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Program Requirements
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 (double-counting) 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)
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MATH 242 Analysis 1 (3 credits)
Overview
Mathematics & Statistics (Sci) : A rigorous presentation of sequences and of real numbers and basic properties of continuous and differentiable functions on the real line.
Terms: Fall 2019
Instructors: Vetois, Jerome (Fall)
Complementary Courses (15 credits)
3 credits selected from:
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MATH 223 Linear Algebra (3 credits)
Overview
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.
Terms: Fall 2019, Winter 2020
Instructors: Kelome, Djivede (Fall) Macdonald, Jeremy (Winter)
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MATH 247 Honours Applied Linear Algebra (3 credits)
Overview
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.
Terms: Winter 2020
Instructors: Hoheisel, Tim (Winter)
6-12 credits selected from:
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ECSE 205 Probability and Statistics for Engineers (3 credits) *
Overview
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.
Terms: Fall 2019, Winter 2020, Summer 2020
Instructors: Hajikhani, Mohammadjavad (Fall) Leib, Harry (Winter) Bajcsy, Jan (Summer)
Not open to students who have taken ECSE 305.
(3-2-4)
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MATH 204 Principles of Statistics 2 (3 credits)
Overview
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.
Terms: Winter 2020
Instructors: Genest, Christian (Winter)
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.
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MATH 240 Discrete Structures (3 credits)
Overview
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.
Terms: Fall 2019, Winter 2020
Instructors: Macdonald, Jeremy; Nica, Bogdan (Fall) Macdonald, Jeremy; Lumley, Allysa (Winter)
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MATH 243 Analysis 2 (3 credits)
Overview
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.
Terms: Winter 2020
Instructors: Hundemer, Axel W (Winter)
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MATH 264 Advanced Calculus for Engineers (3 credits)
Overview
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, Sturm-Liouville problems, and Fourier series.
Terms: Fall 2019, Winter 2020, Summer 2020
Instructors: Wong, Biji; Hurtubise, Jacques Claude (Fall) Bibby, Sean; Hurtubise, Jacques Claude (Winter) Nazari Zahraei Motlagh, Erfan (Summer)
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MATH 271 Linear Algebra and Partial Differential Equations (3 credits) **
Overview
Mathematics & Statistics (Sci) : Applied Linear Algebra. Linear Systems of Ordinary Differential Equations. Power Series Solutions. Partial Differential Equations. Sturm-Liouville Theory and Applications. Fourier Transforms.
Terms: Fall 2019
Instructors: Roth, Charles (Fall)
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MATH 316 Complex Variables (3 credits)
Overview
Mathematics & Statistics (Sci) : Algebra of complex numbers, Cauchy-Riemann equations, complex integral, Cauchy's theorems. Taylor and Laurent series, residue theory and applications.
Terms: Fall 2019
Instructors: Pym, Brent (Fall)
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MATH 319 Introduction to Partial Differential Equations (3 credits) **
Overview
Mathematics & Statistics (Sci) : First order equations, geometric theory; second order equations, classification; Laplace, wave and heat equations, Sturm-Liouville theory, Fourier series, boundary and initial value problems.
Terms: Winter 2020
Instructors: Laborde, Maxime; Hurtubise, Jacques Claude (Winter)
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MATH 323 Probability (3 credits) *
Overview
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.
Terms: Fall 2019, Winter 2020, Summer 2020
Instructors: Correa, Jose Andres; Alam, Shomoita (Fall) Kelome, Djivede; Wolfson, David B (Winter) Kelome, Djivede (Summer)
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MATH 324 Statistics (3 credits) *
Overview
Mathematics & Statistics (Sci) : Sampling distributions, point and interval estimation, hypothesis testing, analysis of variance, contingency tables, nonparametric inference, regression, Bayesian inference.
Terms: Fall 2019, Winter 2020
Instructors: Asgharian-Dastenaei, Masoud (Fall) Luo, Yu; Hurtubise, Jacques Claude (Winter)
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.
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MATH 326 Nonlinear Dynamics and Chaos (3 credits)
Overview
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, Poincare-Bendixson theorem, bifurcations, Hopf bifurcation, the Lorenz equations and chaos.
Terms: Fall 2019
Instructors: Humphries, Antony Raymond (Fall)
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MATH 340 Discrete
Mathematics (3 credits)
Overview
Mathematics & Statistics (Sci) : Discrete Mathematics and applications. Graph Theory: matchings, planarity, and colouring. Discrete probability. Combinatorics: enumeration, combinatorial techniques and proofs.
Terms: Winter 2020
Instructors: Fortier, J茅r么me (Winter)
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MATH 417 Linear Optimization (3 credits)
Overview
Mathematics & Statistics (Sci) : An introduction to linear optimization and its applications: Duality theory, fundamental theorem, sensitivity analysis, convexity, simplex algorithm, interior-point methods, quadratic optimization, applications in game theory.
Terms: Fall 2019
Instructors: Nguyen, Van Quang; Hurtubise, Jacques Claude (Fall)
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MATH 427 Statistical Quality Control (3 credits)
Overview
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.
Terms: Fall 2019
Instructors: Genest, Christian (Fall)
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MATH 447 Introduction to Stochastic Processes (3 credits)
Overview
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.
Terms: Winter 2020
Instructors: Steele, Russell (Winter)
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MATH 475 Honours Partial Differential Equations (3 credits)
Overview
Mathematics & Statistics (Sci) : First order partial differential equations, geometric theory, classification of second order linear equations, Sturm-Liouville problems, orthogonal functions and Fourier series, eigenfunction expansions, separation of variables for heat, wave and Laplace equations, Green's function methods, uniqueness theorems.
Terms: Fall 2019
Instructors: Lin, Jessica (Fall)
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MATH 478 Computational Methods in Applied Mathematics
(3 credits)
Overview
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, Navier-Stokes equations
Terms: Winter 2020
Instructors: Nave, Jean-Christophe (Winter)
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MATH 560 Optimization (4 credits)
Overview
Mathematics & Statistics (Sci) : Line search methods including steepest descent, Newton's (and Quasi-Newton) methods. Trust region methods, conjugate gradient method, solving nonlinear equations, theory of constrained optimization including a rigorous derivation of Karush-Kuhn-Tucker conditions, convex optimization including duality and sensitivity. Interior point methods for linear programming, and conic programming.
Terms: Winter 2020
Instructors: Hoheisel, Tim (Winter)
Prerequisite: Undergraduate background in analysis and linear algebra, with instructor's approval
* Students who take ECSE 205 may not take MATH 323 or MATH 324.
** Students may take MATH 271 or MATH 319 but not both.
0-6 credits chosen from (200- to 500-level) Mathematics and Statistics courses approved for the B.Sc. Major Mathematics or B.Sc. Honours Mathematics programs, or from mathematics courses offered in other units. The courses in this category must be chosen in consultation with, and approved by, the Minor Adviser from the Department of Mathematics and Statistics.
Note: MATH 262, MATH 263 (or any course with substantial overlap in content with these two courses) and/or MATH 338 cannot be credited towards this minor.
