Mathematics, Applied (Faculty of Arts)
Applied Mathematics is a very broad field. In addition to developing a sound basis in Applied Mathematics, one of the objectives of the program is to kindle the students' interest in possible areas of application. To develop an appreciation of the diversity of Applied Mathematics, students are advised to develop some depth (e.g., by completing a minor) in a field related to Applied Mathematics such as Atmospheric and Oceanic Sciences, Biology, Biochemistry, Chemistry, Computer Science, Earth and Planetary Sciences, Economics, Engineering, Management, Physics, Physiology, and Psychology.
DETAILED PROGRAM OUTLINE:
Program Requirement:
Applied Mathematics is a very broad field and students are encouraged to choose a coherent program of complementary courses. Most students specialize in "continuous" or "discrete" applied mathematics, but there are many sensible combinations of courses, and the following informal guidelines should be discussed with the student's adviser. Also, aside from seeking to develop a sound basis in Applied Mathematics, one of the objectives of the program is to kindle the students' interest in possible areas of application. To develop an appreciation of the diversity of Applied Mathematics, students are advised to develop some depth (e.g., by completing a minor) in a field related to Applied Mathematics such as Atmospheric and Oceanic Sciences, Biology, Biochemistry, Chemistry, Computer Science, Earth and Planetary Sciences, Economics, Engineering, Management, Physics, Physiology, and Psychology.
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:

MATH 133 Linear Algebra and Geometry 3 Credits
 Fall
 Winter
 Summer
Offered in the: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. Linear transformations. Eigenvalues and diagonalization.
Offered by: Mathematics and Statistics
 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, except by permission of the Department of Mathematics and Statistics.
 Restriction C: Not open to students who are taking or have taken MATH 134.
 Symbols:
 Terms
 Fall 2020
 Winter 2021
 Instructors
 Rosalie BélangerRioux, Piotr Przytycki
 Djivede A Kelome

MATH 150 Calculus A 4 Credits
 Fall
 Winter
 Summer
Offered in the:Mathematics & Statistics (Sci): Functions, limits and continuity, differentiation, L'Hospital's rule, applications, Taylor polynomials, parametric curves, functions of several variables.
Offered by: Mathematics and Statistics
 Fall
 3 hours lecture, 2 hours tutorial
 Students with no prior exposure to vector geometry are advised to take MATH 133 concurrently. Intended for students with high school calculus who have not received six advanced placement credits
 Restriction: Not open to students who have taken CEGEP objective 00UN or equivalent
 Restriction Note B: Not open to students who have taken or are taking MATH 122, except by permission of the Department of Mathematics and Statistics
 MATH 150 and MATH 151 cover the material of MATH 139, MATH 140, MATH 141, MATH 222
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 Fall 2020
 Instructors
 Charles Roth

MATH 151 Calculus B 4 Credits
 Fall
 Winter
 Summer
Offered in the:Mathematics & Statistics (Sci): Integration, methods and applications, infinite sequences and series, power series, arc length and curvature, multiple integration.
Offered by: Mathematics and Statistics
 Winter
 3 hours lecture; 2 hours tutorial
 Each Tutorial section is enrolment limited
 Prerequisite: MATH 150
 Restriction: Not open to students who have taken CEGEP objective 00UP or equivalent
 Restriction: Not open to students who have taken or are taking MATH 122, except by permission of the Department of Mathematics and Statistics
 Restriction: Not open to students who have taken MATH 152
 Symbols:
 Terms
 Winter 2021
 Instructors
 Charles Roth
In particular, MATH 150/151 and MATH 140/222 are considered equivalent.
Students who have not completed an equivalent of MATH 222 on entering the program must consult an academic adviser and take MATH 222 as a required course in the first semester, increasing the total number of program credits from 60 to 63. Students who have successfully completed MATH 150/151 are not required to take MATH 222.
Note: COMP 202—or an equivalent introduction to computer programming course—is a program prerequisite. U0 students may take COMP 202 as a Freshman Science course; new U1 students should take it as an elective in their first semester.
Students who transfer to Honours in Applied Mathematics from other programs will have credits for previous courses assigned, as appropriate, by the Department.
To be awarded the Honours degree, the student must have, at time of graduation, a CGPA of at least 3.00 in the required and complementary Mathematics courses of the program, as well as an overall CGPA of at least 3.00.
Required Courses
(3942 credits)
* Students with limited programming experience should take COMP 202 or COMP 204 or COMP 208 or equivalent before COMP 250.
** Students select either MATH 251 or MATH 247, but not both.
*** Students who have successfully completed MATH 150/151 or an equivalent of MATH 222 on entering the program are not required to take MATH 222.

COMP 250 Intro to Computer Science 3 Credits*
 Fall
 Winter
 Summer
Offered in the:Computer Science (Sci): Mathematical tools (binary numbers, induction, recurrence relations, asymptotic complexity, establishing correctness of programs), Data structures (arrays, stacks, queues, linked lists, trees, binary trees, binary search trees, heaps, hash tables), Recursive and nonrecursive algorithms (searching and sorting, tree and graph traversal). Abstract data types, inheritance. Selected topics.
Offered by: Computer Science
 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.
 Symbols:
 *
 Terms
 Fall 2020
 Winter 2021
 Instructors
 Giulia Alberini
 Giulia Alberini

COMP 252 Honours Algorithms&Data Struct 3 Credits
 Fall
 Winter
 Summer
Offered in the: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.
Offered by: Computer Science
 3 hours
 Prerequisite: COMP 250 and either MATH 235 or MATH 240
 Restrictions: (1) Open only to students in Honours programs. (2) Students cannot receive credit for both COMP 251 and COMP 252.
 COMP 252 uses basic combinatorial counting methods that are covered in MATH 240 but not in MATH 235. Students who are unfamiliar with these methods should speak with the instructor for guidance.
 Symbols:
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 Winter 2021
 Instructors
 Claude Crepeau

MATH 222 Calculus 3 3 Credits***
 Fall
 Winter
 Summer
Offered in the:Mathematics & Statistics (Sci): Taylor series, Taylor's theorem in one and several variables. Review of vector geometry. Partial differentiation, directional derivative. Extreme of functions of 2 or 3 variables. Parametric curves and arc length. Polar and spherical coordinates. Multiple integrals.
Offered by: Mathematics and Statistics
 Prerequisite: MATH 141. Familiarity with vector geometry or Corequisite: MATH 133
 Restriction: Not open to students who have taken CEGEP course 201303 or MATH 150, MATH 151 or MATH 227
 Symbols:
 ***
 Terms
 Fall 2020
 Winter 2021
 Instructors
 Djivede A Kelome, Jérôme Fortier
 Jerome Vetois

MATH 235 Algebra 1 3 Credits
 Fall
 Winter
 Summer
Offered in the: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.
Offered by: Mathematics and Statistics
 Fall
 3 hours lecture; 1 hour tutorial
 Prerequisite: MATH 133 or equivalent
 Symbols:
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 Fall 2020
 Instructors
 Daniel T Wise

MATH 247 Honours Applied Linear Algebra 3 Credits**
 Fall
 Winter
 Summer
Offered in the: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.
Offered by: Mathematics and Statistics
 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
 Symbols:
 **
 Terms
 Winter 2021
 Instructors
 Tim Hoheisel

MATH 251 Honours Algebra 2 3 Credits**
 Fall
 Winter
 Summer
Offered in the: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.
Offered by: Mathematics and Statistics
 Winter
 Prerequisites: MATH 235 or permission of the Department
 Restriction: Not open to students who are taking or have taken MATH 247
 Symbols:
 **
 Terms
 Winter 2021
 Instructors
 Michael Lipnowski

MATH 255 Honours Analysis 2 3 Credits
 Fall
 Winter
 Summer
Offered in the:Mathematics & Statistics (Sci): Basic pointset topology, metric spaces: open and closed sets, normed and Banach spaces, HÃ¶lder and Minkowski inequalities, sequential compactness, HeineBorel, Banach Fixed Point theorem. Riemann(Stieltjes) integral, Fundamental Theorem of Calculus, Taylor's theorem. Uniform convergence. Infinite series, convergence tests, power series. Elementary functions.
Offered by: Mathematics and Statistics
 Symbols:
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 Winter 2021
 Instructors
 Vojkan Jaksic

MATH 325 Honours ODE's 3 Credits
 Fall
 Winter
 Summer
Offered in the: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.
Offered by: Mathematics and Statistics
 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
 Symbols:
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 Winter 2021
 Instructors
 Antony Raymond Humphries

MATH 350 Honours Discrete Mathematics 3 Credits
 Fall
 Winter
 Summer
Offered in the:Mathematics & Statistics (Sci): Discrete mathematics. Graph Theory: matching theory, connectivity, planarity, and colouring; graph minors and extremal graph theory. Combinatorics: combinatorial methods, enumerative and algebraic combinatorics, discrete probability.
Offered by: Mathematics and Statistics
 Prerequisites: MATH 235 or MATH 240 and MATH 251 or MATH 223.
 Restrictions: Not open to students who have taken or are taking MATH 340. Intended for students in mathematics or computer science honours programs.
 Intended for students in mathematics or computer science honours programs.
 Symbols:
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 Fall 2020
 Instructors
 Sergey Norin

MATH 356 Honours Probability 3 Credits
 Fall
 Winter
 Summer
Offered in the:Mathematics & Statistics (Sci): Sample space, probability axioms, combinatorial probability. Conditional probability, Bayes' Theorem. Distribution theory with special reference to the Binomial, Poisson, and Normal distributions. Expectations, moments, moment generating functions, univariate transformations. Random vectors, independence, correlation, multivariate transformations. Conditional distributions, conditional expectation.Modes of stochastic convergence, laws of large numbers, Central Limit Theorem.
Offered by: Mathematics and Statistics
 Fall
 Prerequisite(s): MATH 243 or MATH 255, and MATH 222 or permission of the Department.
 Restriction: Not open to students who have taken or are taking MATH 323
 Symbols:
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 Fall 2020
 Instructors
 Linan Chen

MATH 357 Honours Statistics 3 Credits
 Fall
 Winter
 Summer
Offered in the: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.
Offered by: Mathematics and Statistics
 Winter
 Prerequisite: MATH 356 or equivalent
 Restriction: Not open to students who have taken or are taking MATH 324
 Symbols:
 Terms
 Winter 2021
 Instructors
 Johanna Neslehova

MATH 358 Honours Advanced Calculus 3 Credits
 Fall
 Winter
 Summer
Offered in the:Mathematics & Statistics (Sci): Pointset topology in Euclidean space; continuity and differentiability of functions in several variables. Implicit and inverse function theorems. Vector fields, divergent and curl operations. Rigorous treatment of multiple integrals: volume and surface area; and Fubini’s theorem. Line and surface integrals, conservative vector fields. Green's theorem, Stokes’ theorem and the divergence theorem.
Offered by: Mathematics and Statistics
 Prerequisites: MATH 222, MATH 247 or MATH 251, MATH 255 or permission of the Department.
 Restrictions: Intended for students in Honours Mathematics programs, Not open to students who have taken or are taking MATH 314 or MATH 248
 Symbols:
 Terms
 Winter 2021
 Instructors
 Pengfei Guan

MATH 376 Honours Nonlinear Dynamics 3 Credits
 Fall
 Winter
 Summer
Offered in the:Mathematics & Statistics (Sci): This course consists of the lectures of MATH 326, but will be assessed at the honours level.
Offered by: Mathematics and Statistics
 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.
 Symbols:
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 Fall 2020
 Instructors
 JeanChristophe Nave

MATH 470 Honours Research Project 3 Credits
 Fall
 Winter
 Summer
Offered in the: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.
Offered by: Mathematics and Statistics
 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
 Symbols:
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 Fall 2020
 Instructors
 Djivede A Kelome

MATH 475 Honours PDE's 3 Credits
 Fall
 Winter
 Summer
Offered in the: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.
Offered by: Mathematics and Statistics
 Prerequisites: MATH 247 or MATH 251 or equivalent, and MATH 248 or MATH 358 or equivalent, MATH 325.
 Restriction: Not open to students who have taken MATH 375.
 Symbols:
 Terms
 Fall 2020
 Instructors
 Jessica Lin
Complementary Courses (21 credits)
3 credits selected from:

MATH 242 Analysis 1 3 Credits
 Fall
 Winter
 Summer
Offered in the:Mathematics & Statistics (Sci): A rigorous presentation of sequences and of real numbers and basic properties of continuous and differentiable functions on the real line.
Offered by: Mathematics and Statistics
 Fall
 Prerequisite: MATH 141
 Restriction(s): Not open to students who are taking or who have taken MATH 254.
 Symbols:
 Terms
 Fall 2020
 Instructors
 Axel W Hundemer

MATH 254 Honours Analysis 1 3 Credits+
 Fall
 Winter
 Summer
Offered in the: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.
Offered by: Mathematics and Statistics
 Prerequisite(s): MATH 141
 Restriction(s): Not open to students who are taking or who have taken MATH 242.
 Symbols:
 +
 Terms
 Fall 2020
 Instructors
 Vojkan Jaksic
+ It is strongly recommended that students take MATH 254.
Advising Notes:
Students interested in continuous applied mathematics are urged to choose these as part of their Complementary Courses: MATH 454, MATH 455 and MATH 478, and are advised to choose additional courses from MATH 387, MATH 397, MATH 555, MATH 560, MATH 574, MATH 578, MATH 579, MATH 580, MATH 581.
Students interested in discrete applied mathematics are advised to choose from these as part of their Complementary Courses: COMP 362, COMP 490, MATH 456, MATH 457, MATH 407, MATH 517, MATH 547, MATH 550, MATH 552, MATH 560.
3 credits selected from:

MATH 249 Honours Complex Variables 3 Credits
 Fall
 Winter
 Summer
Offered in the:Mathematics & Statistics (Sci): Functions of a complex variable; CauchyRiemann equations; Cauchy's theorem and consequences. Taylor and Laurent expansions. Residue calculus; evaluation of real integrals; integral representation of special functions; the complex inversion integral. Conformal mapping; SchwarzChristoffel transformation; Poisson's integral formulas; applications.
Offered by: Mathematics and Statistics
 Winter
 Prerequisite(s): MATH 248 or MATH 358 or equivalent.
 Restriction: Intended for Honours Physics and Engineering students
 Restriction: Not open to students who have taken or are taking MATH 316
 Symbols:
 Terms
 Winter 2021
 Instructors
 Sarah Harrison

MATH 466 Honours Complex Analysis 3 Credits
 Fall
 Winter
 Summer
Offered in the: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.
Offered by: Mathematics and Statistics
 Prerequisite: MATH 255.
 Restriction: Not open to students who have taken or are taking MATH 366, MATH 249, MATH 316 and MATH 381.
 Symbols:
 Terms
 Fall 2020
 Instructors
 Valentino Tosatti
at least 3 credits selected from:

MATH 387 Honours Numerical Analysis 3 Credits
 Fall
 Winter
 Summer
Offered in the:Mathematics & Statistics (Sci): Error analysis. Numerical solutions of equations by iteration. Interpolation. Numerical differentiation and integration. Introduction to numerical solutions of differential equations.
Offered by: Mathematics and Statistics
 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.
 Symbols:
 Terms
 This course is not scheduled for the 20202021 academic year
 Instructors
 There are no professors associated with this course for the 20202021 academic year

MATH 397 Hons Matrix Numerical Analysis 3 Credits
 Fall
 Winter
 Summer
Offered in the: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.
Offered by: Mathematics and Statistics
 Symbols:
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 Winter 2021
 Instructors
 Adam M Oberman
06 credits from the following courses for which no Honours equivalent exists.

MATH 204 Principles of Statistics 2 3 Credits
 Fall
 Winter
 Summer
Offered in the: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.
Offered by: Mathematics and Statistics
 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.
 Symbols:
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 Winter 2021
 Instructors
 Christian Genest

MATH 208 Intro to Statistical Computing 3 Credits
 Fall
 Winter
 Summer
Offered in the:Mathematics & Statistics (Sci): Basic data management. Data visualization. Exploratory data analysis and descriptive statictics. Writing functions. Simulation and parallel computing. Communication data and documenting code for reproducible research.
Offered by: Mathematics and Statistics
 Prerequisite(s): MATH 133
 Symbols:
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 Fall 2020
 Instructors
 Russell Steele

MATH 308 Fundls of Statistical Learning 3 Credits
 Fall
 Winter
 Summer
Offered in the:Mathematics & Statistics (Sci): Theory and application of various techniques for the exploration and analysis of multivariate data: principal component analysis, correspondence analysis, and other visualization and dimensionality reduction techniques; supervised and unsupervised learning; linear discriminant analysis, and clustering techniques. Data applications using appropriate software.
Offered by: Mathematics and Statistics
 Symbols:
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 Winter 2021
 Instructors
 Christian Genest

MATH 329 Theory of Interest 3 Credits
 Fall
 Winter
 Summer
Offered in the:Mathematics & Statistics (Sci): Simple and compound interest, annuities certain, amortization schedules, bonds, depreciation.
Offered by: Mathematics and Statistics
 Winter
 Prerequisite: MATH 141
 Symbols:
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 Winter 2021
 Instructors
 Djivede A Kelome

MATH 338 History & Philosophy of Math 3 Credits
 Fall
 Winter
 Summer
Offered in the: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.
Offered by: Mathematics and Statistics
 Fall
 Symbols:
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 Fall 2020
 Instructors
 There are no professors associated with this course for the 20202021 academic year

MATH 407 Dynamic Programming 3 Credits
 Fall
 Winter
 Summer
Offered in the: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.
Offered by: Mathematics and Statistics
 Symbols:
 Terms
 This course is not scheduled for the 20202021 academic year
 Instructors
 There are no professors associated with this course for the 20202021 academic year

MATH 430 Mathematical Finance 3 Credits
 Fall
 Winter
 Summer
Offered in the:Mathematics & Statistics (Sci): Introduction to concepts of price and hedge derivative securities. The following concepts will be studied in both concrete and continuous time: filtrations, martingales, the change of measure technique, hedging, pricing, absence of arbitrage opportunities and the Fundamental Theorem of Asset Pricing.
Offered by: Mathematics and Statistics
 Symbols:
 Terms
 This course is not scheduled for the 20202021 academic year
 Instructors
 There are no professors associated with this course for the 20202021 academic year

MATH 478 Comput. Meth. in Applied Math 3 Credits
 Fall
 Winter
 Summer
Offered in the:Mathematics & Statistics (Sci): Solution to initial value problems: Linear, Nonlinear Finite Difference Methods: accuracy and stability, Lax equivalence theorem, CFL and von Neumann conditions, Fourier analysis: diffusion, dissipation, dispersion, and spectral methods. Solution of large sparse linear systems: iterative methods, preconditioning, incomplete LU, multigrid, Krylov subspaces, conjugate gradient method. Applications to, e.g., weighted least squares, duality, constrained minimization, calculus of variation, inverse problems, regularization, level set methods, NavierStokes equations
Offered by: Mathematics and Statistics
 Prerequisites: MATH 315 or MATH 325 or MATH 263; MATH 317 or MATH 387 or COMP 350 or MECH 309; or permission of the instructor
 This course will be taught in the winter semester.
 Symbols:
 Terms
 Winter 2021
 Instructors
 JeanChristophe Nave
and the remainder of credits selected from:

COMP 362 Honours Algorithm Design 3 Credits
 Fall
 Winter
 Summer
Offered in the:Computer Science (Sci): Basic algorithmic techniques, their applications and limitations. Problem complexity, how to deal with problems for which no efficient solutions are known.
Offered by: Computer Science
 3 hours
 Prerequisite: COMP 252
 Restriction: Not open to students who have taken or are taking COMP 360.
 Note: COMP 362 can be used instead of COMP 360 to satisfy prerequisites.
 Symbols:
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 Winter 2021
 Instructors
 Bruce Alan Reed

MATH 352 Problem Seminar 1 Credits
 Fall
 Winter
 Summer
Offered in the: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.
Offered by: Mathematics and Statistics
 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.
 Symbols:
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 Fall 2020
 Instructors
 Sergey Norin

MATH 377 Honours Number Theory 3 Credits
 Fall
 Winter
 Summer
Offered in the:Mathematics & Statistics (Sci): This course consists of the lectures of MATH 346, but will be assessed at the honours level.
Offered by: Mathematics and Statistics
 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.
 Symbols:
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 Winter 2021
 Instructors
 Eyal Z Goren

MATH 398 Honours Euclidean Geometry 3 Credits
 Fall
 Winter
 Summer
Offered in the:Mathematics & Statistics (Sci): Honours level: points and lines in a triangle. Quadrilaterals. Angles in a circle. Circumscribed and inscribed circles. Congruent and similar triangles. Area. Power of a point with respect to a circle. Ceva’s theorem. Isometries. Homothety. Inversion.
Offered by: Mathematics and Statistics
 Prerequisite: MATH 133 or equivalent or permission of instructor.
 Restrictions: Not open to students taking or have take MATH 348.
 Symbols:
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 Fall 2020
 Instructors
 Niky Kamran

MATH 454 Honours Analysis 3 3 Credits++
 Fall
 Winter
 Summer
Offered in the:Mathematics & Statistics (Sci): Review of pointset topology: topological space, dense sets, completeness, compactness, connectedness and pathconnectedness, separability. ArzelaAscoli, StoneWeierstrass, Baire category theorems. Measure theory: sigma algebras, Lebesgue measure and integration, L^1 functions. Fatou's lemma, monotone and dominated convergence theorem. Egorov, Lusin's theorems. FubiniTonelli theorem.
Offered by: Mathematics and Statistics
 Symbols:
 ++
 Terms
 Fall 2020
 Instructors
 Jerome Vetois

MATH 455 Honours Analysis 4 3 Credits
 Fall
 Winter
 Summer
Offered in the:Mathematics & Statistics (Sci): Continuation of measure theory. Functional analysis: L^p spaces, linear functionals and dual spaces, HahnBanach theorem, Riesz representation theorem. Hilbert spaces, weak convergence. Spectral theory of compact operator. Introduction to Fourier analysis, Fourier transforms.
Offered by: Mathematics and Statistics
 Symbols:
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 Winter 2021
 Instructors
 Dmitry Jakobson

MATH 456 Honours Algebra 3 3 Credits
 Fall
 Winter
 Summer
Offered in the: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.
Offered by: Mathematics and Statistics
 Prerequisites: MATH 235 and either (MATH 247 or MATH 251).
 Restriction: Not open to students who have taken MATH 370.
 Symbols:
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 Fall 2020
 Instructors
 Eyal Z Goren

MATH 457 Honours Algebra 4 3 Credits
 Fall
 Winter
 Summer
Offered in the: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.
Offered by: Mathematics and Statistics
 Symbols:
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 Winter 2021
 Instructors
 Michael Y Pichot

MATH 458 Honours Differential Geometry 3 Credits
 Fall
 Winter
 Summer
Offered in the: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.
Offered by: Mathematics and Statistics
 Prerequisites: MATH 251 or MATH 247, and MATH 248 or MATH 314 or MATH 358
 Restriction: Not open to students who have taken MATH 380.
 Symbols:
 Terms
 Winter 2021
 Instructors
 Niky Kamran

MATH 480 Honours Independent Study 3 Credits
 Fall
 Winter
 Summer
Offered in the: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.
Offered by: Mathematics and Statistics
 Fall and Winter and Summer
 Please see regulations concerning Project Courses under Faculty Degree Requirements
 Requires approval by the chair before registration
 Symbols:
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 Fall 2020
 Instructors
 Johanna Neslehova

MATH 488 Honours Set Theory 3 Credits
 Fall
 Winter
 Summer
Offered in the:Mathematics & Statistics (Sci): Axioms of set theory, ordinal and cardinal arithmetic, consequences of the axiom of choice, models of set theory, constructible sets and the continuum hypothesis, introduction to independence proofs.
Offered by: Mathematics and Statistics
 Fall
 Prerequisites: MATH 251 or MATH 255 or permission of instructor
 Restrictions :Not open to students who have taken or are taking MATH 590.
 Symbols:
 Terms
 Winter 2021
 Instructors
 Marcin Sabok
++ Not open to students who have taken MATH 354.
All MATH 500level courses.
Other courses with the permission of the Department.