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:
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, normally beginning in the U2 year (please consult the Department of Mathematics and Statistics for this adviser). Selection of courses must be done in conjunction with the Minor advisers.
Note: The Mathematics Minor is open to all students in the Faculty of Engineering (B.Eng. and B.Sc.(Arch.)).
Engineering students must obtain a grade of C or better in courses approved for this Minor.
Course Selection
At least 18 credits must be chosen from the Mathematics and Statistics courses approved for the Mathematics Major or Honours program, or from the following courses:

MATH 249 Honours Complex Variables 3 Credits
 Fall
 Winter
 Summer
Offered in the:Mathematics & Statistics (Sci): Functions of a complex variable; CauchyRiemann equations; Cauchy's theorem and consequences. Taylor and Laurent expansions. Residue calculus; evaluation of real integrals; integral representation of special functions; the complex inversion integral. Conformal mapping; SchwarzChristoffel transformation; Poisson's integral formulas; applications.
Offered by: Mathematics and Statistics
 Winter
 Prerequisite: MATH 248.
 Restriction: Intended for Honours Physics and Engineering students
 Restriction: Not open to students who have taken or are taking MATH 316
 Symbols:
 Terms
 Winter 2020
 Instructors
 Jerome Vetois

MATH 363 Discrete Mathematics 3 Credits
 Fall
 Winter
 Summer
Offered in the:Mathematics & Statistics (Sci): Logic and combinatorics. Mathematical reasoning and methods of proof. Sets, relations, functions, partially ordered sets, lattices, Boolean algebra. Propositional and predicate calculi. Recurrences and graph theory.
Offered by: Mathematics and Statistics
 (306)
 Prerequisites: MATH 263, MATH 264.
 Restriction: Open only to students in the Faculty of Engineering.
 Symbols:
 Terms
 This course is not scheduled for the 20192020 academic year
 Instructors
 There are no professors associated with this course for the 20192020 academic year

MATH 381 Complex Variables & Transforms 3 Credits
 Fall
 Winter
 Summer
Offered in the:Mathematics & Statistics (Sci): Analytic functions, CauchyRiemann equations, simple mappings, Cauchy's theorem, Cauchy's integral formula, Taylor and Laurent expansions, residue calculus. Properties of one and twosided Fourier and Laplace transforms, the complex inversion integral, relation between the Fourier and Laplace transforms, application of transform techniques to the solution of differential equations. The Ztransform and applications to difference equations.
Offered by: Mathematics and Statistics
 Fall and Winter
 (315)
 Prerequisite: MATH 264
 Restriction: Open only to students in the Faculty of Engineering.
 Symbols:
 Terms
 This course is not scheduled for the 20192020 academic year
 Instructors
 There are no professors associated with this course for the 20192020 academic year
The remaining credits may be chosen from mathematicallyallied courses.
The following courses cannot be used toward the Minor:

MATH 222 Calculus 3 3 Credits
 Fall
 Winter
 Summer
Offered in the:Mathematics & Statistics (Sci): Taylor series, Taylor's theorem in one and several variables. Review of vector geometry. Partial differentiation, directional derivative. Extreme of functions of 2 or 3 variables. Parametric curves and arc length. Polar and spherical coordinates. Multiple integrals.
Offered by: Mathematics and Statistics
 Prerequisite: MATH 141. Familiarity with vector geometry or Corequisite: MATH 133
 Restriction: Not open to students who have taken CEGEP course 201303 or MATH 150, MATH 151 or MATH 227
 Symbols:
 Terms
 Fall 2019
 Winter 2020
 Instructors
 Jeremy D Macdonald
 Jérôme Fortier

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:
 Terms
 Fall 2019
 Winter 2020
 Instructors
 Djivede A Kelome
 Jeremy D Macdonald

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:
 Terms
 Winter 2020
 Instructors
 Tim Hoheisel

MATH 248 Honours Vector Calculus 3 Credits
 Fall
 Winter
 Summer
Offered in the:Mathematics & Statistics (Sci): Partial derivatives and differentiation of functions in several variables; Jacobians; maxima and minima; implicit functions. Scalar and vector fields; orthogonal curvilinear coordinates. Multiple integrals; arc length, volume and surface area. Line and surface integrals; irrotational and solenoidal fields; Green's theorem; the divergence theorem. Stokes' theorem; and applications.
Offered by: Mathematics and Statistics
 Fall and Winter and Summer
 Prerequisites: MATH 133 and MATH 222 or consent of Department.
 Restriction: Intended for Honours Physics, Computer Science, Physiology and Engineering students.
 Restriction: Not open to students who have taken or are taking MATH 314 or MATH 358.
 Symbols:
 Terms
 Fall 2019
 Instructors
 Gantumur Tsogtgerel

MATH 262 Intermediate Calculus 3 Credits
 Fall
 Winter
 Summer
Offered in the:Mathematics & Statistics (Sci): Series and power series, including Taylor's theorem. Brief review of vector geometry. Vector functions and curves. Partial differentiation and differential calculus for vector valued functions. Unconstrained and constrained extremal problems. Multiple integrals including surface area and change of variables.
Offered by: Mathematics and Statistics
 (315)
 Prerequisites: MATH 141, MATH 133 or equivalent.
 Restrictions: Open only to students in the Faculty of Engineering. Not open to students who are taking or have taken MATH 151, MATH 152, OR MATH 222.
 Symbols:
 Terms
 Fall 2019
 Winter 2020
 Instructors
 Rosalie BélangerRioux
 Charles Roth

MATH 263 ODEs for Engineers 3 Credits
 Fall
 Winter
 Summer
Offered in the:Mathematics & Statistics (Sci): First order ODEs. Second and higher order linear ODEs. Series solutions at ordinary and regular singular points. Laplace transforms. Linear systems of differential equations with a short review of linear algebra.
Offered by: Mathematics and Statistics
 (315)
 Corequisite: MATH 262.
 Restrictions: Open only to students in the Faculty of Engineering. Not open to students who are taking or have taken MATH 315 or MATH 325.
 Symbols:
 Terms
 Fall 2019
 Winter 2020
 Instructors
 Peter Bartello, Sidney Trudeau

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:
 Terms
 Fall 2019
 Winter 2020
 Instructors
 Rustum Choksi

MATH 270 Applied Linear Algebra 3 Credits
 Fall
 Winter
 Summer
Offered in the:Mathematics & Statistics (Sci): Introduction. Review of basic linear algebra. Vector spaces. Eigenvalues and eigenvectors of matrices. Linear operators.
Offered by: Mathematics and Statistics
 Winter
 (315)
 Prerequisite: MATH 263
 Symbols:
 Terms
 This course is not scheduled for the 20192020 academic year
 Instructors
 There are no professors associated with this course for the 20192020 academic year

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:
 Terms
 Fall 2019
 Instructors
 Charles Roth

MATH 314 Advanced Calculus 3 Credits
 Fall
 Winter
 Summer
Offered in the:Mathematics & Statistics (Sci): Derivative as a matrix. Chain rule. Implicit functions. Constrained maxima and minima. Jacobians. Multiple integration. Line and surface integrals. Theorems of Green, Stokes and Gauss. Fourier series with applications.
Offered by: Mathematics and Statistics
 Prerequisites: MATH 133, MATH 222
 Restriction: Not open to students who have taken or are taking MATH 248 or MATH 358.
 Symbols:
 Terms
 Fall 2019
 Winter 2020
 Instructors
 Charles Roth

MATH 315 Ordinary Differential Eqns 3 Credits
 Fall
 Winter
 Summer
Offered in the:Mathematics & Statistics (Sci): First order ordinary differential equations including elementary numerical methods. Linear differential equations. Laplace transforms. Series solutions.
Offered by: Mathematics and Statistics
 Prerequisite: MATH 222.
 Corequisite: MATH 133.
 Restriction: Not open to students who have taken or are taking MATH 325.
 Symbols:
 Terms
 Fall 2019
 Winter 2020
 Instructors
 Rosalie BélangerRioux

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:
 Terms
 Winter 2020
 Instructors
 Adam M Oberman

MATH 325 Honours ODE's 3 Credits
 Fall
 Winter
 Summer
Offered in the:Mathematics & Statistics (Sci): First and second order equations, linear equations, series solutions, Frobenius method, introduction to numerical methods and to linear systems, Laplace transforms, applications.
Offered by: Mathematics and Statistics
 Fall and Winter
 (306)
 Prerequisite: MATH 222.
 Restriction: Intended for Honours Mathematics, Physics and Engineering programs.
 Restriction: Not open to students who have taken MATH 263 (formerly MATH 261), MATH 315
 Symbols:
 Terms
 Winter 2020
 Instructors
 JeanPhilippe Lessard