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to the new course catalogue, the program and course information displayed below may be temporarily unavailable or outdated.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 Minor Concentration (B.A.) (18 credits)
Offered by: Mathematics and Statistics (Faculty of Science)
Degree: Bachelor of Arts; Bachelor of Arts and Science
Program credit weight: 18
Program Description
The Minor Concentration Mathematics is offered in two versions: an expandable version, for students who wish to leave open the option of expanding the program into a Major Concentration Mathematics, and a non-expandable version for students who know on entry into the Minor that they do not wish to expand it into a major concentration.
The Minor Concentration Mathematics may be taken in conjunction with a major concentration in some other discipline under option A of the Multi-track System. Students planning on taking the Major Concentration Mathematics and the Minor Concentration Mathematics as part of Multi-track option C should select the Supplementary Minor Concentration in Mathematics in place of this Minor concentration.
Under option C, it is not possible to combine the Minor Concentration Mathematics and the Minor Concentration Statistics. Students wishing to do this should instead take the Major Concentration Mathematics under option B (two major concentrations) and select a large number of statistics complementaries.
For more information about the Multi-track System options please refer to the Faculty of Arts regulations under "Faculty Degree Requirements", "About Program Requirements", and "Departmental Programs".
No overlap is permitted with other programs.
Note: For information about Fall 2025 and Winter 2026 course offerings, please check back on May 8, 2025. Until then, the "Terms offered" field will appear blank for most courses while the class schedule is being finalized.
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 18 credits required for the program.
| Course | Title | Credits |
|---|---|---|
| MATH 133 | Linear Algebra and Geometry. | 3 |
Linear Algebra and Geometry. Terms offered: Summer 2025 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 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 The definite integral. Techniques of integration. Applications. Introduction to sequences and series. | ||
Expandable Version: Required Courses (12 credits)
| Course | Title | Credits |
|---|---|---|
| MATH 222 | Calculus 3. | 3 |
Calculus 3. Terms offered: Summer 2025 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. | ||
| MATH 235 | Algebra 1. | 3 |
Algebra 1. Terms offered: this course is not currently offered. 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 236 | Algebra 2. 1 | 3 |
Algebra 2. Terms offered: this course is not currently offered. Linear equations over a field. Introduction to vector spaces. Linear mappings. Matrix representation of linear mappings. Determinants. Eigenvectors and eigenvalues. Diagonalizable operators. Cayley-Hamilton theorem. Bilinear and quadratic forms. Inner product spaces, orthogonal diagonalization of symmetric matrices. Canonical forms. | ||
| MATH 315 | Ordinary Differential Equations. | 3 |
Ordinary Differential Equations. Terms offered: this course is not currently offered. First order ordinary differential equations including elementary numerical methods. Linear differential equations. Laplace transforms. Series solutions. | ||
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Note: Credit cannot be received for both MATH 236 Algebra 2. and MATH 223 Linear Algebra. (listed as a required course in the non-expandable version of this Minor concentration).
Expandable Version: Complementary Courses (6 credits)
Students selecting the expandable version of this program complete 6 credits of complementary courses from the Complementary Course List.
It is strongly recommended that students take MATH 323 Probability. as a complementary course.
Non-Expandable Version: Required Courses (9 credits)
| Course | Title | Credits |
|---|---|---|
| MATH 222 | Calculus 3. | 3 |
Calculus 3. Terms offered: Summer 2025 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. | ||
| MATH 223 | Linear Algebra. 1 | 3 |
Linear Algebra. Terms offered: this course is not currently offered. 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. | ||
| MATH 315 | Ordinary Differential Equations. | 3 |
Ordinary Differential Equations. Terms offered: this course is not currently offered. First order ordinary differential equations including elementary numerical methods. Linear differential equations. Laplace transforms. Series solutions. | ||
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Note: Credit cannot be received for both MATH 223 Linear Algebra. and MATH 236 Algebra 2. (listed as a required course in the expandable version of this Minor concentration).
Non-Expandable Version: Complementary Courses (9 credits)
Students selecting the non-expandable version of this program complete 9 credits of complementary courses from the Complementary Course List.
It is strongly recommended that students take MATH 323 Probability. as a complementary course.
Complementary Course List
| Course | Title | Credits |
|---|---|---|
| MATH 249 | Honours Complex Variables. 1 | 3 |
Honours Complex Variables. Terms offered: this course is not currently offered. Functions of a complex variable; Cauchy-Riemann 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; Schwarz-Christoffel transformation; Poisson's integral formulas; applications. Additional topics if time permits: homotopy of paths and simple connectivity, Riemann sphere, rudiments of analytic continuation. | ||
| MATH 314 | Advanced Calculus. | 3 |
Advanced Calculus. Terms offered: this course is not currently offered. 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. | ||
| MATH 316 | Complex Variables. 1 | 3 |
Complex Variables. Terms offered: this course is not currently offered. Algebra of complex numbers, Cauchy-Riemann equations, complex integral, Cauchy's theorems. Taylor and Laurent series, residue theory and applications. | ||
| MATH 317 | Numerical Analysis. | 3 |
Numerical Analysis. Terms offered: this course is not currently offered. Error analysis. Numerical solutions of equations by iteration. Interpolation. Numerical differentiation and integration. Introduction to numerical solutions of differential equations. | ||
| MATH 318 | Mathematical Logic. | 3 |
Mathematical Logic. Terms offered: this course is not currently offered. Propositional logic: truth-tables, formal proof systems, completeness and compactness theorems, Boolean algebras; first-order logic: formal proofs, Gödel's completeness theorem; axiomatic theories; set theory; Cantor's theorem, axiom of choice and Zorn's lemma, Peano arithmetic; Gödel's incompleteness theorem. | ||
| MATH 319 | Partial Differential Equations . | 3 |
Partial Differential Equations . Terms offered: this course is not currently offered. First order equations, geometric theory; second order equations, classification; Laplace, wave and heat equations, Sturm-Liouville theory, Fourier series, boundary and initial value problems. | ||
| MATH 323 | Probability. | 3 |
Probability. Terms offered: Summer 2025 Sample space, events, conditional probability, independence of events, Bayes' Theorem. Basic combinatorial probability, random variables, discrete and continuous univariate and multivariate distributions. Independence of random variables. Inequalities, weak law of large numbers, central limit theorem. | ||
| MATH 324 | Statistics. | 3 |
Statistics. Terms offered: this course is not currently offered. Sampling distributions, point and interval estimation, hypothesis testing, analysis of variance, contingency tables, nonparametric inference, regression, Bayesian inference. | ||
| MATH 326 | Nonlinear Dynamics and Chaos. | 3 |
Nonlinear Dynamics and Chaos. Terms offered: this course is not currently offered. Linear systems of differential equations, linear stability theory. Nonlinear systems: existence and uniqueness, numerical methods, one and two dimensional flows, phase space, limit cycles, Poincare-Bendixson theorem, bifurcations, Hopf bifurcation, the Lorenz equations and chaos. | ||
| MATH 327 | Matrix Numerical Analysis. | 3 |
Matrix Numerical Analysis. Terms offered: this course is not currently offered. An overview of numerical methods for linear algebra applications and their analysis. Problem classes include linear systems, least squares problems and eigenvalue problems. | ||
| MATH 340 | Discrete Mathematics. | 3 |
Discrete Mathematics. Terms offered: this course is not currently offered. Discrete Mathematics and applications. Graph Theory: matchings, planarity, and colouring. Discrete probability. Combinatorics: enumeration, combinatorial techniques and proofs. | ||
| MATH 346 | Number Theory. | 3 |
Number Theory. Terms offered: this course is not currently offered. Divisibility. Congruences. Quadratic reciprocity. Diophantine equations. Arithmetical functions. | ||
| MATH 348 | Euclidean Geometry. | 3 |
Euclidean Geometry. Terms offered: this course is not currently offered. 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. | ||
| MATH 417 | Linear Optimization. | 3 |
Linear Optimization. Terms offered: this course is not currently offered. An introduction to linear optimization and its applications: Duality theory, fundamental theorem, sensitivity analysis, convexity, simplex algorithm, interior-point methods, quadratic optimization, applications in game theory. | ||
| MATH 451 | Introduction to General Topology. | 3 |
Introduction to General Topology. Terms offered: this course is not currently offered. This course is an introduction to point set topology. Topics include basic set theory and logic, topological spaces, separation axioms, continuity, connectedness, compactness, Tychonoff Theorem, metric spaces, and Baire spaces. | ||
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Note: Either MATH 249 Honours Complex Variables. or MATH 316 Complex Variables. may be taken but not both.