**Second Year** **Courses**

APSC 200: Engineering design and Practice IIIn this course students will participate constructively on teams to create solutions to open-ended complex problems, using standard design methods and tools. This project-based course provides instruction primarily in the first 6 weeks of the semester focusing on problem scoping, creativity and idea generation, decision making incorporating technical, economic, societal, and environmental factors, safety, engineering codes and regulations, and engineering ethics. The final 6 weeks of the course centre around a design project delivered by each discipline. This course is integrated with APSC 293, and coordinated by the same instructor.

APSC 293: Engineering Communications IThis course provides an introduction to effective engineering writing and speaking skills with the emphasis on professional correspondence, engineering reports, oral briefings, and formal oral presentations. These skills are developed in lectures and small group tutorials. This course is integrated with APSC 200, and coordinated by the same instructor.

MTHE 212: Linear AlgebraVector spaces, direct sums, linear transformations, eigenvalues, eigenvectors, inner product spaces, self-adjoint operators, positive operators, singular-value decomposition, minimal polynomials, Jordan canonical form, the projection theorem, applications to approximation and optimization problems.

MTHE 217: Algebraic Structures with ApplicationsThe purpose of the course is to provide an introduction to abstract algebraic systems and to illustrate the concepts with engineering applications. Topics include symbolic logic; switching and logic circuits; set theory, equivalence relations and mappings; the integers and modular arithmetic; groups, cyclic groups, Lagrange’s theorem, group quotients, group homomorphisms and isomorphisms; applications to error-control codes for noisy communication channels.

MTHE 237: Differential Equations for Engineering ScienceTopics include models for dynamical systems, classification of differential equations, methods for solving differential equations, systems of equations and connections with Linear Algebra, stability of dynamical systems and Lyapunov’s method, the Laplace Transform method, and numerical and computer methods.

MTHE 280: Advanced CalculusLimits, Continuity, C’, and linear approximations of functions of several variables. Multiple integrals and Jacobians, Line and surface integrals. The theorems of Green, Stokes, and Gauss.

MTHE 281: Introduction to Real AnalysisTaylor’s theorem, optimization, implicit and inverse function theorems. Elementary topology of Euclidean spaces. Sequences and series of numbers and functions. Pointwise and uniform convergence. Power series.

**Third Year Courses**

MTHE 326: Functions of a Complex VariableComplex numbers, analytic functions, harmonic functions. Cauchy’s theorem. Taylor and Laurent series. Calculus of residues. Rouche’s theorem.

MTHE 335: Mathematics of Engineering SystemsLinear input/output systems and their stability. Frequency-domain and time-domain analysis. Continuous and discrete-time modeling. Fourier, Laplace, and Z-transforms. Sampling and the discrete-time Fourier transform. Applications to modulation of communications signals, filter design, and digital sampling.

MTHE 393: Engineering Design and Practice for Mathematics and EngineeringThis is a project-based design course where methods of applied mathematics are used to solve a complex open-ended engineering problem. The projects involve using system theoretic methods for modelling, analysis, and design applied to engineering problems arising in a variety of engineering disciplines. Students will work in teams and employ design processes to arrive at a solution. The course will include elements of communications, economic analysis, impacts of engineering, professionalism, and engineering ethics.

APSC 221: Economics and Business Practices in EngineeringThis course will provide the student in the Engineering program with the ability to appropriately incorporate selected economic and business practices into the practice of engineering. The practices covered include: business planning for the enterprise, enterprise economic analysis, project management process, project economic analysis, risk analysis and management, quality management and change management. Assignments and examples are based on situations from engineering based industries.

MTHE 328: Real Analysis Metric spaces, topological spaces, compactness, completeness, contraction mappings, sequences and series of functions, uniform convergence, normed linear spaces, Hilbert spaces.

MTHE 351: Probability IProbability theory: probability models; random variables; jointly distributed random variables; transformations and generating functions. Inequalities and limit laws. Distributions: binomial, Poisson, exponential, gamma, normal. Applications: elementary stochastic processes, timetofailure models, binary communication channels with Gaussian noise.

**Fourth Year Courses**

MTHE 493 Engineering Mathemics ProjectThis is the capstone design course for Mathematics and Engineering. Students must work in groups, with a typical group size being between two and four members. Projects are selected early in the year from a list put forward by Mathematics and Engineering faculty members who will also supervise the projects. There is a heavy emphasis on engineering design and professional practice. All projects must be open-ended and design oriented, and students are expected to undertake and demonstrate, in presentations and written work, a process by which the design facets of the project are approached. Projects must involve social, environmental, and economic factors, and students are expected to address these factors comprehensively in presentations and written work. Students are assessed individually and as a group on their professional conduct during the course of the project.

MTHE 494: Mathematics and Engineering SeminarThis is a seminar and course, with an emphasis on communication skills and professional practice. A writing module develops technical writing skills. Students give an engineering presentation to develop their presentation skills. Seminars are given by faculty from the Mathematics and Engineering program, by Mathematics and Engineering alumni on the career paths since completing the program, and by visiting speakers on a variety of professional practice matters, on topics such as workplace safety, workplace equity and human rights, and professional organizations.