Program Requirements
Required Courses (47 credits)
* COMP 250 may be preceded by COMP 202.
** Students select either MATH 251 or MATH 247, but not both.

COMP 250 Introduction to Computer Science (3 credits) *
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 nonrecursive algorithms (searching and sorting, tree and graph traversal). Abstract data types, inheritance. Selected topics.
Terms: Fall 2018, Winter 2019
Instructors: Michael Langer, Giulia Alberini (Fall) Martin Robillard, Giulia Alberini (Winter)

MATH 235 Algebra 1 (3 credits)
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 2018
Instructors: Daniel Wise (Fall)
Fall
3 hours lecture; 1 hour tutorial
Prerequisite: MATH 133 or equivalent

MATH 247 Honours Applied Linear Algebra (3 credits) **
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 2019
Instructors: Tim Hoheisel (Winter)

MATH 248 Honours Advanced Calculus (3 credits)
Overview
Mathematics & Statistics (Sci) : Partial derivatives; implicit functions; Jacobians; maxima and minima; Lagrange multipliers. Scalar and vector fields; orthogonal curvilinear coordinates. Multiple integrals; arc length, volume and surface area. Line integrals; Green's theorem; the divergence theorem. Stokes' theorem; irrotational and solenoidal fields; applications.
Terms: Fall 2018
Instructors: Pengfei Guan (Fall)

MATH 251 Honours Algebra 2 (3 credits) **
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 selfadjoint operators.
Terms: Winter 2019
Instructors: Haining Wang (Winter)

MATH 255 Honours Analysis 2 (3 credits)
Overview
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.
Terms: Winter 2019
Instructors: Rustum Choksi (Winter)

MATH 356 Honours Probability (3 credits)
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, univariate transformations. Random vectors, independence, correlation, multivariate transformations. Conditional distributions, conditional expectation.Modes of stochastic convergence, laws of large numbers, Central Limit Theorem.
Terms: Fall 2018
Instructors: Linan Chen (Fall)

MATH 357 Honours Statistics (3 credits)
Overview
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.
Terms: Winter 2019
Instructors: Masoud AsgharianDastenaei (Winter)

MATH 454 Honours Analysis 3 (3 credits)
Overview
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.
Terms: Fall 2018
Instructors: Dmitry Jakobson (Fall)

MATH 470 Honours Research Project (3 credits)
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 2018, Winter 2019, Summer 2019
Instructors: Djivede Kelome, JeanPhilippe Lessard, David Stephens, Marcin Sabok, Daniel Wise, Dana Louis AddarioBerry, JeanChristophe Nave, Linan Chen, Michael Pichot, Jerome Vetois, Piotr Przytycki (Fall) Djivede Kelome, Dmitry Jakobson, Marcin Sabok, Henri Darmon, Eyal Z Goren, JeanChristophe Nave, Jacques Claude Hurtubise, David Stephens, Antony Raymond Humphries, Niky Kamran, Piotr Przytycki, Daniel Wise (Winter) Djivede Kelome, Jerome Vetois (Summer)
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 523 Generalized Linear Models (4 credits)
Overview
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.
Terms: Winter 2019
Instructors: Johanna Neslehova (Winter)

MATH 533 Honours Regression and Analysis of Variance (4 credits)
Overview
Mathematics & Statistics (Sci) : This course consists of the lectures of MATH 423 but will be assessed at the 500 level.
Terms: Fall 2018
Instructors: Yi Yang (Fall)

MATH 556 Mathematical Statistics 1 (4 credits)
Overview
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.
Terms: Fall 2018
Instructors: Masoud AsgharianDastenaei (Fall)
Fall
Prerequisite: MATH 357 or equivalent

MATH 557 Mathematical Statistics 2 (4 credits)
Overview
Mathematics & Statistics (Sci) : Sampling theory (including largesample theory). Likelihood functions and information matrices. Hypothesis testing, estimation theory. Regression and correlation theory.
Terms: Winter 2019
Instructors: Abbas Khalili Mahmoudabadi (Winter)
Winter
Prerequisite: MATH 556

MATH 587 Advanced Probability Theory 1 (4 credits)
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 2018
Instructors: Linan Chen (Fall)
Complementary Courses (18 credits)
3 credits selected from:
* It is strongly recommended that students take MATH 254.

MATH 242 Analysis 1 (3 credits)
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 2018
Instructors: Jerome Vetois (Fall)

MATH 254 Honours Analysis 1 (3 credits) *
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 2018
Instructors: Axel W Hundemer (Fall)
1215 credits selected from:
* MATH 455 cannot be taken as a substitute for MATH 587. Students may obtain credit for both MATH 587 and MATH 455.

MATH 325 Honours Ordinary Differential Equations (3 credits)
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 2019
Instructors: JeanPhilippe Lessard (Winter)

MATH 350 Graph Theory and Combinatorics (3 credits)
Overview
Mathematics & Statistics (Sci) : Graph models. Graph connectivity, planarity and colouring. Extremal graph theory. Matroids. Enumerative combinatorics and listing.
Terms: Fall 2018
Instructors: Adrian Roshan Vetta (Fall)

MATH 352 Problem Seminar (1 credit)
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 2018
Instructors: Jacques Claude Hurtubise (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 387 Honours Numerical Analysis (3 credits)
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 20182019 academic year.
Instructors: There are no professors associated with this course for the 20182019 academic year.

MATH 397 Honours Matrix Numerical Analysis (3 credits)
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 2019
Instructors: Ivo Panayotov (Winter)

MATH 455 Honours Analysis 4 (3 credits) *
Overview
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.
Terms: Winter 2019
Instructors: Jerome Vetois (Winter)
Restriction(s): Not open to students who have taken MATH 355.

MATH 458 Honours Differential Geometry (3 credits)
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 FaryMilnor theorem on knotted curves, abstract surfaces as 2d manifolds, the Euler characteristic, the GaussBonnet theorem for surfaces.
Terms: Winter 2019
Instructors: Jacques Claude Hurtubise (Winter)

MATH 466 Honours Complex Analysis (3 credits)
Overview
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.
Terms: Fall 2018
Instructors: Sarah Harrison (Fall)

MATH 475 Honours Partial Differential Equations (3 credits)
Overview
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.
Terms: Fall 2018
Instructors: Rustum Choksi (Fall)

MATH 480 Honours Independent Study (3 credits)
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 2018, Winter 2019, Summer 2019
Instructors: Johanna Neslehova, Jacques Claude Hurtubise, Dmitry Jakobson, Sarah Harrison, Dana Louis AddarioBerry, Jonah Gaster (Fall) Johanna Neslehova, Henri Darmon, Michael Lipnowski, Dmitry Jakobson (Winter) Johanna Neslehova, Gantumur Tsogtgerel, Jerome Vetois (Summer)
Fall and Winter and Summer
Please see regulations concerning Project Courses under Faculty Degree Requirements
Requires approval by the chair before registration

MATH 490 Honours Mathematics of Finance (3 credits)
Overview
Mathematics & Statistics (Sci) : This course consists of the lectures of MATH 430, but will be assessed at the honours level.
Terms: This course is not scheduled for the 20182019 academic year.
Instructors: There are no professors associated with this course for the 20182019 academic year.

MATH 524 Nonparametric Statistics (4 credits)
Overview
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.
Terms: Fall 2018
Instructors: Christian Genest (Fall)

MATH 525 Sampling Theory and Applications (4 credits)
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 2019
Instructors: Russell Steele (Winter)

MATH 545 Introduction to Time Series Analysis (4 credits)
Overview
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.
Terms: Fall 2018
Instructors: Russell Steele (Fall)

MATH 547 Stochastic Processes (4 credits)
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 20182019 academic year.
Instructors: There are no professors associated with this course for the 20182019 academic year.

MATH 550 Combinatorics (4 credits)
Overview
Mathematics & Statistics (Sci) : Enumerative combinatorics: inclusionexclusion, generating functions, partitions, lattices and Moebius inversion. Extremal combinatorics: Ramsey theory, Turan's theorem, Dilworth's theorem and extremal set theory. Graph theory: planarity and colouring. Applications of combinatorics.
Terms: This course is not scheduled for the 20182019 academic year.
Instructors: There are no professors associated with this course for the 20182019 academic year.
Intended primarily for honours and graduate students in mathematics.
Restriction: Permission of instructor.

MATH 589 Advanced Probability Theory 2 (4 credits)
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 2019
Instructors: Dana Louis AddarioBerry (Winter)
Winter
Prerequisites: MATH 587 or equivalent

MATH 594 Topics in Mathematics and Statistics
(4 credits)
Overview
Mathematics & Statistics (Sci) : This course covers a topic in mathematics and/or statistics.
Terms: Winter 2019
Instructors: Michael Pichot, Djivede Kelome, Johanna Neslehova (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)
Overview
Mathematics & Statistics (Sci) : This course covers a topic in probability and/or statistics.
Terms: Winter 2019
Instructors: Johanna Neslehova, David Stephens (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.
03 credits from the following courses for which no Honours equivalent exists:

MATH 204 Principles of Statistics 2 (3 credits)
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 2019
Instructors: Christian Genest (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 407 Dynamic Programming (3 credits)
Overview
Mathematics & Statistics (Sci) : Sequential decision problems, resource allocation, transportation problems, equipment replacement, integer programming, network analysis, inventory systems, project scheduling, queuing theory calculus of variations, markovian decision processes, stochastic path problems, reliability, discrete and continuous control processes.
Terms: This course is not scheduled for the 20182019 academic year.
Instructors: There are no professors associated with this course for the 20182019 academic year.

MATH 427 Statistical Quality Control (3 credits)
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 20182019 academic year.
Instructors: There are no professors associated with this course for the 20182019 academic year.