# Honours Probability and Statistics (65 credits)

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Offered by: Mathematics and Statistics     Degree: Bachelor of Arts

### 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) *

Offered by: Computer Science (Faculty of Science)

### Overview

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

Terms: Fall 2017, Winter 2018

Instructors: Michael Langer (Fall) Carlos Gonzalez Oliver, Jérôme Waldispuhl (Winter)

• 3 hours

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

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

• MATH 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 2017

Instructors: Daniel Wise (Fall)

• Fall

• 3 hours lecture; 1 hour tutorial

• Prerequisite: MATH 133 or equivalent

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

Offered by: Mathematics and Statistics (Faculty of Science)

### Overview

Mathematics & Statistics (Sci) : Matrix algebra, determinants, systems of linear equations. Abstract vector spaces, inner product spaces, Fourier series. Linear transformations and their matrix representations. Eigenvalues and eigenvectors, diagonalizable and defective matrices, positive definite and semidefinite matrices. Quadratic and Hermitian forms, generalized eigenvalue problems, simultaneous reduction of quadratic forms. Applications.

Terms: Winter 2018

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)

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 2017

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 2018

Instructors: Jan Vonk (Winter)

• Winter

• Prerequisites: MATH 235 or permission of the Department

• Restriction: Not open to students who are taking or have taken MATH 247

• MATH 255 Honours Analysis 2 (3 credits)

Offered by: Mathematics and Statistics (Faculty of Science)

### Overview

Mathematics & Statistics (Sci) : Basic point-set topology, metric spaces: open and closed sets, normed and Banach spaces, HÃ¶lder and Minkowski inequalities, sequential compactness, Heine-Borel, Banach Fixed Point theorem. Riemann-(Stieltjes) integral, Fundamental Theorem of Calculus, Taylor's theorem. Uniform convergence. Infinite series, convergence tests, power series. Elementary functions.

Terms: Winter 2018

Instructors: Rustum Choksi (Winter)

• MATH 356 Honours Probability (3 credits)

Offered by: Mathematics and Statistics (Faculty of Science)

### Overview

Mathematics & Statistics (Sci) : Sample space, probability axioms, combinatorial probability. Conditional probability, Bayes' Theorem. Distribution theory with special reference to the Binomial, Poisson, and Normal distributions. Expectations, moments, moment generating functions, uni-variate transformations. Random vectors, independence, correlation, multivariate transformations. Conditional distributions, conditional expectation.Modes of stochastic convergence, laws of large numbers, Central Limit Theorem.

Terms: Fall 2017

Instructors: Linan Chen (Fall)

• 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 2018

Instructors: David B Wolfson (Winter)

• 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

• MATH 454 Honours Analysis 3 (3 credits)

Offered by: Mathematics and Statistics (Faculty of Science)

### Overview

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

Terms: Fall 2017

Instructors: Laurent Bruneau (Fall)

• 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 2017, Winter 2018, Summer 2018

Instructors: Djivede Kelome, Gantumur Tsogtgerel, Jerome Vetois, Tim Hoheisel, John A Toth, Niky Kamran, Dana Louis Addario-Berry, Yi Yang, Daniel Wise, Eyal Z Goren (Fall) Djivede Kelome, Anmar Khadra, Linan Chen, Yi Yang, Dmitry Jakobson, Eyal Z Goren, John A Toth, Rustum Choksi, Piotr Przytycki (Winter) Djivede Kelome, Jerome Vetois, Linan Chen (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)

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 2018

Instructors: Johanna Neslehova (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 2017

Instructors: Yi Yang (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 2017

Instructors: Masoud Asgharian-Dastenaei (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 2018

Instructors: Abbas Khalili Mahmoudabadi (Winter)

• MATH 587 Advanced Probability Theory 1 (4 credits)

Offered by: Mathematics and Statistics (Faculty of Science)

### Overview

Mathematics & Statistics (Sci) : Probability spaces. Random variables and their expectations. Convergence of random variables in Lp. Independence and conditional expectation. Introduction to Martingales. Limit theorems including Kolmogorov's Strong Law of Large Numbers.

Terms: Fall 2017

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)

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 2017

Instructors: Jerome Vetois (Fall)

• Fall

• Prerequisite: MATH 141

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

• MATH 254 Honours Analysis 1 (3 credits) *

Offered by: Mathematics and Statistics (Faculty of Science)

### Overview

Mathematics & Statistics (Sci) : Properties of R. Cauchy and monotone sequences, Bolzano- Weierstrass theorem. Limits, limsup, liminf of functions. Pointwise, uniform continuity: Intermediate Value theorem. Inverse and monotone functions. Differentiation: Mean Value theorem, L'Hospital's rule, Taylor's Theorem.

Terms: Fall 2017

Instructors: Axel W Hundemer (Fall)

• Prerequisite(s): MATH 141

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

12-15 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)

Offered by: Mathematics and Statistics (Faculty of Science)

### Overview

Mathematics & Statistics (Sci) : First and second order equations, linear equations, series solutions, Frobenius method, introduction to numerical methods and to linear systems, Laplace transforms, applications.

Terms: Winter 2018

Instructors: Antony Raymond Humphries (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 2017

Instructors: Jan Volec (Fall)

• 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 2017

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 2017

Instructors: Sarah Harrison (Fall)

• 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: Winter 2018

Instructors: Gantumur Tsogtgerel (Winter)

• 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: This course is not scheduled for the 2017-2018 academic year.

Instructors: There are no professors associated with this course for the 2017-2018 academic year.

• MATH 455 Honours Analysis 4 (3 credits) *

Offered by: Mathematics and Statistics (Faculty of Science)

### Overview

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

Terms: Winter 2018

Instructors: Jerome Vetois (Winter)

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

• MATH 458 Honours Differential Geometry (3 credits)

Offered by: Mathematics and Statistics (Faculty of Science)

### Overview

Mathematics & Statistics (Sci) : In addition to the topics of MATH 320, topics in the global theory of plane and space curves, and in the global theory of surfaces are presented. These include: total curvature and the Fary-Milnor theorem on knotted curves, abstract surfaces as 2-d manifolds, the Euler characteristic, the Gauss-Bonnet theorem for surfaces.

Terms: Winter 2018

Instructors: Jacques Claude Hurtubise (Winter)

• Restriction(s): Not open to students who have taken MATH 380.

• MATH 475 Honours Partial Differential Equations (3 credits)

Offered by: Mathematics and Statistics (Faculty of Science)

### Overview

Mathematics & Statistics (Sci) : First order partial differential equations, geometric theory, classification of second order linear equations, Sturm-Liouville problems, orthogonal functions and Fourier series, eigenfunction expansions, separation of variables for heat, wave and Laplace equations, Green's function methods, uniqueness theorems.

Terms: Fall 2017

Instructors: Rustum Choksi (Fall)

• Restriction(s): Not open to students who have taken MATH 375.

• 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 2017, Winter 2018, Summer 2018

Instructors: Axel W Hundemer, Prakash Panangaden, Piotr Przytycki (Fall) Axel W Hundemer, Eyal Z Goren, Tim Hoheisel, Linan Chen, Bogdan Lucian Nica (Winter) Johanna Neslehova, Jessica Lin, Dmitry Jakobson (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)

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 2017-2018 academic year.

Instructors: There are no professors associated with this course for the 2017-2018 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 2017

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 2017-2018 academic year.

Instructors: There are no professors associated with this course for the 2017-2018 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: Fall 2017

Instructors: David Stephens (Fall)

• 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: Winter 2018

Instructors: Dana Louis Addario-Berry (Winter)

• 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 2018

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 2017-2018 academic year.

Instructors: There are no professors associated with this course for the 2017-2018 academic year.

• Winter

• Prerequisites: MATH 587 or equivalent

• MATH 598 Topics in Probability and Statistics (4 credits)

Offered by: Mathematics and Statistics (Faculty of Science)

### Overview

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

Terms: Fall 2017, Winter 2018

Instructors: Johanna Neslehova (Fall) 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.

0-3 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 2018

Instructors: Russell Steele (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)

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 2017-2018 academic year.

Instructors: There are no professors associated with this course for the 2017-2018 academic year.

• 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: Winter 2018

Instructors: Christian Genest (Winter)

Faculty of Arts—2017-2018 (last updated Aug. 23, 2017) (disclaimer)