91Ë¿¹ÏÊÓƵ

Program Requirements

The Minor Concentration Statistics is offered only in a non-expandable version, that is, one that cannot be expanded into the Major Concentration Mathematics.

The Minor Concentration Statistics may be taken in conjunction with a major concentration in some other discipline under option A of the Multi-track System, or together with the Major Concentration Mathematics and a minor concentration (which must be in some other discipline than Mathematics) under option C.

Under option C, it is not possible to combine the Minor Concentration Statistics and the Minor Concentration Mathematics. Students wishing to do this should instead take the Major Concentration Mathematics under option B (two major concentrations) and select a large number of statistics complementaries.

For more information about the Multi-track System options please refer to the Faculty of Arts regulations under "Faculty Degree Requirements", "About Program Requirements", and "Departmental Programs".

No overlap is permitted with other programs.

Program Prerequisites

Students who have not completed the program prerequisite courses listed below or their equivalents will be required to make up any deficiencies in these courses over and above the 18 credits required for the program.

• MATH 133 Linear Algebra and Geometry (3 credits)

  Offered by: Mathematics and Statistics (Faculty of Science)

  Overview

  Mathematics & Statistics (Sci) : 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.

  Terms: Fall 2022, Winter 2023, Summer 2023

  Instructors: Bélanger-Rioux, Rosalie; Mazakian, Hovsep; Gerbelli-Gauthier, Mathilde; Alfieri, Antonio (Fall) Duchesne, Gabriel William (Winter) Leroux-Lapierre, Alexis (Summer)

  • 3 hours lecture, 1 hour tutorial

  • Prerequisite: a course in functions

  • Restriction A: Not open to students who have taken MATH 221 or CEGEP objective 00UQ or equivalent.

  • Restriction B: Not open to students who have taken or are taking MATH 123, except by permission of the Department of Mathematics and Statistics.

  • Restriction C: Not open to students who are taking or have taken MATH 134.

• MATH 140 Calculus 1 (3 credits)

  Offered by: Mathematics and Statistics (Faculty of Science)

  Overview

  Mathematics & Statistics (Sci) : Review of functions and graphs. Limits, continuity, derivative. Differentiation of elementary functions. Antidifferentiation. Applications.

  Terms: Fall 2022, Winter 2023, Summer 2023

  Instructors: Trudeau, Sidney; Huang, Peiyuan; Mellick, Sam (Fall) Collins-Woodfin, Elizabeth (Winter) Lybbert, Reginald (Summer)

  • 3 hours lecture, 1 hour tutorial

  • Prerequisite: High School Calculus

  • Restriction: Not open to students who have taken MATH 120, MATH 139 or CEGEP objective 00UN or equivalent

  • Restriction: Not open to students who have taken or are taking MATH 122, except by permission of the Department of Mathematics and Statistics

  • Each Tutorial section is enrolment limited

• MATH 141 Calculus 2 (4 credits)

  Offered by: Mathematics and Statistics (Faculty of Science)

  Overview

  Mathematics & Statistics (Sci) : The definite integral. Techniques of integration. Applications. Introduction to sequences and series.

  Terms: Fall 2022, Winter 2023, Summer 2023

  Instructors: Macdonald, Jeremy; Xu, Peter (Fall) Trudeau, Sidney; Barill, Gavin; Mazakian, Hovsep (Winter) Abi Younes, Elio; Hassan, Hazem (Summer)

  • Prerequisites: MATH 139 or MATH 140 or MATH 150.

  • Restriction: Not open to students who have taken MATH 121 or CEGEP objective 00UP or equivalent

  • Restriction Note B: Not open to students who have taken or are taking MATH 122, except by permission of the Department of Mathematics and Statistics.

  • Each Tutorial section is enrolment limited

Required Courses (15 credits)

* Note: If the Minor Concentration Statistics is combined with the Major Concentration Mathematics, the required courses MATH 222, MATH 223 and MATH 323 must be replaced by courses selected from the Complementary Courses. Credit cannot be received for both MATH 223 and MATH 236 (listed as a required course in the Major Concentration Mathematics).

• MATH 222 Calculus 3 (3 credits) *

  Offered by: Mathematics and Statistics (Faculty of Science)

  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) Barill, Gavin (Summer)

  • 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.

• MATH 223 Linear Algebra (3 credits) *

  Offered by: Mathematics and Statistics (Faculty of Science)

  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, Mikael (Fall) Macdonald, Jeremy (Winter)

  • 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

• MATH 323 Probability (3 credits) *

  Offered by: Mathematics and Statistics (Faculty of Science)

  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) Asgharian, Masoud; Sajjad, Alia (Winter) Kelome, Djivede (Summer)

  • 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

• MATH 324 Statistics (3 credits)

  Offered by: Mathematics and Statistics (Faculty of Science)

  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)

  Offered by: Mathematics and Statistics (Faculty of Science)

  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)

  • Fall

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

Complementary Courses (3 credits)

3 credits from:

• MATH 204 Principles of Statistics 2 (3 credits)

  Offered by: Mathematics and Statistics (Faculty of Science)

  Overview

  Mathematics & Statistics (Sci) : 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.

  Terms: Winter 2023

  Instructors: Correa, Jose Andres (Winter)

  • Winter

  • Prerequisite: MATH 203 or equivalent. No calculus prerequisites

  • Restriction: This course is intended for students in all disciplines. For extensive course restrictions covering statistics courses see Section 3.6.1 of the Arts and of the Science sections of the calendar regarding course overlaps.

  • 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 208 Introduction to Statistical Computing (3 credits)

  Offered by: Mathematics and Statistics (Faculty of Science)

  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)

  Offered by: Mathematics and Statistics (Faculty of Science)

  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)

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

• MATH 317 Numerical Analysis (3 credits)

  Offered by: Mathematics and Statistics (Faculty of Science)

  Overview

  Mathematics & Statistics (Sci) : Error analysis. Numerical solutions of equations by iteration. Interpolation. Numerical differentiation and integration. Introduction to numerical solutions of differential equations.

  Terms: Fall 2022

  Instructors: Lessard, Jean-Philippe (Fall)

  • Fall

  • Prerequisites: MATH 315 or MATH 325 or MATH 263, and COMP 202 or permission of instructor.

  • Restrictions: Not open to students who have taken COMP 350

• MATH 427 Statistical Quality Control (3 credits)

  Offered by: Mathematics and Statistics (Faculty of Science)

  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 2022-2023 academic year.

  Instructors: There are no professors associated with this course for the 2022-2023 academic year.

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

• MATH 447 Introduction to Stochastic Processes (3 credits)

  Offered by: Mathematics and Statistics (Faculty of Science)

  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: Addario-Berry, Louigi Dana (Winter)

  • 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 by: Mathematics and Statistics (Faculty of Science)

  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, log-linear models. Multinomial models. Overdispersion and Quasilikelihood. Applications to experimental and observational data.

  Terms: Winter 2023

  Instructors: Chatelain, Simon (Winter)

  • Winter

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

• MATH 524 Nonparametric Statistics (4 credits)

  Offered by: Mathematics and Statistics (Faculty of Science)

  Overview

  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.

  Terms: Fall 2022

  Instructors: Neslehova, Johanna (Fall)

  • Fall

  • Prerequisite: MATH 324 or equivalent

  • Restriction: Not open to students who have taken MATH 424

• MATH 525 Sampling Theory and Applications (4 credits)

  Offered by: Mathematics and Statistics (Faculty of Science)

  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)

  • Prerequisite: MATH 324 or equivalent

  • Restriction: Not open to students who have taken MATH 425

• MATH 558 Design of Experiments (4 credits)

  Offered by: Mathematics and Statistics (Faculty of Science)

  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. 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.

  Terms: Winter 2023

  Instructors: Sajjad, Alia (Winter)

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

• MATH 559 Bayesian Theory and Methods (4 credits)

  Offered by: Mathematics and Statistics (Faculty of Science)

  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 2022-2023 academic year.

  Instructors: There are no professors associated with this course for the 2022-2023 academic year.

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