Statistics Major Concentration (B.A. & Sc.) (46 credits)
Offered by: Mathematics and Statistics (Faculty of Science)
Degree: Bachelor of Arts; Bachelor of Arts and Science
Program credit weight: 46
Program Description
The program provides training in statistics with a mathematical core. Taken together with the B.A.; Supplementary Minor Concentration in Statistics, these two programs constitute an equivalent of the B.Sc.; Major in Statistics program offered by the Faculty of Science. 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. Students interested in this accreditation should consult an academic advisor.
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.
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.
Students are strongly advised to complete all required courses by the end of U2.
Where appropriate, Honours courses may be substituted for equivalent courses. Students planning to pursue
graduate studies are encouraged to make such substitutions.
Required Courses (34 credits)
| 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 203 | Principles of Statistics 1. 1 | 3 |
Principles of Statistics 1. Terms offered: Summer 2025, Fall 2025, Winter 2026 Examples of statistical data and the use of graphical means to summarize the data. Basic distributions arising in the natural and behavioural sciences. The logical meaning of a test of significance and a confidence interval. Tests of significance and confidence intervals in the one and two sample setting (means, variances and proportions). | ||
| MATH 204 | Principles of Statistics 2. 2 | 3 |
Principles of Statistics 2. Terms offered: Winter 2026 The concept of degrees of freedom and the analysis of variability. Planning of experiments. Experimental designs. Polynomial and multiple regressions. Statistical computer packages (no previous computing experience is needed). General statistical procedures requiring few assumptions about the probability model. | ||
| MATH 208 | Introduction to Statistical Computing. | 3 |
Introduction to Statistical Computing. Terms offered: Fall 2025 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 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. | ||
| MATH 223 | Linear Algebra. | 3 |
Linear Algebra. Terms offered: Fall 2025, Winter 2026 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 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 323 | Probability. | 3 |
Probability. Terms offered: Summer 2025, Fall 2025, Winter 2026 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. 2 | 3 |
Statistics. Terms offered: Fall 2025, Winter 2026 Sampling distributions, point and interval estimation, hypothesis testing, analysis of variance, contingency tables, nonparametric inference, regression, Bayesian inference. | ||
- 1
Students who have taken an equivalent of MATH 203 Principles of Statistics 1. at CEGEP or elsewhere must replace it by another course from the Complementary course list.
- 2
Students must take MATH 204 Principles of Statistics 2. before taking MATH 324 Statistics..
Complementary Courses (12 credits)
12 credits from:
| Course | Title | Credits |
|---|---|---|
| COMP 551 | Applied Machine Learning. | 4 |
Applied Machine Learning. Terms offered: Fall 2025, Winter 2026 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: Winter 2026 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: Summer 2025, Fall 2025, Winter 2026 A supervised project. | ||
| MATH 420 | Independent Study. 1 | 3 |
Independent Study. Terms offered: Summer 2025, Fall 2025, Winter 2026 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: Fall 2025 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: Fall 2025 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: Winter 2026 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: Winter 2026 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: Fall 2025 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: Winter 2026 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: Fall 2025 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: Winter 2026 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: Fall 2025 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: Winter 2026 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 & Statistics | 4 |
Topics in Probability Statistics Terms offered: Fall 2025, Winter 2026 This course covers a topic in probability and/or statistics. | ||
| WCOM 314 | Communicating Science. 1 | 3 |
Communicating Science. Terms offered: Fall 2025, Winter 2026 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. | ||
- 1
Students can take at most one of MATH 410 Majors Project., MATH 420 Independent Study., MATH 527D1 Statistical Data Science Practicum./MATH 527D2 Statistical Data Science Practicum. and WCOM 314 Communicating Science..