Introduction to commutative algebra, algebraic geometry, and homological algebra. Additional topics at the discretion of the instructor. Prerequisite: MATH 326 or MATH 327 or consent of Department.

Group actions, Sylow Theory, representation theory of finite groups and additional topics at the discretion of the instructor. Prerequisite: MATH 328 or MATH 327 or consent of the Department.

Elementary existence and uniqueness theorems. Systems of equations, stability, perturbation theory. Introduction to numerical methods. Introduction to phase plane analysis. Prerequisite: One of MATH 201, MATH 334, MATH 336, or MA PH 251

Partial differential equations as physical models. Introduction to basic generalized functions. Theory of linear and quasi-linear first-order equations: general solution, initial value problem, generalized solutions and propagation of singularities, characteristic surfaces, shock formation. Theory of fully nonlinear first order equations: complete solution and the initial value problem. Hamilton-Jacobi equation and its applications. Second order linear equations in n dimensions: classification, canonical form, characteristic surfaces and shock formation, initial and boundary value problem. Prerequisite: MATH 300 or MATH 337.

General point-set topology. Compactness, Tychonoff's tbeorem, connectedness. Metric spaces, completeness, Baire's theorem. Urysohn's lemma. Topological manifolds. Homotopy theory, fundamental group, covering spaces. Prerequisite : MATH 216 or 217. Corequisites: MATH 328 or MA PH 464. Offered in alternate years. It may be offered in intervening years if demand is sufficient.

Riemannian geometry of n-space, metric tensors, various curvature concepts and their relationships, covariant differentiation, geodesics, parallel transport. Additional topics at the discretion of the instructor. Prerequisite: MATH 348, or MATH 217 and one of MATH 225 or 227. Note: Offered in alternate years. It may be offered in intervening years if demand is sufficient.

Birth-death processes; continuous-time Markov chains; functional central limit theorem; Brownian motion; weak solutions to stochastic differential equations; weak uniqueness; filtrations; discrete and continuous martingales; martingales problems; strong Markov property; Kolmogorov forward and backward equations; stationary distributions; null and positive recurrence; transience; particle filtering. Prerequisite: STAT 281 or STAT 371. Note: Credit cannot be obtained in MATH 471 if credit has already been in STAT 471.

This course will cover advanced algebraic topics not taught in regular courses in the curriculum or will provide a more in-depth continuation of an existing course. Prerequisite: at least one of MATH 326, MATH 327, MATH 328, MATH 329, or equivalent. Note: Upon approval by the Department of Mathematical and Statistical Sciences, this course may be taken for credit multiple times.

This course is designed to give credit to mature and able students for reading in areas not covered by courses, under the supervision of a staff member. A student, or group of students, wishing to use this course should find a staff member willing to supervise the proposed reading program. A detailed description of the material to be covered should be submitted to the Chair of the Department Honors Committee. (This should include a description of testing methods to be used.) The program will require the approval of both the Honors Committee, and the Chair of the Department. The students' mastery of the material of the course will be tested by a written or oral examination. This course may be taken in Fall or Winter and may be taken any number of times, subject always to the approval mentioned above. Prerequisite: Any 300-level MATH course.

This topics course is designed for new course offerings that may be offered in a given term. Prerequisites: One of MATH 209, 214, or 217 and one of MATH 225 or 227. Additional prerequisites may be required. Note: Credit for this course may be obtained more than once.

This course provides students in Major, Specialization and Honors programs an opportunity to pursue research in mathematics under the direction of a member of the Department. Course requirements include at least one oral presentation and a written final report. Students interested in taking this course should contact the course coordinator two months in advance. Credit for this course may be obtained more than once. Prerequisites: a 300-level MATH course and consent of the course coordinator.

Discrete-time stochastic analysis: Stochastic basis, filtration, stochastic sequences. Absolute continuity of probability measures and conditional expectations. Martingale-like and predictable stochastic sequences. Doob's decomposition. Stopping times and related properties. Uniformly integrable stochastic sequences. Transition from discrete-time to continuous-time stochastic analysis. Introduction to stochastic integration with respect to Brownian motion. Prerequisites: STAT 471 or consent of the Department.

A review and some extensions of single variable complex analysis. Complex linearity and holomorphicity in several variables, Hartog's theorem, Weierstrass preparation theorem, Riemann extension theorem, Weierstrass division theorem, analytic Nullstellensatz, implicit and inverse function theorems, complex manifolds and analytic subvarieties, meromorphic maps. Prerequisite: MATH 411.

Principles of Monte Carlo methods. Essentials of stochastics. Introduction to financial derivatives pricing. Generating random variables. Simulating stochastic differential equations. Application to financial derivatives pricing and interest rate models. Variance reduction techniques. Prerequisite: STAT 471 or FIN 654 or ECON 598 or consent of the Department. Note: This course may not be taken for credit if credit has already been obtained in MATH 408.

Basic data analysis with R, SAS, and Python. Program development with Jupyter notebooks. Cloud computing, collaborative software development, docker containers, kubernets. Internet security, privacy and ethics. Technologies will be updated as new developments arise. Prerequisites: No programming skills are needed.

Continuous semimartingales and quadratic variation. Stochastic integrals for continuous semimartingales. Ito's formula. Change of probability measure (Girsanov transformation). Martingale representation theorem for Brownian filtrations. Stochastic differential equations, diffusions. Introduction to discontinuous semimartingales with emphasis on Poisson processes. Prerequisites: MATH 505 or consent of the Department.

Valuations and their extensions, ramifications; integral dependence, algebraic number fields, ideals and divisors, class number. Prerequisite: MATH 326 or equivalent.

Brief review of set operations and countable sets. Measure theory, integration theory, Lebesgue measure and integrals on R^n, product measure, Tonelli-Fubini theorem. Functions of bounded variation, absolutely continuous functions. Prerequisites: Math 317.

Review of probability tools for discrete financial analysis; Conditional probabilities/expectations. Filtrations, adapted and predictable processes. Martingales, submartingales and supermartingales in discrete-time. Doob decomposition for supermartingales. Predictable representation. Discrete-time financial modes: Arbitrage, complete and incomplete markets. Self-financing property, value and gain processes. Valuation of contingent claims. Binomial model: Model specifications, Perfect hedging. Utility functions and consumption/investment problems. European and American options in discrete time. Futures and forward contracts in discrete time. Transition to the continuous-time framework. Prerequisite: STAT 471 or consent of the Department. Note: This course may not be taken for credit if credit has already been obtained in MATH 415.

Classical Banach spaces. Hahn-Banach, open mapping and closed graphs theorems. Hilbert spaces, orthonormal bases. Elements of spectral theory, spectra of compact operators, spectral theorem for compact self-adjoint operators. Prerequisite: MATH 417. Corequisite: MATH 447.

Locally convex spaces, weak topologies and duality in Banach spaces, weak compactness in Banach spaces, structure of classical Banach spaces, local structures, infinite-dimensional geometry of Banach spaces and applications. Prerequisite: MATH 516. Corequisite: MATH 447 or consent of Department.

Banach algebras and spectral theory, compact and Fredholm operators, the spectral theorem for bounded normal operators, operator algebras, representations of C+-algebras, elementary von Neumann algebra theory, and other topics. Prerequisite: MATH 516. Corequisite: MATH 447 or consent of Department.

Financial markets in continuous-time: Arbitrage, completeness, self-financing strategies. Black Scholes model. Option pricing and hedging: European, American and exotic options. Consumption-investment problem: Utility maximization, optimal portfolio and optimal consumption. Prerequisite: MATH 515. Corequisite: MATH 510 or consent of the Department.

Finite dimensional manifolds/submanifolds; tangent bundle, differential, inverse, and implicit function theorems, partitions of unity; imbeddings, immersions, submersions; vector fields and associated flows; Lie derivative, Lie bracket; tensor analysis, differential forms, orientation, integration, Stokes' theorem; basics of smooth bundle theory, Riemannian metrics; notion of a Lie group with basic examples, smooth Lie group actions, principal bundles. Prerequisite: MATH 446 or 448.

Existence theorems, uniqueness theorems; linear systems (basic theory); stability (basic theory); nonlinear systems (local theory); nonlinear systems (global theory); bifurcations. Prerequisite: MATH 334 or 336, or equivalent.

Asymptotics; boundary value problems; Poincare-Bendixson theory. Additional material will be chosen from among the following topics at the option of the instructor: separation; dichotomies; comparison and oscillation theory; bifurcation theory; nonautonomous systems; dynamical systems; functional differential equations; contingent equations; differential equations in Banach spaces. Prerequisite: MATH 524 or equivalent.

Notions; Elliptic PDE's; Parabolic PDE's; Hyperbolic PDE's; Nonlinear Integrable PDE's. Prerequisite: MATH 436 or equivalent; corequisite: MATH 516.

Particular background from point set topology (pasting and quotienting constructions); homotopy relation between maps and spaces; fundamental group; Seifert VanKampen theorem; covering spaces. Additional topics at the discretion of the instructor. Prerequisites: MATH 227, 317 and 447 or consent of Department.

Direct and iterative methods for solving linear systems, iterative methods for nonlinear systems, polynomial and spline interpolations, least square approximation, numerical differentiation and integration, initial value problems for ODE's (one-step, multistep methods, stiff ODE's). Prerequisite: 400-level MATH course. Students are required to have knowledge of advanced Calculus and introductory knowledge in Analysis and Linear Algebra and some computer programming. Note 1: Restricted to graduate students only. Note 2: May not be taken for credit if credit has already been obtained in MATH 381, 481 or 486 or equivalent.

Finite difference and finite element methods for boundary-value problems of elliptic equations. Numerical algorithms for large systems of linear algebraic equations: direct, classical relaxation, multigrid and preconditioned conjugate gradient methods. Algorithms for vector/parallel computers and the domain decomposition method. Prerequisites: MATH 337, 436 or equivalent and some computer programming.

Asymptotic analysis of integrals: Laplace, stationary phase, and steepest descent methods. Regular and singular perturbations: trained coordinates, multiple scales, asymptotic matching, renormalization techniques, WKB theory, Hamiltonian perturbation theory, center manifolds and stability. Singularities in differential equations. Applications to algebraic, ordinary and partial differential equations. Prerequisite: MATH 438 or equivalent.

Linear part:structure of function spaces, Sobolev spaces, embeddings, topologies, linear operators, adjoint and inverse operators, spectra, distributions, semigroup theory, integral equations, well-posedness and the notion of a solution. Nonlinear part: inequalities, Frechet and Gateaux derivatives, fixed point theorems. Applications from mechanics, reaction-diffusion equations, the Navier-Stokes equations, nonlinear Schrödinger equation. Prerequisite: MATH 438 or equivalent.

Review, theory and extension of Fourier series for square integrable functions; orthonormal systems, Bessel's inequality, completeness, Parseval's identity, Riesz-Fischer Theorem. Extension to Fourier series for functions in other Lebesgue classes; Fejer means, conjugate series, Dirichlet, Fejer and Poisson kernels. Norm convergence; remarks on pointwise convergence. Fourier transforms and series in several dimensions; inverse transform, Plancherel formula, Poisson Formula, maximal functions, Riesz-Thorin Theorem and applications. Elementary distribution theory; D, D', S, S' and some elementary results, Fourier transforms of tempered distributions. Examination of some earlier results with tempered distributions instead of functions and getting familiar with basic concepts. Prerequisite: MATH 418.

Review of basic measure and integration theory. Signed and complex measures. Hahn and Jordan decompositions. The Radon-Nikodym theorem. Lebesgue decomposition. The Lebesgue-Stieltjes integral. Measure theory over locally compact Hausdorff spaces, in particular, the Riesz representation theorem and Haar measures. Hausdorff measure. Introduction to martingales. Prerequisite: One of MATH 417 or MATH 514, and MATH 447 or equivalent.

Fundamentals including continuum hypothesis surface tension, classical thermodynamics, and transport phenomena. Introduction to Cartesian tensors. Kinematics of flow including Lagrangian and Eulerian descriptions, streamline, path line, streak line, vorticity and circulation. Derivation of the conservation laws for mass, momentum, and energy and a detailed description of the Boussinesq approximation. Conservation laws in a rotating frame. Vortex lines and tubes, role of viscosity in vortices, Kelvin's circulation theorem, the vorticity equation in nonrotating and rotating frames. Irrotational flow including its relevance, velocity potential, sources and sinks, and flow past various shapes. Gravity waves in deep and shallow water with and without surface tension in both the linear and nonlinear contexts. Dynamic similarity and Buckingham's Pi Theorem. Prerequisites: One of MATH 311, 411 and MATH 436 or consent of Instructor.

Mathematical modeling in the biological and medical sciences. Students will learn how to apply mathematical methods and theory to a variety of different biological problems. Topics will be taken from: (i) continuous and discrete dynamical systems describing interacting and structured populations, resource management, biological control, reaction kinetics, biological oscillators and switches, the dynamics of infectious diseases and genetics and (ii) models of spatial processes in biology including random walks, pattern formation in morphogenesis and ecology, applications of traveling waves to population dynamics, epidemiology, chemical reactions, and models for neural patterns. Prerequisites: MATH 524 and a 400 or 500 level course on Partial Differential Equations or consent of Instructor.

Developing mathematical models to solve real-world problems, model analysis, fitting model to data, model validation and selection, and interpretation of model outcomes. Types of models include difference equation models, differential equation models, network models, and stochastic models. Prerequisites: Linear algebra and differential equations or consent of the instructor.

Development of mathematical models for the transmission dynamics of infectious diseases, incorporation of important epidemiological factors including disease latency, recovery, relapse and reinfection, isolation and quarantine, vaccination and immunity. Stability and bifurcation analysis of mathematical models. Estimation of model parameters from public health data, and numerical simulations of models. Prediction of the time course of epidemics and long-term patterns of endemic diseases. Prerequisites: MATH 334 or MATH 336, or with instructor's consent.

Group actions, Sylow Theory, solvable and nilpotent groups, Galois Theory. Additional topics at the discretion of the instructor. Prerequisite: MATH 328 or consent of the Department.

Introduction to commutative algebra, algebraic geometry, and homological algebra. Additional topics at the discretion of the instructor. Prerequisite: MATH 326 or consent of the Department.

This course will cover advanced algebraic topics not taught in regular courses in the curriculum or will provide a more in-depth continuation of an existing course. Prerequisite: at least one of MATH 326, MATH 327, MATH 328, MATH 329, or equivalent. Note: Upon approval by the Department of Mathematical and Statistical Sciences, this course may be taken for credit multiple times.

Students registered in this course are supervised by individual staff members in areas of interest of the staff members. Students will be allowed to take this course only in exceptional circumstances and with the permission of the Chairman of the Department. This course shall not be counted against the minimum course requirement for graduate students.

Credit for this course can be obtained twice.

Topics among: Incomplete markets; Models with imperfection (markets with transaction costs, constraints or defaults); Risk measures; Interplay between finance and insurance; Mathematical models for the term structure of interest rates. Prerequisites: MATH 520 or consent of the Department.

Credit for this course may be obtained more than once.

Open only to students taking the MSc non-thesis option in mathematics.

Open only to students taking the MSc non-thesis option in mathematics.

Open only to students taking the MSc non-thesis option in mathematics.

Les nombres, inéquations, fonctions, géométrie analytique, limite, continuité, dérivées et applications, polynôme de Taylor, fonctions exponentielles et logarithmiques, fonctions trigonométriques inverses et hyperboliques, différentielle et calculs approximatifs. Intégration et théorème fondamental du calcul intégral. Méthode des trapèzes et méthode de Simpson. Préalable(s): Mathématiques 30-1 ou l'équivalent et Mathématiques 31. Note(s): (1) Ce cours n'est pas accessible aux étudiants ayant ou postulant des crédits pour MATHQ 114 (ou 113), MATH 117, 134, 144 ou SCI 100. (2) Ce cours est normalement réservé aux étudiants de la Faculty of Engineering. (3) Les étudiants de la Faculty of Engineering qui suivent ce cours obtiendront 3.5 crédits.

Techniques d'intégration et applications du calcul d'intégrales: calcul de longueurs, aires, volumes et masses, intégrales impropres, équations différentielles ordinaires d'ordre un; séparables, linéaires, méthode d'Euler, applications. Séries infinies, séries de Taylor, séries de puissances et critère de convergence d'une série. Coordonnées polaires, rectangulaires, sphériques et cylindriques dans l'espace de trois dimensions, courbes paramétriques dans le plan et l'espace. Volume et aire d'une surface de révolution. Préalable: MATHQ 100. Note(s): (1) Ce cours n'est pas accessible aux étudiants ayant ou postulant des crédits pour MATHQ 115, MATH 118, 146 ou SCI 100. (2) Ce cours est normalement réservé aux étudiants de la Faculty of Engineering. (3) Les étudiants de la Faculty of Engineering qui suivent ce cours obtiendront 3.5 crédits.

Vecteurs et matrices; solution d'équations linéaires; équations de lignes et de plans; déterminants; algèbre matricielle; orthogonalité de GramSchmidt et applications; valeurs propres, vecteurs propres et applications; nombres complexes. Préalable ou concomitant: MATHQ 100. Note(s): (1) Ce cours n'est pas accessible aux étudiants ayant ou postulant des crédits pour MATHQ 120, 125, MATH 125 ou 127. (2) Ce cours est normalement réservé aux étudiants de la Faculty of Engineering. (3) Les étudiants de la Faculty of Engineering qui suivent ce cours obtiendront 3.5 crédits.

Taux de variation et dérivées. Dérivation des fonctions élémentaires, trigonométriques, exponentielles et logarithmiques. L'intégrale définie comme sommation. L'intégration. Le théorème fondamental du calcul intégral. Applications dans le contexte des sciences de la vie ou des Sciences physique, ou des affaires et de l'économie. Préalable(s): Mathématiques 30-1. Note: Ce cours n'est pas accessible aux étudiants ayant ou postulant des crédits pour MATHQ ou MATH 100, 113, 114, 117, 134, 144, 154 ou SCI 100.

Techniques d'intégration et applications de l'intégration. Intégrales impropres. Équations différentielles et modélisation mathématique. Dérivées partielles. Applications dans le contexte des sciences de la vie ou des Sciences physique, ou des affaires et de l'économie. Préalable(s): L'un des cours MATHQ ou MATH 100, 113, 114, 117, 134, 144 ou 154. Note: Ce cours n'est pas accessible aux étudiants ayant ou postulant des crédits pour MATHQ ou MATH 101, 115, 118, 136, 145, 156 ou SCI 100.

Vecteurs et algèbre matricielle. Déterminantes. Système d'équations linéaires. Espaces vectoriels. Valeurs propres et vecteurs propres. Applications. Préalable(s): Mathématiques 30-1 ou l'équivalent. Note: Ce cours n'est pas accessible aux étudiants ayant ou postulant des crédits pour MATHQ 120, MATH 102 ou 127.

Les concepts étudiés ont pour but d'aider l'enseignant à formuler une idée intuitive des concepts qu'il doit enseigner aux élèves. Nous aborderons la théorie élémentaire du nombre, les systèmes de numération, les ensembles de nombres, la théorie élémentaire de probabilité et les raisonnements inductif et déductif. Préalable(s): Mathématiques 30-1 ou 30-2, ou l'approbation du vice-doyen aux affaires académiques. Note(s): (1) Ce cours est réservé aux étudiants du BEd Élémentaire. (2) Les étudiants en sciences ne peuvent pas obtenir de crédits pour ce cours.

Séries infinies. Courbes planes et coordonnées polaires. Géométrie analytique à trois dimensions. Dérivées partielles. Préalable(s): MATHQ 101, 115, MATH 118, 146 ou SCI 100 ou l'équivalent. Note: Ce cours n'est pas accessible aux étudiants ayant ou postulant des crédits pour MATHQ 209 ou MATH 217.

Approche appliquée des mathématiques discrètes, couvrant les codes secrets, la cryptographie à clef publique, codes correcteurs d'erreurs, relations de récurrences, induction, théorie des graphes, algorithmes pour les graphes et algorithmes parallèles. Préalable(s): 3 crédits de niveau 100 en mathématiques ou SCI 100.

Espaces vectoriels. Espaces avec produit scalaire. Exemples d'espace à n dimensions, espace des fonctions continues. Procédé de Gram-Schmidt, factorisation QR, méthode des moindres carrés. Transformations linéaires, changements de base, transformations de similarité et diagonalisation. Diagonalisation orthogonale, formes quadratiques. Applications à une variété de champs, méthodes numériques. Préalable(s): un cours de niveau 100 en algèbre linéaire et Mathématiques 31 ou un autre cours de niveau 100 en calcul. Note: Ce cours n'est pas accessible aux étudiants ayant ou postulant des crédits pour MATH 227.

Géométrie euclidienne de base, congruence, parallélisme, aire et similarité. Développement axiomatique avec emphase sur la résolution de problèmes. Constructions et lieux géométriques, inégalités, maxima et minima, cercles, isométries, et autres sujets. Préalable(s): un cours de MATHQ de niveau 100 ou SCI 100.

Équations différentielles d'ordre un et deux avec des coefficients constants. Courbes, vecteurs tangents, longueur d'arc, intégration en deux et trois dimensions, coordonnées polaires cylindriques et sphériques, intégrales de lignes et de surfaces. Théorèmes de Green, de Stokes et théorème de la divergence. Préalable(s): Un parmi MATH/MATHQ 102, MATH/MATHQ 125 ou MATH 127, et MATH/MATHQ 214. Note: Ce cours n'est pas accessible aux étudiants ayant ou postulant des crédits pour MATH 209 ou MATH 317.

Équations du premier ordre, équations linéaires d'ordre élevé. Solution par séries de puissance. Méthodes de transformée de Laplace. Introduction aux fonctions spéciales. Introduction aux systèmes linéaires. Préalable(s): Un parmi MATH/MATHQ 102, MATH/MATHQ 125 ou MATH 127, et un parmi MATH 209, MATH/MATHQ 214 ou MATH 217. Note: Ce cours n'est pas accessible aux étudiants ayant ou postulant des crédits pour MATH 201, MATH 336, MA PH 251.

Les thèmes choisis par l'instructeur seront puisés dans les mathématiques anciennes (incluant toutes les cultures), classiques ou modernes et examinés d'un point de vue historique. Préalable(s): deux cours de MATHQ de niveau 100 ou SCI 100.

Circuit element definitions. Circuit laws: Ohm's, KVL, KCL. Resistive voltage and current dividers. Basic loop and nodal analysis. Circuit theorems: linearity, Thevenin. Dependent sources. Time domain behavior of inductance and capacitance, energy storage. Sinusoidal signals, complex numbers, phasor and impedance concepts. Diodes: ideal and simple and models. Treatment of RLC circuits in the time domain, frequency domain and s-plane. Prerequisites: MATH 101 and MATH 102.

Number systems, logic gates, Boolean algebra. Karnaugh maps. Combinational networks. State machines. Field programmable gate array (FPGA) implementation. Computer architecture. Assembly language. Addressing modes, subroutines, memory, input-output interfacing, and interrupts.

Introduction to linear systems and signal classification. Convolution. Fourier series expansion and Fourier transform (FT). Sampling and reconstruction. Discrete Fourier transform (DFT) and properties. Spectra analysis. Models of continuous-time systems and discrete-time systems for linear control system Z-transform and inverse Z-transform. Analysis of linear time invariant (LTI) systems. Design of linear time-invariant control systems. Corequisites: MCTR 202 and MATH 201.

Design morphology, analysis and design of components, electro-mechanical system design and risk management concepts, design project aimed at assistive devices or technologies addressing user needs. Corequisite: MCTR 265.

Computer-aided engineering, solid modelling, drafting and design. Introduction to multiphysics simulation. Design project aligned with MCTR 260.

Introduction to object-oriented programming for mechatronic applications. Introduction to data structures and classes with application to mechatronics. Introduction to algorithms. Concepts illustrated on a physical mechatronic system. Prerequisite: ENCMP 100.

Transistors, transistor amplifiers, and op-amp circuits; frequency response and filters; analog signal detection, conditioning, analysis, and conversion; transducers and electronic sensors for measuring common physical properties/phenomena. Understanding properties of signals in time and frequency domain; digitization of analog data; statistics, analysis, and uncertainty of measurement data. Prerequisites: MCTR 202 and MCTR 240.

Linear feedback control systems for command-following, stability, and dynamic response specifications. Frequency response and design techniques, including lead, lag compensators and PID control. An introduction to structural design limitations. Introduction to state space models. Examples emphasizing control of mechatronics systems, using computer-aided design. Prerequisite: MCTR 240. Credit can only be granted for one of MCTR 320, MEC E 420, ECE 360, CH E 446.

Force and torque generation in electric machines. AC and DC machines, permanent magnet synchronous (PMSM) and brushless DC motors (BLDC). Machine characteristics and dynamic models of electric actuators. Linear actuators; power electronics device characteristics; motor drives: H-bridges, inverters; speed control methods; power converters.

Kinematics and dynamics of rigid bodies moving in three dimensions. Spatial kinematics of rigid bodies, Euler angles, tensor of inertia and the Newton-Euler equations of motion for rigid bodies, multi-body dynamics, inverse dynamics for manipulators. Prerequisite: MEC E 250.

Systems engineering definition, relevance, and benefits. The nature of technological systems and the concept of a system life cycle, from need to retirement. Requirements setting, including standards. Modelling system performance, with emphasis on mechatronic systems. System safety, risk, and reliability analysis. Ethical and sustainability considerations in systems design. Design for manufacturability and control. Design de-risking and testing for requirements compliance. Configuration management. Systems thinking and Indigenous perspectives.

Coordinates systems, robot kinematics (forward and inverse), differential kinematics, robot dynamics, path and trajectory planning, position control, force control, impedance control, teleoperation systems.

A project-based course dealing with the design and implementation of a robotic system to accomplish a set of requirements. Integration of sensor technologies, sensor data processing, motion control based on feedback and real-time programming. Design procedures, ethics, safety and risk management, theory of engineering design, role of engineering analysis in design, application of computer-aided design software; component and material selection, codes, and standards; design optimization; system integration and verification through testing; teamwork, and a design project. Corequisite: MCTR 365.

Mechatronic and robotic system design using CAD tools. Concepts of function structure models, material selection, and introduction of load and stress analysis. Integration of sensors and actuators. Simulation of mechanisms, dynamics, kinematics, and heat transfer using commercial software. Emphasis is on numerical model design including testing and verification methods, and the critical interpretation of the computed results. Design project aligned with MCTR 360.

Fundamentals of machine learning methods. Supervised, unsupervised, and reinforcement learning concepts, and fundamentals of fuzzy logic. Review of probability and optimization. Linear regression. Linear classification and logistic regression. Components of modern machine learning approaches, including feature engineering, neural network models, training and evaluation methodology, and deep learning libraries. Object detection and object/human pose regression for robotic applications. Bias in machine learning algorithms. Corequisite: MCTR 399.

Advanced topics in object-oriented programming for mechatronic applications. Advanced data structures, and algorithm analysis and design. Concepts illustrated using a physical mechatronic system and practical mechatronic applications. Introduction to modern robotic and mechatronic operating systems. Prerequisite: MCTR 294.

Analytical and numerical methods with mechatronics applications. Complex numbers, partial differential equations, analytic functions, elementary functions, mappings, integrals, series, residues and poles, integral formulas. Statistical tests. Numerical integration and differentiation, solution methods of boundary value problems. Use of programming languages to implement numerical methods. Critical-thinking applied to problems related to mechatronics systems. Formulation, methodologies, and techniques for numerical solutions of engineering issues, particularly those arising within the field of mechatronics.

System states and state space models. Linearization of nonlinear state-space models. Solving linear time-invariant state-space equations. Controllability and observability, and their algebraic tests. Minimal state-space realizations. State feedback and eigenvalue/pole assignment. Step tracking control design. State estimation and observer design. Observer-based control. Introduction to linear quadratic optimal control. Prerequisite: MCTR 320.

Review of probability, random variables, and stochastic processes. Recursive state estimation: Bayes filter, linear Kalman filter and its extension to nonlinear systems. Practical applications of filtering techniques to mechatronics systems. Prerequisite: MCTR 420.

PART 1: Feasibility study and detailed design of a project which requires students to exercise creative ability, to make assumptions and decisions based on synthesis of technical knowledge, and devise new designs. Advanced design safety review.

PART 2: Feasibility study and detailed design of a project which requires students to exercise creative ability, to make assumptions and decisions based on synthesis of technical knowledge, and devise new designs. Advanced design safety review. Prerequisite: MCTR 460.

Introduction to mobile robots. Means of locomotion and kinematic and dynamic models. Linear and nonlinear motion control theory and filtering applied mobile robots. Map-based and reactive motion planning. Localization and mapping. Visual servoing. Prerequisite: MCTR 394. Corequisite: MCTR 421.

A directed reading and seminar course based on papers taken from the recent literature of medical genetics. The course consists of lectures on a specific topic in medical genetics and oral presentations of the current literature by students. Selected topics vary so that students may take the same course but examining a different topic for additional credit. Prerequisite: consent of the Department of Medical Genetics. Credit may only be obtained in one of MDGEN 401 or MDGEN 601.

The rapid expansion of our understanding of the human genome has created new, exciting possibilities to understanding the root causes of human disease and improve health. However, this also leads to real and potential problems - both ethical and practical. This senior level undergraduate course will consist of four modules each covering different aspects of the scientific theory underlying the practice of Medical Genetics. Topics will include core concepts in human genomics, developmental genetics, genetic variation, Mendelian and non- Mendelian traits, Mendelian disease as examples of key genomic concepts, methodologies that allow for screening of genetic disease and the theory supporting the practice of genetic counselling. This course will be based on didactic understanding of the topics and draw upon examples from the expertise of the instructors. Prerequisites CELL 201 or BIOL 201, 300 level course in CELL or GENET or consent of the Department. Note: Not to be taken by students with credit in CELL 403. In addition, not available to students currently enrolled in CELL 403.

An interactive course designed to provide undergraduate students insight into the role of a genetic counsellor through exploration of key topics. The class meets once a week for a 2-to-3-hour discussion. Each week students will be presented a typical genetic counselling case, which they will then write up and present to the entire class the following week. All students will then participate in the discussion of the case. Midterm(s) and/or finals consist of a 60 min presentation on a choice of various ethical issues currently impacting the field. The course is graded based on presentations, written assignments and participation. Open to undergraduate students with permission of the course instructor. Credit may only be obtained in one of MDGEN 407 or MDGEN 507.

This course provides an overview of the fundamental principles of medical genetics in a pediatric and adult genetics setting including the etiology, inheritance, management, and long-term sequelae of various conditions. Topics will include patterns of single gene and complex inheritance, molecular genetic testing, variant interpretation and personalized genomic medicine. Case examples will be used to reinforce the relevant principles. Readings will be derived from the required texts and from the primary literature. This course is offered as both face to face and synchronous online, but only through the consent of the department. Currently, the course is restricted to students in the Genetic Counselling training program and the Laboratory Medicine Pathology training program.

This course provides an overview of fundamental principles of medical genetics in a prenatal and newborn setting including the etiology, inheritance, management, and long-term sequelae of various conditions. Topics will include patterns of single gene and complex inheritance, population genetics, prenatal diagnosis and screening, cytogenetic analysis, biochemical diagnosis, and newborn screening. Case examples will be used to reinforce the relevant principles. Readings will be derived from the required texts and from the primary literature. This course is offered only through the consent of the department. Currently, the course is restricted to students in the Genetic Counselling training program.

An interactive course designed to provide graduate students insight into the role of a genetic counsellor through exploration of key topics. The class meets once a week for a 2-to-3-hour discussion. Each week students will be presented a typical genetic counselling case, which they will then write up and present to the entire class the following week. All students will then participate in the discussion of the case. Midterm and/or finals consist of a 60 min presentation on a choice of various ethical issues currently impacting the field. The course is graded based on presentations, written assignments and participation. Open to up to 4 students with permission of the course instructor. Credit may only be obtained in one of MDGEN 407 or MDGEN 507.