Offered by:Mathematics and Statistics
Degree:Bachelor of Science
Program Requirement:
The B.Sc.: Honours in Statistics provides training, at the honours level, in statistics, with a solid mathematical core, and basic training in computing. With a suitable selection of complementary courses, the program can focus on probability, mathematical statistics, applied statistics, actuarial science and finance, or data science. With satisfactory performance in an appropriate selection of courses, this program can lead to the professional accreditation A.Stat from the Statistical Society of Canada, which is regarded as the entry level requirement for a Statistician practicing in Canada.
Program Requirements (63 credits)
Students may complete this program with a minimum of 60 credits or a maximum of 63 credits depending on whether or not they are required to take MATH 222.
Program Prerequisites
The minimum requirement for entry into the Honours program is that the student has completed with high standing the following courses or their equivalents:
-
MATH 133
Linear Algebra and Geometry
3 Credits
Offered in the:
- Fall
- Winter
- Summer
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.
Offered by: Mathematics and Statistics
- 3 hours lecture, 1 hour tutorial
- Prerequisite: a course in functions
- Restriction(s): 1) Not open to students who have taken CEGEP objective 00UQ or equivalent. 2) Not open to students who have taken or are taking MATH 123, except by permission of the Department of Mathematics and Statistics.
- Terms
- Fall 2024
- Winter 2025
- Summer 2025
- Instructors
- Jeremy Macdonald, Antoine Giard, Miguel Ayala, Romain Branchereau
- Th茅o Pinet
-
MATH 150
Calculus A
4 Credits
Offered in the:
- Fall
- Winter
- Summer
Mathematics & Statistics (Sci): Functions, limits and continuity, differentiation, L'Hospital's rule, applications, Taylor polynomials, parametric curves, functions of several variables.
Offered by: Mathematics and Statistics
- Fall
- 3 hours lecture, 2 hours tutorial
- Students with no prior exposure to vector geometry are advised to take MATH 133 concurrently. Intended for students with high school calculus who have not received six advanced placement credits
- Restriction(s): 1) Not open to students who have taken or are taking MATH 139 or MATH 140 or CEGEP objective 00UN or equivalent. 2) Not open to students who have taken or are taking MATH 122,except by permission of the Department of Mathematics and Statistics.
- MATH 150 and MATH 151 cover the material of MATH 139, MATH 140, MATH 141, MATH 222
-
MATH 151
Calculus B
4 Credits
Offered in the:
- Fall
- Winter
- Summer
Mathematics & Statistics (Sci): Integration, methods and applications, infinite sequences and series, power series, arc length and curvature, multiple integration.
Offered by: Mathematics and Statistics
- Winter
- 3 hours lecture; 2 hours tutorial
- Each Tutorial section is enrolment limited
- Prerequisite: MATH 150
- Restriction(s): 1) Not open to students who have taken or are taking MATH 141 or CEGEP objective 00UP or equivalent. 2) Not open to students who have taken or are taking MATH 122, except by permission of the Department of Mathematic sand Statistics.
In particular, MATH 150/MATH 151 and MATH 140/MATH 141/MATH 222 are considered equivalent.
Required Courses (28-31 credits)
* Students with limited programming experience should take COMP 202/COMP 204/COMP 208 or equivalent before COMP 250.
** Students select either MATH 251 or MATH 247, but not both.
*** Students who have successfully completed MATH 150/MATH 151 or an equivalent of MATH 222 on entering the program are not required to take MATH 222.
Students who have not completed an equivalent of MATH 222 on entering the program must consult an academic adviser and take MATH 222 as a required course in the first semester, increasing the total number of program credits from 60 to 63. Students who have successfully completed MATH 150/MATH 151 are not required to take MATH 222.
Note: Students with limited knowledge of computer programming should take COMP 202/COMP 204/COMP 208 or equivalent before COMP 250. U0 students may take COMP 202 as a Freshman Science course; new U1 students should take one of these courses as an elective in their first semester.
Note: Students who wish to take MATH 204 as a complementary course are strongly advised to take MATH 203 beforehand, in their first semester or their first year.
Students who transfer to Honours in Mathematics from other programs will have credits for previous courses assigned, as appropriate, by the Department.
To be awarded the Honours degree, the student must have, at time of graduation, a CGPA of at least 3.00 in the required and complementary Mathematics courses of the program, as well as an overall CGPA of at least 3.00.
-
COMP 250
Intro to Computer Science
3 Credits*
Offered in the:
- Fall
- Winter
- Summer
Computer Science (Sci): Mathematical tools (binary numbers, induction,recurrence relations, asymptotic complexity,establishing correctness of programs). Datastructures (arrays, stacks, queues, linked lists,trees, binary trees, binary search trees, heaps,hash tables). Recursive and non-recursivealgorithms (searching and sorting, tree andgraph traversal). Abstract data types. Objectoriented programming in Java (classes andobjects, interfaces, inheritance). Selected topics.
Offered by: Computer Science
- Terms
- Instructors
- Giulia Alberini
- Giulia Alberini
-
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 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
- Fall 2024
- Winter 2025
- Summer 2025
- Instructors
- Brent Pym, Damien Tageddine
- Hovsep Mazakian
-
MATH 235
Algebra 1
3 Credits
Offered in the:
- Fall
- Winter
- Summer
Mathematics & Statistics (Sci): Sets, functions and relations. Methods of proof. Complex numbers. Divisibility theory for integers and modular arithmetic. Divisibility theory for polynomials. Rings, ideals and quotient rings. Fields and construction of fields from polynomial rings. Groups, subgroups and cosets; homomorphisms and quotient groups.
Offered by: Mathematics and Statistics
- Fall
- 3 hours lecture; 1 hour tutorial
- Prerequisite: MATH 133 or equivalent
- Restrictions: Not open to students who have taken or are taking MATH 245.
-
MATH 247
Honours Applied Linear Algebra
3 Credits**
Offered in the:
- Fall
- Winter
- Summer
Mathematics & Statistics (Sci): Matrix algebra, determinants, systems of linear equations. Abstract vector spaces, inner product spaces, Fourier series. Linear transformations and their matrix representations. Eigenvalues and eigenvectors, diagonalizable and defective matrices, positive definite and semidefinite matrices. Quadratic and Hermitian forms, generalized eigenvalue problems, simultaneous reduction of quadratic forms. Applications.
Offered by: Mathematics and Statistics
- Winter
- Prerequisite: MATH 133 or equivalent.
- Restriction: Intended for Honours Physics and Engineering students
- Restriction: Not open to students who have taken or are taking MATH 236, MATH 223 or MATH 251
-
MATH 251
Honours Algebra 2
3 Credits**
Offered in the:
- Fall
- Winter
- Summer
Mathematics & Statistics (Sci): Linear equations over a field. Introduction to vector spaces. Linear maps and their matrix representation. Determinants. Canonical forms. Duality. Bilinear and
quadratic forms. Real and complex inner product spaces. Diagonalization of self-adjoint operators.
Offered by: Mathematics and Statistics
- Winter
- Prerequisites: MATH 235 or permission of the Department
- Restriction: Not open to students who are taking or have taken MATH 247
-
MATH 255
Honours Analysis 2
3 Credits
Offered in the:
- Fall
- Winter
- Summer
Mathematics & Statistics (Sci): Basic point-set topology, metric spaces: open and closed sets, normed and Banach spaces, H脙露lder and Minkowski inequalities, sequential compactness, Heine-Borel, Banach Fixed Point theorem. Riemann-(Stieltjes) integral, Fundamental Theorem of Calculus, Taylor's theorem. Uniform convergence. Infinite series, convergence tests, power series. Elementary functions.
Offered by: Mathematics and Statistics
-
MATH 356
Honours Probability
3 Credits
Offered in the:
- Fall
- Winter
- Summer
Mathematics & Statistics (Sci): Sample space, probability axioms, combinatorial probability. Conditional probability, Bayes' Theorem. Distribution theory with special reference to the Binomial, Poisson, and Normal distributions. Expectations, moments, moment generating functions, uni-variate transformations. Random vectors, independence, correlation, multivariate transformations. Conditional distributions, conditional expectation.Modes of stochastic convergence, laws of large numbers, Central Limit Theorem.
Offered by: Mathematics and Statistics
- Fall
- Prerequisite(s): MATH 243 or MATH 255, and MATH 222 or permission of the Department.
- Restriction: Not open to students who have taken or are taking MATH 323
-
MATH 357
Honours Statistics
3 Credits
Offered in the:
- Fall
- Winter
- Summer
Mathematics & Statistics (Sci): Sampling distributions. Point estimation. Minimum variance unbiased estimators,
sufficiency, and completeness. Confidence intervals. Hypothesis tests, Neyman-Pearson Lemma, uniformly most powerful tests. Likelihood ratio tests for normal samples. Asymptotic sampling distributions and inference.
Offered by: Mathematics and Statistics
- Winter
- Prerequisite: MATH 356 or equivalent
- Restriction: Not open to students who have taken or are taking MATH 324
-
MATH 470
Honours Research Project
3 Credits
Offered in the:
- Fall
- Winter
- Summer
Mathematics & Statistics (Sci): The project will contain a significant research component that requires substantial independent work consisting of a written report and oral examination or presentation.
Offered by: Mathematics and Statistics
- Fall and Winter and Summer
- Requires Departmental Approval
- Students are advised to start contacting potential project supervisors early during their U2 year.
- Prerequisite: appropriate honours courses with approval of the project supervisor
- Terms
- Instructors
- Jose Andres Correa, Louigi Dana Addario-Berry, Dmitry Jakobson, Henri Darmon, Johanna Neslehova, Jean-Christophe Nave, Sergey Norin, Linan Chen, Anmar Khadra, Kiwon Lee, Jessica Lin
- Djivede A Kelome
-
MATH 533
Regression and ANOVA
4 Credits
Offered in the:
- Fall
- Winter
- Summer
Mathematics & Statistics (Sci): Multivariate normal and chi-squared distributions; quadratic forms. Multiple linear
regression estimators and their properties. General linear hypothesis tests. Prediction and confidence intervals. Asymptotic properties of least squares estimators. Weighted least squares. Variable selection and regularization. Selected advanced topics in regression. Applications to experimental and observational
data.
Offered by: Mathematics and Statistics
Complementary Courses (32 credits)
Advising notes:
- Students wishing to pursue mathematical statistics in graduate school are advised to take MATH 587 and recommended to take honours mathematics courses as complementary courses in Part II, in particular MATH 358, MATH 454 (preferably prior to MATH 587), and MATH 455.
- Students wishing to pursue applied statistics and/or careers as statisticians in industry or government are advised to take MATH 523, MATH 524, MATH 547, at least one of MATH 525 and MATH 558, and as many courses as possible from Part III of the list of Complementary Courses below. Students interested in obtaining the A-Stat accreditation from the Statistical Society of Canada should discuss their course selection with the academic adviser.
-Students with interest in probability are advised to choose from the following as part of their Complementary Courses: MATH 547, MATH 587, MATH 589.
- Students with interest in actuarial science are advised to choose from the following as part of their Complementary Courses: MATH 329, MATH 430, MATH 524, MATH 545, MATH 547.
- Students with interest in data science and machine learning are advised to choose from the following as part of their Complementary Courses: COMP 206, COMP 251, COMP 370, COMP 424, COMP 551, MATH 308, MATH 350, MATH 378, MATH 462 and MATH 517,MATH 562, and MATH 563.
Part I: 3 credits selected from:
* It is strongly recommended that students take MATH 254.
-
MATH 242
Analysis 1
3 Credits
Offered in the:
- Fall
- Winter
- Summer
Mathematics & Statistics (Sci): A rigorous presentation of sequences and of real numbers and basic properties of continuous and differentiable functions on the real line.
Offered by: Mathematics and Statistics
- Fall
- Prerequisite: MATH 141
- Restriction(s): Not open to students who are taking or who have taken MATH 254.
-
MATH 254
Honours Analysis 1
3 Credits*
Offered in the:
- Fall
- Winter
- Summer
Mathematics & Statistics (Sci): Properties of R. Cauchy and monotone sequences, Bolzano- Weierstrass theorem. Limits, limsup, liminf of functions. Pointwise, uniform continuity: Intermediate Value theorem. Inverse and monotone functions. Differentiation: Mean Value theorem, L'Hospital's rule, Taylor's Theorem.
Offered by: Mathematics and Statistics
- Prerequisite(s): MATH 141
- Restriction(s): Not open to students who are taking or who have taken MATH 242.
Part II: 6-11 credits in mathematics and computer science selected from:
+ Students can select either MATH 248 or MATH 358, but not both.
++ Students may obtain credit for both MATH 455 and MATH 587.
-
COMP 206
Intro to Software Systems
3 Credits
Offered in the:
- Fall
- Winter
- Summer
Computer Science (Sci): Comprehensive overview of programming in C, use of system calls and libraries, debugging and testing of code; use of developmental tools like make, version control systems.
Offered by: Computer Science
- Terms
- Instructors
- Jacob T Errington
- Joseph P Vybihal, Max Kopinsky
-
COMP 252
Honours Algorithms&Data Struct
3 Credits
Offered in the:
- Fall
- Winter
- Summer
Computer Science (Sci): The design and analysis of data structures and algorithms. The description of various computational problems and the algorithms that can be used to solve them, along with their associated data structures. Proving the correctness of algorithms and determining their computational complexity.
Offered by: Computer Science
- 3 hours
- Prerequisite: COMP 250 and either MATH 235 or MATH 240
- Restrictions: (1) Open only to students in Honours programs. (2) Students cannot receive credit for both COMP 251 and COMP 252.
- COMP 252 uses basic combinatorial counting methods that are covered in MATH 240 but not in MATH 235. Students who are unfamiliar with these methods should speak with the instructor for guidance.
-
MATH 248
Honours Vector Calculus
3 Credits+
Offered in the:
- Fall
- Winter
- Summer
Mathematics & Statistics (Sci): Partial derivatives and differentiation of functions in several variables; Jacobians;
maxima and minima; implicit functions. Scalar and vector fields; orthogonal curvilinear coordinates. Multiple integrals; arc length, volume and surface area. Line and surface integrals; irrotational and solenoidal fields; Green's theorem; the divergence theorem. Stokes' theorem; and applications.
Offered by: Mathematics and Statistics
- Fall and Winter and Summer
- Prerequisites: MATH 133 and MATH 222 or consent of Department.
- Restriction: Intended for Honours Physics, Computer Science, Physiology and Engineering students.
- Restriction: Not open to students who have taken or are taking MATH 314 or MATH 358.
-
MATH 325
Honours ODE's
3 Credits
Offered in the:
- Fall
- Winter
- Summer
Mathematics & Statistics (Sci): First and second order equations, linear equations, series solutions, Frobenius method, introduction to numerical methods and to linear systems, Laplace transforms, applications.
Offered by: Mathematics and Statistics
- Fall and Winter
- (3-0-6)
- Prerequisite: MATH 222.
- Restriction: Intended for Honours Mathematics, Physics and Engineering programs.
- Restriction: Not open to students who have taken MATH 263 (formerly MATH 261), MATH 315
-
MATH 350
Honours Discrete Mathematics
3 Credits
Offered in the:
- Fall
- Winter
- Summer
Mathematics & Statistics (Sci): Discrete mathematics. Graph Theory: matching theory, connectivity, planarity, and colouring; graph minors and extremal graph theory. Combinatorics: combinatorial methods, enumerative and algebraic combinatorics, discrete probability.
Offered by: Mathematics and Statistics
- Prerequisites: MATH 235 or MATH 240 and MATH 251 or MATH 223.
- Restrictions: Not open to students who have taken or are taking MATH 340. Intended for students in mathematics or computer science honours programs.
- Intended for students in mathematics or computer science honours programs.
-
MATH 352
Problem Seminar
1 Credits
Offered in the:
- Fall
- Winter
- Summer
Mathematics & Statistics (Sci): Seminar in Mathematical Problem Solving. The problems considered will be of the type that occur in the Putnam competition and in other similar mathematical competitions.
Offered by: Mathematics and Statistics
- Prerequisite: Enrolment in a math related program or permission of the instructor. Requires departmental approval.
- Prerequisite: Enrolment in a math related program or permission of the instructor.
-
MATH 358
Honours Advanced Calculus
3 Credits+
Offered in the:
- Fall
- Winter
- Summer
Mathematics & Statistics (Sci): Point-set topology in Euclidean space; continuity and differentiability of functions in several variables. Implicit and inverse function theorems. Vector fields, divergent and curl operations. Rigorous treatment of multiple integrals: volume and surface area; and Fubini鈥檚 theorem. Line and surface integrals, conservative vector fields. Green's theorem, Stokes鈥� theorem and the divergence theorem.
Offered by: Mathematics and Statistics
-
MATH 376
Honours Nonlinear Dynamics
3 Credits
Offered in the:
- Fall
- Winter
- Summer
Mathematics & Statistics (Sci): This course consists of the lectures of MATH 326, but will be assessed at the honours level.
Offered by: Mathematics and Statistics
- Fall
- Prerequisites: MATH 222, MATH 223
- Restrictions: Intended primarily for Honours students. Not open to students who have taken or are taking MATH 326.
- Note: Additionally, a special project or projects may be assigned.
-
MATH 387
Honours Numerical Analysis
3 Credits
Offered in the:
- Fall
- Winter
- Summer
Mathematics & Statistics (Sci): Error analysis. Numerical solutions of equations by iteration. Interpolation. Numerical differentiation and integration. Introduction to numerical solutions of differential equations.
Offered by: Mathematics and Statistics
- Taught in alternate years
- Winter (even years)
- Prerequisites: MATH 325 or MATH 315, COMP 202 or permission of instructor.
- Corequisites: MATH 255 or MATH 243.
- Restriction: Intended primarily for Honours students.
- Terms
- This course is not scheduled for the 2024-2025 academic year
- Instructors
- There are no professors associated with this course for the 2024-2025 academic year
-
MATH 397
Hons Matrix Numerical Analysis
3 Credits
Offered in the:
- Fall
- Winter
- Summer
Mathematics & Statistics (Sci): The course consists of the lectures of MATH 327 plus additional work involving theoretical assignments and/or a project. The final examination for this course may be different from that of MATH 327.
Offered by: Mathematics and Statistics
- Terms
- This course is not scheduled for the 2024-2025 academic year
- Instructors
- There are no professors associated with this course for the 2024-2025 academic year
-
MATH 398
Honours Euclidean Geometry
3 Credits
Offered in the:
- Fall
- Winter
- Summer
Mathematics & Statistics (Sci): Honours level: points and lines in a triangle. Quadrilaterals. Angles in a circle. Circumscribed and inscribed circles. Congruent and similar triangles. Area.
Power of a point with respect to a circle. Ceva鈥檚 theorem. Isometries. Homothety. Inversion.
Offered by: Mathematics and Statistics
- Prerequisite: MATH 133 or equivalent or permission of instructor.
- Restrictions: Not open to students taking or have take MATH 348.
- Terms
- This course is not scheduled for the 2024-2025 academic year
- Instructors
- There are no professors associated with this course for the 2024-2025 academic year
-
MATH 454
Honours Analysis 3
3 Credits
Offered in the:
- Fall
- Winter
- Summer
Mathematics & Statistics (Sci): Measure theory: sigma-algebras, Lebesgue measure in R^n and integration, L^1 functions, Fatou's lemma, monotone and dominated convergence theorem, Egorov鈥檚 theorem, Lusin's theorem, Fubini-Tonelli theorem, differentiation of the integral, differentiability of functions of bounded variation, absolutely continuous functions, fundamental theorem of calculus.
Offered by: Mathematics and Statistics
- Prerequisite(s): MATH 255
- Restriction: Not open to students who have taken MATH 354.
-
MATH 455
Honours Analysis 4
3 Credits++
Offered in the:
- Fall
- Winter
- Summer
Mathematics & Statistics (Sci): Review of point-set topology: topological spaces, dense sets, completeness, compactness, connectedness and path-connectedness, separability, Baire category theorem, Arzela-Ascoli theorem, Stone-Weierstrass theorem..Functional analysis: L^p spaces, linear functionals and dual spaces, Hilbert spaces, Riesz representation theorems. Fourier series and transform, Riemann-Lebesgue Lemma,Fourier inversion formula, Plancherel theorem, Parseval鈥檚 identity, Poisson summation formula.
Offered by: Mathematics and Statistics
- Prerequisite: MATH 454 or equivalent.
- Restriction(s): Not open to students who have taken MATH 355.
-
MATH 458
Honours Differential Geometry
3 Credits
Offered in the:
- Fall
- Winter
- Summer
Mathematics & Statistics (Sci): In addition to the topics of MATH 320, topics in the global theory of plane and space curves, and in the global theory of surfaces are presented. These include: total curvature and the Fary-Milnor theorem on knotted curves, abstract surfaces as 2-d manifolds, the Euler characteristic, the Gauss-Bonnet theorem for surfaces.
Offered by: Mathematics and Statistics
-
MATH 466
Honours Complex Analysis
3 Credits
Offered in the:
- Fall
- Winter
- Summer
Mathematics & Statistics (Sci): Functions of a complex variable, Cauchy-Riemann equations, Cauchy's theorem and its consequences. Uniform convergence on compacta. Taylor and Laurent series, open mapping theorem, Rouch茅's theorem and the argument principle. Calculus of residues. Fractional linear transformations and conformal mappings.
Offered by: Mathematics and Statistics
-
MATH 475
Honours PDE's
3 Credits
Offered in the:
- Fall
- Winter
- Summer
Mathematics & Statistics (Sci): First order partial differential equations, geometric theory, classification of second order linear equations, Sturm-Liouville problems, orthogonal functions and Fourier series, eigenfunction expansions, separation of variables for heat, wave and Laplace equations, Green's function methods, uniqueness theorems.
Offered by: Mathematics and Statistics
-
MATH 478
Comput. Meth. in Applied Math
3 Credits
Offered in the:
- Fall
- Winter
- Summer
Mathematics & Statistics (Sci): Solution to initial value problems: Linear, Nonlinear Finite Difference Methods: accuracy and stability, Lax equivalence theorem, CFL and von Neumann conditions,
Fourier analysis: diffusion, dissipation, dispersion, and spectral methods. Solution of large sparse linear systems: iterative methods, preconditioning, incomplete
LU, multigrid, Krylov subspaces, conjugate gradient method. Applications to, e.g., weighted least squares, duality, constrained minimization, calculus of variation,
inverse problems, regularization, level set methods, Navier-Stokes equations
Offered by: Mathematics and Statistics
-
MATH 480
Honours Independent Study
3 Credits
Offered in the:
- Fall
- Winter
- Summer
Mathematics & Statistics (Sci): Reading projects permitting independent study under the guidance of a staff member specializing in a subject where no appropriate course is available. Arrangements must be made with an instructor and the Chair before registration.
Offered by: Mathematics and Statistics
- Fall and Winter and Summer
- Please see regulations concerning Project Courses under Faculty Degree Requirements
- Requires approval by the chair before registration
- Terms
- Instructors
- Louigi Dana Addario-Berry
- Djivede A Kelome
-
MATH 527D1
Stat. Data Science Practicum
3 Credits
Offered in the:
- Fall
- Winter
- Summer
Mathematics & Statistics (Sci): The holistic skills required for doing statistical data science in practice. Data science life cycle from a statistics-centric perspective and from the perspective of a statistician working in the larger data science environment. Group-based projects with industry, government, or university partners. Statistical collaboration and consulting conducted in coordination with the Data Science Solutions Hub (DaS^2H) of the Computational and Data Systems Initiative (CDSI).
Offered by: Mathematics and Statistics
- Terms
- Instructors
- Jose Andres Correa, Eric Kolaczyk
-
MATH 527D2
Stat. Data Science Practicum
3 Credits
Offered in the:
- Fall
- Winter
- Summer
Mathematics & Statistics (Sci): See MATH 527D1 for course description.
Offered by: Mathematics and Statistics
- Terms
- Instructors
- Jose Andres Correa, Eric Kolaczyk
and any 500-level course offered by the Department of Mathematics and Statistics not listed in Part III below.
Part III: 18-23 credits in probability and statistics selected as follows:
15-23 credits selected from:
+++ Students must take MATH 204 before taking MATH 357 or MATH 533. Moreover, it is strongly advised to take MATH 203 before taking MATH 204.
-
MATH 204
Principles of Statistics 2
3 Credits+++
Offered in the:
- Fall
- Winter
- Summer
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.
Offered by: Mathematics and Statistics
- 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 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 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
-
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
-
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; 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
-
MATH 547
Stochastic Processes
4 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
-
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
-
MATH 557
Mathematical Statistics 2
4 Credits
Offered in the:
- Fall
- Winter
- Summer
Mathematics & Statistics (Sci): 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.
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. 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
-
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鈥檚 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鈥擧astings. Nonparametric Bayesian inference.
Offered by: Mathematics and Statistics
- Terms
- This course is not scheduled for the 2024-2025 academic year
- Instructors
- There are no professors associated with this course for the 2024-2025 academic year
-
MATH 587
Advanced Probability Theory 1
4 Credits
Offered in the:
- Fall
- Winter
- Summer
Mathematics & Statistics (Sci): Probability spaces. Random variables and their expectations. Convergence of random variables in Lp. Independence and conditional expectation. Introduction to Martingales. Limit theorems including Kolmogorov's Strong Law of Large Numbers.
Offered by: Mathematics and Statistics
- Terms
- Instructors
- Louigi Dana Addario-Berry
-
MATH 589
Advanced Probability Theory 2
4 Credits
Offered in the:
- Fall
- Winter
- Summer
Mathematics & Statistics (Sci): Characteristic functions: elementary properties, inversion formula, uniqueness, convolution and continuity theorems. Weak convergence. Central limit theorem. Additional topic(s) chosen (at discretion of instructor) from: Martingale Theory; Brownian motion, stochastic calculus.
Offered by: Mathematics and Statistics
- Winter
- Prerequisites: MATH 587 or equivalent
0-3 credits from the following courses for which no Honours equivalent exists:
-
MATH 329
Theory of Interest
3 Credits
Offered in the:
- Fall
- Winter
- Summer
Mathematics & Statistics (Sci): Simple and compound interest, annuities certain, amortization schedules, bonds, depreciation.
Offered by: Mathematics and Statistics
- Terms
- This course is not scheduled for the 2024-2025 academic year
- Instructors
- There are no professors associated with this course for the 2024-2025 academic year
-
MATH 378
Nonlinear Optimization
3 Credits
Offered in the:
- Fall
- Winter
- Summer
Mathematics & Statistics (Sci): Optimization terminology. Convexity. First- and second-order optimality conditions for unconstrained problems. Numerical methods for unconstrained optimization:
Gradient methods, Newton-type methods, conjugate gradient methods, trust-region methods. Least squares problems (linear + nonlinear). Optimality conditions for smooth constrained optimization problems (KKT theory). Lagrangian duality. Augmented Lagrangian methods. Active-set method for quadratic programming. SQP methods.
Offered by: Mathematics and Statistics
- Terms
- This course is not scheduled for the 2024-2025 academic year
- Instructors
- There are no professors associated with this course for the 2024-2025 academic year
-
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 2024-2025 academic year
- Instructors
- There are no professors associated with this course for the 2024-2025 academic year
0-8 credits selected from:
+++ Students may select either MATH 594 or MATH 598 but not both.
-
COMP 370
Introduction to Data
Science
3 Credits
Offered in the:
- Fall
- Winter
- Summer
Computer Science (Sci): Comprehensive introduction to the data science process. Orientation to the use and configuration of core data science toolkits, data collection and annotation fundamentals, principles of responsible data science, the use of quantitative tools in data science, and presentation of data science findings.
Offered by: Computer Science
- Prerequisites: COMP 206 and COMP 250
- Restrictions: Not open to students who have taken COMP 598 when the topic was "Introduction to Data Science" or "Data Science".
-
COMP 424
Artificial Intelligence
3 Credits
Offered in the:
- Fall
- Winter
- Summer
Computer Science (Sci): Introduction to search methods. Knowledge representation using logic and probability. Planning and decision making under uncertainty. Introduction to machine learning.
Offered by: Computer Science
- Terms
- Instructors
- David P Meger, Golnoosh Farnadi
-
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 Pr茅mont-Schwarz, Reihaneh Rabbany
- Yue Li
-
COMP 579
Reinforcement Learning
4 Credits
Offered in the:
- Fall
- Winter
- Summer
Computer Science (Sci): Bandit algorithms, finite Markov decision processes, dynamic programming, Monte-Carlo Methods, temporal-difference learning, bootstrapping, planning, approximation methods, on versus off policy learning, policy gradient methods temporal
abstraction and inverse reinforcement learning.
Offered by: Computer Science
- Prerequisite: A university level course in machine learning such as COMP 451 or COMP 551. Background in calculus, linear algebra, probability at the level of MATH 222, MATH 223, MATH 323, respectively.
- Terms
- Instructors
- Doina Precup, Isabeau Pr茅mont-Schwarz
-
COMP 588
Probabilistic Graphical Models
4 Credits
Offered in the:
- Fall
- Winter
- Summer
Computer Science (Sci): Representation, inference and learning with graphical models; directed and undirected graphical models; exact inference; approximate inference using deterministic optimization based methods, stochastic sampling based methods; learning with complete and partial observations.
Offered by: Computer Science
-
MATH 430
Mathematical Finance
3 Credits
Offered in the:
- Fall
- Winter
- Summer
Mathematics & Statistics (Sci): Introduction to concepts of price and hedge derivative securities. The following concepts will be studied in both concrete and continuous time: filtrations, martingales, the change of measure technique, hedging, pricing, absence of arbitrage opportunities and the Fundamental Theorem of Asset Pricing.
Offered by: Mathematics and Statistics
-
MATH 462
Machine Learning
3 Credits
Offered in the:
- Fall
- Winter
- Summer
Mathematics & Statistics (Sci): Introduction to supervised learning: decision trees, nearest neighbors, linear models, neural networks. Probabilistic learning: logistic regression, Bayesian methods, naive Bayes. Classification with linear models and convex losses. Unsupervised learning: PCA, k-means, encoders, and decoders. Statistical learning theory: PAC learning and VC dimension. Training models with gradient descent and stochastic gradient descent. Deep neural networks. Selected topics chosen from: generative models, feature representation learning, computer vision.
Offered by: Mathematics and Statistics
- Terms
- This course is not scheduled for the 2024-2025 academic year
- Instructors
- There are no professors associated with this course for the 2024-2025 academic year
-
MATH 510
Quantitative Risk Management
4 Credits
Offered in the:
- Fall
- Winter
- Summer
Mathematics & Statistics (Sci): Basics concepts in quantitative risk management: types of financial risk, loss distribution, risk measures, regulatory framework. Empirical properties of financial data, models for stochastic volatility. Extreme-value theory models for maxima and threshold exceedances. Multivariate models, copulas, and dependence measures. Risk aggregation.
Offered by: Mathematics and Statistics
-
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 2024-2025 academic year
- Instructors
- There are no professors associated with this course for the 2024-2025 academic year
-
MATH 594
Topics in Mathematics&Stats
4 Credits+++
Offered in the:
- Fall
- Winter
- Summer
Mathematics & Statistics (Sci): This course covers a topic in mathematics and/or statistics.
Offered by: Mathematics and Statistics
- Prerequisites: At least 30 credits in required or complementary courses from the Honours Mathematics, Honours Applied Mathematics, or Honours Probability and Statistics programs. Additional prerequisites may be imposed by the Department of Mathematics and Statistics depending on the nature of the topic.
- Restrictions: Requires permission of the Department of Mathematics and Statistics
-
MATH 598
Topics in Probability & Stats
4 Credits+++
Offered in the:
- Fall
- Winter
- Summer
Mathematics & Statistics (Sci): This course covers a topic in probability and/or statistics.
Offered by: Mathematics and Statistics
- Prerequisite(s): At least 30 credits in required or complementary courses from the Honours in Probability and Statistics program including MATH 356. Additional prerequisites may be imposed by the Department of Mathematics and Statistics depending on the nature of the topic.
- Restriction(s): Requires permission of the Department of Mathematics and Statistics.
- Terms
- Instructors
- Louigi Dana Addario-Berry, Johanna Neslehova
- Masoud Asgharian, Abbas Khalili