Mathematics (Probability and Statistics  Faculty of Arts)
The Honours in Probability and Statistics is available to students enrolled in both the Faculty of Arts and the Faculty of Science.
Note: Students entering a Mathematics program are normally expected to have completed MATH 133; MATH 139 or MATH 140; MATH 141; or their equivalents. Otherwise, they will be required to make up any deficiencies in these courses over and above the program credits.If you are interested in the program, consult the program outline below.
DETAILED PROGRAM OUTLINE:
Program Requirement:
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
 Fall
 Winter
 Summer
Offered in the: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; quadratic loci in two and three dimensions.
Offered by: Mathematics and Statistics
 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, MATH 130 or MATH 131, except by permission of the Department of Mathematics and Statistics.
 Restriction C: Not open to students who are taking or have taken MATH 134.
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 Fall 2019
 Winter 2020
 Instructors
 Rosalie BélangerRioux

MATH 150 Calculus A 4 Credits
 Fall
 Winter
 Summer
Offered in the: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: 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 or MATH 130 or MATH 131, 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
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 Fall 2019
 Instructors
 Charles Roth

MATH 151 Calculus B 4 Credits
 Fall
 Winter
 Summer
Offered in the: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: 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 or MATH 130 or MATH 131, except by permission of the Department of Mathematics and Statistics
 Restriction: Not open to students who have taken MATH 152
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 Winter 2020
 Instructors
 Charles Roth
In particular, MATH 150/151 and MATH 140/141/222 are considered equivalent.
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 Intro to Computer Science 3 Credits*
 Fall
 Winter
 Summer
Offered in the: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 nonrecursive algorithms (searching and sorting, tree and graph traversal). Abstract data types, inheritance. Selected topics.
Offered by: Computer Science
 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.
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 Fall 2019
 Winter 2020
 Instructors
 Michael Langer, Giulia Alberini
 Giulia Alberini

MATH 208 Intro to Statistical Computing 3 Credits
 Fall
 Winter
 Summer
Offered in the: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.
Offered by: Mathematics and Statistics
 Prerequisite(s): MATH 133
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 Fall 2019
 Instructors
 Russell Steele

MATH 222 Calculus 3 3 Credits***
 Fall
 Winter
 Summer
Offered in the:Mathematics & Statistics (Sci): Taylor series, Taylor's theorem in one and several variables. Review of vector geometry. Partial differentiation, directional derivative. Extreme of functions of 2 or 3 variables. Parametric curves and arc length. Polar and spherical coordinates. Multiple integrals.
Offered by: Mathematics and Statistics
 Prerequisite: MATH 141. Familiarity with vector geometry or Corequisite: MATH 133
 Restriction: Not open to students who have taken CEGEP course 201303 or MATH 150, MATH 151 or MATH 227
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 Fall 2019
 Winter 2020
 Instructors
 Jeremy D Macdonald, Broderick J Causley
 Jérôme Fortier

MATH 235 Algebra 1 3 Credits
 Fall
 Winter
 Summer
Offered in the: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.
Offered by: Mathematics and Statistics
 Fall
 3 hours lecture; 1 hour tutorial
 Prerequisite: MATH 133 or equivalent
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 Fall 2019
 Instructors
 Daniel T Wise

MATH 247 Honours Applied Linear Algebra 3 Credits**
 Fall
 Winter
 Summer
Offered in the: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
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 Winter 2020
 Instructors
 Tim Hoheisel

MATH 251 Honours Algebra 2 3 Credits**
 Fall
 Winter
 Summer
Offered in the: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 selfadjoint 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
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 Winter 2020
 Instructors
 Henri Darmon

MATH 255 Honours Analysis 2 3 Credits
 Fall
 Winter
 Summer
Offered in the:Mathematics & Statistics (Sci): Basic pointset topology, metric spaces: open and closed sets, normed and Banach spaces, HÃ¶lder and Minkowski inequalities, sequential compactness, HeineBorel, 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
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 Winter 2020
 Instructors
 Pengfei Guan

MATH 356 Honours Probability 3 Credits
 Fall
 Winter
 Summer
Offered in the: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, univariate 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
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 Fall 2019
 Instructors
 Abbas Khalili Mahmoudabadi

MATH 357 Honours Statistics 3 Credits
 Fall
 Winter
 Summer
Offered in the:Mathematics & Statistics (Sci): Data analysis. Estimation and hypothesis testing. Power of tests. Likelihood ratio criterion. The chisquared goodness of fit test. Introduction to regression analysis and analysis of variance.
Offered by: Mathematics and Statistics
 Winter
 Prerequisite: MATH 356 or equivalent
 Corequisite(s): MATH 255 Honours Analysis 2
 Restriction: Not open to students who have taken or are taking MATH 324
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 Winter 2020
 Instructors
 Johanna Neslehova

MATH 470 Honours Research Project 3 Credits
 Fall
 Winter
 Summer
Offered in the: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
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 Fall 2019
 Winter 2020
 Instructors
 Djivede A Kelome, Henri Darmon, Michael Y Pichot, Michael Lipnowski, Johanna Neslehova, Peter Bartello, Marcin Sabok
 Djivede A Kelome

MATH 533 Honours Regression and ANOVA 4 Credits
 Fall
 Winter
 Summer
Offered in the:Mathematics & Statistics (Sci): This course consists of the lectures of MATH 423 but will be assessed at the 500 level.
Offered by: Mathematics and Statistics
 Prerequisites: MATH 357, MATH 247 or MATH 251.
 Restriction: Not open to have taken or are taking MATH 423.
 Note: An additional project or projects assigned by the instructor that require a more detailed treatment of the major results and concepts covered in MATH 423.
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 Fall 2019
 Instructors
 Yi Yang
Complementary Courses (32 credits)
Advising notes:
 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 AStat 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
 Fall
 Winter
 Summer
Offered in the: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.
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 Fall 2019
 Instructors
 Jerome Vetois

MATH 254 Honours Analysis 1 3 Credits*
 Fall
 Winter
 Summer
Offered in the: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.
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 Fall 2019
 Instructors
 Axel W Hundemer
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 Intro to Software Systems 3 Credits
 Fall
 Winter
 Summer
Offered in the: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
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 Fall 2019
 Winter 2020
 Instructors
 Joseph P Vybihal
 Joseph P Vybihal

COMP 252 Honours Algorithms&Data Struct 3 Credits
 Fall
 Winter
 Summer
Offered in the: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.
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 Winter 2020
 Instructors
 Luc P Devroye

MATH 248 Honours Vector Calculus 3 Credits+
 Fall
 Winter
 Summer
Offered in the: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.
 Symbols:
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 Fall 2019
 Instructors
 Gantumur Tsogtgerel

MATH 325 Honours ODE's 3 Credits
 Fall
 Winter
 Summer
Offered in the: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
 (306)
 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
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 Winter 2020
 Instructors
 JeanPhilippe Lessard

MATH 350 Honours Discrete Mathematics 3 Credits
 Fall
 Winter
 Summer
Offered in the: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.
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 Fall 2019
 Instructors
 Sergey Norin

MATH 352 Problem Seminar 1 Credits
 Fall
 Winter
 Summer
Offered in the: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.
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 Fall 2019
 Instructors
 Sergey Norin

MATH 358 Honours Advanced Calculus 3 Credits+
 Fall
 Winter
 Summer
Offered in the:Mathematics & Statistics (Sci): Pointset 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.
Offered by: Mathematics and Statistics
 Prerequisites: MATH 222, MATH 247 or MATH 251, MATH 255 or permission of the Department.
 Restrictions: Intended for students in Honours Mathematics programs, Not open to students who have taken or are taking MATH 314 or MATH 248
 Symbols:
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 Winter 2020
 Instructors
 Pengfei Guan

MATH 376 Honours Nonlinear Dynamics 3 Credits
 Fall
 Winter
 Summer
Offered in the: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.
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 Fall 2019
 Instructors
 Antony Raymond Humphries

MATH 387 Honours Numerical Analysis 3 Credits
 Fall
 Winter
 Summer
Offered in the: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.
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 Winter 2020
 Instructors
 Antony Raymond Humphries

MATH 397 Hons Matrix Numerical Analysis 3 Credits
 Fall
 Winter
 Summer
Offered in the: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
 Symbols:
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 This course is not scheduled for the 20192020 academic year
 Instructors
 There are no professors associated with this course for the 20192020 academic year

MATH 398 Honours Euclidean Geometry 3 Credits
 Fall
 Winter
 Summer
Offered in the: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.
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.
 Symbols:
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 Fall 2019
 Instructors
 Michael Lipnowski

MATH 454 Honours Analysis 3 3 Credits
 Fall
 Winter
 Summer
Offered in the:Mathematics & Statistics (Sci): Review of pointset topology: topological space, dense sets, completeness, compactness, connectedness and pathconnectedness, separability. ArzelaAscoli, StoneWeierstrass, 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. FubiniTonelli theorem.
Offered by: Mathematics and Statistics
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 Fall 2019
 Instructors
 Jerome Vetois

MATH 455 Honours Analysis 4 3 Credits++
 Fall
 Winter
 Summer
Offered in the:Mathematics & Statistics (Sci): Continuation of measure theory. Functional analysis: L^p spaces, linear functionals and dual spaces, HahnBanach theorem, Riesz representation theorem. Hilbert spaces, weak convergence. Spectral theory of compact operator. Introduction to Fourier analysis, Fourier transforms.
Offered by: Mathematics and Statistics
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 Winter 2020
 Instructors
 Dmitry Jakobson

MATH 458 Honours Differential Geometry 3 Credits
 Fall
 Winter
 Summer
Offered in the: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 FaryMilnor theorem on knotted curves, abstract surfaces as 2d manifolds, the Euler characteristic, the GaussBonnet theorem for surfaces.
Offered by: Mathematics and Statistics
 Prerequisites: MATH 251 or MATH 247, and MATH 248 or MATH 314 or MATH 358
 Prerequisites: MATH 251 or MATH 247, and MATH 248 or MATH 314.
 Restriction: Not open to students who have taken MATH 380.
 Symbols:
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 Winter 2020
 Instructors
 Jacques Claude Hurtubise

MATH 466 Honours Complex Analysis 3 Credits
 Fall
 Winter
 Summer
Offered in the:Mathematics & Statistics (Sci): Functions of a complex variable, CauchyRiemann 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.
Offered by: Mathematics and Statistics
 Prerequisite: MATH 255.
 Restriction: Not open to students who have taken or are taking MATH 366, MATH 249, MATH 316 and MATH 381.
 Symbols:
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 Fall 2019
 Instructors
 Sarah Harrison

MATH 475 Honours PDE's 3 Credits
 Fall
 Winter
 Summer
Offered in the:Mathematics & Statistics (Sci): First order partial differential equations, geometric theory, classification of second order linear equations, SturmLiouville 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
 Prerequisites: MATH 247 or MATH 251 or equivalent, and MATH 248 or MATH 358 or equivalent, MATH 325.
 Restriction: Not open to students who have taken MATH 375.
 Symbols:
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 Fall 2019
 Instructors
 Jessica Lin

MATH 478 Comput. Meth. in Applied Math 3 Credits
 Fall
 Winter
 Summer
Offered in the: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, NavierStokes equations
Offered by: Mathematics and Statistics
 Prerequisites: MATH 315 or MATH 325 or MATH 263; MATH 317 or MATH 387 or COMP 350 or MECH 309; or permission of the instructor
 This course will be taught in the winter semester.
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 Winter 2020
 Instructors
 JeanChristophe Nave

MATH 480 Honours Independent Study 3 Credits
 Fall
 Winter
 Summer
Offered in the: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
 Symbols:
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 Fall 2019
 Winter 2020
 Instructors
 Johanna Neslehova
 Johanna Neslehova
and any 500level 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 524 Nonparametric Statistics 4 Credits
 Fall
 Winter
 Summer
Offered in the:Mathematics & Statistics (Sci): Distribution free procedures for 2sample problem: Wilcoxon rank sum, SiegelTukey, Smirnov tests. Shift model: power and estimation. Single sample procedures: Sign, Wilcoxon signed rank tests. Nonparametric ANOVA: KruskalWallis, Friedman tests. Association: Spearman's rank correlation, Kendall's tau. Goodness of fit: Pearson's chisquare, likelihood ratio, KolmogorovSmirnov tests. Statistical software packages used.
Offered by: Mathematics and Statistics
 Symbols:
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 This course is not scheduled for the 20192020 academic year
 Instructors
 There are no professors associated with this course for the 20192020 academic year

MATH 547 Stochastic Processes 4 Credits
 Fall
 Winter
 Summer
Offered in the: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
 Prerequisites: MATH 356 and either MATH 247 or MATH 251.
 Restriction: Not open to students who have taken or are taking MATH 447.
 Symbols:
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 This course is not scheduled for the 20192020 academic year
 Instructors
 There are no professors associated with this course for the 20192020 academic year

MATH 556 Mathematical Statistics 1 4 Credits
 Fall
 Winter
 Summer
Offered in the:Mathematics & Statistics (Sci): Distribution theory, stochastic models and multivariate transformations. Families of distributions including locationscale families, exponential families, convolution families, exponential dispersion models and hierarchical models. Concentration inequalities. Characteristic functions. Convergence in probability, almost surely, in Lp and in distribution. Laws of large numbers and Central Limit Theorem. Stochastic simulation.
Offered by: Mathematics and Statistics
 Fall
 Prerequisite: MATH 357 or equivalent
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 Fall 2019
 Instructors
 David A Stephens

MATH 557 Mathematical Statistics 2 4 Credits
 Fall
 Winter
 Summer
Offered in the:Mathematics & Statistics (Sci): Sampling theory (including largesample theory). Likelihood functions and information matrices. Hypothesis testing, estimation theory. Regression and correlation theory.
Offered by: Mathematics and Statistics
 Winter
 Prerequisite: MATH 556
 Symbols:
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 Winter 2020
 Instructors
 Masoud AsgharianDastenaei

MATH 587 Advanced Probability Theory 1 4 Credits
 Fall
 Winter
 Summer
Offered in the: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
 Symbols:
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 Fall 2019
 Instructors
 Dana Louis AddarioBerry

MATH 589 Advanced Probability Theory 2 4 Credits
 Fall
 Winter
 Summer
Offered in the: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
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 Winter 2020
 Instructors
 Dana Louis AddarioBerry
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+++
 Fall
 Winter
 Summer
Offered in the: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.
 Symbols:
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 Terms
 Winter 2020
 Instructors
 Christian Genest

MATH 523 Generalized Linear Models 4 Credits
 Fall
 Winter
 Summer
Offered in the:Mathematics & Statistics (Sci): Modern discrete data analysis. Exponential families, orthogonality, link functions. Inference and model selection using analysis of deviance. Shrinkage (Bayesian, frequentist viewpoints). Smoothing. Residuals. Quasilikelihood. Contingency tables: logistic regression, loglinear models. Censored data. Applications to current problems in medicine, biological and physical sciences. R software.
Offered by: Mathematics and Statistics
 Symbols:
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 Winter 2020
 Instructors
 Johanna Neslehova

MATH 525 Sampling Theory & Applications 4 Credits
 Fall
 Winter
 Summer
Offered in the: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
 Symbols:
 Terms
 This course is not scheduled for the 20192020 academic year
 Instructors
 There are no professors associated with this course for the 20192020 academic year

MATH 545 Intro to Time Series Analysis 4 Credits
 Fall
 Winter
 Summer
Offered in the:Mathematics & Statistics (Sci): Stationary processes; estimation and forecasting of ARMA models; nonstationary and seasonal models; statespace models; financial time series models; multivariate time series models; introduction to spectral analysis; long memory models.
Offered by: Mathematics and Statistics
 Symbols:
 Terms
 Winter 2020
 Instructors
 Russell Steele
03 credits from the following courses for which no Honours equivalent exists:

MATH 329 Theory of Interest 3 Credits
 Fall
 Winter
 Summer
Offered in the:Mathematics & Statistics (Sci): Simple and compound interest, annuities certain, amortization schedules, bonds, depreciation.
Offered by: Mathematics and Statistics
 Winter
 Prerequisite: MATH 141
 Symbols:
 Terms
 Winter 2020
 Instructors
 There are no professors associated with this course for the 20192020 academic year

MATH 427 Statistical Quality Control 3 Credits
 Fall
 Winter
 Summer
Offered in the: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
 Symbols:
 Terms
 Fall 2019
 Instructors
 Christian Genest
The remaining credits selected from:
+++ Students may select either MATH 594 or MATH 598 but not both.

COMP 424 Artificial Intelligence 3 Credits
 Fall
 Winter
 Summer
Offered in the: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
 Symbols:
 Terms
 Winter 2020
 Instructors
 Jackie Cheung

COMP 551 Applied Machine Learning 4 Credits
 Fall
 Winter
 Summer
Offered in the:Computer Science (Sci): Selected topics in machine learning and data mining, including clustering, neural networks, support vector machines, decision trees. Methods include feature selection and dimensionality reduction, error estimation and empirical validation, algorithm design and parallelization, and handling of large data sets. Emphasis on good methods and practices for deployment of real systems.
Offered by: Computer Science
 Prerequisite(s): MATH 323 or ECSE 205 or ECSE 305 or equivalent
 Restriction(s): Not open to students who have taken COMP 598 when topic was "Applied Machine Learning"
 Some background in Artificial Intelligence is recommended, e.g. COMP424 or ECSE526, but not required.
 Symbols:
 Terms
 Fall 2019
 Winter 2020
 Instructors
 William L Hamilton
 Mohsen Ravanbakhsh, Reihaneh Rabbany

MATH 430 Mathematical Finance 3 Credits
 Fall
 Winter
 Summer
Offered in the: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
 Symbols:
 Terms
 Winter 2020
 Instructors
 Djivede A Kelome

MATH 540 Life Actuarial Mathematics 4 Credits
 Fall
 Winter
 Summer
Offered in the: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.
Offered by: Mathematics and Statistics
 Symbols:
 Terms
 This course is not scheduled for the 20192020 academic year
 Instructors
 There are no professors associated with this course for the 20192020 academic year

MATH 541 Nonlife Actuarial Models 4 Credits
 Fall
 Winter
 Summer
Offered in the: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, heavytail distributions, and extremes; dynamic risk models based on stochastic processes and ruin theory.
Offered by: Mathematics and Statistics
 Symbols:
 Terms
 This course is not scheduled for the 20192020 academic year
 Instructors
 There are no professors associated with this course for the 20192020 academic year

MATH 594 Topics in Mathematics&Stats 4 Credits+++
 Fall
 Winter
 Summer
Offered in the: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
 Symbols:
 +++
 Terms
 This course is not scheduled for the 20192020 academic year
 Instructors
 There are no professors associated with this course for the 20192020 academic year

MATH 598 Topics in Probability & Stats 4 Credits+++
 Fall
 Winter
 Summer
Offered in the: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.
 Symbols:
 +++
 Terms
 Winter 2020
 Instructors
 Jessica Lin