Mathematics (Faculty of Engineering)
Mathematics and statistics are omnipresent in today's world of information and technology. Their theories, models, and methods are integral to the way we analyze, understand, and build the world around us. They play a key role in nearly every effort to push the boundaries of science, engineering, medicine, and social sciences and contribute, in a major way, to solving some of the most pressing human, environmental, and economic problems of our time.
The Minor in Mathematics for Engineering students may be taken in addition to the courses required for the B.Eng. degree. Minor programs normally consist of 1824 credits, allowing 912 credits of overlap with the degree program. The real credit cost to the student is typically 9 to 15 credits, representing one term beyond the B.Eng. degree program.
DETAILED PROGRAM OUTLINE:
Program Requirement:
The B.Eng.; Minor in Mathematics provides students with an even stronger foundation in mathematics to further develop their knowledge of this subject. Students enrolled in the B.Eng.; Minor in Mathematics complete a series of mathematics courses offered by the Department of Mathematics and Statistics, or other units offering mathematics courses.
Minor Adviser: Faculty Student Adviser in the McGIll Engineering Student Centre (Student Affairs Office) (Frank Dawson Adams Building, Room 22) AND an adviser designated by the Department of Mathematics and Statistics. (Please consult the Department of Mathematics and Statistics for the name of this adviser.) Selection of courses must be undertaken in conjunction with the Minor Advisers, normally beginning in the U2 year.
Note: The B.Eng.; Minor in Mathematics is open to all students in the Faculty of Engineering (including students registered in the B.Sc.(Arch.)). A maximum of 9 credits of overlap (doublecounting) with the degree program is allowed.
Engineering students must obtain a grade of C or better in courses approved for this Minor.
Required Course (3 credits)

MATH 242 Analysis 1 3 Credits
 Fall
 Winter
 Summer
Offered in the:Mathematics & Statistics (Sci): A rigorous presentation of sequences and of real numbers and basic properties of continuous and differentiable functions on the real line.
Offered by: Mathematics and Statistics
 Fall
 Prerequisite: MATH 141
 Restriction(s): Not open to students who are taking or who have taken MATH 254.
 Symbols:
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 Fall 2020
 Instructors
 Axel W Hundemer
Complementary Courses (15 credits)
3 credits selected from:

MATH 223 Linear Algebra 3 Credits
 Fall
 Winter
 Summer
Offered in the:Mathematics & Statistics (Sci): Review of matrix algebra, determinants and systems of linear equations. Vector spaces, linear operators and their matrix representations, orthogonality. Eigenvalues and eigenvectors, diagonalization of Hermitian matrices. Applications.
Offered by: Mathematics and Statistics
 Fall and Winter
 Prerequisite: MATH 133 or equivalent
 Restriction: Not open to students in Mathematics programs nor to students who have taken or are taking MATH 236, MATH 247 or MATH 251. It is open to students in Faculty Programs
 Symbols:
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 Fall 2020
 Winter 2021
 Instructors
 Michael Y Pichot

MATH 247 Honours Applied Linear Algebra 3 Credits
 Fall
 Winter
 Summer
Offered in the:Mathematics & Statistics (Sci): Matrix algebra, determinants, systems of linear equations. Abstract vector spaces, inner product spaces, Fourier series. Linear transformations and their matrix representations. Eigenvalues and eigenvectors, diagonalizable and defective matrices, positive definite and semidefinite matrices. Quadratic and Hermitian forms, generalized eigenvalue problems, simultaneous reduction of quadratic forms. Applications.
Offered by: Mathematics and Statistics
 Winter
 Prerequisite: MATH 133 or equivalent.
 Restriction: Intended for Honours Physics and Engineering students
 Restriction: Not open to students who have taken or are taking MATH 236, MATH 223 or MATH 251
 Symbols:
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 Winter 2021
 Instructors
 Tim Hoheisel
612 credits selected from:

ECSE 205 Prob and Stats for Engineers 3 Credits*
 Fall
 Winter
 Summer
Offered in the:Electrical Engineering: Probability: basic probability model, conditional probability, Bayes rule, random variables and vectors, distribution and density functions, common distributions in engineering, expectation, moments, independence, laws of large numbers, central limit theorem. Statistics: descriptive measures of engineering data, sampling distributions, estimation of mean and variance, confidence intervals, hypothesis testing, linear regression.
Offered by: Electrical & Computer Engr
 Not open to students who have taken ECSE 305.
 (324)
 Symbols:
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 Fall 2020
 Winter 2021
 Instructors
 Harry Leib
 Harry Leib

MATH 204 Principles of Statistics 2 3 Credits
 Fall
 Winter
 Summer
Offered in the:Mathematics & Statistics (Sci): The concept of degrees of freedom and the analysis of variability. Planning of experiments. Experimental designs. Polynomial and multiple regressions. Statistical computer packages (no previous computing experience is needed). General statistical procedures requiring few assumptions about the probability model.
Offered by: Mathematics and Statistics
 Winter
 Prerequisite: MATH 203 or equivalent. No calculus prerequisites
 Restriction: This course is intended for students in all disciplines. For extensive course restrictions covering statistics courses see Section 3.6.1 of the Arts and of the Science sections of the calendar regarding course overlaps.
 You may not be able to receive credit for this course and other statistic courses. Be sure to check the Course Overlap section under Faculty Degree Requirements in the Arts or Science section of the Calendar.
 Symbols:
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 Winter 2021
 Instructors
 Christian Genest

MATH 240 Discrete Structures 3 Credits
 Fall
 Winter
 Summer
Offered in the:Mathematics & Statistics (Sci): Introduction to discrete mathematics and applications. Logical reasoning and methods of proof. Elementary number theory and cryptography: prime numbers, modular equations, RSA encryption. Combinatorics: basic enumeration, combinatorial methods, recurrence equations. Graph theory: trees, cycles, planar graphs.
Offered by: Mathematics and Statistics
 Fall and Winter
 Corequisite: MATH 133.
 Restriction: For students in any Computer Science, Computer Engineering, or Software Engineering programs. Others only with the instructor's permission. Not open to students who have taken or are taking MATH 235.
 Symbols:
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 Fall 2020
 Winter 2021
 Instructors
 Dana Louis AddarioBerry, Elliot Paquette
 Adrian Roshan Vetta, Jérôme Fortier

MATH 243 Analysis 2 3 Credits
 Fall
 Winter
 Summer
Offered in the:Mathematics & Statistics (Sci): Definition and properties of Riemann integral, Fundamental Theorem of Calculus, Taylor's theorem. Infinite series: alternating, telescoping series, rearrangements, conditional and absolute convergence, convergence tests. Power series and Taylor series. Elementary functions. Introduction to metric spaces.
Offered by: Mathematics and Statistics
 Symbols:
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 Winter 2021
 Instructors
 Axel W Hundemer

MATH 264 Adv Calculus for Engineers 3 Credits
 Fall
 Winter
 Summer
Offered in the:Mathematics & Statistics (Sci): Review of multiple integrals. Differential and integral calculus of vector fields including the theorems of Gauss, Green, and Stokes. Introduction to partial differential equations, separation of variables, SturmLiouville problems, and Fourier series.
Offered by: Mathematics and Statistics
 (315)
 Prerequisite: MATH 262 or MATH 151 or MATH 152 or equivalent.
 Corequisite: MATH 263
 Restrictions: Open only to students in the Faculty of Engineering. Not open to students who are taking or have taken MATH 319 or MATH 475.
 Symbols:
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 Fall 2020
 Winter 2021
 Instructors
 Jerome Vetois
 Rustum Choksi

MATH 271 Linear Algebra and PDE's 3 Credits**
 Fall
 Winter
 Summer
Offered in the:Mathematics & Statistics (Sci): Applied Linear Algebra. Linear Systems of Ordinary Differential Equations. Power Series Solutions. Partial Differential Equations. SturmLiouville Theory and Applications. Fourier Transforms.
Offered by: Mathematics and Statistics
 Fall and Winter
 (315)
 Prerequisites: MATH 263, MATH 264.
 Not open to students who have taken MATH 266.
 Symbols:
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 Terms
 Fall 2020
 Instructors
 Charles Roth

MATH 316 Complex Variables 3 Credits
 Fall
 Winter
 Summer
Offered in the:Mathematics & Statistics (Sci): Algebra of complex numbers, CauchyRiemann equations, complex integral, Cauchy's theorems. Taylor and Laurent series, residue theory and applications.
Offered by: Mathematics and Statistics
 Fall
 Prerequisites: MATH 314 or equivalent and MATH 243.
 Restriction: Not open to students who have taken or are taking MATH 249, MATH 366, MATH 381 or MATH 466.
 Symbols:
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 Fall 2020
 Instructors
 Brent Pym

MATH 319 Intro to Partial Diff Equas 3 Credits**
 Fall
 Winter
 Summer
Offered in the:Mathematics & Statistics (Sci): First order equations, geometric theory; second order equations, classification; Laplace, wave and heat equations, SturmLiouville theory, Fourier series, boundary and initial value problems.
Offered by: Mathematics and Statistics
 Symbols:
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 Terms
 Winter 2021
 Instructors
 Peter Bartello

MATH 323 Probability 3 Credits*
 Fall
 Winter
 Summer
Offered in the:Mathematics & Statistics (Sci): Sample space, events, conditional probability, independence of events, Bayes' Theorem. Basic combinatorial probability, random variables, discrete and continuous univariate and multivariate distributions. Independence of random variables. Inequalities, weak law of large numbers, central limit theorem.
Offered by: Mathematics and Statistics
 Prerequisites: MATH 141 or equivalent.
 Restriction: Intended for students in Science, Engineering and related disciplines, who have had differential and integral calculus
 Restriction: Not open to students who have taken or are taking MATH 356
 Symbols:
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 Terms
 Fall 2020
 Winter 2021
 Instructors
 David B Wolfson, Alia Sajjad
 David B Wolfson, Alia Sajjad

MATH 324 Statistics 3 Credits*
 Fall
 Winter
 Summer
Offered in the:Mathematics & Statistics (Sci): Sampling distributions, point and interval estimation, hypothesis testing, analysis of variance, contingency tables, nonparametric inference, regression, Bayesian inference.
Offered by: Mathematics and Statistics
 Fall and Winter
 Prerequisite: MATH 323 or equivalent
 Restriction: Not open to students who have taken or are taking MATH 357
 You may not be able to receive credit for this course and other statistic courses. Be sure to check the Course Overlap section under Faculty Degree Requirements in the Arts or Science section of the Calendar.
 Symbols:
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 Terms
 Fall 2020
 Winter 2021
 Instructors
 Masoud AsgharianDastenaei
 Yi Yang

MATH 326 Nonlinear Dynamics and Chaos 3 Credits
 Fall
 Winter
 Summer
Offered in the:Mathematics & Statistics (Sci): Linear systems of differential equations, linear stability theory. Nonlinear systems: existence and uniqueness, numerical methods, one and two dimensional flows, phase space, limit cycles, PoincareBendixson theorem, bifurcations, Hopf bifurcation, the Lorenz equations and chaos.
Offered by: Mathematics and Statistics
 Fall
 Prerequisites: MATH 222, MATH 223
 Restriction: Not open to students who have taken or are taking MATH 376
 Symbols:
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 Fall 2020
 Instructors
 JeanChristophe Nave

MATH 340 Discrete Mathematics 3 Credits
 Fall
 Winter
 Summer
Offered in the:Mathematics & Statistics (Sci): Discrete Mathematics and applications. Graph Theory: matchings, planarity, and colouring. Discrete probability. Combinatorics: enumeration, combinatorial techniques and proofs.
Offered by: Mathematics and Statistics
 Winter
 Prerequisites: MATH 235 or MATH 240 or MATH 242.
 Corequisites: MATH 223 or MATH 236.
 Restriction: Restriction: Not open to students who have taken or are taking MATH 350.
 Symbols:
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 Winter 2021
 Instructors
 Jérôme Fortier

MATH 417 Linear Optimization 3 Credits
 Fall
 Winter
 Summer
Offered in the:Mathematics & Statistics (Sci): An introduction to linear optimization and its applications: Duality theory, fundamental theorem, sensitivity analysis, convexity, simplex algorithm, interiorpoint methods, quadratic optimization, applications in game theory.
Offered by: Mathematics and Statistics
 Prerequisites: COMP 202, and MATH 223 or MATH 236, and MATH 314 or equivalent
 Restriction: Not open to students who have taken or are taking MATH 487 or MATH 517.
 Symbols:
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 Fall 2020
 Instructors
 Tim Hoheisel

MATH 427 Statistical Quality Control 3 Credits
 Fall
 Winter
 Summer
Offered in the:Mathematics & Statistics (Sci): Introduction to quality management; variability and productivity. Quality measurement: capability analysis, gauge capability studies. Process control: control charts for variables and attributes. Process improvement: factorial designs, fractional replications, response surface methodology, Taguchi methods. Acceptance sampling: operating characteristic curves; single, multiple and sequential acceptance sampling plans for variables and attributes.
Offered by: Mathematics and Statistics
 Symbols:
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 This course is not scheduled for the 20202021 academic year
 Instructors
 There are no professors associated with this course for the 20202021 academic year

MATH 447 Intro. to Stochastic Processes 3 Credits
 Fall
 Winter
 Summer
Offered in the:Mathematics & Statistics (Sci): Conditional probability and conditional expectation, generating functions. Branching processes and random walk. Markov chains, transition matrices, classification of states, ergodic theorem, examples. Birth and death processes, queueing theory.
Offered by: Mathematics and Statistics
 Winter
 Prerequisite: MATH 323
 Restriction: Not open to students who have taken or are taking MATH 547.
 Symbols:
 Terms
 Winter 2021
 Instructors
 Elliot Paquette

MATH 475 Honours PDE's 3 Credits
 Fall
 Winter
 Summer
Offered in the:Mathematics & Statistics (Sci): First order partial differential equations, geometric theory, classification of second order linear equations, SturmLiouville problems, orthogonal functions and Fourier series, eigenfunction expansions, separation of variables for heat, wave and Laplace equations, Green's function methods, uniqueness theorems.
Offered by: Mathematics and Statistics
 Prerequisites: MATH 247 or MATH 251 or equivalent, and MATH 248 or MATH 358 or equivalent, MATH 325.
 Restriction: Not open to students who have taken MATH 375.
 Symbols:
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 Fall 2020
 Instructors
 Jessica Lin

MATH 478 Comput. Meth. in Applied Math 3 Credits
 Fall
 Winter
 Summer
Offered in the:Mathematics & Statistics (Sci): Solution to initial value problems: Linear, Nonlinear Finite Difference Methods: accuracy and stability, Lax equivalence theorem, CFL and von Neumann conditions, Fourier analysis: diffusion, dissipation, dispersion, and spectral methods. Solution of large sparse linear systems: iterative methods, preconditioning, incomplete LU, multigrid, Krylov subspaces, conjugate gradient method. Applications to, e.g., weighted least squares, duality, constrained minimization, calculus of variation, inverse problems, regularization, level set methods, NavierStokes equations
Offered by: Mathematics and Statistics
 Prerequisites: MATH 315 or MATH 325 or MATH 263; MATH 317 or MATH 387 or COMP 350 or MECH 309; or permission of the instructor
 This course will be taught in the winter semester.
 Symbols:
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 Winter 2021
 Instructors
 JeanChristophe Nave

MATH 560 Optimization 4 Credits
 Fall
 Winter
 Summer
Offered in the:Mathematics & Statistics (Sci): Line search methods including steepest descent, Newton's (and QuasiNewton) methods. Trust region methods, conjugate gradient method, solving nonlinear equations, theory of constrained optimization including a rigorous derivation of KarushKuhnTucker conditions, convex optimization including duality and sensitivity. Interior point methods for linear programming, and conic programming.
Offered by: Mathematics and Statistics
 Prerequisite: Undergraduate background in analysis and linear algebra, with instructor's approval
 Symbols:
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 Winter 2021
 Instructors
 Courtney Paquette
* Students who take ECSE 205 may not take MATH 323 or MATH 324.
** Students may take MATH 271 or MATH 319 but not both.