Mathematics & Engineering Courses

MTHE 217 
Algebraic Structures with Applications 
F 30.5 3.5 
The purpose of the course is to provide an introduction to abstract algebraic systems, and to illustrate the concepts with applications to communication engineering. Topics covered are: symbolic logic, switching and logic circuits; set theory and mappings; equivalence relations; the integers; introduction to Boolean algebras; group theory, groups, subgroups, cyclic groups, cosets and Lagrange's theorem, quotient groups, homomorphisms and isomorphisms; applications to errorcontrol codes, binary block codes for noisy communication channels, nearest neighbor decoding, code error detection/correction capabilities, group (linear) codes, coset decoding, generator and parity check matrices, syndrome decoding; basic properties of rings and fields. (30/0/0/12/0)
PREREQUISITE: APSC 174

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MTHE 224 
Applied Mathematics for Civil Engineers 
F 3.51 4.5 
The course will discuss the application of linear differential equations with constant coefficients, and systems of linear equations within the realm of civil engineering. Additionally, the course will explore relevant data analysis techniques including: graphical and statistical analysis and presentation of experimental data, random sampling, estimation using confidence intervals, linear regression, residuals and correlation. (54/0/0/0/0)
PREREQUISITES: APSC 142, APSC 172, APSC 174

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MTHE 225 
Ordinary Differential Equations 
F 30.5 3.5 
First order differential equations, linear differential equations with constant coefficients, and applications, Laplace transforms, systems of linear equations. (42/0/0/0/0)
PREREQUISITES: APSC 171, APSC 172, APSC 174

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MATH 226 
Ordinary Differential Equations 

First order differential equations, linear differential equations with constant coefficients, and applications, Laplace transforms, systems of linear equations. (36/0/0/0/0) ~ COURSE DELETED IN 2008/09 ~
PREREQUISITES: APSC 171, APSC 172, APSC 174

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MTHE 227 
Vector Analysis 
F 300 3 
Review of multiple integrals. Differentiation and integration of vectors; line, surface and volume integrals; gradient, divergence and curl; conservative fields and potential. Spherical and cylindrical coordinates, solid angle. Green's and Stokes' theorems, the divergence theorem. (36/0/0/0/0)
PREREQUISITES: APSC 171, APSC 172, APSC 174

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MTHE 228 
Complex Analysis 
W 30.5 3.5 
Complex arithmetic, complex plane. Differentiation, analytic functions. Elementary functions. Elementary functions. Contour integration, Cauchy's Theorem and Integral Formula. Taylor and Laurent series, residues with applications to evaluation of integrals. (42/0/0/0/0)
PREREQUISITES: APSC 171, APSC 172, APSC 174

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MTHE 232 
Differential Equations 
W 300 3 
Introduction to ordinary differential equations and their applications to the physical and social sciences. Topics may include: numerical solutions, power series and series solutions, Laplace transforms. (36/0/0/0/0)
PREREQUISITES: APSC 171, APSC 172, APSC 174
EXCLUSIONS: MATH 225, MATH 226, MATH 231, MATH 235, MATH 237

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MTHE 235 
Differential Equations for Electrical and Computer Engineers 
F 300 3 
First order differential equations, linear differential equations with constant coefficients. Laplace transforms. Systems of linear differential equations. Examples involving the use of differential equations in solving circuits will be presented. (27/0/0/9/0)
PREREQUISITES: APSC 171, APSC 172, APSC 174

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MTHE 237 
Differential Equations and Computer Methods 
F 3.50 3.5 
Topics include models for dynamical systems, classification of
differential equations, methods for solving differential equations,
variation of parameters, systems of differential equations and
connections with Linear Algebra, Laplace Transforms, numerical methods
for solutions, stability of dynamical systems, nonlinear equations and
Lyapunov's method. Computer methods (symbolic
and numerical) are introduced in the laboratory component of
the course.
(18/11/0/13/0)
PREREQUISITES: APSC 171, APSC 172, APSC 174
EXCLUSIONS: MATH 231, MTHE 232 (MATH 232)

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MATH 239 
Applied Mathematical Modeling 

A survey of important mathematical techniques used to model processes in a variety of fields. Topics include multivariable calculus and optimization, game theory, discretetime dynamical systems, and dynamic optimization. Examples will be drawn from several areas including biology, economics, and medicine. (18/9/5/4/0) ~ COURSE DELETED IN 2008/09 ~
PREREQUISITES: APSC 172 or MATH 120 or MATH 121 or MATH 126, APSC 174 or MATH 110 or MATH 111 recommended

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MTHE 272 
Application of Numerical Methods 
W 3.50 3.5 
An introductory course on the effective use of computers in science and
engineering. Topics include: solving linear and nonlinear equations,
interpolation, integration, and numerical solution of ordinary
differential equations. Extensive use is made of MATLAB,
a high level interactive numerical package
(20/0/0/11/11)
PREREQUISITES: APSC 174 or equivalent (Note: some programming experience is important for the course) Must be registered in BSCE

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MTHE 280 
Advanced Calculus 
F 30.5 3.5 
Limits, 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. (42/0/0/0/0)
PREREQUISITES: APSC 172, APSC 174
EXCLUSIONS: MATH 221, MTHE 227 (MATH 227)

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MTHE 281 
Introduction to Real Analysis 
W 30.5 3.5 
Taylor'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. (42/0/0/0/0)
PREREQUISITES: APSC 172

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MTHE 312 
Linear Algebra 
W 30.5 3.5 
Vector spaces, linear transformations and matrices. Linear equations. Determinants. Eigenvalues and eigenvectors. Normal forms. Linear functions and dual spaces. Bilinear functions, quadratic and hermitian forms. Inner product spaces, the projection theorem and applications to approximation and optimization problems. (42/0/0/0/0)
PREREQUISITES: MTHE 217 (MATH 217) or permission of the instructor

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MTHE 326 
Functions of a Complex Variable 
F 300 3 
Complex numbers, analytic functions, harmonic functions. Cauchy's theorem. Taylor and Laurent series. Calculus of residues. Rouche's theorem. (36/0/0/0/0)
PREREQUISITES: MTHE 280 (MATH 280), MTHE 281 (MATH 281)

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MTHE 332 
Introduction to Control 
W 30.5 3.5 
Modeling control systems, linearization around an equilibrium point.
Block diagrams, impulse response, transfer function, frequency response.
Controllability and observability, LTI realizations. Feedback and
stability, Lyapunov stability criterion, pole placement, Routh
criterion. Input/output stability, design of PID controllers, Bode
plots,
Nyquist plots, Nyquist stability criterion, robust controllers.
(0/0/0/31/11)
PREREQUISITE: MTHE 326 (MATH 326)

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MTHE 333 
ControlRobotics Lab I 
W 010 1 
This laboratory introduces the use of motion control devices such as optical encoders, pulse width amplifiers and armature controlled DC servo motors. The experiments complement the analytical and theoretical work on control taken in other third year courses. Students design and implement proportional, proportionalderivative, and proportionalintegralderivative controllers. (0/0/0/4/8)

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MTHE 334 
Mathematical Methods for Engineering and Physics 
F 30.5 3.5 
Motivation for signal spaces. Banach and Hilbert spaces of continuous
and discretetime signals. Spaces of continuous and not necessarily
continuous signals. The four Fourier transforms: continuousdiscrete
Fourier transform; continuouscontinuous Fourier transform;
discretecontinuous Fourier transform; discretediscrete Fourier
transform. Transform inversion using Fourier series and Fourier
integrals. (28/0/0/14/0)
PREREQUISITES: MTHE 237 (MATH 237), MTHE 281 (MATH 281)

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MTHE 335 
Mathematics of Engineering Systems 
W 30.5 3.5 
Linear input/output systems and their stability. Frequencydomain and timedomain analysis. Continuous and discretetime modeling. Fourier, Laplace, and Ztransforms. Sampling and the discretetime Fourier transform. Applications to modulation of communications signals, filter design, and digital sampling. (0/11/0/20/11)
PREREQUISITES: MTHE 334 (MATH 334), MTHE 326 (MATH 326) or MTHE 228 (MATH 228)

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MTHE 337 
Introduction to Operations Research Models 
W 300 3 
Formulation and solution of some industrial and business problems using mathematical models. Review of probability. Markov chains and applications to inventory problems. Introduction to queuing theory and applications. Machine maintenance planning; optimal number of servers. Simulation and Monte Carlo methods. Reliability and replacement problems. Inventory and production planning problems. One, or possibly two, topics chosen from constrained optimization, network flow analysis and dynamic programming. (18/0/0/9/9)
PREREQUISITES: STAT 256 or MTHE 267 (STAT 267) or equivalent or permission of the instructor

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MTHE 338 
Topics in Applied Mathematics 
F 30.5 3.5 
Methods and theory for ordinary and partial differential equations. Review of eigenvectors and eigenmodes in solutions to systems of ordinary differential equations. The principle of linear superposition and eigenfunction expansion, orthogonality, and inner product on a vector space of functions. The method of separation of variables in rectangular and cylindrical coordinate systems; sinusoidal and Bessel orthogonal functions. The wave, diffusion, and Laplace's (potential) equation. SturmLiouville theory: eigenvalue problems and orthogonal functions. Fourier transform and, time permitting, Laplace transform techniques. (28/0/0/14/0)
PREREQUISITES: MTHE 227 (MATH 227) or MTHE 280 (MATH 280), MATH 226 or MTHE 237 (MATH 237) or MTHE 232 (MATH 232), or permission of the instructor

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MTHE 339 
Evolutionary Game Theory 
W 300 3 
This course highlights the usefulness of game theoretical approaches in solving problems in the natural sciences and economics. Basic ideas of game theory, including Nash equilibrium and mixed strategies; stability using approaches developed for the study of dynamical systems, including evolutionary stability and replicator dynamics; the emergence of cooperative behaviour; limitations of applying the theory to human behaviour. (18/9/9/0/0)
PREREQUISITES: APSC 172 or MATH 120 (or MATH 121); APSC 174 or MATH 110 (or MATH 111) recommended

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MTHE 406 
Introduction to Coding Theory 
W 300 3 
Construction 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. (14/0/0/12/10)
PREREQUISITES: MATH 212 or MTHE 217 (MATH 217)

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MTHE 418 
Number Theory and Cryptography 
F 300 3 
Time estimates for arithmetic and elementary number theory algorithms (division algorithm, Euclidean algorithm, congruences), modular arithmetic, finite fields, quadratic residues. Design of simple cryptographic systems, public key and RSA systems. Primality and factoring: pseudoprimes, Pollard's rhomethod, index calculus. Elliptic curve cryptography. (18/0/0/9/9) Offered in Winter Term in evennumbered years
PREREQUISITES: MATH 210 or MATH 212 or MTHE 217 (MATH 217) or MATH 211 with permission of the instructor

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MTHE 430 
Modern Control Theory 
F 3.5.5 4 
This course covers core topics in modern control theory: linearization
of a nonlinear system around a given trajectory, existence and
uniqueness theory for nonlinear and linear ordinary differential
equations, the transition matrix of a linear timevarying system,
controllability and observability for linear systems, weighting patterns
and minimal realizations, feedback stabilization, linear state
observers, free endpoint and fixed endpoint optimal control problems,
the Riccati equation, the linear quadratic regulator. Laboratory
experiments illustrate design considerations in implementing the lecture
material.
(28/0/0/20/0)
PREREQUISITES: MTHE 237 (MATH 237), MTHE 312 (MATH 312), MTHE 326 (MATH 326), MTHE 332 (MATH 332), or permission of the instructor

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MTHE 437 
Advanced Topics in Applied Mathematics 
W 300 3 
Subject matter to vary from year to year. (9/0/0/9/18) ~ COURSE NOT OFFERED IN 20112012 ~
PREREQUISITE: Permission of the instructor

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MTHE 439 
Lagrangian Mechanics, Dynamics, and Control 
W 30.5 3.5 
Geometric mechanical system modelling, including configuration space,
tangent bundle, kinetic energy, inertia, and force.
EulerLagrange equations using affine connections. The last part of the
course develops one of the following three applications, depending on
instructor and student interest: (1) mechanical systems with
nonholonomic constraints; (2) control theory for mechanical systems; (3)
equilibria and stability.
(20/0/0/11/11)
PREREQUISITES: MTHE 280 (MATH 280), MTHE 281 (MATH 281), MTHE 237 (MATH 237) or MATH 231, or permission of the instructor

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MTHE 472 
Control of Stochastic Systems 
W 300 3 
Optimal control of stochastic systems with applications in various fields of engineering and applied mathematics. Topics include statespace models, development of control laws by dynamic programming, controlled Markov chain models, control with complete and partial information, linear and nonlinear filtering, estimation, Martingales, stochastic stability, convergence of policies, dual effect of control, adaptive control, team decisions, numerical methods, value and policy iteration algorithms. (0/0/0/18/18)
PREREQUISITES: MTHE 351 (STAT 351), MTHE 332 (MATH 332), or permission of the instructor

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MTHE 474 
Information Theory 
F 300 3 
An introduction to the fundamental principles of the theory of communication. Topics include: information measures, entropy, mutual information, divergence; modeling of information sources, discrete memoryless sources, Markov sources, entropy rate, source redundancy; fundamentals of lossless data compression, block encoding, variablelength encoding, Kraft inequality, design of ShannonFano and Huffman codes; fundamentals of channel coding, channel capacity, noisy channel coding theorem, channels with memory, lossless information transmission theorem; continuousalphabet sources and channels, differential entropy, capacity of discretetime and bandlimited continuoustime Gaussian channels; ratedistortion theory, lossy data compression, ratedistortion theorem, lossy information transmission theorem. (9/0/0/17/10)
PREREQUISITES: STAT 251 or MTHE 351 (STAT 351) or ELEC 326

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MTHE 477 
Data Compression and Source Coding 
W 300 3 
Fundamentals of the theoretical and practical (algorithmic) aspects of lossless
and lossy data compression. Topics include: adaptive Huffman coding, arithmetic
coding, the fundamental performance limits of universal lossless coding,
LempelZiv and related dictionary based methods, the BurrowsWheeler transform,
elements of Kolmogorov complexity theory, ratedistortion theory, scalar and
vector quantization, applications to speech and image coding. (0/0/0/21/15)
PREREQUISITE: MTHE 474 (MATH 474)

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MTHE 478 
Topics in Communication Theory 
F/W 300 3 
Subject 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 errorcontrol coding; design and performance analysis of communication networks; and other related topics. (0/0/0/18/18) ~ COURSE NOT OFFERED IN 20112012 ~
PREREQUISITE: Permission of the instructor

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MTHE 484 
Data Networks 
W 300 3 
This 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. (10/0/0/26/0) ~ COURSE NOT OFFERED IN 20112012 ~
PREREQUISITES: MTHE 455 (STAT 455) or permission of the instructor

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MTHE 493 
Engineering Mathematics Project 
F 003 W 031.5 7.5 
This is the fourth year thesis course  each student does supervised research on an engineering topic and reports on this periodically throughout the year, and at the end of the year. Research topics are selected from a list distributed early in the fall term, or by consultation with faculty members. Projects typically involve the design and implementation of some piece of equipment, or software; emphasis is placed on projects where engineering and mathematics fit together nicely. (For example, design and construction of a hovercraft, and the controller, has appeared as a team project in the last few years.) A written proposal for your project is due at the end of the fourth week of the first term, and a draft of the Engineering Design Chapter of the Thesis on January 31st. Communication skills are stressed in the proposal, in the interim oral report in the first term, in the Engineering Design Chapter and in the final oral and written reports on the results of the investigation. Typically thesis projects are done by teams of up to four students. Mathematics and Engineering faculty members supervise the projects. (0/0/23/40/27)

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MTHE 494 
Mathematics and Engineering Seminar 
F 300 3 
The first objective of this seminar is to give the students exposure to and insight into various aspects of the profession and practice of engineering. There will be speakers on professional engineers' organizations and the role and responsibility of the professional engineer, health and safety considerations in the engineering workplace, as well as technical topics relating to various careers in engineering (by Mathematics and Engineering alumni) and ongoing research activities (by Mathematics and Engineering faculty and faculty from other departments at Queen's). A second important objective is to develop the students' communications skills (both written and oral). Instruction on effective technical writing and reporting is provided over several lectures at the beginning of the term. Each student is required to write essays on four talks (which will be professionally marked) and to give an oral presentation on an engineering topic. (0/0/26/10/0)

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