Mathematics Joint Honours Component (B.A. & Sc.) (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.
Degree Requirements — B.A. & Sc. students
This program is offered as part of a Bachelor of Arts & Science (B.A. & Sc.) degree.
To graduate, students must satisfy both their program requirements and their degree requirements.
- The program requirements (i.e., the specific courses that make up this program) are listed under the Course Tab (above).
- The degree requirements—including the mandatory Foundation program, appropriate degree structure, and any additional components—are outlined on the Degree Requirements page.
Students are responsible for ensuring that this program fits within the overall structure of their degree and that all degree requirements are met. Consult the Degree Planning Guide on the SOUSA website for additional guidance.
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 133 | Linear 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. | ||
| MATH 140 | Calculus 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. | ||
| MATH 141 | Calculus 2. | 4 |
Calculus 2. Terms offered: Summer 2025, Fall 2025, Winter 2026 The definite integral. Techniques of integration. Applications. Introduction to sequences and series. | ||
| MATH 222 | Calculus 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. | ||
Required Courses (9 credits)
| Course | Title | Credits |
|---|---|---|
| MATH 235 | Algebra 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. | ||
| MATH 251 | Honours 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. | ||
| MATH 255 | Honours 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. | ||
Complementary Courses (27 credits)
3 credits selected from:
| Course | Title | Credits |
|---|---|---|
| MATH 242 | Analysis 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. | ||
| MATH 254 | Honours Analysis 1. 1 | 3 |
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. | ||
- 1
It is strongly recommended that students take MATH 254 Honours Analysis 1..
3 credits selected from:
| Course | Title | Credits |
|---|---|---|
| MATH 248 | Honours 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. | ||
| MATH 358 | Honours Advanced Calculus. 1 | 3 |
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. | ||
- 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 325 | Honours 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. | ||
| MATH 356 | Honours 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. | ||
| MATH 357 | Honours 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. | ||
| MATH 454 | Honours Analysis 3. 1 | 3 |
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. | ||
| MATH 455 | Honours Analysis 4. 2 | 3 |
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. | ||
| MATH 456 | Honours Algebra 3. 3 | 3 |
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. | ||
| MATH 457 | Honours Algebra 4. 4 | 3 |
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. | ||
| MATH 458 | Honours Differential Geometry. 5 | 3 |
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. | ||
| MATH 466 | Honours 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. | ||