Mathematics Major Concentration (B.A.) (46 credits)
Offered by: Mathematics and Statistics (Faculty of Science)
Degree: Bachelor of Arts
Program credit weight: 46
Program Description
The B.A.; Major Concentration in Mathematics aims to provide an overview of the foundations of mathematics.
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.
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.
Guidelines for Course Selection
Students who received advanced standing or the CEGEP equivalent of the 100-level Math courses listed below are no longer required to take them. Whenever an exemption without credits is granted for a 200-level and above required Math course, the latter must be replaced with a complementary course chosen in consultation with a program advisor.
Where appropriate, Honours-level courses may be substituted for their Majors-level counterparts. Students planning to undertake graduate studies in mathematics are urged to make such substitutions. If there is no major counterpart available for a course, please see a departmental advisor to discuss its inclusion into your program as a complementary course in the lower section.
Students interested in computer science should consider the courses MATH 317, MATH 318, MATH 327, MATH 340, MATH 417, and take the Minor Concentration Computer Science.
Students interested in probability and statistics should consider either taking the Minor Concentration Statistics under option C or taking the major concentration in statistics.
Students interested in applied mathematics should consider the courses MATH 317, MATH 319, MATH 324, MATH 326, MATH 327, and MATH 417.
Students interested in careers in business, industry or government should consider the courses MATH 317, MATH 319, MATH 327, MATH 417, MATH 423, and MATH 447.
Students who have done well in MATH 242 and MATH 235 at the end of their first term should consider, in consultation with their adviser and the instructors of the courses involved, the possibility of entering an Honours program in Mathematics, in Applied Mathematics, in Probability and Statistics, or a Joint Honours program in Mathematics and another discipline.
Required Courses (28 Credits)
| 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. | ||
| 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. | 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 242 | Analysis 1. | 3 |
Analysis 1. Terms offered: this course is not currently offered. A rigorous presentation of sequences and of real numbers and basic properties of continuous and differentiable functions on the real line. | ||
| MATH 243 | Analysis 2. | 3 |
Analysis 2. Terms offered: this course is not currently offered. Definition and properties of Riemann integral, Fundamental Theorem of Calculus, Taylor's theorem. Infinite series: alternating, telescoping series, rearrangements, conditional and absolute convergence, convergence tests. Power series and Taylor series. Elementary functions. Introduction to metric spaces. | ||
| 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. | ||
Complementary Courses (18 Credits)
9-18 credits from:
| 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 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. | ||
| 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 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 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 378 | Nonlinear Optimization . | 3 |
Nonlinear Optimization . Terms offered: this course is not currently offered. Optimization terminology. Convexity. First- and second-order optimality conditions for unconstrained problems. Numerical methods for unconstrained optimization: Gradient methods, Newton-type methods, conjugate gradient methods, trust-region methods. Least squares problems (linear + nonlinear). Optimality conditions for smooth constrained optimization problems (KKT theory). Lagrangian duality. Augmented Lagrangian methods. Active-set method for quadratic programming. SQP methods. | ||
| 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. | ||
- 1
Note: Either MATH 249 Honours Complex Variables. or MATH 316 Complex Variables. may be taken but not both.
0-3 credits from:
| Course | Title | Credits |
|---|---|---|
| MATH 329 | Theory of Interest. | 3 |
Theory of Interest. Terms offered: this course is not currently offered. Simple and compound interest, annuities certain, amortization schedules, bonds, depreciation. | ||
| MATH 338 | History and Philosophy of Mathematics. | 3 |
History and Philosophy of Mathematics. Terms offered: this course is not currently offered. 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, culminating in the discovery of the infinitesimal and integral calculus by Newton and Leibnitz. Demonstration of how mathematics was done in past centuries, and involves the practice of mathematics, including detailed calculations, arguments based on geometric reasoning, and proofs. | ||
0-9 credits from:
| Course | Title | Credits |
|---|---|---|
| MATH 208 | Introduction to Statistical Computing. | 3 |
Introduction to Statistical Computing. Terms offered: this course is not currently offered. Basic data management. Data visualization. Exploratory data analysis and descriptive statistics. Writing functions. Simulation and parallel computing. Communication data and documenting code for reproducible research. | ||
| MATH 308 | Fundamentals of Statistical Learning. | 3 |
Fundamentals of Statistical Learning. Terms offered: this course is not currently offered. Theory and application of various techniques for the exploration and analysis of multivariate data: principal component analysis, correspondence analysis, and other visualization and dimensionality reduction techniques; supervised and unsupervised learning; linear discriminant analysis, and clustering techniques. Data applications using appropriate software. | ||
| 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 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 335 | Groups, Tilings and Algorithms. | 3 |
Groups, Tilings and Algorithms. Terms offered: this course is not currently offered. Transformation groups of the plane. Inversions and Moebius transformations. The hyperbolic plane. Tilings in dimension 2 and 3. Group presentations and Cayley graphs. Free groups and Schreier's theorem. Coxeter groups. Dehn's Word and Conjugacy Problems. Undecidability of the Word Problem for semigroups. Regular languages and automatic groups. Automaticity of Coxeter groups. | ||
| 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 352 | Problem Seminar. | 1 |
Problem Seminar. Terms offered: this course is not currently offered. 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. | ||
| MATH 410 | Majors Project. | 3 |
Majors Project. Terms offered: this course is not currently offered. A supervised project. | ||
| MATH 420 | Independent Study. | 3 |
Independent Study. Terms offered: this course is not currently offered. 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. | ||
| MATH 423 | Applied Regression. | 3 |
Applied Regression. Terms offered: this course is not currently offered. Multiple regression estimators and their properties. Hypothesis tests and confidence intervals. Analysis of variance. Prediction and prediction intervals. Model diagnostics. Model selection. Introduction to weighted least squares. Basic contingency table analysis. Introduction to logistic and Poisson regression. Applications to experimental and observational data. | ||
| MATH 427 | Statistical Quality Control. | 3 |
Statistical Quality Control. Terms offered: this course is not currently offered. Introduction to quality management; variability and productivity. Quality measurement: capability analysis, gauge capability studies. Process control: control charts for variables and attributes. Process improvement: factorial designs, fractional replications, response surface methodology, Taguchi methods. Acceptance sampling: operating characteristic curves; single, multiple and sequential acceptance sampling plans for variables and attributes. | ||
| MATH 430 | Mathematical Finance. | 3 |
Mathematical Finance. Terms offered: this course is not currently offered. Introduction to concepts of price and hedge derivative securities. The following concepts will be studied in both concrete and continuous time: filtrations, martingales, the change of measure technique, hedging, pricing, absence of arbitrage opportunities and the Fundamental Theorem of Asset Pricing. | ||
| MATH 447 | Introduction to Stochastic Processes. | 3 |
Introduction to Stochastic Processes. Terms offered: this course is not currently offered. Conditional probability and conditional expectation, generating functions. Branching processes and random walk. Markov chains, transition matrices, classification of states, ergodic theorem, examples. Birth and death processes, queueing theory. | ||
| MATH 463 | Convex Optimization. | 3 |
Convex Optimization. Terms offered: this course is not currently offered. Introduction to convex analysis and convex optimization: Convex sets and functions, subdifferential calculus, conjugate functions, Fenchel duality, proximal calculus. Subgradient methods, proximal-based methods. Conditional gradient method, ADMM. Applications including data classification, network-flow problems, image processing, convex feasibility problems, DC optimization, sparse optimization, and compressed sensing. | ||
| MATH 478 | Computational Methods in Applied Mathematics . | 3 |
Computational Methods in Applied Mathematics . Terms offered: this course is not currently offered. 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, Navier-Stokes equations | ||