Offered by:Mathematics and Statistics
Degree:Bachelor of Science
Program Requirement:
(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
Offered in the:
 Fall
 Winter
 Summer
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.
Offered by: Mathematics and Statistics
 Terms
 Instructors
 Brent Pym, Damien Tageddine

MATH 223
Linear Algebra
3 Credits
Offered in the:
 Fall
 Winter
 Summer
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.
Offered by: Mathematics and Statistics
 Terms
 Instructors
 Shereen Elaidi, Hugues Bellemare
 Jeremy Macdonald

MATH 323
Probability
3 Credits
Offered in the:
 Fall
 Winter
 Summer
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.
Offered by: Mathematics and Statistics
 Prerequisites: MATH 141 or equivalent.
 Restriction: Intended for students in Science, Engineering and related disciplines, who have had differential and integral calculus
 Restriction: Not open to students who have taken or are taking MATH 356
 Terms
 Instructors
 Alia Sajjad
 Tharshanna Nadarajah

MATH 324
Statistics
3 Credits
Offered in the:
 Fall
 Winter
 Summer
Mathematics & Statistics (Sci): Sampling distributions, point and interval estimation, hypothesis testing, analysis of variance, contingency tables, nonparametric inference, regression, Bayesian inference.
Offered by: Mathematics and Statistics
 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.
 Terms
 Instructors
 Tharshanna Nadarajah
 Masoud Asgharian

MATH 423
Applied Regression
3 Credits
Offered in the:
 Fall
 Winter
 Summer
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.
Offered by: Mathematics and Statistics
Complementary Courses (912 credits)
912 credits selected from:

CHEM 593
Statcl Mechs&MchnLrng for Chem
3 Credits
Offered in the:
 Fall
 Winter
 Summer
Chemistry: Intermediate topics in statistical mechanics and related machine learning: ensemble theory, critical phenomena, static and timedependent phenomena, linear response and fluctuations, Monte Carlo and molecular dynamics simulation methods, data driven simulation methods: MaxEnt modeling, generative machine learning, active learning.
Offered by: Chemistry

COMP 451
Fundls of Machine Learning
3 Credits
Offered in the:
 Fall
 Winter
 Summer
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.
Offered by: Computer Science

COMP 551
Applied Machine Learning
4 Credits
Offered in the:
 Fall
 Winter
 Summer
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.
Offered by: Computer Science
 Terms
 Instructors
 Isabeau PrémontSchwarz, Reihaneh Rabbany
 Yue Li

GEOG 351
Quantitative Methods
3 Credits
Offered in the:
 Fall
 Winter
 Summer
Geography: Multiple regression and correlation, logit models, discrete choice models, gravity models, facility location algorithms, survey design, population projection.
Offered by: Geography
 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
Intro to Statistical Computing
3 Credits
Offered in the:
 Fall
 Winter
 Summer
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.
Offered by: Mathematics and Statistics

MATH 209
FundlsofStatclModlng&Infrnce
3 Credits
Offered in the:
 Fall
 Winter
 Summer
Mathematics & Statistics (Sci): 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.
Offered by: Mathematics and Statistics

MATH 308
Fundls of Statistical Learning
3 Credits
Offered in the:
 Fall
 Winter
 Summer
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.
Offered by: Mathematics and Statistics

MATH 427
Statistical Quality Control
3 Credits
Offered in the:
 Fall
 Winter
 Summer
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.
Offered by: Mathematics and Statistics
 Terms
 This course is not scheduled for the 20242025 academic year
 Instructors
 There are no professors associated with this course for the 20242025 academic year

MATH 447
Intro. to Stochastic Processes
3 Credits
Offered in the:
 Fall
 Winter
 Summer
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.
Offered by: Mathematics and Statistics
 Winter
 Prerequisite: MATH 323
 Restriction: Not open to students who have taken or are taking MATH 547.

MATH 523
Generalized Linear Models
4 Credits
Offered in the:
 Fall
 Winter
 Summer
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.
Offered by: Mathematics and Statistics

MATH 524
Nonparametric Statistics
4 Credits
Offered in the:
 Fall
 Winter
 Summer
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.
Offered by: Mathematics and Statistics
 Fall
 Prerequisite: MATH 324 or equivalent
 Restriction: Not open to students who have taken MATH 424

MATH 525
Sampling Theory & Applications
4 Credits
Offered in the:
 Fall
 Winter
 Summer
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.
Offered by: Mathematics and Statistics
 Prerequisite: MATH 324 or equivalent
 Restriction: Not open to students who have taken MATH 425

MATH 545
Intro to Time Series Analysis
4 Credits
Offered in the:
 Fall
 Winter
 Summer
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.
Offered by: Mathematics and Statistics

MATH 556
Mathematical Statistics 1
4 Credits
Offered in the:
 Fall
 Winter
 Summer
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.
Offered by: Mathematics and Statistics

MATH 557
Mathematical Statistics 2
4 Credits
Offered in the:
 Fall
 Winter
 Summer
Mathematics & Statistics (Sci): Sufficiency, minimal and complete sufficiency, ancillarity. Fisher and KullbackLeibler
information. Elements of decision theory. Theory of estimation and hypothesis testing from the Bayesian and frequentist perspective. Elements of asymptotic statistics including largesample behaviour of maximum likelihood estimators, likelihoodratio tests, and chisquared goodnessoffit tests.
Offered by: Mathematics and Statistics

MATH 558
Design of Experiments
4 Credits
Offered in the:
 Fall
 Winter
 Summer
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.
Offered by: Mathematics and Statistics

MATH 559
Bayesian Theory and Methods
4 Credits
Offered in the:
 Fall
 Winter
 Summer
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.
Offered by: Mathematics and Statistics
 Terms
 This course is not scheduled for the 20242025 academic year
 Instructors
 There are no professors associated with this course for the 20242025 academic year

MATH 562
Theory of Machine Learning
4 Credits
Offered in the:
 Fall
 Winter
 Summer
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.
Offered by: Mathematics and Statistics
 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".
 Terms
 This course is not scheduled for the 20242025 academic year
 Instructors
 There are no professors associated with this course for the 20242025 academic year

PHYS 362
Statistical Mechanics
3 Credits
Offered in the:
 Fall
 Winter
 Summer
Physics: Quantum states and ensemble averages. FermiDirac, BoseEinstein and Boltzmann distribution functions and their applications.
Offered by: Physics
 Winter
 3 hours lectures
 Prerequisites: MATH 248 or equivalents, PHYS 253.
 Restriction: Honours students, or permission of the instructor
 Restriction: Not open to students taking or having passed PHYS 333
 Terms
 Instructors
 Jack C Sankey (Childress)

PHYS 559
Advanced Statistical Mechanics
3 Credits
Offered in the:
 Fall
 Winter
 Summer
Physics: Scattering and structure factors. Review of thermodynamics and statistical mechanics; correlation functions (static); mean field theory; critical phenomena; broken symmetry; fluctuations, roughening.
Offered by: Physics
 Fall
 3 hours lectures
 Restriction: U3 Honours students, graduate students, or permission of the instructor

SOCI 504
Quantitative Methods 1
3 Credits
Offered in the:
 Fall
 Winter
 Summer
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.
Offered by: Sociology
No more than 6 credits from the above list of complementary courses may be taken outside the Department of Mathematics and Statistics.