Program Requirement:
Students who wish to study at the Honours level in two Arts disciplines may apply to combine Joint Honours program components from two Arts disciplines. For a list of available Joint Honours programs, see "Overview of Programs Offered" and "Joint Honours Programs".
To remain in the Joint Honours program and receive the Joint Honours degree, a student must maintain the standards set by each discipline, as well as by the Faculty. In the Mathematics courses of the program a GPA of 3.00 and a CGPA of 3.00 must be maintained. Students who have difficulty in maintaining the required level should change to another program before entering their final year.
Program Prerequisites
Students who have not completed the program prerequisite courses listed below or their equivalents will be required to make up any deficiencies in these courses over and above the 36 credits required for the program.

MATH 133
Linear Algebra and Geometry
3 Credits
Offered in the:
 Fall
 Winter
 Summer
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. Linear transformations. Eigenvalues and diagonalization.
Offered by: Mathematics and Statistics
 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, except by permission of the Department of Mathematics and Statistics.
 Restriction C: Not open to students who are taking or have taken MATH 134.
 Terms
 This course is not scheduled for the 20232024 academic year
 Instructors
 There are no professors associated with this course for the 20232024 academic year

MATH 140
Calculus 1
3 Credits
Offered in the:
 Fall
 Winter
 Summer
Mathematics & Statistics (Sci): Review of functions and graphs. Limits, continuity, derivative. Differentiation of elementary functions. Antidifferentiation. Applications.
Offered by: Mathematics and Statistics
 3 hours lecture, 1 hour tutorial
 Prerequisite: High School Calculus
 Restriction: Not open to students who have taken MATH 120, MATH 139 or CEGEP objective 00UN or equivalent
 Restriction: Not open to students who have taken or are taking MATH 122, except by permission of the Department of Mathematics and Statistics
 Each Tutorial section is enrolment limited
 Terms
 This course is not scheduled for the 20232024 academic year
 Instructors
 There are no professors associated with this course for the 20232024 academic year

MATH 141
Calculus 2
4 Credits
Offered in the:
 Fall
 Winter
 Summer
Mathematics & Statistics (Sci): The definite integral. Techniques of integration. Applications. Introduction to sequences and series.
Offered by: Mathematics and Statistics
 Prerequisites: MATH 139 or MATH 140 or MATH 150.
 Restriction: Not open to students who have taken MATH 121 or CEGEP objective 00UP or equivalent
 Restriction Note B: Not open to students who have taken or are taking MATH 122, except by permission of the Department of Mathematics and Statistics.
 Each Tutorial section is enrolment limited
 Terms
 This course is not scheduled for the 20232024 academic year
 Instructors
 There are no professors associated with this course for the 20232024 academic year

MATH 222
Calculus 3
3 Credits
Offered in the:
 Fall
 Winter
 Summer
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
 Terms
 This course is not scheduled for the 20232024 academic year
 Instructors
 There are no professors associated with this course for the 20232024 academic year
Required Courses (9 credits)

MATH 235
Algebra 1
3 Credits
Offered in the:
 Fall
 Winter
 Summer
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.
Offered by: Mathematics and Statistics
 Fall
 3 hours lecture; 1 hour tutorial
 Prerequisite: MATH 133 or equivalent
 Terms
 This course is not scheduled for the 20232024 academic year
 Instructors
 There are no professors associated with this course for the 20232024 academic year

MATH 251
Honours Algebra 2
3 Credits
Offered in the:
 Fall
 Winter
 Summer
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.
Offered by: Mathematics and Statistics
 Winter
 Prerequisites: MATH 235 or permission of the Department
 Restriction: Not open to students who are taking or have taken MATH 247
 Terms
 This course is not scheduled for the 20232024 academic year
 Instructors
 There are no professors associated with this course for the 20232024 academic year

MATH 255
Honours Analysis 2
3 Credits
Offered in the:
 Fall
 Winter
 Summer
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.
Offered by: Mathematics and Statistics
 Terms
 This course is not scheduled for the 20232024 academic year
 Instructors
 There are no professors associated with this course for the 20232024 academic year
Complementary Courses (27 credits)
3 credits selected from:

MATH 242
Analysis 1
3 Credits
Offered in the:
 Fall
 Winter
 Summer
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.
 Terms
 This course is not scheduled for the 20232024 academic year
 Instructors
 There are no professors associated with this course for the 20232024 academic year

MATH 254
Honours Analysis 1
3 Credits*
Offered in the:
 Fall
 Winter
 Summer
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.
Offered by: Mathematics and Statistics
 Prerequisite(s): MATH 141
 Restriction(s): Not open to students who are taking or who have taken MATH 242.
 Terms
 This course is not scheduled for the 20232024 academic year
 Instructors
 There are no professors associated with this course for the 20232024 academic year
* It is strongly recommended that students take MATH 254.
3 credits selected from:

MATH 248
Honours Vector Calculus
3 Credits
Offered in the:
 Fall
 Winter
 Summer
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.
 Terms
 This course is not scheduled for the 20232024 academic year
 Instructors
 There are no professors associated with this course for the 20232024 academic year

MATH 358
Honours Advanced Calculus
3 Credits
Offered in the:
 Fall
 Winter
 Summer
Mathematics & Statistics (Sci): Pointset topology in Euclidean space; continuity and differentiability of functions in several variables. Implicit and inverse function theorems. Vector fields, divergent and curl operations. Rigorous treatment of multiple integrals: volume and surface area; and Fubini’s theorem. Line and surface integrals, conservative vector fields. Green's theorem, Stokes’ theorem and the divergence theorem.
Offered by: Mathematics and Statistics
 Terms
 This course is not scheduled for the 20232024 academic year
 Instructors
 There are no professors associated with this course for the 20232024 academic year
** It is strongly recommended that students take MATH 358.
15 credits selected from the list below. The remaining credits are to be chosen from the full list of available Honours courses in Mathematics and Statistics.
* Not open to students who have taken MATH 354.
** Not open to students who have taken MATH 355.
*** Not open to students who have taken MATH 370.
+ Not open to students who have taken MATH 371.
++ Not open to students who have taken MATH 380.

MATH 325
Honours ODE's
3 Credits
Offered in the:
 Fall
 Winter
 Summer
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
 Terms
 This course is not scheduled for the 20232024 academic year
 Instructors
 There are no professors associated with this course for the 20232024 academic year

MATH 356
Honours Probability
3 Credits
Offered in the:
 Fall
 Winter
 Summer
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.
Offered by: Mathematics and Statistics
 Fall
 Prerequisite(s): MATH 243 or MATH 255, and MATH 222 or permission of the Department.
 Restriction: Not open to students who have taken or are taking MATH 323
 Terms
 This course is not scheduled for the 20232024 academic year
 Instructors
 There are no professors associated with this course for the 20232024 academic year

MATH 357
Honours Statistics
3 Credits
Offered in the:
 Fall
 Winter
 Summer
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.
Offered by: Mathematics and Statistics
 Winter
 Prerequisite: MATH 356 or equivalent
 Restriction: Not open to students who have taken or are taking MATH 324
 Terms
 This course is not scheduled for the 20232024 academic year
 Instructors
 There are no professors associated with this course for the 20232024 academic year

MATH 454
Honours Analysis 3
3 Credits*
Offered in the:
 Fall
 Winter
 Summer
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.
Offered by: Mathematics and Statistics
 Prerequisite: MATH 255 or equivalent.
 Restriction: Not open to students who have taken MATH 354.
 Terms
 This course is not scheduled for the 20232024 academic year
 Instructors
 There are no professors associated with this course for the 20232024 academic year

MATH 455
Honours Analysis 4
3 Credits**
Offered in the:
 Fall
 Winter
 Summer
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.
Offered by: Mathematics and Statistics
 Prerequisite: MATH 454 or equivalent.
 Restriction(s): Not open to students who have taken MATH 355.
 Terms
 This course is not scheduled for the 20232024 academic year
 Instructors
 There are no professors associated with this course for the 20232024 academic year

MATH 456
Honours Algebra 3
3 Credits***
Offered in the:
 Fall
 Winter
 Summer
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.
Offered by: Mathematics and Statistics
 Terms
 This course is not scheduled for the 20232024 academic year
 Instructors
 There are no professors associated with this course for the 20232024 academic year

MATH 457
Honours Algebra 4
3 Credits+
Offered in the:
 Fall
 Winter
 Summer
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.
Offered by: Mathematics and Statistics
 Prerequisite: MATH 456 or equivalent
 Restriction(s): Not open to students who have taken MATH 371.
 Terms
 This course is not scheduled for the 20232024 academic year
 Instructors
 There are no professors associated with this course for the 20232024 academic year

MATH 458
Honours Differential Geometry
3 Credits++
Offered in the:
 Fall
 Winter
 Summer
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.
Offered by: Mathematics and Statistics
 Terms
 This course is not scheduled for the 20232024 academic year
 Instructors
 There are no professors associated with this course for the 20232024 academic year

MATH 466
Honours Complex Analysis
3 Credits
Offered in the:
 Fall
 Winter
 Summer
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.
Offered by: Mathematics and Statistics
 Terms
 This course is not scheduled for the 20232024 academic year
 Instructors
 There are no professors associated with this course for the 20232024 academic year