Program Requirements
Applied Mathematics is a very broad field and students are encouraged to choose a coherent program of complementary courses. Most students specialize in "continuous" or "discrete" applied mathematics, but there are many sensible combinations of courses, and the following informal guidelines should be discussed with the student's adviser. Also, aside from seeking to develop a sound basis in Applied Mathematics, one of the objectives of the program is to kindle the students' interest in possible areas of application. To develop an appreciation of the diversity of Applied Mathematics, students are advised to develop some depth (e.g., by completing a minor) in a field related to Applied Mathematics such as Atmospheric and Oceanic Sciences, Biology, Biochemistry, Chemistry, Computer Science, Earth and Planetary Sciences, Economics, Engineering, Management, Physics, Physiology, and Psychology.
Students may complete this program with a minimum of 60 credits or a maximum of 63 credits depending if they are exempt from MATH 222.
Program Prerequisites
The minimum requirement for entry into the Honours program is that the student has completed with high standing the following courses below or their equivalents:

MATH 133 Linear Algebra and Geometry (3 credits)
Overview
Mathematics & Statistics (Sci) : Systems of linear equations, matrices, inverses, determinants; geometric vectors in three dimensions, dot product, cross product, lines and planes; introduction to vector spaces, linear dependence and independence, bases; quadratic loci in two and three dimensions.
Terms: Fall 2018, Winter 2019, Summer 2019
Instructors: Jerome Fortier, Liangming Shen, Yann Batiste Pequignot, Damian Osajda (Fall) Jerome Fortier (Winter)
3 hours lecture, 1 hour tutorial
Prerequisite: a course in functions
Restriction A: Not open to students who have taken MATH 221 or CEGEP objective 00UQ or equivalent.
Restriction B: Not open to students who have taken or are taking MATH 123, MATH 130 or MATH 131, except by permission of the Department of Mathematics and Statistics.
Restriction C: Not open to students who are taking or have taken MATH 134.

MATH 150 Calculus A (4 credits)
Overview
Mathematics & Statistics (Sci) : Functions, limits and continuity, differentiation, L'Hospital's rule, applications, Taylor polynomials, parametric curves, functions of several variables.
Terms: Fall 2018
Instructors: Charles Roth (Fall)
Fall
3 hours lecture, 2 hours tutorial
Students with no prior exposure to vector geometry are advised to take MATH 133 concurrently. Intended for students with high school calculus who have not received six advanced placement credits
Restriction: Not open to students who have taken CEGEP objective 00UN or equivalent
Restriction Note B: Not open to students who have taken or are taking MATH 122 or MATH 130 or MATH 131, except by permission of the Department of Mathematics and Statistics
MATH 150 and MATH 151 cover the material of MATH 139, MATH 140, MATH 141, MATH 222

MATH 151 Calculus B (4 credits)
Overview
Mathematics & Statistics (Sci) : Integration, methods and applications, infinite sequences and series, power series, arc length and curvature, multiple integration.
Terms: Winter 2019
Instructors: Charles Roth (Winter)
Winter
3 hours lecture; 2 hours tutorial
Each Tutorial section is enrolment limited
Prerequisite: MATH 150
Restriction: Not open to students who have taken CEGEP objective 00UP or equivalent
Restriction: Not open to students who have taken or are taking MATH 122 or MATH 130 or MATH 131, except by permission of the Department of Mathematics and Statistics
Restriction: Not open to students who have taken MATH 152
In particular, MATH 150/151 and MATH 140/222 are considered equivalent.
Students who have not completed and equivalent of MATH 222 on entering the program must consult and academic adviser and take MATH 222 as a required course in the first semester, increasing the total number of program credits from 60 to 63. Students who have successfully completed MATH 150/151 are not required to take MATH 222.
Note: COMP 202—or an equivalent introduction to computer programming course—is a program prerequisite. U0 students may take COMP 202 as a Freshman Science course; new U1 students should take it as an elective in their first semester.
Students who transfer to Honours in Mathematics from other programs will have credits for previous courses assigned, as appropriate, by the Department.
To be awarded the Honours degree, the student must have, at time of graduation, a CGPA of at least 3.00 in the required and complementary Mathematics courses of the program, as well as an overall CGPA of at least 3.00.
Required Courses
(3942 credits)
* Students with limited programming experience should take COMP 202 or equivalent before COMP 250.
** Students select either MATH 251 or MATH 247, but not both.
*** Students who have successfully completed MATH 150/151 or an equivalent of MATH 222 on entering the program are not required to take MATH 222.

COMP 250 Introduction to Computer Science (3 credits) *
Overview
Computer Science (Sci) : Mathematical tools (binary numbers, induction, recurrence relations, asymptotic complexity, establishing correctness of programs), Data structures (arrays, stacks, queues, linked lists, trees, binary trees, binary search trees, heaps, hash tables), Recursive and nonrecursive algorithms (searching and sorting, tree and graph traversal). Abstract data types, inheritance. Selected topics.
Terms: Fall 2018, Winter 2019
Instructors: Michael Langer, Giulia Alberini (Fall) Martin Robillard, Giulia Alberini (Winter)

COMP 252 Honours Algorithms and Data Structures (3 credits)
Overview
Computer Science (Sci) : The design and analysis of data structures and algorithms. The description of various computational problems and the algorithms that can be used to solve them, along with their associated data structures. Proving the correctness of algorithms and determining their computational complexity.
Terms: Winter 2019
Instructors: Adrian Roshan Vetta (Winter)
3 hours
Restrictions: (1) Open only to students in Honours programs. (2) Students cannot receive credit for both COMP 251 and COMP 252.
COMP 252 uses basic combinatorial counting methods that are covered in MATH 240 but not in MATH 235. Students who are unfamiliar with these methods should speak with the instructor for guidance.

MATH 222 Calculus 3 (3 credits) ***
Overview
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.
Terms: Fall 2018, Winter 2019, Summer 2019
Instructors: Jeremy Macdonald, Dmitry Faifman (Fall) Lars Sektnan (Winter)

MATH 235 Algebra 1 (3 credits)
Overview
Mathematics & Statistics (Sci) : Sets, functions and relations. Methods of proof. Complex numbers. Divisibility theory for integers and modular arithmetic. Divisibility theory for polynomials. Rings, ideals and quotient rings. Fields and construction of fields from polynomial rings. Groups, subgroups and cosets; group actions on sets.
Terms: Fall 2018
Instructors: Daniel Wise (Fall)
Fall
3 hours lecture; 1 hour tutorial
Prerequisite: MATH 133 or equivalent

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 2019
Instructors: Tim Hoheisel (Winter)

MATH 248 Honours Advanced Calculus (3 credits)
Overview
Mathematics & Statistics (Sci) : Partial derivatives; implicit functions; Jacobians; maxima and minima; Lagrange multipliers. Scalar and vector fields; orthogonal curvilinear coordinates. Multiple integrals; arc length, volume and surface area. Line integrals; Green's theorem; the divergence theorem. Stokes' theorem; irrotational and solenoidal fields; applications.
Terms: Fall 2018
Instructors: Pengfei Guan (Fall)

MATH 251 Honours Algebra 2 (3 credits) **
Overview
Mathematics & Statistics (Sci) : Linear equations over a field. Introduction to vector spaces. Linear maps and their matrix representation. Determinants. Canonical forms. Duality. Bilinear and quadratic forms. Real and complex inner product spaces. Diagonalization of selfadjoint operators.
Terms: Winter 2019
Instructors: Haining Wang (Winter)

MATH 255 Honours Analysis 2 (3 credits)
Overview
Mathematics & Statistics (Sci) : Basic pointset topology, metric spaces: open and closed sets, normed and Banach spaces, HÃ¶lder and Minkowski inequalities, sequential compactness, HeineBorel, Banach Fixed Point theorem. Riemann(Stieltjes) integral, Fundamental Theorem of Calculus, Taylor's theorem. Uniform convergence. Infinite series, convergence tests, power series. Elementary functions.
Terms: Winter 2019
Instructors: Rustum Choksi (Winter)

MATH 325 Honours Ordinary Differential Equations (3 credits)
Overview
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.
Terms: Winter 2019
Instructors: JeanPhilippe Lessard (Winter)

MATH 350 Graph Theory and Combinatorics (3 credits)
Overview
Mathematics & Statistics (Sci) : Graph models. Graph connectivity, planarity and colouring. Extremal graph theory. Matroids. Enumerative combinatorics and listing.
Terms: Fall 2018
Instructors: Adrian Roshan Vetta (Fall)

MATH 356 Honours Probability (3 credits)
Overview
Mathematics & Statistics (Sci) : Sample space, probability axioms, combinatorial probability. Conditional probability, Bayes' Theorem. Distribution theory with special reference to the Binomial, Poisson, and Normal distributions. Expectations, moments, moment generating functions, univariate transformations. Random vectors, independence, correlation, multivariate transformations. Conditional distributions, conditional expectation.Modes of stochastic convergence, laws of large numbers, Central Limit Theorem.
Terms: Fall 2018
Instructors: Linan Chen (Fall)

MATH 357 Honours Statistics (3 credits)
Overview
Mathematics & Statistics (Sci) : Data analysis. Estimation and hypothesis testing. Power of tests. Likelihood ratio criterion. The chisquared goodness of fit test. Introduction to regression analysis and analysis of variance.
Terms: Winter 2019
Instructors: Masoud AsgharianDastenaei (Winter)

MATH 376 Honours Nonlinear Dynamics (3 credits)
Overview
Mathematics & Statistics (Sci) : This course consists of the lectures of MATH 326, but will be assessed at the honours level.
Terms: Fall 2018
Instructors: JeanPhilippe Lessard (Fall)

MATH 470 Honours Research Project (3 credits)
Overview
Mathematics & Statistics (Sci) : The project will contain a significant research component that requires substantial independent work consisting of a written report and oral examination or presentation.
Terms: Fall 2018, Winter 2019
Instructors: Djivede Kelome, JeanPhilippe Lessard, David Stephens, Marcin Sabok, Daniel Wise, Dana Louis AddarioBerry, JeanChristophe Nave, Linan Chen, Michael Pichot, Jerome Vetois, Piotr Przytycki (Fall) Djivede Kelome, Dmitry Jakobson, Marcin Sabok, Henri Darmon, Eyal Z Goren, JeanChristophe Nave, Jacques Claude Hurtubise, David Stephens, Antony Raymond Humphries, Niky Kamran, Piotr Przytycki, Daniel Wise (Winter)
Fall and Winter and Summer
Requires Departmental Approval
Students are advised to start contacting potential project supervisors early during their U2 year.
Prerequisite: appropriate honours courses with approval of the project supervisor

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, SturmLiouville 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 2018
Instructors: Rustum Choksi (Fall)
Complementary Courses (21 credits)
3 credits selected from:

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 2018
Instructors: Jerome Vetois (Fall)

MATH 254 Honours Analysis 1 (3 credits) +
Overview
Mathematics & Statistics (Sci) : Properties of R. Cauchy and monotone sequences, Bolzano Weierstrass theorem. Limits, limsup, liminf of functions. Pointwise, uniform continuity: Intermediate Value theorem. Inverse and monotone functions. Differentiation: Mean Value theorem, L'Hospital's rule, Taylor's Theorem.
Terms: Fall 2018
Instructors: Axel W Hundemer (Fall)
+ It is strongly recommended that students take MATH 254.
Advising Notes:
Students interested in continuous applied mathematics are urged to choose these as part of their Complementary Courses: MATH 454, MATH 455 and MATH 478, and are advised to choose additional courses from MATH 387, MATH 397, MATH 555, MATH 560, MATH 574, MATH 578, MATH 579, MATH 580, MATH 581.
Students interested in discrete applied mathematics are advised to choose from these as part of their Complementary Courses: COMP 362, COMP 490, MATH 456, MATH 457, MATH 407, MATH 517, MATH 547, MATH 550, MATH 552, MATH 560.
3 credits selected from:

MATH 249 Honours Complex Variables (3 credits)
Overview
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.
Terms: Winter 2019
Instructors: Charles Roth (Winter)

MATH 466 Honours Complex Analysis (3 credits)
Overview
Mathematics & Statistics (Sci) : Functions of a complex variable, CauchyRiemann equations, Cauchy's theorem and its consequences. Uniform convergence on compacta. Taylor and Laurent series, open mapping theorem, Rouché's theorem and the argument principle. Calculus of residues. Fractional linear transformations and conformal mappings.
Terms: Fall 2018
Instructors: Sarah Harrison (Fall)
at least 3 credits selected from:

MATH 387 Honours Numerical Analysis (3 credits)
Overview
Mathematics & Statistics (Sci) : Error analysis. Numerical solutions of equations by iteration. Interpolation. Numerical differentiation and integration. Introduction to numerical solutions of differential equations.
Terms: This course is not scheduled for the 20182019 academic year.
Instructors: There are no professors associated with this course for the 20182019 academic year.

MATH 397 Honours Matrix Numerical Analysis (3 credits)
Overview
Mathematics & Statistics (Sci) : The course consists of the lectures of MATH 327 plus additional work involving theoretical assignments and/or a project. The final examination for this course may be different from that of MATH 327.
Terms: Winter 2019
Instructors: Ivo Panayotov (Winter)
06 credits from the following courses for which no Honours equivalent exists.

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 2019
Instructors: Christian Genest (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.

MATH 329 Theory of Interest (3 credits)
Overview
Mathematics & Statistics (Sci) : Simple and compound interest, annuities certain, amortization schedules, bonds, depreciation.
Terms: Winter 2019
Instructors: Djivede Kelome (Winter)
Winter
Prerequisite: MATH 141

MATH 338 History and Philosophy of Mathematics (3 credits)
Overview
Mathematics & Statistics (Sci) : Egyptian, Babylonian, Greek, Indian and Arab contributions to mathematics are studied together with some modern developments they give rise to, for example, the problem of trisecting the angle. European mathematics from the Renaissance to the 18th century is discussed in some detail.
Terms: Fall 2018
Instructors: Thomas F Fox (Fall)
Fall

MATH 407 Dynamic Programming (3 credits)
Overview
Mathematics & Statistics (Sci) : Sequential decision problems, resource allocation, transportation problems, equipment replacement, integer programming, network analysis, inventory systems, project scheduling, queuing theory calculus of variations, markovian decision processes, stochastic path problems, reliability, discrete and continuous control processes.
Terms: This course is not scheduled for the 20182019 academic year.
Instructors: There are no professors associated with this course for the 20182019 academic year.

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, NavierStokes equations
Terms: Winter 2019
Instructors: JeanChristophe Nave (Winter)
and the remainder of credits selected from:

COMP 362 Honours Algorithm Design (3 credits)
Overview
Computer Science (Sci) : Basic algorithmic techniques, their applications and limitations. Problem complexity, how to deal with problems for which no efficient solutions are known.
Terms: Winter 2019
Instructors: Bruce Alan Reed (Winter)

MATH 352 Problem Seminar (1 credit)
Overview
Mathematics & Statistics (Sci) : Seminar in Mathematical Problem Solving. The problems considered will be of the type that occur in the Putnam competition and in other similar mathematical competitions.
Terms: Fall 2018
Instructors: Jacques Claude Hurtubise (Fall)
Prerequisite: Enrolment in a math related program or permission of the instructor. Requires departmental approval.
Prerequisite: Enrolment in a math related program or permission of the instructor.

MATH 377 Honours Number Theory (3 credits)
Overview
Mathematics & Statistics (Sci) : This course consists of the lectures of MATH 346, but will be assessed at the honours level.
Terms: Winter 2019
Instructors: Michael Lipnowski (Winter)
Winter
Prerequisite: Enrolment in Mathematics Honours program or consent of instructor
Restriction: Not open to students who have taken or are taking MATH 346.
Note: Additionally, a special project or projects may be assigned.

MATH 398 Honours Euclidean Geometry
(3 credits)
Overview
Mathematics & Statistics (Sci) : Honours level: points and lines in a triangle. Quadrilaterals. Angles in a circle. Circumscribed and inscribed circles. Congruent and similar triangles. Area. Power of a point with respect to a circle. Ceva’s theorem. Isometries. Homothety. Inversion.
Terms: Fall 2018
Instructors: Piotr Przytycki (Fall)

MATH 454 Honours Analysis 3 (3 credits) ++
Overview
Mathematics & Statistics (Sci) : Review of pointset topology: topological space, dense sets, completeness, compactness, connectedness and pathconnectedness, separability. ArzelaAscoli, StoneWeierstrass, Baire category theorems. Measure theory: sigma algebras, Lebesgue measure and integration, L^1 functions. Fatou's lemma, monotone and dominated convergence theorem. Egorov, Lusin's theorems. FubiniTonelli theorem.
Terms: Fall 2018
Instructors: Dmitry Jakobson (Fall)

MATH 455 Honours Analysis 4 (3 credits)
Overview
Mathematics & Statistics (Sci) : Continuation of measure theory. Functional analysis: L^p spaces, linear functionals and dual spaces, HahnBanach theorem, Riesz representation theorem. Hilbert spaces, weak convergence. Spectral theory of compact operator. Introduction to Fourier analysis, Fourier transforms.
Terms: Winter 2019
Instructors: Jerome Vetois (Winter)
Restriction(s): Not open to students who have taken MATH 355.

MATH 456 Honours Algebra 3 (3 credits)
Overview
Mathematics & Statistics (Sci) : Introduction to monoids, groups, permutation groups; the isomorphism theorems for groups; the theorems of Cayley, Lagrange and Sylow; structure of groups of low order. Introduction to ring theory; integral domains, fields, quotient field of an integral domain; polynomial rings; unique factorization domains.
Terms: Fall 2018
Instructors: Michael Pichot (Fall)

MATH 457 Honours Algebra 4 (3 credits)
Overview
Mathematics & Statistics (Sci) : Introduction to modules and algebras; finitely generated modules over a principal ideal domain. Field extensions; finite fields; Galois groups; the fundamental theorem of Galois theory; application to the classical problem of solvability by radicals.
Terms: Winter 2019
Instructors: Michael Pichot (Winter)
Restriction(s): Not open to students who have taken MATH 371.

MATH 458 Honours Differential Geometry (3 credits)
Overview
Mathematics & Statistics (Sci) : In addition to the topics of MATH 320, topics in the global theory of plane and space curves, and in the global theory of surfaces are presented. These include: total curvature and the FaryMilnor theorem on knotted curves, abstract surfaces as 2d manifolds, the Euler characteristic, the GaussBonnet theorem for surfaces.
Terms: Winter 2019
Instructors: Jacques Claude Hurtubise (Winter)

MATH 480 Honours Independent Study (3 credits)
Overview
Mathematics & Statistics (Sci) : Reading projects permitting independent study under the guidance of a staff member specializing in a subject where no appropriate course is available. Arrangements must be made with an instructor and the Chair before registration.
Terms: Fall 2018, Winter 2019
Instructors: Johanna Neslehova, Jacques Claude Hurtubise, Dmitry Jakobson, Sarah Harrison, Dana Louis AddarioBerry, Jonah Gaster (Fall) Johanna Neslehova, Henri Darmon, Michael Lipnowski, Dmitry Jakobson (Winter)
Fall and Winter and Summer
Please see regulations concerning Project Courses under Faculty Degree Requirements
Requires approval by the chair before registration

MATH 488 Honours Set Theory (3 credits)
Overview
Mathematics & Statistics (Sci) : Axioms of set theory, ordinal and cardinal arithmetic, consequences of the axiom of choice, models of set theory, constructible sets and the continuum hypothesis, introduction to independence proofs.
Terms: Winter 2019
Instructors: Marcin Sabok (Winter)

MATH 490 Honours Mathematics of Finance (3 credits)
Overview
Mathematics & Statistics (Sci) : This course consists of the lectures of MATH 430, but will be assessed at the honours level.
Terms: This course is not scheduled for the 20182019 academic year.
Instructors: There are no professors associated with this course for the 20182019 academic year.
++ Not open to students who have taken MATH 354.
All MATH 500level courses.
Other courses with the permission of the Department.