Program Requirements
(2427 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.
Required Courses (15 credits)

MATH 222 Calculus 3 (3 credits)
Overview
Mathematics & Statistics (Sci) : 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.
Terms: Fall 2022, Winter 2023, Summer 2023
Instructors: Paquette, Elliot; Wrobel, Konrad (Fall) Trudeau, Sidney (Winter)

MATH 223 Linear Algebra (3 credits)
Overview
Mathematics & Statistics (Sci) : 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.
Terms: Fall 2022, Winter 2023
Instructors: Macdonald, Jeremy; Pichot, Michael (Fall) Macdonald, Jeremy (Winter)

MATH 323 Probability (3 credits)
Overview
Mathematics & Statistics (Sci) : 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.
Terms: Fall 2022, Winter 2023, Summer 2023
Instructors: Nadarajah, Tharshanna; Sajjad, Alia (Fall) Sajjad, Alia; Asgharian, Masoud (Winter)

MATH 324 Statistics (3 credits)
Overview
Mathematics & Statistics (Sci) : Sampling distributions, point and interval estimation, hypothesis testing, analysis of variance, contingency tables, nonparametric inference, regression, Bayesian inference.
Terms: Fall 2022, Winter 2023
Instructors: Nadarajah, Tharshanna (Fall) Nadarajah, Tharshanna (Winter)
Fall and Winter
Prerequisite: MATH 323 or equivalent
Restriction: Not open to students who have taken or are taking MATH 357
You may not be able to receive credit for this course and other statistic courses. Be sure to check the Course Overlap section under Faculty Degree Requirements in the Arts or Science section of the Calendar.

MATH 423 Applied Regression (3 credits)
Overview
Mathematics & Statistics (Sci) : 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.
Terms: Fall 2022
Instructors: Nadarajah, Tharshanna (Fall)
Complementary Courses (912 credits)
912 credits selected from:

CHEM 593 Statistical Mechanics (3 credits)
Overview
Chemistry : Intermediate topics in statistical mechanics, including: modern and classical theories of real gases and liquids, critical phenomena and the renormalization group, timedependent phenomena, linear response and fluctuations, inelastic scattering, Monte Carlo and molecular dynamics methods.
Terms: This course is not scheduled for the 20222023 academic year.
Instructors: There are no professors associated with this course for the 20222023 academic year.

COMP 451 Fundamentals of Machine Learning (3 credits)
Overview
Computer Science (Sci) : 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.
Terms: Fall 2022
Instructors: Ravanbakhsh, Siamak (Fall)

COMP 551 Applied Machine Learning (4 credits)
Overview
Computer Science (Sci) : 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.
Terms: Fall 2022, Winter 2023
Instructors: Li, Yue (Fall) Rabbany, Reihaneh (Winter)
Prerequisite(s): MATH 323 or ECSE 205 or ECSE 305 or equivalent
Restriction(s): Not open to students who have taken or are taking COMP 451. Not open to students who have taken or are taking ECSE 551.
Some background in Artificial Intelligence is recommended, e.g. COMP424 or ECSE526, but not required.

GEOG 351 Quantitative Methods (3 credits)
Overview
Geography : Multiple regression and correlation, logit models, discrete choice models, gravity models, facility location algorithms, survey design, population projection.
Terms: Winter 2023
Instructors: There are no professors associated with this course for the 20222023 academic year.
Winter
3 hours
Prerequisite: GEOG 202 or equivalent or permission of instructor
You may not be able to get credit for this course and other statistic courses. Be sure to check the Course Overlap section under Faculty Degree Requirements in the Arts or Science section of the Calendar.

MATH 208 Introduction to Statistical Computing (3 credits)
Overview
Mathematics & Statistics (Sci) : 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.
Terms: Fall 2022
Instructors: Steele, Russell (Fall)
Prerequisite(s): MATH 133

MATH 308 Fundamentals of Statistical Learning (3 credits)
Overview
Mathematics & Statistics (Sci) : 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.
Terms: Winter 2023
Instructors: Alam, Shomoita (Winter)

MATH 427 Statistical Quality Control (3 credits)
Overview
Mathematics & Statistics (Sci) : 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.
Terms: This course is not scheduled for the 20222023 academic year.
Instructors: There are no professors associated with this course for the 20222023 academic year.

MATH 447 Introduction to Stochastic Processes (3 credits)
Overview
Mathematics & Statistics (Sci) : 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.
Terms: Winter 2023
Instructors: AddarioBerry, Louigi Dana (Winter)

MATH 523 Generalized Linear Models (4 credits)
Overview
Mathematics & Statistics (Sci) : 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, loglinear models. Multinomial models. Overdispersion and Quasilikelihood. Applications to experimental and observational data.
Terms: Winter 2023
Instructors: Neslehova, Johanna (Winter)

MATH 524 Nonparametric Statistics (4 credits)
Overview
Mathematics & Statistics (Sci) : Distribution free procedures for 2sample problem: Wilcoxon rank sum, SiegelTukey, Smirnov tests. Shift model: power and estimation. Single sample procedures: Sign, Wilcoxon signed rank tests. Nonparametric ANOVA: KruskalWallis, Friedman tests. Association: Spearman's rank correlation, Kendall's tau. Goodness of fit: Pearson's chisquare, likelihood ratio, KolmogorovSmirnov tests. Statistical software packages used.
Terms: Fall 2022
Instructors: Neslehova, Johanna (Fall)

MATH 525 Sampling Theory and Applications (4 credits)
Overview
Mathematics & Statistics (Sci) : 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.
Terms: Winter 2023
Instructors: Yang, Archer Yi (Winter)

MATH 545 Introduction to Time Series Analysis (4 credits)
Overview
Mathematics & Statistics (Sci) : Stationary processes; estimation and forecasting of ARMA models; nonstationary and seasonal models; statespace models; financial time series models; multivariate time series models; introduction to spectral analysis; long memory models.
Terms: This course is not scheduled for the 20222023 academic year.
Instructors: There are no professors associated with this course for the 20222023 academic year.

MATH 556 Mathematical Statistics 1 (4 credits)
Overview
Mathematics & Statistics (Sci) : Distribution theory, stochastic models and multivariate transformations. Families of distributions including locationscale 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.
Terms: Fall 2022
Instructors: Stephens, David (Fall)
Fall
Prerequisite: MATH 357 or equivalent

MATH 557 Mathematical Statistics 2 (4 credits)
Overview
Mathematics & Statistics (Sci) : Sampling theory (including largesample theory). Likelihood functions and information matrices. Hypothesis testing, estimation theory. Regression and correlation theory.
Terms: Winter 2023
Instructors: Asgharian, Masoud (Winter)
Winter
Prerequisite: MATH 556

MATH 558 Design of Experiments (4 credits)
Overview
Mathematics & Statistics (Sci) : 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. Rowcolumn designs. Latin squares. Model and analysis for fixed row and column effects. Splitplot 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.
Terms: Winter 2023
Instructors: Sajjad, Alia (Winter)

MATH 559 Bayesian Theory and Methods (4 credits)
Overview
Mathematics & Statistics (Sci) : 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.
Terms: This course is not scheduled for the 20222023 academic year.
Instructors: There are no professors associated with this course for the 20222023 academic year.

MATH 562 Theory of Machine Learning (4 credits)
Overview
Mathematics & Statistics (Sci) : 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.
Terms: Winter 2023
Instructors: Oberman, Adam (Winter)
Prerequisites: MATH 462 or COMP 451 or (COMP 551, MATH 222, MATH 223 and MATH 324) or ECSE 551.
Restrictions: Not open to students who have taken or are taking COMP 562. Not open to students who have taken COMP 599 when the topic was "Statistical Learning Theory" or "Mathematical Topics for Machine Learning". Not open to students who have taken COMP 598 when the topic was"Mathematical Foundations of Machine Learning".

PHYS 362 Statistical Mechanics (3 credits)
Overview
Physics : Quantum states and ensemble averages. FermiDirac, BoseEinstein and Boltzmann distribution functions and their applications.
Terms: Winter 2023
Instructors: Liu, Adrian (Winter)

PHYS 559 Advanced Statistical Mechanics (3 credits)
Overview
Physics : Scattering and structure factors. Review of thermodynamics and statistical mechanics; correlation functions (static); mean field theory; critical phenomena; broken symmetry; fluctuations, roughening.
Terms: Fall 2022
Instructors: Coish, Bill (Fall)
Fall
3 hours lectures
Restriction: U3 Honours students, graduate students, or permission of the instructor

SOCI 504 Quantitative Methods 1 (3 credits)
Overview
Sociology (Arts) : 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 maximumlikelihood approach to statistical inference. Emphasis on the assumptions behind regression models and correct interpretation of results. Assignments will emphasize practical aspects of quantitative analysis.
Terms: Fall 2022
Instructors: Clark, Shelley (Fall)
No more than 6 credits from the above list of complementary courses may be taken outside the Department of Mathematics and Statistics.