Mathematics Minor (B.Eng.) (18 credits)
Offered by: Mathematics and Statistics (Faculty of Science)
Degree: Bachelor of Engineering
Program credit weight: 18
Program Description
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.
Note: For information about Fall 2025 and Winter 2026 course offerings, please check back on May 8, 2025. Until then, the "Terms offered" field will appear blank for most courses while the class schedule is being finalized.
Required Course (3 credits)
| Course | Title | Credits |
|---|---|---|
| MATH 242 | Analysis 1. | 3 |
Analysis 1. Terms offered: this course is not currently offered. A rigorous presentation of sequences and of real numbers and basic properties of continuous and differentiable functions on the real line. | ||
Complementary Courses (15 credits)
3 credits selected from:
| Course | Title | Credits |
|---|---|---|
| MATH 223 | Linear Algebra. | 3 |
Linear Algebra. Terms offered: this course is not currently offered. 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. | ||
| MATH 247 | Honours Applied Linear Algebra. | 3 |
Honours Applied Linear Algebra. Terms offered: this course is not currently offered. 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. | ||
6-12 credits selected from:
| Course | Title | Credits |
|---|---|---|
| ECSE 205 | Probability and Statistics for Engineers 1 | 3 |
Probability and Statistics for Engineers Terms offered: Summer 2025 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. | ||
| MATH 204 | Principles of Statistics 2. | 3 |
Principles of Statistics 2. Terms offered: this course is not currently offered. 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. | ||
| MATH 240 | Discrete Structures. | 3 |
Discrete Structures. Terms offered: this course is not currently offered. 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. | ||
| MATH 243 | Analysis 2. | 3 |
Analysis 2. Terms offered: this course is not currently offered. 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. | ||
| MATH 264 | Advanced Calculus for Engineers. | 3 |
Advanced Calculus for Engineers. Terms offered: Summer 2025 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. | ||
| MATH 271 | Linear Algebra and Partial Differential Equations. 2 | 3 |
Linear Algebra and Partial Differential Equations. Terms offered: this course is not currently offered. Applied Linear Algebra. Linear Systems of Ordinary Differential Equations. Power Series Solutions. Partial Differential Equations. Sturm-Liouville Theory and Applications. Fourier Transforms. | ||
| MATH 316 | Complex Variables. | 3 |
Complex Variables. Terms offered: this course is not currently offered. Algebra of complex numbers, Cauchy-Riemann equations, complex integral, Cauchy's theorems. Taylor and Laurent series, residue theory and applications. | ||
| MATH 319 | Partial Differential Equations . 2 | 3 |
Partial Differential Equations . Terms offered: this course is not currently offered. First order equations, geometric theory; second order equations, classification; Laplace, wave and heat equations, Sturm-Liouville theory, Fourier series, boundary and initial value problems. | ||
| MATH 323 | Probability. 1 | 3 |
Probability. Terms offered: Summer 2025 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. | ||
| MATH 324 | Statistics. 1 | 3 |
Statistics. Terms offered: this course is not currently offered. Sampling distributions, point and interval estimation, hypothesis testing, analysis of variance, contingency tables, nonparametric inference, regression, Bayesian inference. | ||
| MATH 326 | Nonlinear Dynamics and Chaos. | 3 |
Nonlinear Dynamics and Chaos. Terms offered: this course is not currently offered. 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. | ||
| MATH 340 | Discrete Mathematics. | 3 |
Discrete Mathematics. Terms offered: this course is not currently offered. Discrete Mathematics and applications. Graph Theory: matchings, planarity, and colouring. Discrete probability. Combinatorics: enumeration, combinatorial techniques and proofs. | ||
| MATH 378 | Nonlinear Optimization . | 3 |
Nonlinear Optimization . Terms offered: this course is not currently offered. Optimization terminology. Convexity. First- and second-order optimality conditions for unconstrained problems. Numerical methods for unconstrained optimization: Gradient methods, Newton-type methods, conjugate gradient methods, trust-region methods. Least squares problems (linear + nonlinear). Optimality conditions for smooth constrained optimization problems (KKT theory). Lagrangian duality. Augmented Lagrangian methods. Active-set method for quadratic programming. SQP methods. | ||
| MATH 417 | Linear Optimization. | 3 |
Linear Optimization. Terms offered: this course is not currently offered. 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. | ||
| MATH 427 | Statistical Quality Control. | 3 |
Statistical Quality Control. Terms offered: this course is not currently offered. 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. | ||
| MATH 447 | Introduction to Stochastic Processes. | 3 |
Introduction to Stochastic Processes. Terms offered: this course is not currently offered. 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. | ||
| MATH 463 | Convex Optimization. | 3 |
Convex Optimization. Terms offered: this course is not currently offered. Introduction to convex analysis and convex optimization: Convex sets and functions, subdifferential calculus, conjugate functions, Fenchel duality, proximal calculus. Subgradient methods, proximal-based methods. Conditional gradient method, ADMM. Applications including data classification, network-flow problems, image processing, convex feasibility problems, DC optimization, sparse optimization, and compressed sensing. | ||
| MATH 475 | Honours Partial Differential Equations. | 3 |
Honours Partial Differential Equations. Terms offered: this course is not currently offered. 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. | ||
| MATH 478 | Computational Methods in Applied Mathematics . | 3 |
Computational Methods in Applied Mathematics . Terms offered: this course is not currently offered. 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 | ||
| MATH 563 | Honours Convex Optimization . | 4 |
Honours Convex Optimization . Terms offered: this course is not currently offered. Honours level introduction to convex analysis and convex optimization: Convex sets and functions, subdifferential calculus, conjugate functions, Fenchel duality, proximal calculus. Subgradient methods, proximal-based methods. Conditional gradient method, ADMM. Applications including data classification, network-flow problems, image processing, convex feasibility problems, DC optimization, sparse optimization, and compressed sensing. | ||
- 1
Students who take ECSE 205 Probability and Statistics for Engineers may not take MATH 323 Probability. or MATH 324 Statistics..
- 2
Students may take MATH 271 Linear Algebra and Partial Differential Equations. or MATH 319 Partial Differential Equations . 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 Intermediate Calculus., MATH 263 Ordinary Differential Equations for Engineers. (or any course with substantial overlap in content with these two courses) and/or MATH 338 History and Philosophy of Mathematics. cannot be credited towards this minor.