**Systems and Robotics**

The interface between engineering systems and robotics is an area that demands sophisticated mathematical abilities. This area is characterized by the use of sophisticated control methods with electronic/digital implementations, active structural materials, and other topics from classical mechanical design. The Systems and Robotics option blends mathematics, electrical engineering, and mechanics into one cohesive program.

In addition to the common core of mathematics courses, students in Systems and Robotics take courses in electronics, microprocessor systems, and electric machines from the Electrical and Computer Engineering Department, dynamics and mechanics from Physics, and advanced systems engineering and control courses offered by the Mathematics and Statistics Department. Graduates of the program are exceptionally well-prepared for careers in systems engineering, mechatronics, and robotics, as well as careers in any field requiring strong analytical skills.

**Second Year Courses**

ELEC 221: Electric CircuitsThis course introduces the circuit analysis techniques which are used in subsequent courses in electronics, power, and signals and systems. Circuits containing resistance, capacitance, inductance, and independent and dependent voltage and current sources will be studied. Emphasis is placed on DC, AC, and transient analysis techniques.

ELEC 271: Digital SystemsBoolean algebra applied to digital systems; logic gates; combinational logic design; electronic circuits for logic gates; arithmetic circuits; latches and flipflops, registers and counters; synchronous sequential logic and state machine design; implementation in programmable logic chips.

ENPH 225: MechanicsExtension of classical mechanics and engineering applications. Plane dynamics, relative motion and forces in moving and accelerated reference frames. Introduction to general three-dimensional motion of a rigid body, inertia tensor and steady-state precession. The laws of conservation of mass, momentum and energy.

ELEC 252: Electronics IThis course is an introduction to semiconductor electronics for students in the Electrical Engineering program and related programs. Topics studied include: operational amplifiers; dc and small signal models for diodes, basic principles of bipolar transistors and field effect transistors, dc analysis of electronic circuits and practical applications of the devices to the design of power supplies, amplifiers and digital logic circuits.

ELEC 274: Computer Architecture Number and data representation. Logical structure of computers. Instruction set architecture. Instruction execution sequencing. Assembly-language programming. Input/output interfaces and programming. Processor datapath and control unit design. Semiconductor memory technology and memory hierarchy design.

**Third Year Courses**

ELEC 278: Fundamentals of Information StructuresFundamentals of Data Structures and Algorithms: arrays, linked lists, stacks, queues, deques, asymptotic notation, hash and scatter tables, recursion, trees and search trees, heaps and priority queues, sorting, and graphs. Advanced programming in the C language. Introduction to object oriented programming concepts in the context of data structures.

ENPH 239: Electricity and MagnetismThe experimental basis and mathematical description of electrostatics, magnetostatics and electromagnetic induction, together with a discussion of the properties of dielectrics and ferromagnetics, are presented. Both the integral and vector forms of Maxwell’s equations are deduced.

MTHE 353: Probability IIIntermediate probability theory as a basis for further study in mathematical statistics and stochastic processes; probability measures, expectations; modes of convergence of sequences of random variables; conditional expectations; independent systems of random variables; Gaussian systems; characteristic functions; Law of large numbers, Central limit theory; some notions of dependence.

ELEC 371: Microprocessor Interfacing and Embedded SystemsMicroprocessor bus organization and memory interfaces; parallel input/output interface design; assembly-language and high-level-language programming; interrupts and exceptions; timers; embedded systems organization and design considerations; integration in microcontrollers and programmable logic chips; interfacing with sensors and actuators; embedded system case studies.

MTHE 337: Intro To Operations ResearchSome probability distributions, simulation, Markov chains, queuing theory, dynamic programming, inventory theory.

**Fourth Year Courses**

MTHE 430: Modern Control TheoryThis course covers core topics in modern control theory: Linearization, existence and uniqueness of trajectories for nonlinear and linear systems, the transition matrix, controllability, observabiity, minimal realizations, feedback stabilization, linear state observers, optimal control theory, the linear quadratic regulator, dynamic programming.

MTHE 472: Control of Stochastic SystemsThis course concerns the optimization, control, and stabilization of dynamical systems under probabilistic uncertainty with applications in engineering systems and applied mathematics. Topics include: controlled and control-free Markov chains and stochastic stability; martingale methods for stability and stochastic learning; dynamic programming and optimal control for finite horizons, infinite horizons, and average cost problems; partially observed models, non-linear filtering and Kalman Filtering; linear programming and numerical methods; reinforcement learning and stochastic approximation methods; decentralized stochastic control, and continuous-time stochastic control.

MTHE 474: Information TheoryTopics include: information measures, entropy, mutual information, modeling of information sources, lossless data compression, block encoding, variable-length encoding, Kraft inequality, fundamentals of channel coding, channel capacity, rate-distortion theory, lossy data compression, rate-distortion theorem.

**Technical Electives**

In the fourth year of the program, students choose four technical electives to compliment the core courses and explore their individual interests. At least one must be chosen from List I and the remaining from List I or List II so that they satisfy certain engineering design and engineering science criteria. Course offerings change year to year.

See the current Academic Calendar for a complete list of offered technical electives.

### List I

MTHE 406: Introduction To Coding TheoryConstruction and properties of finite fields. Polynomials, vector spaces, block codes over finite fields. Hamming distance and other code parameters. Bounds relating code parameters. Cyclic codes and their structure as ideals. Weight distribution. Special codes and their relation to designs and projective planes. Decoding algorithms.

MTHE 434: Optimization Theory with Applications to Machine LearningTheory of convex sets and functions; separation theorems; primal-dual properties; geometric treatment of optimization problems; algorithmic procedures for solving constrained optimization programs; applications of optimization theory to machine learning.

MTHE 439: Lagrangian Mechanics, Dynamics, and ControlGeometric modelling, including configuration space, tangent bundle, kinetic energy, inertia, and force. Euler-Lagrange equations using affine connections. The last part of the course develops one of the following three applications: mechanical systems with nonholonomic constraints; control theory for mechanical systems; equilibria and stability.

MTHE 477: Data Compression and Source CodingTopics include: arithmetic coding, universal lossless coding, Lempel-Ziv and related dictionary based methods, rate-distortion theory, scalar and vector quantization, predictive and transform coding, applications to speech and image coding.

MTHE 478: Topics In Communication TheorySubject matter will vary from year to year. Possible subjects include: constrained coding and applications to magnetic and optical recording; data compression; theory and practice of error-control coding; design and performance analysis of communication networks; and other related topics.

MTHE 484: Data NetworksThis course covers performance models for data networking, delay models and loss models; analysis of multiple access systems, routing, and flow control; multiplexing; priority systems; satellite multiple access, wireless networking, wireless sensor networks. Knowledge of networking protocols is not required.

MTHE 454: Statistical Spectrum EstimationMany systems evolve with an inherent amount of randomness in time and/or space. The focus of this course is on developing and analyzing methods for analyzing time series. Because most of the common time–domain methods are unreliable, the emphasis is on frequency–domain methods, i.e. methods that work and expose the bias that plagues most time–domain techniques. Slepian sequences (discrete prolate spheroidal sequences) and multi–taper methods of spectrum estimation are covered in detail.

MTHE 455: Stochastic Processes and ApplicationsMarkov chains, birth and death processes, random walk problems, elementary renewal theory, Markov processes, Brownian motion and Poisson processes, queuing theory, branching processes.

MTHE 433: Continuum Mechanics with ApplicationsContinuum mechanics lays the foundations for the study of the mechanical behavior of solids and fluids. After a review of vector and tensor analysis, the kinematics of continua are introduced. Emphasis is given to the concepts of stress, strain and deformation. The fundamental laws of conservation of mass, balances of (linear and angular) momentum and energy are presented together with the constitutive models. Applications of these models are given in the theory of linearized elasticity and fluid dynamics.

MTHE 437: Topics In Applied MathematicsTopic: An Introduction to Stochastic Differential Equations (with Applications to Mathematical Finance and Engineering) The aim of this course is to provide a rigorous introduction to the theory of stochastic calculus and stochastic differential equations, and to survey some of its most important applications, especially in Mathematical Finance. The Itô stochastic integral and its associated “Itô Calculus” will be derived in the general framework of continuous semimartingales, leading to a detailed treatment of stochastic differential equations (SDEs) and their properties. The theory thus developed will be applied to selected problems in Mathematical Finance (option pricing and hedging, trading strategies and arbitrage) and Engineering (boundary-value problems, filtering, optimal control). Numerical aspects of SDEs will also be discussed.

MTHE 418: Number Theory & CryptographyTime estimates for arithmetic and elementary number theory algorithms (division algorithm, Euclidean algorithm, congruences), modular arithmetic, finite fields, quadratic residues. Simple cryptographic systems; public key, RSA. Primality and factoring: pseudoprimes, Pollard’s rho-method, index calculus. Elliptic curve cryptography.

MTHE 457: Statistical LearningIntroduction to the theory and application of statistical algorithms. Topics include classification, smoothing, model selection, optimization, sampling, supervised and unsupervised learning.

### List II

ELEC 353: Electronics IITransistor-level modeling and design of analog and digital electronic circuits. Differential amplifiers, Gilbert Cell multipliers, multi-stage amplifiers, amplifier frequency response, negative feedback amplifiers, LC-tank and crystal oscillators, two-port networks. Advanced concepts in logic design. Students learn the basics of computer aided design (CAD) of integrated circuits including schematic simulation, layout, design rules, layout versus schematic verification and extracted circuit simulation. Laboratory work is design-oriented and students are introduced to advanced test and measurement techniques using vector network analyzers.

ELEC 421: Digital Signal Processing: Filters and System DesignSampling theorem, filter realization structures, quantization errors and finite word length effects, digital signal processor programming, finite and infinite impulse response filter design techniques, discrete and fast Fourier transform.

ELEC 431: Power ElectronicsThis course introduces the basic concepts of power electronics, which include power semiconductor devices and switching power converters. Emphasis is placed on the analysis and design of various power electronics circuits. Their industrial application, such as in telecommunications and computing, will also be discussed. More specifically, the course will cover the characteristics of switching devices, especially that of MOSFET. The course will also cover the operation of various switching converters such as phase controlled ACto- DC converters, AC voltage controllers, DC-to-DC switching converters, DC-to-AC inverters and switching power supplies. The requirements and configurations of power systems for telecommunications will be introduced. The techniques to analyze and design these power systems using available components will also be discussed. Computer simulation will be used to analyze the detailed operation of switching converters.

ELEC 448: Introduction to Robotics - Mechanics and ControlRobotics is an interdisciplinary subject concerning areas of mechanics, electronics, information theory, control systems and automation. This course provides an introduction to robotics and covers fundamental aspects of modeling and control of robot manipulators. Topics include history and application of robotics in industry, rigid body kinematics, manipulator forward, inverse and differential kinematics, workspace, singularity, redundancy, manipulator dynamics, trajectory generation, actuators, sensors, and manipulator position and contact force control strategies. Applications studied using MATLAB/Simulink software simulation and laboratory experiments.

MECH 456: Introduction To RoboticsThis course will cover the following topics in the field of robotics: historical development; robot components (sensors, actuators, and end effectors, and their selection criteria); basic categories of robots (serial and parallel manipulators, mobile robots); mobility/constraint analysis; workspace analysis; rigid body kinematics (homogeneous transformation, angle and axis of rotation, Euler angles); manipulator kinematics and motion trajectories (displacement and velocity analyses, differential relations, Jacobian matrix); non redundant and redundant sensing/actuation of manipulators; manipulator statics (force and stiffness); singularities; and manipulator dynamics.

ELEC 454: Analog ElectronicsTopics include; an introduction to noise and distortion in electronic circuits, analysis and design of biasing circuits, references, ADCs and DACs, power amps, mixers, modulators and PLLs along with a short introduction to analog filter design.

ELEC 457: Integrated Circuits and System ApplicationIn the first part of this course modern microelectronic circuits are covered and in the second part these circuits are used in new and emerging applications. Topics include: active and passive filtering circuits, phase locked loops, frequency synthesizers, RF modulators, clock and data recovery circuits, RF energy harvesting, ultra low-power circuits, biotelemetry systems, biological sensors, neurostimulator circuits, introduction to radiometry and radar imaging.

ELEC 461: Digital CommunicationsRepresentation of signals and noise, Gaussian processes, correlation functions and power spectra. Linear systems and random processes. Performance analysis and design of coherent and noncoherent communication systems, phase-shift-keying, frequency-shift,-keying, and M-ary communication systems. Optimum receivers and signal space concepts. Information and its measure, source encoding, channel capacity and error correcting coding.

ELEC 464: Wireless CommunicationsFundamental principles and practice of current wireless communications systems and technologies. Historical context, the wireless channel including path loss, shadowing, fading, and system modes in use. Capacity limitations on transmission rate, transmission of data by signaling over wireless channels via digital modulation, optimum receivers, countermeasures to fading and interference via diversity and equalization, multiple user systems including multiple access FDMA, TDMA, CDMA, FDMA/TDMA, uplink and downlink; capacity and power control, design of cellular networks. Selected standards and emerging trends are also surveyed.

ELEC 483: Microwave and RF Circuits and SystemsThis course introduces the analysis and design of microwave components and systems. Topics include: modelling of high frequency circuits; transmission lines; scattering parameters; impedance matching; passive microwave components; amplifiers, mixers and oscillators; noise in receivers; elemental antennas and simple and phased arrays; communication links – microwave land, cellular and satellite systems; performance and link budget analysis.

ELEC 486: Fiber Optic CommunicationThis course introduces fundamental principles and applications of fiber optic communication systems. Topics include Fabry-Perot and distributed feedback semiconductor lasers, planar dielectric waveguides, propagation characteristics of single-mode optical fibers, p-i-n and avalanche photodiodes, and digital receiver performance. Device technology and system design applications are considered.

MECH 452: Mechatronics EngineeringThis is a course in mechatronic systems design. Mechatronics Engineering, an integration of computer, electrical and mechanical engineering, is studied in a series of workshops that focus on electronics, microcontrollers, programmable logic controllers and mobile robots. The lectures provide the theoretical background to the workshops, and include discussion of related industrial and commercial applications. The knowledge and experience gained in the lectures and workshops is applied to a team design project. Students will use their knowledge of electric circuits, microcontrollers and control systems typically acquired in MECH 210, MECH 217 and MECH 350.

MINE 472: Mining Systems, Automation, and RoboticsIn order to address issues related to safety, productivity, and remote operations, the world’s mineral resources industry has been gradually shifting towards the increased use of automated systems and roboticallyenhanced machines. It is important, therefore, that graduate engineers understand how these new technologies work so as to improve and make best use of them. This online course introduces senior students to the fundamental tools and techniques of automation and robotics as applied to modern mining practice. Enrolment is open to students from a range of engineering disciplines. This course provides an introduction to the basics of systems control, examples of how methods of automatic control can be applied to mining equipment and associated industrial vehicles, as well as to the fundamentals of sensing and navigation as applied to the design of robotic mobile equipment.