Joint Honours Component (B. A.)

Please note: Due to the ongoing transition to the new course catalogue, the program and course information displayed below may be temporarily unavailable or outdated. In particular, details about whether a course will be offered in an upcoming term may be inaccurate. Official course scheduling information for Fall 2025 will be available on Minerva during the first week of May. We appreciate your patience and understanding during this transition.


Mathematics Joint Honours Component (B.A.) (36 credits)

Offered by: Mathematics and Statistics (Faculty of Science)
Degree: Bachelor of Arts; Bachelor of Arts and Science
Program credit weight: 36

Program Description

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.

Degree Requirements — B.A. students

To be eligible for a B.A. degree, a student must fulfil all Faculty and program requirements as indicated in Degree Requirements for the Faculty of Arts.

We recommend that students consult an Arts OASIS advisor for degree planning.

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.

Course Title Credits
MATH 133Linear Algebra and Geometry.3

Linear Algebra and Geometry.

Terms offered: Summer 2025, Fall 2025, Winter 2026

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.

See course page for more information

MATH 140Calculus 1.3

Calculus 1.

Terms offered: Summer 2025, Fall 2025, Winter 2026

Review of functions and graphs. Limits, continuity, derivative. Differentiation of elementary functions. Antidifferentiation. Applications.

See course page for more information

MATH 141Calculus 2.4

Calculus 2.

Terms offered: Summer 2025, Fall 2025, Winter 2026

The definite integral. Techniques of integration. Applications. Introduction to sequences and series.

See course page for more information

MATH 222Calculus 3.3

Calculus 3.

Terms offered: Summer 2025, Fall 2025, Winter 2026

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.

See course page for more information

Required Courses (9 credits)

Course Title Credits
MATH 235Algebra 1.3

Algebra 1.

Terms offered: Fall 2025

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; homomorphisms and quotient groups.

See course page for more information

MATH 251Honours Algebra 2.3

Honours Algebra 2.

Terms offered: Winter 2026

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 self-adjoint operators.

See course page for more information

MATH 255Honours Analysis 2.3

Honours Analysis 2.

Terms offered: Winter 2026

Basic point-set topology, metric spaces: open and closed sets, normed and Banach spaces, Hölder and Minkowski inequalities, sequential compactness, Heine-Borel, Banach Fixed Point theorem. Riemann-(Stieltjes) integral, Fundamental Theorem of Calculus, Taylor's theorem. Uniform convergence. Infinite series, convergence tests, power series. Elementary functions.

See course page for more information

Complementary Courses (27 credits)

3 credits selected from:

Course Title Credits
MATH 242Analysis 1.3

Analysis 1.

Terms offered: Fall 2025

A rigorous presentation of sequences and of real numbers and basic properties of continuous and differentiable functions on the real line.

See course page for more information

MATH 254Honours Analysis 1. 13

Honours Analysis 1.

Terms offered: Fall 2025

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.

See course page for more information

1

It is strongly recommended that students take MATH 254 Honours Analysis 1..

3 credits selected from:

Course Title Credits
MATH 248Honours Vector Calculus.3

Honours Vector Calculus.

Terms offered: Fall 2025

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.

See course page for more information

MATH 358Honours Advanced Calculus. 13

Honours Advanced Calculus.

Terms offered: Winter 2026

Point-set 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.

See course page for more information

1

It is strongly recommended that students take MATH 358 Honours Advanced Calculus..

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.

Course Title Credits
MATH 325Honours Ordinary Differential Equations.3

Honours Ordinary Differential Equations.

Terms offered: Winter 2026

First and second order equations, linear equations, series solutions, Frobenius method, introduction to numerical methods and to linear systems, Laplace transforms, applications.

See course page for more information

MATH 356Honours Probability.3

Honours Probability.

Terms offered: Fall 2025

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, uni-variate transformations. Random vectors, independence, correlation, multivariate transformations. Conditional distributions, conditional expectation.Modes of stochastic convergence, laws of large numbers, Central Limit Theorem.

See course page for more information

MATH 357Honours Statistics.3

Honours Statistics.

Terms offered: Winter 2026

Sampling distributions. Point estimation. Minimum variance unbiased estimators, sufficiency, and completeness. Confidence intervals. Hypothesis tests, Neyman-Pearson Lemma, uniformly most powerful tests. Likelihood ratio tests for normal samples. Asymptotic sampling distributions and inference.

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MATH 454Honours Analysis 3. 13

Honours Analysis 3.

Terms offered: Fall 2025

Measure theory: sigma-algebras, Lebesgue measure in R^n and integration, L^1 functions, Fatou's lemma, monotone and dominated convergence theorem, Egorov’s theorem, Lusin's theorem, Fubini-Tonelli theorem, differentiation of the integral, differentiability of functions of bounded variation, absolutely continuous functions, fundamental theorem of calculus.

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MATH 455Honours Analysis 4. 23

Honours Analysis 4.

Terms offered: Winter 2026

Review of point-set topology: topological spaces, dense sets, completeness, compactness, connectedness and path-connectedness, separability, Baire category theorem, Arzela-Ascoli theorem, Stone-Weierstrass theorem..Functional analysis: L^p spaces, linear functionals and dual spaces, Hilbert spaces, Riesz representation theorems. Fourier series and transform, Riemann-Lebesgue Lemma,Fourier inversion formula, Plancherel theorem, Parseval’s identity, Poisson summation formula.

See course page for more information

MATH 456Honours Algebra 3. 33

Honours Algebra 3.

Terms offered: Fall 2025

Groups, quotient groups and the isomorphism theorems. Group actions. Groups of prime order and the class equation. Sylow's theorems. Simplicity of the alternating group. Semidirect products. Principal ideal domains and unique factorization domains. Modules over a ring. Finitely generated modules over a principal ideal domain with applications to canonical forms.

See course page for more information

MATH 457Honours Algebra 4. 43

Honours Algebra 4.

Terms offered: Winter 2026

Representations of finite groups. Maschke's theorem. Schur's lemma. Characters, their orthogonality, and character tables. Field extensions. Finite and cyclotomic fields. Galois extensions and Galois groups. The fundamental theorem of Galois theory. Solvability by radicals.

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MATH 458Honours Differential Geometry. 53

Honours Differential Geometry.

Terms offered: Winter 2026

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 Fary-Milnor theorem on knotted curves, abstract surfaces as 2-d manifolds, the Euler characteristic, the Gauss-Bonnet theorem for surfaces.

See course page for more information

MATH 466Honours Complex Analysis.3

Honours Complex Analysis.

Terms offered: this course is not currently offered.

Functions of a complex variable, Cauchy-Riemann 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.

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