriented modelling.
Terms: This course is not scheduled for the 2015-2016 academic year.
Instructors: There are no professors associated with this course for the 2015-2016 academic year.
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COMP 540 Matrix Computations (3 credits)
Overview
Computer Science (Sci) : Designing and programming reliable numerical algorithms. Stability of algorithms and condition of problems. Reliable and efficient algorithms for solution of equations, linear least squares problems, the singular value decomposition, the eigenproblem and related problems. Perturbation analysis of problems. Algorithms for structured matrices.
Terms: Fall 2015
Instructors: Chang, Xiao-Wen (Fall)
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COMP 566 Discrete Optimization 1 (3 credits)
Overview
Computer Science (Sci) : Use of computer in solving problems in discrete optimization. Linear programming and extensions. Network simplex method. Applications of linear programming. Vertex enumeration. Geometry of linear programming. Implementation issues and robustness. Students will do a project on an application of their choice.
Terms: This course is not scheduled for the 2015-2016 academic year.
Instructors: There are no professors associated with this course for the 2015-2016 academic year.
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MATH 578 Numerical Analysis 1 (4 credits)
Overview
Mathematics & Statistics (Sci) : Development, analysis and effective use of numerical methods to solve problems arising in applications. Topics include direct and iterative methods for the solution of linear equations (including preconditioning), eigenvalue problems, interpolation, approximation, quadrature, solution of nonlinear systems.
Terms: Fall 2015
Instructors: Oberman, Adam (Fall)
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MATH 579 Numerical Differential Equations (4 credits)
Overview
Mathematics & Statistics (Sci) : Numerical solution of initial and boundary value problems in science and engineering: ordinary differential equations; partial differential equations of elliptic, parabolic and hyperbolic type. Topics include Runge Kutta and linear multistep methods, adaptivity, finite elements, finite differences, finite volumes, spectral methods.
Terms: Winter 2016
Instructors: Oberman, Adam (Winter)
List B - Applications and Specialized Methods Courses:
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ATOC 512 Atmospheric and Oceanic Dynamics (3 credits)
Overview
Atmospheric & Oceanic Sciences : Introduction to the fluid dynamics of large-scale flows of the atmosphere and oceans. Stratification of atmosphere and oceans. Equations of state, thermodynamics and momentum. Kinematics, circulation, and vorticity. Hydrostatic and quasi-geostrophic flows. Brief introduction to wave motions, flow over topography, Ekman boundary layers, turbulence.
Terms: Fall 2015
Instructors: Straub, David N (Fall)
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ATOC 513 Waves and Stability (3 credits)
Overview
Atmospheric & Oceanic Sciences : Linear theory of waves in rotating and stratified media. Geostrophic adjustment and model initialization. Wave propagation in slowly varying media. Mountain waves; waves in shear flows. Barotropic, baroclinic, symmetric, and Kelvin-Helmholtz instability. Wave-mean flow interaction. Equatorially trapped waves.
Terms: Winter 2016
Instructors: Merlis, Timothy (Winter)
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ATOC 515 Turbulence in Atmosphere and Oceans (3 credits)
Overview
Atmospheric & Oceanic Sciences : Application of statistical and semi-empirical methods to the study of geophysical turbulence. Reynolds' equations, dimensional analysis, and similarity. The surface and planetary boundary layers. Oceanic mixed layer. Theories of isotropic two- and three- dimensional turbulence: energy and enstrophy inertial ranges. Beta turbulence.
Terms: This course is not scheduled for the 2015-2016 academic year.
Instructors: There are no professors associated with this course for the 2015-2016 academic year.
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CIVE 572 Computational Hydraulics (3 credits)
Overview
Civil Engineering : Computation of unsteady flows in open channels; abrupt waves, flood waves, tidal propagations; method of characteristics; mathematical modelling of river and coastal currents.
Terms: Fall 2015
Instructors: Chu, Vincent H; Karimpour Ghannadi, Shooka (Fall)
(3-0-6)
Prerequisite: CIVE 327 or equivalent
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CIVE 603 Structural Dynamics (4 credits)
Overview
Civil Engineering : Dynamic loads on structures; equations of motion of linear single- and multiple-degree-of-freedom systems and of continuous systems; free and forced vibrations; damping in structures; modal superposition and time-history analysis; earthquake effects; provisions of the National Building Code of Canada for seismic analysis.
Terms: This course is not scheduled for the 2015-2016 academic year.
Instructors: There are no professors associated with this course for the 2015-2016 academic year.
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COMP 557 Fundamentals of Computer Graphics (3 credits)
Overview
Computer Science (Sci) : The study of fundamental mathematical, algorithmic and representational issues in computer graphics. The topics to be covered are: overview of graphics process, projective geometry, homogeneous coordinates, projective transformations, quadrics and tensors, line-drawing, surface modelling and object modelling reflectance models and rendering, texture mapping, polyhedral representations, procedural modelling, and animation.
Terms: Fall 2015
Instructors: Kry, Paul (Fall)
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COMP 558 Fundamentals of Computer Vision (3 credits)
Overview
Computer Science (Sci) : Biological vision, edge detection, projective geometry and camera modelling, shape from shading and texture, stereo vision, optical flow, motion analysis, object representation, object recognition, graph theoretic methods, high level vision, applications.
Terms: This course is not scheduled for the 2015-2016 academic year.
Instructors: There are no professors associated with this course for the 2015-2016 academic year.
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COMP 567 Discrete Optimization 2 (3 credits)
Overview
Computer Science (Sci) : Formulation, solution and applications of integer programs. Branch and bound, cutting plane, and column generation algorithms. Combinatorial optimization. Polyhedral methods. A large emphasis will be placed on modelling. Students will select and present a case study of an application of integer programming in an area of their choice.
Terms: Winter 2016
Instructors: Lamghari, Amina; Dimitrakopoulos, Roussos (Winter)
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COMP 621 Program Analysis and Transformations (4 credits)
Overview
Computer Science (Sci) : Program analysis and transformations are used in optimizing compilers and other automatic tools such as bug-finders, verification tools and software engineering applications. Course topics include the design of intermediate representations, control flow analysis, data flow analysis at both the intra- and inter-procedural level and program transformations for performance improvement.
Terms: Fall 2015
Instructors: Hendren, Laurie (Fall)
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COMP 642 Numerical Estimation Methods (4 credits)
Overview
Computer Science (Sci) : Efficient and reliable numerical algorithms in estimation and their applications. Linear models and least squares estimation. Maximum-likelihood estimation. Kalman filtering. Adaptive estimation, GPS measurements and mathematical models for positioning. Position estimation. Fault detection and exclusion.
Terms: Winter 2016
Instructors: Chang, Xiao-Wen (Winter)
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COMP 767 Advanced Topics: Applications 2 (4 credits)
Overview
Computer Science (Sci) : Advanced topics in computing systems.
Terms: This course is not scheduled for the 2015-2016 academic year.
Instructors: There are no professors associated with this course for the 2015-2016 academic year.
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ECSE 507 Optimization and Optimal Control (3 credits)
Overview
Electrical Engineering : General introduction to optimization methods including steepest descent, conjugate gradient, Newton algorithms. Generalized matrix inverses and the least squared error problem. Introduction to constrained optimality; convexity and duality; interior point methods. Introduction to dynamic optimization; existence theory, relaxed controls, the Pontryagin Maximum Principle. Sufficiency of the Maximum Principle.
Terms: Winter 2016
Instructors: Michalska, Hannah (Winter)
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ECSE 532 Computer Graphics (3 credits)
Overview
Electrical Engineering : Introduction to computer graphics systems and display devices: raster scan, scan conversion, graphical input and interactive techniques - window environments; display files: graphics languages and data structures: 2D transformations; 3D computer graphics, hidden line removal and shading; graphics system design; applications. Laboratory project involving the preparation and running of graphics programs.
Terms: This course is not scheduled for the 2015-2016 academic year.
Instructors: There are no professors associated with this course for the 2015-2016 academic year.
(3-0-6)
Prerequisite: ECSE 322
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ECSE 547 Finite Elements in Electrical Engineering (3 credits)
Overview
Electrical Engineering : Finite elements for electrostatics. Energy minimization. Semi-conductors. Nonlinear magnetics and Newton-Raphson. Axisymmetric problems. Capacitance, inductance, and resistance through finite elements. Resonance: cavities, waveguides. High order and curvilinear elements.
Terms: Winter 2016
Instructors: McFee, Steve J (Winter)
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ECSE 549 Expert Systems in Electrical Design (3 credits)
Overview
Electrical Engineering : Design processes in electrical engineering. Hierarchical design. Computer aided design. Expert system technology. Device representations, heuristics and structures, algebraic models. Design versus diagnosis, "Shallow" and "Deep" systems, second generation (multi-paradigm) systems. Shells and their uses in design systems. Knowledge acquisition systems.
Terms: Fall 2015
Instructors: Lowther, David Alister (Fall)
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MATH 555 Fluid Dynamics (4 credits)
Overview
Mathematics & Statistics (Sci) : Kinematics. Dynamics of general fluids. Inviscid fluids, Navier-Stokes equations. Exact solutions of Navier-Stokes equations. Low and high Reynolds number flow.
Terms: This course is not scheduled for the 2015-2016 academic year.
Instructors: There are no professors associated with this course for the 2015-2016 academic year.
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MATH 560 Optimization (4 credits)
Overview
Mathematics & Statistics (Sci) : Line search methods including steepest descent, Newton's (and Quasi-Newton) methods. Trust region methods, conjugate gradient method, solving nonlinear equations, theory of constrained optimization including a rigorous derivation of Karush-Kuhn-Tucker conditions, convex optimization including duality and sensitivity. Interior point methods for linear programming, and conic programming.
Terms: This course is not scheduled for the 2015-2016 academic year.
Instructors: There are no professors associated with this course for the 2015-2016 academic year.
Prerequisite: Undergraduate background in analysis and linear algebra, with instructor's approval
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MATH 761 Advanced Topics in Applied Mathematics 1 (4 credits)
Overview
Mathematics & Statistics (Sci) : This course covers an advanced topic in applied mathematics.
Terms: Winter 2016
Instructors: Nave, Jean-Christophe; Poullet, Pascal (Winter)
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MECH 533 Subsonic Aerodynamics (3 credits)
Overview
Mechanical Engineering : Kinematics: equations of motion; vorticity and circulation, conformal mapping and flow round simple bodies. Two-dimensional flow round aerofoils. Three-dimensional flows; high and low aspect-ratio wings; airscrews. Wind tunnel interference. Similarity rules for subsonic irrotational flows.
Terms: Fall 2015
Instructors: Cortelezzi, Luca (Fall)
(3-1-5)
Prerequisite (Undergraduate): MECH 331
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MECH 537 High-Speed Aerodynamics (3 credits)
Overview
Mechanical Engineering : Equations of compressible flows. Planar and conical shock waves. Expansion and shock wave interference; shock tubes. Method of characteristics. Supersonic nozzle design. Aerofoil theory in high subsonic, supersonic and hypersonic flows. Conical flows. Yawed, delta and polygonal wings; rolling and pitching rotations. Wing-body systems. Elements of transonic flows.
Terms: Fall 2015
Instructors: Mateescu, Dan (Fall)
(3-0-6)
Pre/Corequisite (Undergraduate): MECH 533
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MECH 538 Unsteady Aerodynamics (3 credits)
Overview
Mechanical Engineering : Fundamental equations of unsteady compressible flows in fixed or moving reference frames. Unsteady flows past bodies in translation and having oscillatory motions. Oscillations of cylindrical pipes or shells subjected to internal flows. Vortex theory of oscillating aerofoils in incompressible flows. Theodorsen's method. Unsteady compressible flow past oscillating aerofoils.
Terms: This course is not scheduled for the 2015-2016 academic year.
Instructors: There are no professors associated with this course for the 2015-2016 academic year.
(3-0-6)
Prerequisite (Undergraduate): MECH 533
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MECH 539 Computational Aerodynamics (3 credits)
Overview
Mechanical Engineering : Fundamental equations. Basic flow singularities. Boundary element methods. Source, doublet and vortex panel methods for 2D and 3D incompressible and compressible flows. Method of characteristics. Euler equations for inviscid rotational flows. Finite-difference and finite-volume methods. Explicit and implicit time-integration methods. Quasi 1D solutions. Nozzle and confined aerofoil applications.
Terms: Winter 2016
Instructors: Nadarajah, Sivakumaran (Winter)
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MECH 541 Kinematic Synthesis (3 credits)
Overview
Mechanical Engineering : The role of kinematic synthesis within the design process. Degree of freedom. Kinematic pairs and bonds. Groups and subgroups of displacements. Applications to the qualitative synthesis of parallel-kinematics machines with three and four degrees of freedom. Function, motion and path generation problems in planar, spherical and spatial four-bar linkages. Extensions to six-bar linkages. Cam mechanisms.
Terms: Winter 2016
Instructors: Angeles, Jorge (Winter)
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MECH 572 Introduction to Robotics (3 credits)
Overview
Mechanical Engineering : Overview of the field of robotics. Kinematics, statics, singularity analysis and workspace of serial robots with decoupled architecture. Direct and inverse kinematics and dynamics. Algorithms for manipulator kinematics and dynamics.
Terms: Fall 2015
Instructors: Angeles, Jorge (Fall)
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MECH 573 Mechanics of Robotic Systems (3 credits)
Overview
Mechanical Engineering : Manipulator performance and design. Pick-and-place and continuous-path operations. Computation of rigid-body angular velocity and acceleration from point-data measurements. Inverse kinematics of serial manipulators with coupled architectures; kinetostatics of multifingered hands and walking machines. Kinematics and dynamics of parallel manipulators and wheeled mobile robots.
Terms: This course is not scheduled for the 2015-2016 academic year.
Instructors: There are no professors associated with this course for the 2015-2016 academic year.
(3-0-6)
Prerequisite: MECH 309 or MATH 317, and MECH 572 or permission of the instructor.
Since the course is open to both undergraduate and graduate students, and B- is the minimum passing mark for graduate students, this minimum mark will be relaxed for undergraduates. The regulations applicable to undergraduates will apply accordingly.
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MECH 577 Optimum Design (3 credits)
Overview
Mechanical Engineering : The role of optimization within the design process: Design methodology and philosophy. Constrained optimization: The Kuhn-Tucker conditions. Techniques of linear and non-linear programming. The simplex and the complex methods. Sensitivity of the design to manufacturing errors. Robustness of the design to manufacturing and operation errors.
Terms: This course is not scheduled for the 2015-2016 academic year.
Instructors: There are no professors associated with this course for the 2015-2016 academic year.
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MECH 610 Fundamentals of Fluid Dynamics (4 credits)
Overview
Mechanical Engineering : Conservation laws control volume analysis, Navier Stokes Equations and some exact solutions, dimensional analysis and limiting forms of Navier Stokes Equations. Vorticity, Potential flow and lift, boundary layer theory, drag, turbulence.
Terms: Winter 2016
Instructors: Lee, Timothy (Winter)
Prerequisite: MECH 605 or permission of instructor
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MECH 620 Advanced Computational Aerodynamics (4 credits)
Overview
Mechanical Engineering : Explicit and implicit time-integration methods; 2D and 3D finite-difference and finite-volume formulations for subsonic, transonic and supersonic rotational flows. Shock-fitting versus shock-capturing methods. Solution of the Navier-Stokes equations using artificial compressibility. Spectral methods. Lagrangian formulation. Time-accurate methods for unsteady flows with oscillating boundaries.
Terms: This course is not scheduled for the 2015-2016 academic year.
Instructors: There are no professors associated with this course for the 2015-2016 academic year.
Evening course
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MECH 632 Advanced Mechanics of Materials (4 credits)
Overview
Mechanical Engineering : Review of stress, strain, equilibrium and boundary conditions. Constitutive equations for linear and non-linear elasticity; viscoelasticity; rubber elasticity. Implementation of nonlinear constitutive relations for mechanical engineering applications. Material selection charts and overview of the major classes of materials (metals, polymers, ceramics, cellular materials, composites and biomaterials). Microscale mechanisms and their relation to macroscopic performance. Plasticity in metals: deformation maps, micromechanics, failure criteria, post-yield flow, creep and temperature effects. Structure and properties of polymers, models for plasticity and crazing. Fracture and fatigue, Weibull statistics for ceramics and glasses. Selected advanced topics and discussion of modern materials.
Terms: Fall 2015
Instructors: Barthelat, Francois (Fall)
Evening course
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MECH 642 Advanced Dynamics (4 credits)
Overview
Mechanical Engineering : Variational methods. Hamilton's principle and equations of motion of engineering systems. Lagrangian formulations for discrete systems. Methods of discretizing continuous systems. Rigid body dynamics. Dynamic behaviour of linear and nonlinear systems. Response of engineering systems to deterministic inputs by classical methods. Stability of linear and nonlinear systems.
Terms: Winter 2016
Instructors: Kovecses, Jozsef (Winter)
Evening course
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MECH 650 Fundamentals of Heat Transfer (4 credits)
Overview
Mechanical Engineering : Heat conduction: analytical solutions; integral solutions; solid-liquid phase-change. Forced and natural convection: nondimensionalization; boundary layer theory; design correlations for external and internal flows; basic ideas of turbulence modelling. Mixed convection. Boiling and condensation. Radiation heat transfer: basic concepts; black-body enclosure theory; gray-body enclosure theory; participating media.
Terms: Winter 2016
Instructors: Baliga, Bantwal (Winter)
Evening course
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MECH 654 Compt. Fluid Flow and Heat Transfer (4 credits)
Overview
Mechanical Engineering : A study of numerical methods for solving complex problems involving fluid flow and heat transfer. Finite volume methods, and overview of control-volume finite element methods. Methods for solving large systems of coupled nonlinear algebraic discretized equations. Mathematical models for turbulence.
Terms: This course is not scheduled for the 2015-2016 academic year.
Instructors: There are no professors associated with this course for the 2015-2016 academic year.
Evening course