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Program Requirements

Program Prerequisites

The minimum requirement for entry into the Honours program is that the student has completed with high standing the following courses below or their equivalents. In addition, a student who has not completed the equivalent of MATH 222 must take it in the first term without receiving credits toward the credits required in the Honours program.

Students who transfer to Honours in Mathematics from other programs will have credits for previous courses assigned, as appropriate, by the Department.

To remain in an Honours program and to be awarded the Honours degree, the student must maintain a 3.00 GPA in the required and complementary Mathematics courses of the program, as well as an overall CGPA of 3.00.

• MATH 133 Linear Algebra and Geometry (3 credits)

  Offered by: Mathematics and Statistics (Faculty of Science)

  Overview

  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.

  Terms: Fall 2015, Winter 2016, Summer 2016

  Instructors: Disegni, Daniel; Kelome, Djivede; Baratin, Aristide; Anderson, William J (Fall) Novytska, Yuliya; Kelome, Djivede (Winter) Baratin, Aristide (Summer)

  • 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.

• MATH 140 Calculus 1 (3 credits)

  Offered by: Mathematics and Statistics (Faculty of Science)

  Overview

  Mathematics & Statistics (Sci) : Review of functions and graphs. Limits, continuity, derivative. Differentiation of elementary functions. Antidifferentiation. Applications.

  Terms: Fall 2015, Winter 2016, Summer 2016

  Instructors: Hundemer, Axel W; Hu, Ying; Wallace, Michael (Fall) Vonk, Jan (Winter) Jakobson, Dmitry (Summer)

  • 3 hours lecture, 1 hour tutorial

  • Prerequisite: High School Calculus

  • Restriction: Not open to students who have taken MATH 120, MATH 139 or CEGEP objective 00UN 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

  • Each Tutorial section is enrolment limited

• MATH 141 Calculus 2 (4 credits)

  Offered by: Mathematics and Statistics (Faculty of Science)

  Overview

  Mathematics & Statistics (Sci) : The definite integral. Techniques of integration. Applications. Introduction to sequences and series.

  Terms: Fall 2015, Winter 2016, Summer 2016

  Instructors: Pang, Chung Yin Amy (Fall) Shokoohi, Farhad; Hundemer, Axel W; Barsheshat, Yariv (Winter) Al Balushi, Ibrahim; ³ÉÈËVRÊÓƵivray, Annaliza (Summer)

  • Prerequisites: MATH 139 or MATH 140 or MATH 150.

  • Restriction: Not open to students who have taken MATH 121 or CEGEP objective 00UP 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.

  • Each Tutorial section is enrolment limited

Required Courses (48 credits)

* MATH 314 may be substituted for MATH 248 if MATH 222 had to be taken in the Fall.

** Not open to students who have taken MATH 354.

*** Not open to students who have taken MATH 355.

^ Not open to students who have taken MATH 380.

+ Not open to students who have taken MATH 370.

++ Not open to students who have taken MATH 371.

+++ Not open to students who have taken MATH 375.

• 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 2015

  Instructors: Goren, Eyal Z (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 2015

  Instructors: Hundemer, Axel W (Fall)

  • Fall

  • Prerequisite: MATH 141

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

• 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 2015

  Instructors: Guan, Pengfei (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 2016

  Instructors: Przytycki, Piotr (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 2016

  Instructors: Jaksic, Vojkan (Winter)

  • Winter

  • Prerequisites: MATH 242 or MATH 254 or permission of the Department

• 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 2015, Winter 2016

  Instructors: Li, JunFang (Fall) Humphries, Antony Raymond (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 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 2015

  Instructors: Khalili Mahmoudabadi, Abbas (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 2016

  Instructors: Asgharian-Dastenaei, Masoud (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 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 2015

  Instructors: Koosis, Paul (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 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 2015

  Instructors: Drury, Stephen W (Fall)

• 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 2016

  Instructors: Drury, Stephen W (Winter)

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

• MATH 456 Honours Algebra 3 (3 credits) +

  Offered by: Mathematics and Statistics (Faculty of Science)

  Overview

  Mathematics & Statistics (Sci) : Introduction to monoids, groups, permutation groups; the isomorphism theorems for groups; the theorems of Cayley, Lagrange and Sylow; structure of groups of low order. Introduction to ring theory; integral domains, fields, quotient field of an integral domain; polynomial rings; unique factorization domains.

  Terms: Fall 2015

  Instructors: Barrera, Daniel (Fall)

  • Restriction(s): Not open to students who have taken MATH 370.

• MATH 457 Honours Algebra 4 (3 credits) ++

  Offered by: Mathematics and Statistics (Faculty of Science)

  Overview

  Mathematics & Statistics (Sci) : Introduction to modules and algebras; finitely generated modules over a principal ideal domain. Field extensions; finite fields; Galois groups; the fundamental theorem of Galois theory; application to the classical problem of solvability by radicals.

  Terms: Winter 2016

  Instructors: Barrera, Daniel (Winter)

  • Restriction(s): Not open to students who have taken MATH 371.

• 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 2016

  Instructors: Przytycki, Piotr (Winter)

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

• 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 2015, Winter 2016, Summer 2016

  Instructors: Kelome, Djivede; Norin, Sergey; Sabok, Marcin; Darmon, Henri; Jaksic, Vojkan; Wise, Daniel (Fall) Kelome, Djivede; Goren, Eyal Z; Darmon, Henri; Jaksic, Vojkan; Kamran, Niky; Vetta, Adrian Roshan; Asgharian-Dastenaei, Masoud; Jakobson, Dmitry (Winter) Kelome, Djivede; Pichot, Michael; Hurtubise, Jacques Claude; Stephens, David (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 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 2015

  Instructors: Choksi, Rustum (Fall)

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

Complementary Courses (12 credits)

12 credits selected from:

• 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 2015

  Instructors: Norin, Sergey (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 2015

  Instructors: Norin, Sergey (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 376 Honours Nonlinear Dynamics (3 credits)

  Offered by: Mathematics and Statistics (Faculty of Science)

  Overview

  Mathematics & Statistics (Sci) : This course consists of the lectures of MATH 326, but will be assessed at the honours level.

  Terms: Fall 2015

  Instructors: Nave, Jean-Christophe (Fall)

  • 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.

• MATH 377 Honours Number Theory (3 credits)

  Offered by: Mathematics and Statistics (Faculty of Science)

  Overview

  Mathematics & Statistics (Sci) : This course consists of the lectures of MATH 346, but will be assessed at the honours level.

  Terms: This course is not scheduled for the 2015-2016 academic year.

  Instructors: There are no professors associated with this course for the 2015-2016 academic year.

  • Winter

  • Prerequisite: Enrolment in Mathematics Honours program or consent of instructor

  • Restriction: Not open to students who have taken or are taking MATH 346.

  • Note: Additionally, a special project or projects may be assigned.

• 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 2016

  Instructors: Tsogtgerel, Gantumur (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 2015-2016 academic year.

  Instructors: There are no professors associated with this course for the 2015-2016 academic year.

  • 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 2015, Winter 2016, Summer 2016

  Instructors: Jaksic, Vojkan; Chen, Linan; Shepherd, Frederick (Fall) Jaksic, Vojkan; Stephens, David; Guan, Pengfei (Winter) Jaksic, Vojkan; Jakobson, Dmitry (Summer)

  • Fall and Winter and Summer

  • Please see regulations concerning Project Courses under Faculty Degree Requirements

  • Requires approval by the chair before registration

• MATH 487 Honours Mathematical Programming (3 credits)

  Offered by: Mathematics and Statistics (Faculty of Science)

  Overview

  Mathematics & Statistics (Sci) : The course consists of the lectures of MATH 417, but will be assessed at the honours level.

  Terms: Fall 2015

  Instructors: Shepherd, Frederick (Fall)

  • Prerequisites: MATH 248, MATH 251 and COMP 202 or COMP 250 or permission of instructor.

  • Restriction: Intended primarily for honours students. Not open to students who have taken or are taking MATH 417.

  • Note: Additionally, a special project or projects may be assigned.

• MATH 488 Honours Set Theory (3 credits)

  Offered by: Mathematics and Statistics (Faculty of Science)

  Overview

  Mathematics & Statistics (Sci) : Axioms of set theory. Operations on sets. Ordinal and cardinal numbers. Well-orderings, transfinite induction and recursion. Consequences of the axiom of choice. Boolean algebras. Cardinal arithmetic.

  Terms: This course is not scheduled for the 2015-2016 academic year.

  Instructors: There are no professors associated with this course for the 2015-2016 academic year.

  • Fall

  • Prerequisites: MATH 251 or MATH 255 or permission of instructor

all MATH 500-level courses.

Honours-level courses from related disciplines:

* COMP 250 may be preceded by COMP 202.

• 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 2015, Winter 2016

  Instructors: Blanchette, Mathieu; Waldispuhl, Jérôme (Fall) Crepeau, Claude (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.

• COMP 252 Honours Algorithms and Data Structures (3 credits)

  Offered by: Computer Science (Faculty of Science)

  Overview

  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.

  Terms: Winter 2016

  Instructors: Devroye, Luc P (Winter)

  • 3 hours

  • Prerequisite: COMP 250 and MATH 240

  • Restrictions: Open only to students registered in following programs: Honours in Computer Science, Joint Honours in Mathematics and Computer Science, Honours in Applied Mathematics, Honours in Mathematics. Not open to students who have taken or are taking COMP 251.

  • Note: COMP 252 can be used instead of COMP 251 to satisfy prerequisites.

no more than 6 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 2016

  Instructors: Wallace, Michael (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 329 Theory of Interest (3 credits)

  Offered by: Mathematics and Statistics (Faculty of Science)

  Overview

  Mathematics & Statistics (Sci) : Simple and compound interest, annuities certain, amortization schedules, bonds, depreciation.

  Terms: Winter 2016

  Instructors: Kelome, Djivede (Winter)

  • Winter

  • Prerequisite: MATH 141

• MATH 338 History and Philosophy of Mathematics (3 credits)

  Offered by: Mathematics and Statistics (Faculty of Science)

  Overview

  Mathematics & Statistics (Sci) : Egyptian, Babylonian, Greek, Indian and Arab contributions to mathematics are studied together with some modern developments they give rise to, for example, the problem of trisecting the angle. European mathematics from the Renaissance to the 18th century is discussed in some detail.

  Terms: Fall 2015

  Instructors: Fox, Thomas F (Fall)

  • Fall

• MATH 348 Topics in Geometry (3 credits)

  Offered by: Mathematics and Statistics (Faculty of Science)

  Overview

  Mathematics & Statistics (Sci) : Selected topics - the particular selection may vary from year to year. Topics include: isometries in the plane, symmetry groups of frieze and ornamental patterns, equidecomposibility, non-Euclidean geometry and problems in discrete geometry.

  Terms: This course is not scheduled for the 2015-2016 academic year.

  Instructors: There are no professors associated with this course for the 2015-2016 academic year.

  • Prerequisite: MATH 133 or equivalent or permission of instructor.

• 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 2015-2016 academic year.

  Instructors: There are no professors associated with this course for the 2015-2016 academic year.

  • Winter

  • Prerequisites: COMP 202; MATH 223 or MATH 236, MATH 314, MATH 315 and MATH 323

Students may select other courses with the permission of the Department.