Statistics Concentration (Supplementary Minor) (18 credits)
Offered by: Mathematics and Statistics (Faculty of Science)
Degree: Bachelor of Arts
Program credit weight: 18
Program Description
Students may complete this program with a minimum of 18 credits or a maximum of 20 credits.
Taken together with the B.A.; Major Concentration in Statistics, this program constitutes an equivalent of the B.Sc.; Major in Statistics program offered by the Faculty of Science. It provides training in statistics, with a mathematical core and basic training in computing. With satisfactory performance in an appropriate selection of courses, these two programs can lead to the accreditation "A.Stat" from the Statistical Society of Canada, which is regarded as the entry level requirement for a statistician practicing in Canada.
This supplementary minor concentration is open only to students registered in the B.A.; Major Concentration in Statistics. Taken together, these two programs constitute a program equivalent to the B.Sc.; Major in Statistics offered by the Faculty of Science. No course overlap between the B.A.; Major Concentration in Statistics and the B.A.; Supplementary Minor Concentration in Statistics is permitted.
Note that according to the Faculty of Arts Multi-Track System degree requirements, option C, students registered in the B.A.; Supplementary Minor Concentration in Statistics must also complete another minor concentration in a discipline other than Mathematics and Statistics. For more information about the Multi-Track System options, please refer to Faculty of Arts regulations under "Faculty Degree Requirements," "About Program Requirements," and "Departmental Programs."
This supplementary minor concentration is open only to students registered in the B.A.; Major Concentration in Statistics. Taken together, these two programs constitute a program equivalent to the B.Sc.; Major in Statistics offered by the Faculty of Science. No course overlap between the B.A.; Major Concentration in Statistics and the B.A.; Supplementary Minor Concentration in Statistics is permitted.
Note that according to the Faculty of Arts Multi-Track System degree requirements, option C, students registered in the B.A.; Supplementary Minor Concentration in Statistics must also complete another minor concentration in a discipline other than Mathematics and Statistics. For more information about the Multi-Track System options, please refer to Faculty of Arts regulations under "Faculty Degree Requirements," "About Program Requirements," and "Departmental Programs."
Guidelines for Course Selection
Students are strongly advised to complete all required courses and all Part I and Part II complementary courses by the end of U2, except for MATH 423 Applied Regression..
Where appropriate, Honours courses may be substituted for equivalent courses. Students planning to pursue graduate studies are encouraged to make such substitutions, and to take MATH 556 Mathematical Statistics 1. and MATH 557 Mathematical Statistics 2. as complementary courses.
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.
Required Courses (6 credits)
| Course | Title | Credits |
|---|---|---|
| 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 423 | Applied Regression. 1 | 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. | ||
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If MATH 423 Applied Regression. has been taken as part of the B.A.; Major Concentration in Statistics, another 3-credit complementary course from Part II must be taken.
Complementary Courses (12-14 credits)
Part I: 3 credits selected from1:
| Course | Title | Credits |
|---|---|---|
| COMP 202 | Foundations of Programming. | 3 |
Foundations of Programming. Terms offered: Summer 2025 Introduction to computer programming in a high level language: variables, expressions, primitive types, methods, conditionals, loops. Introduction to algorithms, data structures (arrays, strings), modular software design, libraries, file input/output, debugging, exception handling. Selected topics. | ||
| COMP 204 | Computer Programming for Life Sciences. | 3 |
Computer Programming for Life Sciences. Terms offered: this course is not currently offered. Computer Science (Sci): Computer programming in a high level language: variables, expressions, types, functions, conditionals, loops, objects and classes. Introduction to algorithms, modular software design, libraries, file input/output, debugging. Emphasis on applications in the life sciences. | ||
| COMP 208 | Computer Programming for Physical Sciences and Engineering . | 3 |
Computer Programming for Physical Sciences and Engineering . Terms offered: this course is not currently offered. Programming and problem solving in a high level computer language: variables, expressions, types, functions, conditionals, loops, objects and classes. Introduction to algorithms such as searching and sorting. Modular software design, libraries, file input and output, debugging. Emphasis on applications in Physical Sciences and Engineering, such as root finding, numerical integration, diffusion, Monte Carlo methods. | ||
| COMP 250 | Introduction to Computer Science. | 3 |
Introduction to Computer Science. Terms offered: this course is not currently offered. Mathematical tools (binary numbers, induction,recurrence relations, asymptotic complexity,establishing correctness of programs). Datastructures (arrays, stacks, queues, linked lists,trees, binary trees, binary search trees, heaps,hash tables). Recursive and non-recursivealgorithms (searching and sorting, tree andgraph traversal). Abstract data types. Objectoriented programming in Java (classes andobjects, interfaces, inheritance). Selected topics. | ||
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Students who have sufficient knowledge in programming are encouraged to take COMP 250 Introduction to Computer Science..
Part II: 3 credits selected from:
| Course | Title | Credits |
|---|---|---|
| COMP 350 | Numerical Computing. 1 | 3 |
Numerical Computing. Terms offered: this course is not currently offered. Computer representation of numbers, IEEE Standard for Floating Point Representation, computer arithmetic and rounding errors. Numerical stability. Matrix computations and software systems. Polynomial interpolation. Least-squares approximation. Iterative methods for solving a nonlinear equation. Discretization methods for integration and differential equations. | ||
| 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. | 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. 1 | 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 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 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 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 350 | Honours Discrete Mathematics . | 3 |
Honours Discrete Mathematics . Terms offered: this course is not currently offered. Discrete mathematics. Graph Theory: matching theory, connectivity, planarity, and colouring; graph minors and extremal graph theory. Combinatorics: combinatorial methods, enumerative and algebraic combinatorics, discrete probability. | ||
| 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 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 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. | ||
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Students can take either MATH 317 Numerical Analysis. or COMP 350 Numerical Computing., but not both.
Part III: 6-8 credits selected from:
| Course | Title | Credits |
|---|---|---|
| COMP 551 | Applied Machine Learning. | 4 |
Applied Machine Learning. Terms offered: this course is not currently offered. Selected topics in machine learning and data mining, including clustering, neural networks, support vector machines, decision trees. Methods include feature selection and dimensionality reduction, error estimation and empirical validation, algorithm design and parallelization, and handling of large data sets. Emphasis on good methods and practices for deployment of real systems. | ||
| 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 410 | Majors Project. 1 | 3 |
Majors Project. Terms offered: this course is not currently offered. A supervised project. | ||
| MATH 420 | Independent Study. 1 | 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 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 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 523 | Generalized Linear Models. | 4 |
Generalized Linear Models. Terms offered: this course is not currently offered. Exponential families, link functions. Inference and parameter estimation for generalized linear models; model selection using analysis of deviance. Residuals. Contingency table analysis, logistic regression, multinomial regression, Poisson regression, log-linear models. Multinomial models. Overdispersion and Quasilikelihood. Applications to experimental and observational data. | ||
| MATH 524 | Nonparametric Statistics. | 4 |
Nonparametric Statistics. Terms offered: this course is not currently offered. Distribution free procedures for 2-sample problem: Wilcoxon rank sum, Siegel-Tukey, Smirnov tests. Shift model: power and estimation. Single sample procedures: Sign, Wilcoxon signed rank tests. Nonparametric ANOVA: Kruskal-Wallis, Friedman tests. Association: Spearman's rank correlation, Kendall's tau. Goodness of fit: Pearson's chi-square, likelihood ratio, Kolmogorov-Smirnov tests. Statistical software packages used. | ||
| MATH 525 | Sampling Theory and Applications. | 4 |
Sampling Theory and Applications. Terms offered: this course is not currently offered. Simple random sampling, domains, ratio and regression estimators, superpopulation models, stratified sampling, optimal stratification, cluster sampling, sampling with unequal probabilities, multistage sampling, complex surveys, nonresponse. | ||
| MATH 527D1 | Statistical Data Science Practicum. 1 | 3 |
Statistical Data Science Practicum. Terms offered: this course is not currently offered. The holistic skills required for doing statistical data science in practice. Data science life cycle from a statistics-centric perspective and from the perspective of a statistician working in the larger data science environment. Group-based projects with industry, government, or university partners. Statistical collaboration and consulting conducted in coordination with the Data Science Solutions Hub (DaS^2H) of the Computational and Data Systems Initiative (CDSI). | ||
| MATH 527D2 | Statistical Data Science Practicum. 1 | 3 |
Statistical Data Science Practicum. Terms offered: this course is not currently offered. See MATH 527D1 for course description. | ||
| MATH 545 | Introduction to Time Series Analysis. | 4 |
Introduction to Time Series Analysis. Terms offered: this course is not currently offered. Stationary processes; estimation and forecasting of ARMA models; non-stationary and seasonal models; state-space models; financial time series models; multivariate time series models; introduction to spectral analysis; long memory models. | ||
| MATH 556 | Mathematical Statistics 1. | 4 |
Mathematical Statistics 1. Terms offered: this course is not currently offered. Distribution theory, stochastic models and multivariate transformations. Families of distributions including location-scale families, exponential families, convolution families, exponential dispersion models and hierarchical models. Concentration inequalities. Characteristic functions. Convergence in probability, almost surely, in Lp and in distribution. Laws of large numbers and Central Limit Theorem. Stochastic simulation. | ||
| MATH 557 | Mathematical Statistics 2. | 4 |
Mathematical Statistics 2. Terms offered: this course is not currently offered. Sufficiency, minimal and complete sufficiency, ancillarity. Fisher and Kullback-Leibler information. Elements of decision theory. Theory of estimation and hypothesis testing from the Bayesian and frequentist perspective. Elements of asymptotic statistics including large-sample behaviour of maximum likelihood estimators, likelihood-ratio tests, and chi-squared goodness-of-fit tests. | ||
| MATH 558 | Design of Experiments. | 4 |
Design of Experiments. Terms offered: this course is not currently offered. Introduction to concepts in statistically designed experiments. Randomization and replication. Completely randomized designs. Simple linear model and analysis of variance. Introduction to blocking. Orthogonal block designs. Models and analysis for block designs. Factorial designs and their analysis. Row-column designs. Latin squares. Model and analysis for fixed row and column effects. Split-plot designs, model and analysis. Relations and operations on factors. Orthogonal factors. Orthogonal decomposition. Orthogonal plot structures. Hasse diagrams. Applications to real data and ethical issues. | ||
| MATH 559 | Bayesian Theory and Methods. | 4 |
Bayesian Theory and Methods. Terms offered: this course is not currently offered. Subjective probability, Bayesian statistical inference and decision making, de Finetti’s representation. Bayesian parametric methods, optimal decisions, conjugate models, methods of prior specification and elicitation, approximation methods. Hierarchical models. Computational approaches to inference, Markov chain Monte Carlo methods, Metropolis—Hastings. Nonparametric Bayesian inference. | ||
| MATH 598 | Topics in Probability and Statistics. | 4 |
Topics in Probability and Statistics. Terms offered: this course is not currently offered. This course covers a topic in probability and/or statistics. | ||
| WCOM 314 | Communicating Science. 1 | 3 |
Communicating Science. Terms offered: this course is not currently offered. Production of written and oral assignments (in English) designed to communicate scientific problems and findings to varied audiences Analysis of the disciplinary conventions of scientific discourse in terms of audience, purpose, organization, and style; comparative rhetorical analysis of academic and popular genres, including abstracts, lab reports, research papers, print and online journalism. | ||
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Students can take at most one of MATH 410 Majors Project., MATH 420 Independent Study., MATH 527D1 Statistical Data Science Practicum./MATH 571D2 and WCOM 314 Communicating Science..