Statistics Minor (B.Sc.) (27 credits)
Offered by: Mathematics and Statistics (Faculty of Science)
Degree: Bachelor of Science
Program credit weight: 27
Program Description
(24-27 credits)
Students may complete this program with a minimum of 24 credits or a maximum of 27 credits.
The Minor may be taken in conjunction with any primary program in the Faculty of Science (other than those with a main component in Statistics). Students should declare their intention to follow the Minor Statistics at the beginning of the penultimate year and must obtain approval for the selection of courses to fulfil the requirements for the Minor from the Departmental Chief Adviser (or delegate).
All courses counted towards the Minor must be passed with a grade of C or better. Generally, no more than 6 credits of overlap are permitted between the Minor and the primary program. However, with an approved choice of substantial courses, the overlap restriction may be relaxed to 9 credits for students whose primary program requires 60 credits or more, and to 12 credits when the primary program requires 72 credits or more.
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 (15 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. | 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 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 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. | ||
Complementary Courses (9-12 credits)
9-12 credits selected from:
| Course | Title | Credits |
|---|---|---|
| CHEM 593 | Statistical Mechanics and Machine Learning for Chemistry. | 3 |
Statistical Mechanics and Machine Learning for Chemistry. Terms offered: this course is not currently offered. Intermediate topics in statistical mechanics and related machine learning: ensemble theory, critical phenomena, static and time-dependent phenomena, linear response and fluctuations, Monte Carlo and molecular dynamics simulation methods, data driven simulation methods: MaxEnt modeling, generative machine learning, active learning. | ||
| COMP 451 | Fundamentals of Machine Learning. | 3 |
Fundamentals of Machine Learning. Terms offered: this course is not currently offered. Introduction to the computational, statistical and mathematical foundations of machine learning. Algorithms for both supervised learning and unsupervised learning. Maximum likelihood estimation, neural networks, and regularization. | ||
| 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. | ||
| GEOG 351 | Quantitative Methods. | 3 |
Quantitative Methods. Terms offered: this course is not currently offered. Multiple regression and correlation, logit models, discrete choice models, gravity models, facility location algorithms, survey design, population projection. | ||
| 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 209 | Fundamentals of Statistical Modeling and Inference. | 3 |
Fundamentals of Statistical Modeling and Inference. Terms offered: this course is not currently offered. Introduction to statistical modelling, likelihood principle and maximum likelihood estimation, Bayesian principle and Bayesian estimation, with emphasis on their application in statistical analysis and data science. | ||
| 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 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 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 562 | Theory of Machine Learning. | 4 |
Theory of Machine Learning. Terms offered: this course is not currently offered. Concentration inequalities, PAC model, VC dimension, Rademacher complexity, convex optimization, gradient descent, boosting, kernels, support vector machines, regression and learning bounds. Further topics selected from: Gaussian processes, online learning, regret bounds, basic neural network theory. | ||
| PHYS 362 | Statistical Mechanics. | 3 |
Statistical Mechanics. Terms offered: this course is not currently offered. Quantum states and ensemble averages. Fermi-Dirac, Bose-Einstein and Boltzmann distribution functions and their applications. | ||
| PHYS 559 | Advanced Statistical Mechanics. | 3 |
Advanced Statistical Mechanics. Terms offered: this course is not currently offered. Scattering and structure factors. Review of thermodynamics and statistical mechanics; correlation functions (static); mean field theory; critical phenomena; broken symmetry; fluctuations, roughening. | ||
| SOCI 504 | Quantitative Methods 1. | 3 |
Quantitative Methods 1. Terms offered: this course is not currently offered. An introduction to basic regression techniques commonly used in the social sciences. Covers the least squares linear regression model in depth and may introduce models for discrete dependent variables as well as the maximum-likelihood approach to statistical inference. Emphasis on the assumptions behind regression models and correct interpretation of results. Assignments will emphasize practical aspects of quantitative analysis. | ||
No more than 6 credits from the above list of complementary courses may be taken outside the Department of Mathematics and Statistics.