Minor Statistics (B. Sc.)

Offered by:Mathematics and Statistics
Degree:Bachelor of Science

Program Requirement:

(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.

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

  • Prerequisite: MATH 141. Familiarity with vector geometry or Corequisite: MATH 133
  • Restriction: Not open to students who have taken MATH 150, MATH 151 or MATH 262.

  • Terms
    • Fall 2023
    • Winter 2024
    • Summer 2024
  • Instructors
    • Patrick Allen, Marcin Sabok
    • Sidney Trudeau
• 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

  • Fall and Winter
  • Prerequisite: MATH 133 or equivalent
  • Restriction: Not open to students in Mathematics programs nor to students who have taken or are taking MATH 236, MATH 247 or MATH 251. It is open to students in Faculty Programs

  • Terms
    • Fall 2023
    • Winter 2024
  • Instructors
    • Djivede A Kelome, Mikael Y Pichot
    • Mikael Y Pichot
• 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
    • Fall 2023
    • Winter 2024
    • Summer 2024
  • Instructors
    • Alia Sajjad, Tharshanna Nadarajah
    • 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
    • Fall 2023
    • Winter 2024
  • Instructors
    • Tharshanna Nadarajah
    • Oliver Russell
• 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

  • Fall
  • Prerequisites: MATH 324, and MATH 223 or MATH 236

  • Terms
    • Fall 2023
  • Instructors
    • Tharshanna Nadarajah

Complementary Courses (9-12 credits)

9-12 credits selected from:

• CHEM 593 Statistical Mechanics 3 Credits

  Offered in the:
  • Fall
  • Winter
  • Summer

  
  

  Chemistry: Intermediate topics in statistical mechanics, including: modern and classical theories of real gases and liquids, critical phenomena and the renormalization group, time-dependent phenomena, linear response and fluctuations, inelastic scattering, Monte Carlo and molecular dynamics methods.

  Offered by: Chemistry

  • Winter
  • Term paper
  • Prerequisite: CHEM 345. Recommended: CHEM 365

  • Terms
    • Winter 2024
  • Instructors
    • Yelena Simine
• 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

  • Prerequisite: COMP 251, MATH 222, MATH 223, and MATH 323.
  • Restriction: Not open to students who are taking or have taken COMP 551.

  • Terms
    • Fall 2023
  • Instructors
    • Siamak Ravanbakhsh
• 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

  • Prerequisite(s): MATH 323 or ECSE 205, COMP 202, MATH 133, MATH 222 (or their equivalents).
  • Restriction(s): Not open to students who have taken or are taking COMP 451, ECSE 551, or PSYC 560.
  • Some background in Artificial Intelligence is recommended, e.g. COMP-424 or ECSE-526, but not required.

  • Terms
    • Fall 2023
    • Winter 2024
  • Instructors
    • Isabeau Prémont-Schwarz, Reihaneh Rabbany
    • Yue Li, Isabeau Prémont-Schwarz
• 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.

  • Terms
    • Winter 2024
  • Instructors
    • There are no professors associated with this course for the 2023-2024 academic year
• 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

  • Prerequisite(s): MATH 133

  • Terms
    • Fall 2023
  • Instructors
    • Kiwon Lee
• 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

  • Prerequisite(s): MATH 208, one of MATH 223, MATH 236, MATH 247, MATH 251; MATH 323 or MATH 356.

  • Terms
    • Winter 2024
  • Instructors
    • Archer Yi Yang
• 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

  • Prerequisites: MATH 203 or equivalent, and MATH 204 or MATH 324.

  • Terms
    • This course is not scheduled for the 2023-2024 academic year
  • Instructors
    • There are no professors associated with this course for the 2023-2024 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.

  • Terms
    • Winter 2024
  • Instructors
    • Elizabeth W Collins-Woodfin
• 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, log-linear models. Multinomial models. Overdispersion and Quasilikelihood. Applications to experimental and observational data.

  Offered by: Mathematics and Statistics

  • Winter
  • Prerequisite: MATH 423 or MATH 533 or EPIB 697.

  • Terms
    • Winter 2024
  • Instructors
    • Russell Steele
• MATH 524 Nonparametric Statistics 4 Credits

  Offered in the:
  • Fall
  • Winter
  • Summer

  
  

  Mathematics & Statistics (Sci): 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.

  Offered by: Mathematics and Statistics

  • Fall
  • Prerequisite: MATH 324 or equivalent
  • Restriction: Not open to students who have taken MATH 424

  • Terms
    • This course is not scheduled for the 2023-2024 academic year
  • Instructors
    • There are no professors associated with this course for the 2023-2024 academic year
• 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

  • Terms
    • Winter 2024
  • Instructors
    • Mohamed Mehdi Dagdoug
• 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; non-stationary and seasonal models; state-space models; financial time series models; multivariate time series models; introduction to spectral analysis; long memory models.

  Offered by: Mathematics and Statistics

  • Prerequisite: MATH 324 or MATH 357 or equivalent

  • Terms
    • This course is not scheduled for the 2023-2024 academic year
  • Instructors
    • There are no professors associated with this course for the 2023-2024 academic year
• 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 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.

  Offered by: Mathematics and Statistics

  • Fall
  • Prerequisite: MATH 357 or equivalent

  • Terms
    • Fall 2023
  • Instructors
    • Masoud Asgharian
• MATH 557 Mathematical Statistics 2 4 Credits

  Offered in the:
  • Fall
  • Winter
  • Summer

  
  

  Mathematics & Statistics (Sci): Sampling theory (including large-sample theory). Likelihood functions and information matrices. Hypothesis testing, estimation theory. Regression and correlation theory.

  Offered by: Mathematics and Statistics

  • Winter
  • Prerequisite: MATH 556

  • Terms
    • Winter 2024
  • Instructors
    • Masoud Asgharian
• 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. 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.

  Offered by: Mathematics and Statistics

  • Prerequisites: MATH 223, MATH 236, MATH 247, MATH 251, or equivalent. MATH 208 or equivalent. MATH 324, MATH 357, or equivalent.

  • Terms
    • Winter 2024
  • Instructors
    • Alia Sajjad
• 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

  • Prerequisite: MATH 324, MATH 357, MATH 557, or equivalent, and MATH 208 or equivalent.

  • Terms
    • Fall 2023
  • Instructors
    • David A Stephens
• 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 2023-2024 academic year
  • Instructors
    • There are no professors associated with this course for the 2023-2024 academic year
• PHYS 362 Statistical Mechanics 3 Credits

  Offered in the:
  • Fall
  • Winter
  • Summer

  
  

  Physics: Quantum states and ensemble averages. Fermi-Dirac, Bose-Einstein 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
    • Winter 2024
  • Instructors
    • Adrian C Liu
• 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

  • Terms
    • Fall 2023
  • Instructors
    • Bill Coish
• 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 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.

  Offered by: Sociology

  • Prerequisites: SOCI 350 and SOCI 461 or equivalents

  • Terms
    • Fall 2023
  • Instructors
    • Shelley D Clark

No more than 6 credits from the above list of complementary courses may be taken outside the Department of Mathematics and Statistics.