Program Requirements
Required Courses (46 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) : An introduction to the design of computer algorithms, including basic data structures, analysis of algorithms, and establishing correctness of programs. Overview of topics in computer science.
Terms: Fall 2010, Winter 2011
Instructors: Doina Precup (Fall) Michael Langer (Winter)
 3 hours
 Prerequisites: Familiarity with a high level programming language and CEGEP level Math.
 Restrictions: COMP 203 and COMP 250 are considered to be equivalent from a prerequisite point of view, and cannot both be taken for credit.

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 2010
Instructors: Heekyoung Hahn (Fall)
 Fall
 3 hours lecture; 1 hour tutorial
 Prerequisite: MATH 133 or equivalent

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 2010
Instructors: Reem Adel Yassawi (Fall)
 Fall
 Prerequisite: MATH 141

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 2011
Instructors: Axel W Hundemer (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 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 2010
Instructors: Pengfei Guan (Fall)
 Fall and Winter and Summer
 Prerequisites: MATH 133 and MATH 222 or consent of Department.
 Restriction: Intended for Honours Mathematics, Physics and Engineering students
 Restriction: Not open to students who have taken or are taking MATH 314

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 2011
Instructors: James G Loveys (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)
Overview
Mathematics & Statistics (Sci) : Series of functions including power series. Riemann integration in one variable. Elementary functions.
Terms: Winter 2011
Instructors: Vojkan Jaksic (Winter)
 Winter
 Prerequisites: MATH 242 or permission of the Department

MATH 354 Honours Analysis 3 (3 credits)
Overview
Mathematics & Statistics (Sci) : Introduction to metric spaces. Multivariable differential calculus, implicit and inverse function theorems.
Terms: Fall 2010
Instructors: Dmitry Jakobson (Fall)
 Fall
 Prerequisite: MATH 255 or equivalent

MATH 355 Honours Analysis 4 (3 credits)
Overview
Mathematics & Statistics (Sci) : Lebesque measure, integration and Fubini's theorem. Abstract measure and integration. Convergence theorems. Introduction to Hilbert spaces, L_2 spaces, Fourier series. Fourier integrals (if time allows).
Terms: Winter 2011
Instructors: Dmitry Jakobson (Winter)
 Winter
 Prerequisite: MATH 354 or equivalent.

MATH 356 Honours Probability (3 credits)
Overview
Mathematics & Statistics (Sci) : Basic combinatorial probability. Introductory distribution theory of univariate and multivariate distributions with special reference to the Binomial, Poisson, Gamma and Normal distributions. Characteristic functions. Weak law of large numbers. Central limit theorem.
Terms: Fall 2010
Instructors: Johanna Neslehova (Fall)
 Fall
 Prerequisite: MATH 255 or MATH 243
 Restriction: Not open to students who have taken or are taking MATH 323

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 2011
Instructors: Masoud AsgharianDastenaei (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)
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 2010, Winter 2011
Instructors: Djivede Kelome (Fall) Djivede Kelome (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 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. Sliced inverse regression. Contingency tables: logistic regression, loglinear models. Censored data. Applications to current problems in medicine, biological and physical sciences. GLIM, S, software.
Terms: Winter 2011
Instructors: David Stephens (Winter)
 Winter
 Prerequisite: MATH 423 or EPIB 697
 Restriction: Not open to students who have taken MATH 426

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 2010
Instructors: Abbas Khalili Mahmoudabadi (Fall)
 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.

MATH 556 Mathematical Statistics 1 (4 credits)
Overview
Mathematics & Statistics (Sci) : Probability and distribution theory (univariate and multivariate). Exponential families. Laws of large numbers and central limit theorem.
Terms: Fall 2010
Instructors: Johanna Neslehova (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 2011
Instructors: Christian Genest (Winter)
 Winter
 Prerequisite: MATH 556
Complementary Courses (15 credits)
The remaining credits selected from:

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: Fall 2010, Winter 2011
Instructors: Antony Raymond Humphries (Fall) Ivo Klemes (Winter)
 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

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: Winter 2011
Instructors: Bruce Alan Reed (Winter)
 Prerequisites: MATH 235 or MATH 240 and MATH 251 or MATH 223.
 Restrictions: Not open to students who have taken or are taking MATH 343 or MATH 340.
 Intended for students in mathematics or computer science honours programs.

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 2010
Instructors: James G Loveys (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 366 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: This course is not scheduled for the 20102011 academic year.
Instructors: There are no professors associated with this course for the 20102011 academic year.
 Prerequisite: MATH 248.
 Corequisite: MATH 354.
 Restriction: Not open to students who have taken or are taking MATH 466, MATH 249, MATH 316, MATH 381.

MATH 375 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 2010
Instructors: Charles Roth (Fall)
 Fall
 Prerequisites: MATH 247 or MATH 251 or equivalent, MATH 248 or equivalent, MATH 325

MATH 380 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 2011
Instructors: Pengfei Guan (Winter)
 Winter
 Prerequisites: MATH 251 or MATH 247, and MATH 248 or MATH 314

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 20102011 academic year.
Instructors: There are no professors associated with this course for the 20102011 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)
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 2011
Instructors: Antony Raymond Humphries (Winter)
 Winter
 Prerequisites: MATH 251 or MATH 247, COMP 202 or permission of the instructor.

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 2010, Winter 2011
Instructors: Axel W Hundemer (Fall) Axel W Hundemer (Winter)
 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 20102011 academic year.
Instructors: There are no professors associated with this course for the 20102011 academic year.
 Prerequisites: MATH 222, MATH 323 or equivalent. (Intended primarily for honours students.)
 Restrictions: Not open to students who have taken MATH 330. Not open to students who have taken or are taking MATH 430.
 Note: Additionally, a special project or projects may be assigned.

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 2010
Instructors: Christian Genest (Fall)
 Fall
 Prerequisite: MATH 324 or equivalent
 Restriction: Not open to students who have taken MATH 424

MATH 525 Sampling Theory and Applications (4 credits)
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: This course is not scheduled for the 20102011 academic year.
Instructors: There are no professors associated with this course for the 20102011 academic year.
 Prerequisite: MATH 324 or equivalent
 Restriction: Not open to students who have taken MATH 425

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 20102011 academic year.
Instructors: There are no professors associated with this course for the 20102011 academic year.
 Intended primarily for honours and graduate students in mathematics.
 Restriction: Permission of instructor.

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 2010
Instructors: Dana Louis AddarioBerry (Fall)
 Fall
 Prerequisite: MATH 356 or equivalent and approval 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 2011
Instructors: Dana Louis AddarioBerry (Winter)
 Winter
 Prerequisites: MATH 587 or equivalent
With at most 3 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 2011
Instructors: There are no professors associated with this course for the 20102011 academic year.
 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 20102011 academic year.
Instructors: There are no professors associated with this course for the 20102011 academic year.
 Winter
 Prerequisites: COMP 202; MATH 223 or MATH 236, MATH 314, MATH 315 and MATH 323

MATH 447 Introduction to Stochastic Processes (3 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: Winter 2011
Instructors: Dana Louis AddarioBerry (Winter)
 Winter
 Prerequisite: MATH 323
 Restriction: Not open to students who have taken or are taking MATH 547.