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# Honours Probability and Statistics (63 credits)

Offered by: Mathematics and Statistics     Degree: Bachelor of Science

### Program Requirements

The program provides training in probability and statistics, with a solid mathematical core, and basic training in computing. It prepares students for graduate school in probability, statistics, or data science. It also offers a path to a variety of careers in industry or government in the statistical sciences. With a suitable selection of complementary courses, students 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 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 2020, Winter 2021, Summer 2021

Instructors: Bélanger-Rioux, Rosalie; Ball, Gavin; Aigner, Florian; Przytycki, Piotr (Fall) Kelome, Djivede (Winter)

• 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 150 Calculus A (4 credits)

Offered by: Mathematics and Statistics (Faculty of Science)

### Overview

Mathematics & Statistics (Sci) : Functions, limits and continuity, differentiation, L'Hospital's rule, applications, Taylor polynomials, parametric curves, functions of several variables.

Terms: Fall 2020

Instructors: Roth, Charles (Fall)

• 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: Not open to students who have taken CEGEP objective 00UN 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

• MATH 150 and MATH 151 cover the material of MATH 139, MATH 140, MATH 141, MATH 222

• MATH 151 Calculus B (4 credits)

Offered by: Mathematics and Statistics (Faculty of Science)

### Overview

Mathematics & Statistics (Sci) : Integration, methods and applications, infinite sequences and series, power series, arc length and curvature, multiple integration.

Terms: Winter 2021

Instructors: Roth, Charles (Winter)

• Winter

• 3 hours lecture; 2 hours tutorial

• Each Tutorial section is enrolment limited

• Prerequisite: MATH 150

• Restriction: Not open to students who have taken CEGEP objective 00UP 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

• Restriction: Not open to students who have taken MATH 152

In particular, MATH 150/151 and MATH 140/141/222 are considered equivalent.

#### Required Courses (28-31 credits)

* Students with limited programming experience should take COMP 202/204/208 or equivalent before COMP 250.

** Students select either MATH 251 or MATH 247, but not both.

*** Students who have successfully completed MATH 150/151 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 150/151 are not required to take MATH 222.

Note: Students with limited knowledge of computer programming should take COMP 202/204/208 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 as a Freshman Science course or as an elective in their first semester.

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 Introduction to Computer Science (3 credits) *

Offered by: Computer Science (Faculty of Science)

### Overview

Computer Science (Sci) : Mathematical tools (binary numbers, induction, recurrence relations, asymptotic complexity, establishing correctness of programs), Data structures (arrays, stacks, queues, linked lists, trees, binary trees, binary search trees, heaps, hash tables), Recursive and non-recursive algorithms (searching and sorting, tree and graph traversal). Abstract data types, inheritance. Selected topics.

Terms: Fall 2020, Winter 2021

Instructors: Alberini, Giulia (Fall) Alberini, Giulia (Winter)

• 3 hours

• Prerequisites: Familiarity with a high level programming language and CEGEP level Math.

• Students with limited programming experience should take COMP 202 or equivalent before COMP 250. See COMP 202 Course Description for a list of topics.

• 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 statictics. Writing functions. Simulation and parallel computing. Communication data and documenting code for reproducible research.

Terms: Fall 2020

Instructors: Steele, Russell (Fall)

• 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 2020, Winter 2021, Summer 2021

Instructors: Fortier, Jérôme; Kelome, Djivede (Fall) Vetois, Jerome (Winter)

• MATH 235 Algebra 1 (3 credits)

Offered by: Mathematics and Statistics (Faculty of Science)

### Overview

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; group actions on sets.

Terms: Fall 2020

Instructors: Wise, Daniel (Fall)

• Fall

• 3 hours lecture; 1 hour tutorial

• Prerequisite: MATH 133 or equivalent

• MATH 247 Honours Applied Linear Algebra (3 credits) **

Offered by: Mathematics and Statistics (Faculty of Science)

### Overview

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.

Terms: Winter 2021

Instructors: Hoheisel, Tim (Winter)

• 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 by: Mathematics and Statistics (Faculty of Science)

### Overview

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.

Terms: Winter 2021

Instructors: Lipnowski, Michael (Winter)

• 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 by: Mathematics and Statistics (Faculty of Science)

### Overview

Mathematics & Statistics (Sci) : Basic point-set topology, metric spaces: open and closed sets, normed and Banach spaces, HÃ¶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.

Terms: Winter 2021

Instructors: Jaksic, Vojkan (Winter)

• MATH 356 Honours Probability (3 credits)

Offered by: Mathematics and Statistics (Faculty of Science)

### Overview

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.

Terms: Fall 2020

Instructors: Chen, Linan (Fall)

• 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 by: Mathematics and Statistics (Faculty of Science)

### Overview

Mathematics & Statistics (Sci) : Data analysis. Estimation and hypothesis testing. Power of tests. Likelihood ratio criterion. The chi-squared goodness of fit test. Introduction to regression analysis and analysis of variance.

Terms: Winter 2021

Instructors: Neslehova, Johanna (Winter)

• 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 by: Mathematics and Statistics (Faculty of Science)

### Overview

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.

Terms: Fall 2020, Winter 2021

Instructors: Kelome, Djivede; Jakobson, Dmitry; Steele, Russell; Paquette, Elliot; Neslehova, Johanna; Vetta, Adrian Roshan; Hoheisel, Tim (Fall) Kelome, Djivede; Pichot, Michael; Jakobson, Dmitry; Lin, Jessica; Nave, Jean-Christophe; Khalili Mahmoudabadi, Abbas; Vetois, Jerome; Neslehova, Johanna (Winter)

• 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

• MATH 533 Regression and Analysis of Variance (4 credits)

Offered by: Mathematics and Statistics (Faculty of Science)

### Overview

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.

Terms: Fall 2020

#### Complementary Courses (32 credits)

- Students wishing to pursue probability or mathematical statistics in graduate school are strongly advised to take MATH 587 and recommended to take honours mathematics courses as complementary courses in Part 11, in particular MATH 358, MATH 454 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, 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 advisor.

- 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 540, MATH 541, 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 424, COMP 551, MATH 350, and MATH 517.

Part 1: 3 credits selected from:

* It is strongly recommended that students take MATH 254.

• MATH 242 Analysis 1 (3 credits)

Offered by: Mathematics and Statistics (Faculty of Science)

### Overview

Mathematics & Statistics (Sci) : A rigorous presentation of sequences and of real numbers and basic properties of continuous and differentiable functions on the real line.

Terms: Fall 2020

Instructors: Hundemer, Axel W (Fall)

• 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 by: Mathematics and Statistics (Faculty of Science)

### Overview

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.

Terms: Fall 2020

Instructors: Jaksic, Vojkan; Hundemer, Axel W; Hurtubise, Jacques Claude (Fall)

• Prerequisite(s): MATH 141

• Restriction(s): Not open to students who are taking or who have taken MATH 242.

Part II: at least 6 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 Introduction to Software Systems (3 credits)

Offered by: Computer Science (Faculty of Science)

### Overview

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.

Terms: Fall 2020, Winter 2021

Instructors: D'silva, Joseph (Fall) D'silva, Joseph; Vybihal, Joseph P (Winter)

• COMP 252 Honours Algorithms and Data Structures (3 credits)

Offered by: Computer Science (Faculty of Science)

### Overview

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.

Terms: Winter 2021

Instructors: Crepeau, Claude (Winter)

• 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 by: Mathematics and Statistics (Faculty of Science)

### Overview

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.

Terms: Fall 2020

Instructors: Guan, Pengfei (Fall)

• 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 Ordinary Differential Equations (3 credits)

Offered by: Mathematics and Statistics (Faculty of Science)

### Overview

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.

Terms: Winter 2021

Instructors: Humphries, Antony Raymond (Winter)

• 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 by: Mathematics and Statistics (Faculty of Science)

### Overview

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.

Terms: Fall 2020

Instructors: Norin, Sergey (Fall)

• 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 credit)

Offered by: Mathematics and Statistics (Faculty of Science)

### Overview

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.

Terms: Fall 2020

Instructors: Norin, Sergey (Fall)

• 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 by: Mathematics and Statistics (Faculty of Science)

### Overview

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’s theorem. Line and surface integrals, conservative vector fields. Green's theorem, Stokes’ theorem and the divergence theorem.

Terms: Winter 2021

Instructors: Guan, Pengfei (Winter)

• MATH 376 Honours Nonlinear Dynamics (3 credits)

Offered by: Mathematics and Statistics (Faculty of Science)

### Overview

Mathematics & Statistics (Sci) : This course consists of the lectures of MATH 326, but will be assessed at the honours level.

Terms: Fall 2020

Instructors: Nave, Jean-Christophe (Fall)

• 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 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: This course is not scheduled for the 2020-2021 academic year.

Instructors: There are no professors associated with this course for the 2020-2021 academic year.

• 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.

• MATH 397 Honours Matrix Numerical Analysis (3 credits)

Offered by: Mathematics and Statistics (Faculty of Science)

### Overview

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.

Terms: Winter 2021

Instructors: Saldanha Salvador, Tiago Miguel (Winter)

• MATH 398 Honours Euclidean Geometry (3 credits)

Offered by: Mathematics and Statistics (Faculty of Science)

### Overview

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’s theorem. Isometries. Homothety. Inversion.

Terms: Fall 2020

Instructors: Kamran, Niky (Fall)

• Prerequisite: MATH 133 or equivalent or permission of instructor.

• Restrictions: Not open to students taking or have take MATH 348.

• MATH 454 Honours Analysis 3 (3 credits)

Offered by: Mathematics and Statistics (Faculty of Science)

### Overview

Mathematics & Statistics (Sci) : Review of point-set topology: topological space, dense sets, completeness, compactness, connectedness and path-connectedness, separability. Arzela-Ascoli, Stone-Weierstrass, Baire category theorems. Measure theory: sigma algebras, Lebesgue measure and integration, L^1 functions. Fatou's lemma, monotone and dominated convergence theorem. Egorov, Lusin's theorems. Fubini-Tonelli theorem.

Terms: Fall 2020

Instructors: Vetois, Jerome (Fall)

• Prerequisite: MATH 255 or equivalent.

• Restriction: Not open to students who have taken MATH 354.

• MATH 455 Honours Analysis 4 (3 credits) ++

Offered by: Mathematics and Statistics (Faculty of Science)

### Overview

Mathematics & Statistics (Sci) : Continuation of measure theory. Functional analysis: L^p spaces, linear functionals and dual spaces, Hahn-Banach theorem, Riesz representation theorem. Hilbert spaces, weak convergence. Spectral theory of compact operator. Introduction to Fourier analysis, Fourier transforms.

Terms: Winter 2021

Instructors: Jakobson, Dmitry (Winter)

• Prerequisite: MATH 454 or equivalent.

• Restriction(s): Not open to students who have taken MATH 355.

• MATH 458 Honours Differential Geometry (3 credits)

Offered by: Mathematics and Statistics (Faculty of Science)

### Overview

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.

Terms: Winter 2021

Instructors: Kamran, Niky (Winter)

• MATH 466 Honours Complex Analysis (3 credits)

Offered by: Mathematics and Statistics (Faculty of Science)

### Overview

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, Rouché's theorem and the argument principle. Calculus of residues. Fractional linear transformations and conformal mappings.

Terms: Fall 2020

Instructors: Tosatti, Valentino; Hurtubise, Jacques Claude (Fall)

• MATH 475 Honours Partial Differential Equations (3 credits)

Offered by: Mathematics and Statistics (Faculty of Science)

### Overview

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.

Terms: Fall 2020

Instructors: Lin, Jessica (Fall)

• MATH 478 Computational Methods in Applied Mathematics (3 credits)

Offered by: Mathematics and Statistics (Faculty of Science)

### Overview

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

Terms: Winter 2021

Instructors: Nave, Jean-Christophe (Winter)

• MATH 480 Honours Independent Study (3 credits)

Offered by: Mathematics and Statistics (Faculty of Science)

### Overview

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.

Terms: Fall 2020, Winter 2021

Instructors: Neslehova, Johanna; Sabok, Marcin; Stephens, David; Yang, Yi; Darmon, Henri (Fall) Neslehova, Johanna; Jakobson, Dmitry; Tserunyan, Anush; Allen, Patrick (Winter)

• Fall and Winter and Summer

• Please see regulations concerning Project Courses under Faculty Degree Requirements

• Requires approval by the chair before registration

and any 500-level course offered by the Department of Mathematics and Statistics not listed in Part III below.

Part III: at least 18 credits in probability and statistics selected as follows:

At least 8 credits selected from:

• 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 2021

Instructors: Genest, Christian (Winter)

• 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 2020

Instructors: Wolfson, David B (Fall)

• Fall

• Prerequisite: MATH 324 or equivalent

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

• MATH 547 Stochastic Processes (4 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: This course is not scheduled for the 2020-2021 academic year.

Instructors: There are no professors associated with this course for the 2020-2021 academic year.

• MATH 556 Mathematical Statistics 1 (4 credits)

Offered by: Mathematics and Statistics (Faculty of Science)

### Overview

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.

Terms: Fall 2020

• Fall

• Prerequisite: MATH 357 or equivalent

• MATH 557 Mathematical Statistics 2 (4 credits)

Offered by: Mathematics and Statistics (Faculty of Science)

### Overview

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

Terms: Winter 2021

Instructors: Asgharian-Dastenaei, Masoud (Winter)

• MATH 587 Advanced Probability Theory 1 (4 credits)

Offered by: Mathematics and Statistics (Faculty of Science)

### Overview

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.

Terms: Fall 2020

Instructors: Chen, Linan (Fall)

• MATH 589 Advanced Probability Theory 2 (4 credits)

Offered by: Mathematics and Statistics (Faculty of Science)

### Overview

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.

Terms: Winter 2021

Instructors: Chen, Linan (Winter)

• Winter

• Prerequisites: MATH 587 or equivalent

At least 7 credits selected from:

+++ Students must take MATH 204 before taking MATH 357 or MATH 533. Moreover, it is advisable to take MATH 203 as a Freshman Science course or as an elective before taking MATH 204.

• 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 2021

Instructors: Genest, Christian (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 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 2021

Instructors: Neslehova, Johanna (Winter)

• 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 2021

Instructors: Steele, Russell (Winter)

• Prerequisite: MATH 324 or equivalent

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

• MATH 545 Introduction to Time Series Analysis (4 credits)

Offered by: Mathematics and Statistics (Faculty of Science)

### Overview

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.

Terms: This course is not scheduled for the 2020-2021 academic year.

Instructors: There are no professors associated with this course for the 2020-2021 academic year.

0-3 credits from the following courses for which no Honours equivalent exists:

• MATH 329 Theory of Interest (3 credits)

Offered by: Mathematics and Statistics (Faculty of Science)

### Overview

Mathematics & Statistics (Sci) : Simple and compound interest, annuities certain, amortization schedules, bonds, depreciation.

Terms: Winter 2021

Instructors: Kelome, Djivede (Winter)

• 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 2020-2021 academic year.

Instructors: There are no professors associated with this course for the 2020-2021 academic year.

The remaining credits selected from:

+++ Students may select either MATH 594 or MATH 598 but not both.

• COMP 424 Artificial Intelligence (3 credits)

Offered by: Computer Science (Faculty of Science)

### Overview

Computer Science (Sci) : Introduction to search methods. Knowledge representation using logic and probability. Planning and decision making under uncertainty. Introduction to machine learning.

Terms: Winter 2021

Instructors: Cheung, Jackie (Winter)

• COMP 451 Fundamentals of Machine Learning (3 credits)

Offered by: Computer Science (Faculty of Science)

### Overview

Computer Science (Sci) : Introduction to the computational, statistical and mathematical foundations of machine learning. Algorithms for both supervised learning and unsupervised learning. Maximum likelihood estimation, neural networks, and regularization.

Terms: Winter 2021

Instructors: Hamilton, William (Winter)

• COMP 551 Applied Machine Learning (4 credits)

Offered by: Computer Science (Faculty of Science)

### Overview

Computer Science (Sci) : Selected topics in machine learning and data mining, including clustering, neural networks, support vector machines, decision trees. Methods include feature selection and dimensionality reduction, error estimation and empirical validation, algorithm design and parallelization, and handling of large data sets. Emphasis on good methods and practices for deployment of real systems.

Terms: Fall 2020, Winter 2021

Instructors: Ravanbakhsh, Mohsen (Fall) Rabbany, Reihaneh (Winter)

• Prerequisite(s): MATH 323 or ECSE 205 or ECSE 305 or equivalent

• Restriction(s): Not open to students who have taken or are taking COMP 451.

• Some background in Artificial Intelligence is recommended, e.g. COMP-424 or ECSE-526, but not required.

• MATH 430 Mathematical Finance (3 credits)

Offered by: Mathematics and Statistics (Faculty of Science)

### Overview

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.

Terms: This course is not scheduled for the 2020-2021 academic year.

Instructors: There are no professors associated with this course for the 2020-2021 academic year.

• MATH 540 Life Actuarial Mathematics (4 credits)

Offered by: Mathematics and Statistics (Faculty of Science)

### Overview

Mathematics & Statistics (Sci) : Life tables and distributions; force of mortality; premium, net premium, and reserve valuation for life insurance and annuity contracts (discrete and continuous case); cash flow analysis for portfolios of life insurance and annuities; asset liability management; numerical techniques for multiple decrement and state models; portfolio valuation of aggregate risks.

Terms: This course is not scheduled for the 2020-2021 academic year.

Instructors: There are no professors associated with this course for the 2020-2021 academic year.

• MATH 541 Nonlife Actuarial Models (4 credits)

Offered by: Mathematics and Statistics (Faculty of Science)

### Overview

Mathematics & Statistics (Sci) : Stochastic models and inference for loss severity and claim frequency distributions; computational techniques for the aggregation of independent risks (Panjer's algorithm, FFT, etc.); risk measures and quantitative risk management applications; models and inference for multivariate data, heavy-tail distributions, and extremes; dynamic risk models based on stochastic processes and ruin theory.

Terms: This course is not scheduled for the 2020-2021 academic year.

Instructors: There are no professors associated with this course for the 2020-2021 academic year.

• MATH 594 Topics in Mathematics and Statistics (4 credits) +++

Offered by: Mathematics and Statistics (Faculty of Science)

### Overview

Mathematics & Statistics (Sci) : This course covers a topic in mathematics and/or statistics.

Terms: Winter 2021

Instructors: Norin, Sergey (Winter)

• 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 and Statistics (4 credits) +++

Offered by: Mathematics and Statistics (Faculty of Science)

### Overview

Mathematics & Statistics (Sci) : This course covers a topic in probability and/or statistics.

Terms: Fall 2020, Winter 2021

Instructors: Stephens, David (Fall) Stephens, David (Winter)

• 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.

Faculty of Science—2020-2021 (last updated Mar. 27, 2020) (disclaimer)