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Honours Probability and Statistics (64 credits)

Offered by: Mathematics and Statistics     Degree: Bachelor of Science

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) *

    Offered by: Computer Science (Faculty of Science)

    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 2014, Winter 2015

    Instructors: Mathieu Blanchette, Jérôme Waldispuhl, Hamed Hatami (Fall) Martin Robillard (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)

    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 2014

    Instructors: Payman L Kassaei (Fall)

    • Fall
    • 3 hours lecture; 1 hour tutorial
    • Prerequisite: MATH 133 or equivalent
  • 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 2014

    Instructors: Axel W Hundemer (Fall)

    • Fall
    • Prerequisite: MATH 141
    • Restriction(s): Not open to students who are taking or who have taken MATH 254.
  • 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 2015

    Instructors: Piotr Przytycki (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)

    Offered by: Mathematics and Statistics (Faculty of Science)

    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 2014

    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) **

    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 2015

    Instructors: Piotr Przytycki (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, Hölder 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 2015

    Instructors: Vojkan Jaksic (Winter)

    • Winter
    • Prerequisites: MATH 242 or MATH 254 or permission of the Department
  • MATH 354 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 2014

    Instructors: Stephen W Drury (Fall)

    • Fall
    • Prerequisite: MATH 255 or equivalent
  • 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 2014

    Instructors: Abbas Khalili Mahmoudabadi (Fall)

    • Fall
    • Prerequisite(s): MATH 133 or MATH 134, and MATH 222 or permisson of the Department.
    • Corequisite(s): MATH 242 or MATH 254
  • 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 2015

    Instructors: David B Wolfson (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 2014, Winter 2015

    Instructors: Djivede Kelome, Antony Raymond Humphries, Jean-Christophe Nave, Gantumur Tsogtgerel, Adrian Roshan Vetta (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)

    Offered by: Mathematics and Statistics (Faculty of Science)

    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. Quasi-likelihood. Contingency tables: logistic regression, log-linear models. Censored data. Applications to current problems in medicine, biological and physical sciences. R software.

    Terms: Winter 2015

    Instructors: Russell Steele (Winter)

    • Winter
    • Prerequisite: MATH 423
    • Restriction: Not open to students who have taken MATH 426
  • MATH 533 Honours Regression and Analysis of Variance (4 credits)

    Offered by: Mathematics and Statistics (Faculty of Science)

    Overview

    Mathematics & Statistics (Sci) : This course consists of the lectures of MATH 423 but will be assessed at the 500 level.

    Terms: Fall 2014

    Instructors: David Stephens (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)

    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 2014

    Instructors: David Stephens (Fall)

    • 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 2015

    Instructors: Abbas Khalili Mahmoudabadi (Winter)

    • Winter
    • Prerequisite: MATH 556

Complementary Courses (18 credits)

At least 3 credits from:

  • MATH 355 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 2015

    Instructors: Stephen W Drury (Winter)

    • Winter
    • Prerequisite: MATH 354 or equivalent.
  • 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 2014

    Instructors: Linan Chen (Fall)

    • Fall
    • Prerequisite(s): MATH 356 and MATH 255 or MATH 243 or equivalent.

The remaining credits selected from:

  • 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: Fall 2014, Winter 2015

    Instructors: Antony Raymond Humphries (Fall) Charles Roth (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 Graph Theory and Combinatorics (3 credits)

    Offered by: Mathematics and Statistics (Faculty of Science)

    Overview

    Mathematics & Statistics (Sci) : Graph models. Graph connectivity, planarity and colouring. Extremal graph theory. Matroids. Enumerative combinatorics and listing.

    Terms: Fall 2014

    Instructors: Sergey Norin (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 343 or MATH 340.
    • 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 2014

    Instructors: Sergey Norin (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)

    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 2014

    Instructors: Dmitry Jakobson (Fall)

    • 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)

    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 2014

    Instructors: Adam Oberman (Fall)

    • Fall
    • Prerequisites: MATH 247 or MATH 251 or equivalent, MATH 248 or equivalent, MATH 325
  • MATH 380 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 2015

    Instructors: Niky Kamran (Winter)

    • Winter
    • Prerequisites: MATH 251 or MATH 247, and MATH 248 or MATH 314
  • 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 2014-2015 academic year.

    Instructors: There are no professors associated with this course for the 2014-2015 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 2015

    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)

    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 2014, Winter 2015

    Instructors: Vojkan Jaksic, Michael Pichot (Fall) Vojkan Jaksic (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)

    Offered by: Mathematics and Statistics (Faculty of Science)

    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 2014-2015 academic year.

    Instructors: There are no professors associated with this course for the 2014-2015 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)

    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 2014

    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)

    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: This course is not scheduled for the 2014-2015 academic year.

    Instructors: There are no professors associated with this course for the 2014-2015 academic year.

    • 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 2014-2015 academic year.

    Instructors: There are no professors associated with this course for the 2014-2015 academic year.

    • Prerequisite: MATH 324 or MATH 357 or equivalent
  • 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 2014-2015 academic year.

    Instructors: There are no professors associated with this course for the 2014-2015 academic year.

    • Prerequisites: MATH 356 and either MATH 247 or MATH 251.
    • Restriction: Not open to students who have taken or are taking MATH 447.
  • MATH 550 Combinatorics (4 credits)

    Offered by: Mathematics and Statistics (Faculty of Science)

    Overview

    Mathematics & Statistics (Sci) : Enumerative combinatorics: inclusion-exclusion, 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: Winter 2015

    Instructors: Sergey Norin (Winter)

    • Intended primarily for honours and graduate students in mathematics.
    • Restriction: Permission of instructor.
  • 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: This course is not scheduled for the 2014-2015 academic year.

    Instructors: There are no professors associated with this course for the 2014-2015 academic year.

    • Winter
    • Prerequisites: MATH 587 or equivalent
  • MATH 598 Topics in Probability & 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: This course is not scheduled for the 2014-2015 academic year.

    Instructors: There are no professors associated with this course for the 2014-2015 academic year.

    • 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.

With at most 3 credits from the following courses for which no Honours equivalent exists:

  • 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 2015

    Instructors: There are no professors associated with this course for the 2014-2015 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)

    Offered by: Mathematics and Statistics (Faculty of Science)

    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 2014-2015 academic year.

    Instructors: There are no professors associated with this course for the 2014-2015 academic year.

    • Winter
    • Prerequisites: COMP 202; MATH 223 or MATH 236, MATH 314, MATH 315 and MATH 323
  • 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 2014-2015 academic year.

    Instructors: There are no professors associated with this course for the 2014-2015 academic year.

    • Prerequisites: MATH 323 + MATH 324
Faculty of Science—2014-2015 (last updated Feb. 18, 2014) (disclaimer)