Mathematics (Faculty of Science)
Mathematics and statistics are omnipresent in today's world of information and technology. Their theories, models, and methods are integral to the way we analyze, understand, and build the world around us. They play a key role in nearly every effort to push the boundaries of science, engineering, medicine, and social sciences and contribute, in a major way, to solving some of the most pressing human, environmental, and economic problems of our time.
The department’s programs provide a broad and solid mathematical and statistical education that paves the way to many interesting career options in academia, government, and industry. Top students typically get admitted to prestigious graduate schools around the world and often become leaders in their areas of research in academic or industrial settings. Its graduates at all levels are in high demand in government departments, health research centers, banks, insurance and pharmaceutical companies, statistical agencies, and multinational hightechnology industries.
DETAILED PROGRAM OUTLINES:
Program Requirement:
Program Prerequisites
Students entering the Major program are normally expected to have completed the courses below or their equivalents. Otherwise, they will be required to make up any deficiencies in these courses over and above the 54 credits of required courses.

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; quadratic loci in two and three dimensions.
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, 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.
 Symbols:
 Terms
 Fall 2019
 Winter 2020
 Instructors
 Rosalie BélangerRioux

MATH 140 Calculus 1 3 Credits
 Fall
 Winter
 Summer
Offered in the:Mathematics & Statistics (Sci): Review of functions and graphs. Limits, continuity, derivative. Differentiation of elementary functions. Antidifferentiation. Applications.
Offered by: Mathematics and Statistics
 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
 Symbols:
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 Fall 2019
 Winter 2020
 Instructors
 Sidney Trudeau
 Jérôme Fortier

MATH 141 Calculus 2 4 Credits
 Fall
 Winter
 Summer
Offered in the:Mathematics & Statistics (Sci): The definite integral. Techniques of integration. Applications. Introduction to sequences and series.
Offered by: Mathematics and Statistics
 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
 Symbols:
 Terms
 Fall 2019
 Winter 2020
 Instructors
 Jeremy D Macdonald, Sidney Trudeau
Guidelines for Selection of Courses in the Major Program
The following informal guidelines should be discussed with the student's adviser. Where appropriate, Honours courses may be substituted for equivalent Major courses. Students planning to pursue graduate studies are encouraged to make such substitutions.
Students interested in computer science are advised to choose courses from the following: MATH 317, MATH 318, MATH 327, MATH 335, MATH 340, MATH 407, MATH 417 and to complete the Computer Science Minor.
Students interested in probability and statistics are advised to take MATH 204, MATH 324, MATH 407, MATH 423, MATH 447, MATH 523, MATH 525.
Students interested in applied mathematics should take MATH 317, MATH 319, MATH 324, MATH 326, MATH 327, MATH 407, MATH 417.
Students considering a career in secondary school teaching are advised to take MATH 318, MATH 338, MATH 346, MATH 348.
Students interested in careers in business, industry or government are advised to select courses from the following list:
MATH 317, MATH 319, MATH 327, MATH 329, MATH 407, MATH 417, MATH 423, MATH 430, MATH 447, MATH 523, MATH 525.
Required Courses (27 credits)
Note: Students who have done well in MATH 235 and MATH 242 should consider entering the Honours stream by registering in MATH 251 and MATH 255 instead of MATH 236 and MATH 243.
* Students may select either MATH 249 or MATH 316 but not both.
** Students who have successfully completed a course equivalent to MATH 222 with a grade of C or better may omit MATH 222, but must replace it with 3 credits of elective courses.

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:
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 Terms
 Fall 2019
 Winter 2020
 Instructors
 Jeremy D Macdonald
 Jérôme Fortier

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 2019
 Instructors
 Daniel T Wise

MATH 236 Algebra 2 3 Credits
 Fall
 Winter
 Summer
Offered in the:Mathematics & Statistics (Sci): Linear equations over a field. Introduction to vector spaces. Linear mappings. Matrix representation of linear mappings. Determinants. Eigenvectors and eigenvalues. Diagonalizable operators. CayleyHamilton theorem. Bilinear and quadratic forms. Inner product spaces, orthogonal diagonalization of symmetric matrices. Canonical forms.
Offered by: Mathematics and Statistics
 Winter
 Prerequisite: MATH 235
 Symbols:
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 Winter 2020
 Instructors
 There are no professors associated with this course for the 20192020 academic year

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:
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 Fall 2019
 Instructors
 Jerome Vetois

MATH 243 Analysis 2 3 Credits
 Fall
 Winter
 Summer
Offered in the:Mathematics & Statistics (Sci): Definition and properties of Riemann integral, Fundamental Theorem of Calculus, Taylor's theorem. Infinite series: alternating, telescoping series, rearrangements, conditional and absolute convergence, convergence tests. Power series and Taylor series. Elementary functions. Introduction to metric spaces.
Offered by: Mathematics and Statistics
 Symbols:
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 Winter 2020
 Instructors
 Axel W Hundemer

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: MATH 248.
 Restriction: Intended for Honours Physics and Engineering students
 Restriction: Not open to students who have taken or are taking MATH 316
 Symbols:
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 Winter 2020
 Instructors
 Jerome Vetois

MATH 314 Advanced Calculus 3 Credits
 Fall
 Winter
 Summer
Offered in the:Mathematics & Statistics (Sci): Derivative as a matrix. Chain rule. Implicit functions. Constrained maxima and minima. Jacobians. Multiple integration. Line and surface integrals. Theorems of Green, Stokes and Gauss. Fourier series with applications.
Offered by: Mathematics and Statistics
 Prerequisites: MATH 133, MATH 222
 Restriction: Not open to students who have taken or are taking MATH 248 or MATH 358.
 Symbols:
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 Fall 2019
 Winter 2020
 Instructors
 Charles Roth

MATH 315 Ordinary Differential Eqns 3 Credits
 Fall
 Winter
 Summer
Offered in the:Mathematics & Statistics (Sci): First order ordinary differential equations including elementary numerical methods. Linear differential equations. Laplace transforms. Series solutions.
Offered by: Mathematics and Statistics
 Prerequisite: MATH 222.
 Corequisite: MATH 133.
 Restriction: Not open to students who have taken or are taking MATH 325.
 Symbols:
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 Fall 2019
 Winter 2020
 Instructors
 Rosalie BélangerRioux

MATH 316 Complex Variables 3 Credits*
 Fall
 Winter
 Summer
Offered in the:Mathematics & Statistics (Sci): Algebra of complex numbers, CauchyRiemann equations, complex integral, Cauchy's theorems. Taylor and Laurent series, residue theory and applications.
Offered by: Mathematics and Statistics
 Fall
 Prerequisites: MATH 314 or equivalent and MATH 243.
 Restriction: Not open to students who have taken or are taking MATH 249, MATH 366, MATH 381 or MATH 466.
 Symbols:
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 Terms
 Fall 2019
 Instructors
 Brent Pym

MATH 323 Probability 3 Credits
 Fall
 Winter
 Summer
Offered in the:Mathematics & Statistics (Sci): Sample space, events, conditional probability, independence of events, Bayes' Theorem. Basic combinatorial probability, random variables, discrete and continuous univariate and multivariate distributions. Independence of random variables. Inequalities, weak law of large numbers, central limit theorem.
Offered by: Mathematics and Statistics
 Prerequisites: MATH 141 or equivalent.
 Restriction: Intended for students in Science, Engineering and related disciplines, who have had differential and integral calculus
 Restriction: Not open to students who have taken or are taking MATH 356
 Symbols:
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 Fall 2019
 Winter 2020
 Instructors
 Jose Andres Correa
 David B Wolfson, Djivede A Kelome
Complementary Courses (27 credits)
27 credits selected as follows:
612 credits selected from the following:

MATH 317 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
 Fall
 Prerequisites: MATH 315 or MATH 325 or MATH 263, and COMP 202 or permission of instructor.
 Restrictions: Not open to students who have taken COMP 350
 Symbols:
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 Fall 2019
 Instructors
 Peter Bartello

MATH 324 Statistics 3 Credits
 Fall
 Winter
 Summer
Offered in the:Mathematics & Statistics (Sci): Sampling distributions, point and interval estimation, hypothesis testing, analysis of variance, contingency tables, nonparametric inference, regression, Bayesian inference.
Offered by: Mathematics and Statistics
 Fall and Winter
 Prerequisite: MATH 323 or equivalent
 Restriction: Not open to students who have taken or are taking MATH 357
 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:
 Terms
 Fall 2019
 Winter 2020
 Instructors
 Masoud AsgharianDastenaei

MATH 335 Computational Algebra 3 Credits
 Fall
 Winter
 Summer
Offered in the:Mathematics & Statistics (Sci): Computational aspects of modern algebra. Computing in groups: algorithms, algorithmic problems in groups, finitely generated abelian groups, free groups and automata, finitely presented groups. Computing in rings: elementary notions of ring theory, ideals of polynomial rings in several variables, Groebner bases, elements of field theory.
Offered by: Mathematics and Statistics
 Prerequisites: MATH 235 and MATH 236.
 Note: This course is intended primarily for students in the Major Program in Mathematics and the Joint Major Program in Mathematics and Computer Science.
 Symbols:
 Terms
 This course is not scheduled for the 20192020 academic year
 Instructors
 There are no professors associated with this course for the 20192020 academic year

MATH 340 Discrete Structures 2 3 Credits
 Fall
 Winter
 Summer
Offered in the:Mathematics & Statistics (Sci): Review of mathematical writing, proof techniques, graph theory and counting. Mathematical logic. Graph connectivity, planar graphs and colouring. Probability and graphs. Introductory group theory, isomorphisms and automorphisms of graphs. Enumeration and listing.
Offered by: Mathematics and Statistics
 Winter
 Prerequisites: MATH 235 or MATH 240 or MATH 242.
 Corequisites: MATH 223 or MATH 236.
 Restriction: Not open to students who have taken or are taking MATH 343 or MATH 350.
 Symbols:
 Terms
 Winter 2020
 Instructors
 Jérôme Fortier
1521 credits selected from the following: at least 6 credits must be at the 400 or 500 level.

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 2020
 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 2019
 Instructors
 Russell Steele

MATH 318 Mathematical Logic 3 Credits
 Fall
 Winter
 Summer
Offered in the:Mathematics & Statistics (Sci): Propositional logic: truthtables, formal proof systems, completeness and compactness theorems, Boolean algebras; firstorder logic: formal proofs, Gödel's completeness theorem; axiomatic theories; set theory; Cantor's theorem, axiom of choice and Zorn's lemma, Peano arithmetic; Gödel's incompleteness theorem.
Offered by: Mathematics and Statistics
 Symbols:
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 Fall 2019
 Instructors
 Marcin Sabok

MATH 319 Intro to Partial Diff Equas 3 Credits
 Fall
 Winter
 Summer
Offered in the:Mathematics & Statistics (Sci): First order equations, geometric theory; second order equations, classification; Laplace, wave and heat equations, SturmLiouville theory, Fourier series, boundary and initial value problems.
Offered by: Mathematics and Statistics
 Symbols:
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 Winter 2020
 Instructors
 Adam M Oberman

MATH 320 Differential Geometry 3 Credits
 Fall
 Winter
 Summer
Offered in the:Mathematics & Statistics (Sci): Review of Euclidean geometry. Local theory of plane and space curves: the Frenet formulas. Local theory of surfaces: the first and second fundamental forms, the shape operator, the mean and Gaussian curvatures, surfaces of revolution with prescribed curvature, ruled and developable surfaces. Geodesic curves on surfaces of revolution. The GaussCodazzi equations, rigidity.
Offered by: Mathematics and Statistics
 Symbols:
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 This course is not scheduled for the 20192020 academic year
 Instructors
 There are no professors associated with this course for the 20192020 academic year

MATH 326 Nonlinear Dynamics and Chaos 3 Credits
 Fall
 Winter
 Summer
Offered in the:Mathematics & Statistics (Sci): Linear systems of differential equations, linear stability theory. Nonlinear systems: existence and uniqueness, numerical methods, one and two dimensional flows, phase space, limit cycles, PoincareBendixson theorem, bifurcations, Hopf bifurcation, the Lorenz equations and chaos.
Offered by: Mathematics and Statistics
 Fall
 Prerequisites: MATH 222, MATH 223
 Restriction: Not open to students who have taken or are taking MATH 376
 Symbols:
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 Fall 2019
 Instructors
 Antony Raymond Humphries

MATH 327 Matrix Numerical Analysis 3 Credits
 Fall
 Winter
 Summer
Offered in the:Mathematics & Statistics (Sci): An overview of numerical methods for linear algebra applications and their analysis. Problem classes include linear systems, least squares problems and eigenvalue problems.
Offered by: Mathematics and Statistics
 Winter
 Prerequisites: MATH 223 or MATH 236 or MATH 247 or MATH 251, COMP 202 or consent of instructor.
 Symbols:
 Terms
 This course is not scheduled for the 20192020 academic year
 Instructors
 There are no professors associated with this course for the 20192020 academic year

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:
 Terms
 Winter 2020
 Instructors
 There are no professors associated with this course for the 20192020 academic year

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:
 Terms
 Fall 2019
 Instructors
 There are no professors associated with this course for the 20192020 academic year

MATH 346 Number Theory 3 Credits
 Fall
 Winter
 Summer
Offered in the:Mathematics & Statistics (Sci): Divisibility. Congruences. Quadratic reciprocity. Diophantine equations. Arithmetical functions.
Offered by: Mathematics and Statistics
 Winter
 Prerequisite: MATH 235 or consent of instructor
 Restriction: Not open to students who have taken or are taking MATH 377.
 Symbols:
 Terms
 This course is not scheduled for the 20192020 academic year
 Instructors
 There are no professors associated with this course for the 20192020 academic year

MATH 348 Euclidean Geometry 3 Credits
 Fall
 Winter
 Summer
Offered in the:Mathematics & Statistics (Sci): 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.
 Restriction: Not open to students who have taken MATH 398.
 Symbols:
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 Fall 2019
 Instructors
 Michael Lipnowski

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 2019
 Instructors
 Sergey Norin

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 20192020 academic year
 Instructors
 There are no professors associated with this course for the 20192020 academic year

MATH 410 Majors Project 3 Credits
 Fall
 Winter
 Summer
Offered in the:Mathematics & Statistics (Sci): A supervised project.
Offered by: Mathematics and Statistics
 Prerequisite: Students must have 21 completed credits of the required mathematics courses in their program, including all required 200 level mathematics courses.
 Requires departmental approval.
 Symbols:
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 Fall 2019
 Winter 2020
 Instructors
 Djivede A Kelome, Russell Steele
 Djivede A Kelome

MATH 417 Linear Optimization 3 Credits
 Fall
 Winter
 Summer
Offered in the:Mathematics & Statistics (Sci): An introduction to linear optimization and its applications: Duality theory, fundamental theorem, sensitivity analysis, convexity, simplex algorithm, interiorpoint methods, quadratic optimization, applications in game theory.
Offered by: Mathematics and Statistics
 Prerequisites: COMP 202, and MATH 223 or MATH 236, and MATH 314 or equivalent
 Restriction: Not open to students who have taken or are taking MATH 487 or MATH 517.
 Symbols:
 Terms
 Fall 2019
 Instructors
 There are no professors associated with this course for the 20192020 academic year

MATH 423 Regression&Anal of Variance 3 Credits
 Fall
 Winter
 Summer
Offered in the:Mathematics & Statistics (Sci): Leastsquares estimators and their properties. Analysis of variance. Linear models with general covariance. Multivariate normal and chisquared distributions; quadratic forms. General linear hypothesis: Ftest and ttest. Prediction and confidence intervals. Transformations and residual plot. Balanced designs.
Offered by: Mathematics and Statistics
 Fall
 Prerequisites: MATH 324, and MATH 223 or MATH 236
 Restriction: Not open to students who have taken or are taking MATH 533.
 Symbols:
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 Fall 2019
 Instructors
 Yi Yang

MATH 427 Statistical Quality Control 3 Credits
 Fall
 Winter
 Summer
Offered in the: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.
Offered by: Mathematics and Statistics
 Symbols:
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 Fall 2019
 Instructors
 Christian Genest

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:
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 Winter 2020
 Instructors
 Djivede A Kelome

MATH 447 Intro. to Stochastic Processes 3 Credits
 Fall
 Winter
 Summer
Offered in the: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.
Offered by: Mathematics and Statistics
 Winter
 Prerequisite: MATH 323
 Restriction: Not open to students who have taken or are taking MATH 547.
 Symbols:
 Terms
 Winter 2020
 Instructors
 Russell Steele

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:
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 Winter 2020
 Instructors
 JeanChristophe Nave

MATH 523 Generalized Linear Models 4 Credits
 Fall
 Winter
 Summer
Offered in the:Mathematics & Statistics (Sci): Modern discrete data analysis. Exponential families, orthogonality, link functions. Inference and model selection using analysis of deviance. Shrinkage (Bayesian, frequentist viewpoints). Smoothing. Residuals. Quasilikelihood. Contingency tables: logistic regression, loglinear models. Censored data. Applications to current problems in medicine, biological and physical sciences. R software.
Offered by: Mathematics and Statistics
 Symbols:
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 Winter 2020
 Instructors
 Johanna Neslehova

MATH 525 Sampling Theory & Applications 4 Credits
 Fall
 Winter
 Summer
Offered in the: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.
Offered by: Mathematics and Statistics
 Symbols:
 Terms
 This course is not scheduled for the 20192020 academic year
 Instructors
 There are no professors associated with this course for the 20192020 academic year

MATH 545 Intro to Time Series Analysis 4 Credits
 Fall
 Winter
 Summer
Offered in the:Mathematics & Statistics (Sci): Stationary processes; estimation and forecasting of ARMA models; nonstationary and seasonal models; statespace models; financial time series models; multivariate time series models; introduction to spectral analysis; long memory models.
Offered by: Mathematics and Statistics
 Symbols:
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 Winter 2020
 Instructors
 Russell Steele
If necessary, 6 additional credits in Mathematics or related disciplines selected in consultation with the Adviser.
Program Requirement:
The Minor may be taken in conjunction with any primary program in the Faculty of Science (other than programs in Mathematics). Students should declare their intention to follow the Minor Mathematics at the beginning of the penultimate year and should obtain approval for the selection of courses to fulfil the requirements for the Minor from the Departmental Chief Adviser (or delegate).
It is strongly recommended that students in the Minor program take MATH 323. The remaining credits may be freely chosen from the required and complementary courses for majors and honours students in Mathematics, with the obvious exception of courses that involve duplication of material. Alternatively, up to 6 credits may be allowed for appropriate courses from other departments.
Generally, no more than 6 credits of overlap are permitted between the Minor and the primary program. However, with an approved choice of substantial courses, the overlap restriction may be relaxed to 9 credits for students whose primary program requires 60 credits or more, and to 12 credits when the primary program requires 72 credits or more.
Required Courses (9 credits)
* MATH 223 may be replaced by MATH 235 and MATH 236. In this case, the complementary credit requirement is reduced by 3 credits.

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 2019
 Winter 2020
 Instructors
 Jeremy D Macdonald
 Jérôme Fortier

MATH 223 Linear Algebra 3 Credits*
 Fall
 Winter
 Summer
Offered in the:Mathematics & Statistics (Sci): Review of matrix algebra, determinants and systems of linear equations. Vector spaces, linear operators and their matrix representations, orthogonality. Eigenvalues and eigenvectors, diagonalization of Hermitian matrices. Applications.
Offered by: Mathematics and Statistics
 Fall and Winter
 Prerequisite: MATH 133 or equivalent
 Restriction: Not open to students in Mathematics programs nor to students who have taken or are taking MATH 236, MATH 247 or MATH 251. It is open to students in Faculty Programs
 Symbols:
 *
 Terms
 Fall 2019
 Winter 2020
 Instructors
 Djivede A Kelome
 Jeremy D Macdonald

MATH 315 Ordinary Differential Eqns 3 Credits
 Fall
 Winter
 Summer
Offered in the:Mathematics & Statistics (Sci): First order ordinary differential equations including elementary numerical methods. Linear differential equations. Laplace transforms. Series solutions.
Offered by: Mathematics and Statistics
 Prerequisite: MATH 222.
 Corequisite: MATH 133.
 Restriction: Not open to students who have taken or are taking MATH 325.
 Symbols:
 Terms
 Fall 2019
 Winter 2020
 Instructors
 Rosalie BélangerRioux
Complementary Courses (15 credits)
15 credits selected from the required and complementary courses for majors and honours students in Mathematics, with MATH 323 strongly recommended; alternatively, up to 6 credits may be allowed for appropriate courses from other departments.
Program Requirement:
Program Prerequisites
Students entering the Core Science Component in Mathematics are normally expected to have completed the courses below or their equivalents. Otherwise, they will be required to make up any deficiencies in these courses over and above the 45 credits required for the program.

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; quadratic loci in two and three dimensions.
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, 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.
 Symbols:
 Terms
 Fall 2019
 Winter 2020
 Instructors
 Rosalie BélangerRioux

MATH 140 Calculus 1 3 Credits
 Fall
 Winter
 Summer
Offered in the:Mathematics & Statistics (Sci): Review of functions and graphs. Limits, continuity, derivative. Differentiation of elementary functions. Antidifferentiation. Applications.
Offered by: Mathematics and Statistics
 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
 Symbols:
 Terms
 Fall 2019
 Winter 2020
 Instructors
 Sidney Trudeau
 Jérôme Fortier

MATH 141 Calculus 2 4 Credits
 Fall
 Winter
 Summer
Offered in the:Mathematics & Statistics (Sci): The definite integral. Techniques of integration. Applications. Introduction to sequences and series.
Offered by: Mathematics and Statistics
 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
 Symbols:
 Terms
 Fall 2019
 Winter 2020
 Instructors
 Jeremy D Macdonald, Sidney Trudeau
Guidelines for Selection of Courses
The following informal guidelines should be discussed with the student's adviser. Where appropriate, Honours courses may be substituted for equivalent Major courses. Students planning to pursue graduate studies are encouraged to make such substitutions.
Students interested in computer science are advised to choose courses from the following: MATH 317, MATH 318, MATH 327, MATH 328, MATH 335, MATH 340, MATH 407, MATH 417 and to complete the Computer Science Minor.
Students interested in probability and statistics are advised to take MATH 204, MATH 324, MATH 407, MATH 423, MATH 447, MATH 523, MATH 525.
Students interested in applied mathematics should take MATH 317, MATH 319, MATH 324, MATH 326, MATH 327, MATH 407, MATH 417.
Students considering a career in secondary school teaching are advised to take MATH 318, MATH 328, MATH 338, MATH 339, MATH 346, MATH 348.
Students interested in careers in business, industry or government are advised to select courses from the following list:
MATH 317, MATH 319, MATH 327, MATH 329, MATH 407, MATH 417, MATH 423, MATH 430, MATH 447, MATH 523, MATH 525.
Required Courses (27 credits)
* Students may select either MATH 249 or MATH 316 but not both.
** Students who have successfully completed a course equivalent to MATH 222 with a grade of C or better may omit MATH 222, but must replace it with 3 credits of elective courses.

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 2019
 Winter 2020
 Instructors
 Jeremy D Macdonald
 Jérôme Fortier

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:
 Terms
 Fall 2019
 Instructors
 Daniel T Wise

MATH 236 Algebra 2 3 Credits
 Fall
 Winter
 Summer
Offered in the:Mathematics & Statistics (Sci): Linear equations over a field. Introduction to vector spaces. Linear mappings. Matrix representation of linear mappings. Determinants. Eigenvectors and eigenvalues. Diagonalizable operators. CayleyHamilton theorem. Bilinear and quadratic forms. Inner product spaces, orthogonal diagonalization of symmetric matrices. Canonical forms.
Offered by: Mathematics and Statistics
 Winter
 Prerequisite: MATH 235
 Symbols:
 Terms
 Winter 2020
 Instructors
 There are no professors associated with this course for the 20192020 academic year

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 2019
 Instructors
 Jerome Vetois

MATH 243 Analysis 2 3 Credits
 Fall
 Winter
 Summer
Offered in the:Mathematics & Statistics (Sci): Definition and properties of Riemann integral, Fundamental Theorem of Calculus, Taylor's theorem. Infinite series: alternating, telescoping series, rearrangements, conditional and absolute convergence, convergence tests. Power series and Taylor series. Elementary functions. Introduction to metric spaces.
Offered by: Mathematics and Statistics
 Symbols:
 Terms
 Winter 2020
 Instructors
 Axel W Hundemer

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: MATH 248.
 Restriction: Intended for Honours Physics and Engineering students
 Restriction: Not open to students who have taken or are taking MATH 316
 Symbols:
 *
 Terms
 Winter 2020
 Instructors
 Jerome Vetois

MATH 314 Advanced Calculus 3 Credits
 Fall
 Winter
 Summer
Offered in the:Mathematics & Statistics (Sci): Derivative as a matrix. Chain rule. Implicit functions. Constrained maxima and minima. Jacobians. Multiple integration. Line and surface integrals. Theorems of Green, Stokes and Gauss. Fourier series with applications.
Offered by: Mathematics and Statistics
 Prerequisites: MATH 133, MATH 222
 Restriction: Not open to students who have taken or are taking MATH 248 or MATH 358.
 Symbols:
 Terms
 Fall 2019
 Winter 2020
 Instructors
 Charles Roth

MATH 315 Ordinary Differential Eqns 3 Credits
 Fall
 Winter
 Summer
Offered in the:Mathematics & Statistics (Sci): First order ordinary differential equations including elementary numerical methods. Linear differential equations. Laplace transforms. Series solutions.
Offered by: Mathematics and Statistics
 Prerequisite: MATH 222.
 Corequisite: MATH 133.
 Restriction: Not open to students who have taken or are taking MATH 325.
 Symbols:
 Terms
 Fall 2019
 Winter 2020
 Instructors
 Rosalie BélangerRioux

MATH 316 Complex Variables 3 Credits*
 Fall
 Winter
 Summer
Offered in the:Mathematics & Statistics (Sci): Algebra of complex numbers, CauchyRiemann equations, complex integral, Cauchy's theorems. Taylor and Laurent series, residue theory and applications.
Offered by: Mathematics and Statistics
 Fall
 Prerequisites: MATH 314 or equivalent and MATH 243.
 Restriction: Not open to students who have taken or are taking MATH 249, MATH 366, MATH 381 or MATH 466.
 Symbols:
 *
 Terms
 Fall 2019
 Instructors
 Brent Pym

MATH 323 Probability 3 Credits
 Fall
 Winter
 Summer
Offered in the:Mathematics & Statistics (Sci): Sample space, events, conditional probability, independence of events, Bayes' Theorem. Basic combinatorial probability, random variables, discrete and continuous univariate and multivariate distributions. Independence of random variables. Inequalities, weak law of large numbers, central limit theorem.
Offered by: Mathematics and Statistics
 Prerequisites: MATH 141 or equivalent.
 Restriction: Intended for students in Science, Engineering and related disciplines, who have had differential and integral calculus
 Restriction: Not open to students who have taken or are taking MATH 356
 Symbols:
 Terms
 Fall 2019
 Winter 2020
 Instructors
 Jose Andres Correa
 David B Wolfson, Djivede A Kelome
Complementary Courses (18 credits)
18 credits selected from the following list, with at least 6 credits selected from:

MATH 317 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
 Fall
 Prerequisites: MATH 315 or MATH 325 or MATH 263, and COMP 202 or permission of instructor.
 Restrictions: Not open to students who have taken COMP 350
 Symbols:
 Terms
 Fall 2019
 Instructors
 Peter Bartello

MATH 324 Statistics 3 Credits
 Fall
 Winter
 Summer
Offered in the:Mathematics & Statistics (Sci): Sampling distributions, point and interval estimation, hypothesis testing, analysis of variance, contingency tables, nonparametric inference, regression, Bayesian inference.
Offered by: Mathematics and Statistics
 Fall and Winter
 Prerequisite: MATH 323 or equivalent
 Restriction: Not open to students who have taken or are taking MATH 357
 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:
 Terms
 Fall 2019
 Winter 2020
 Instructors
 Masoud AsgharianDastenaei

MATH 335 Computational Algebra 3 Credits
 Fall
 Winter
 Summer
Offered in the:Mathematics & Statistics (Sci): Computational aspects of modern algebra. Computing in groups: algorithms, algorithmic problems in groups, finitely generated abelian groups, free groups and automata, finitely presented groups. Computing in rings: elementary notions of ring theory, ideals of polynomial rings in several variables, Groebner bases, elements of field theory.
Offered by: Mathematics and Statistics
 Prerequisites: MATH 235 and MATH 236.
 Note: This course is intended primarily for students in the Major Program in Mathematics and the Joint Major Program in Mathematics and Computer Science.
 Symbols:
 Terms
 This course is not scheduled for the 20192020 academic year
 Instructors
 There are no professors associated with this course for the 20192020 academic year

MATH 340 Discrete Structures 2 3 Credits
 Fall
 Winter
 Summer
Offered in the:Mathematics & Statistics (Sci): Review of mathematical writing, proof techniques, graph theory and counting. Mathematical logic. Graph connectivity, planar graphs and colouring. Probability and graphs. Introductory group theory, isomorphisms and automorphisms of graphs. Enumeration and listing.
Offered by: Mathematics and Statistics
 Winter
 Prerequisites: MATH 235 or MATH 240 or MATH 242.
 Corequisites: MATH 223 or MATH 236.
 Restriction: Not open to students who have taken or are taking MATH 343 or MATH 350.
 Symbols:
 Terms
 Winter 2020
 Instructors
 Jérôme Fortier
the remainder of the 18 credits to be selected from:

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:
 Terms
 Winter 2020
 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:
 Terms
 Fall 2019
 Instructors
 Russell Steele

MATH 318 Mathematical Logic 3 Credits
 Fall
 Winter
 Summer
Offered in the:Mathematics & Statistics (Sci): Propositional logic: truthtables, formal proof systems, completeness and compactness theorems, Boolean algebras; firstorder logic: formal proofs, Gödel's completeness theorem; axiomatic theories; set theory; Cantor's theorem, axiom of choice and Zorn's lemma, Peano arithmetic; Gödel's incompleteness theorem.
Offered by: Mathematics and Statistics
 Symbols:
 Terms
 Fall 2019
 Instructors
 Marcin Sabok

MATH 319 Intro to Partial Diff Equas 3 Credits
 Fall
 Winter
 Summer
Offered in the:Mathematics & Statistics (Sci): First order equations, geometric theory; second order equations, classification; Laplace, wave and heat equations, SturmLiouville theory, Fourier series, boundary and initial value problems.
Offered by: Mathematics and Statistics
 Symbols:
 Terms
 Winter 2020
 Instructors
 Adam M Oberman

MATH 320 Differential Geometry 3 Credits
 Fall
 Winter
 Summer
Offered in the:Mathematics & Statistics (Sci): Review of Euclidean geometry. Local theory of plane and space curves: the Frenet formulas. Local theory of surfaces: the first and second fundamental forms, the shape operator, the mean and Gaussian curvatures, surfaces of revolution with prescribed curvature, ruled and developable surfaces. Geodesic curves on surfaces of revolution. The GaussCodazzi equations, rigidity.
Offered by: Mathematics and Statistics
 Symbols:
 Terms
 This course is not scheduled for the 20192020 academic year
 Instructors
 There are no professors associated with this course for the 20192020 academic year

MATH 326 Nonlinear Dynamics and Chaos 3 Credits
 Fall
 Winter
 Summer
Offered in the:Mathematics & Statistics (Sci): Linear systems of differential equations, linear stability theory. Nonlinear systems: existence and uniqueness, numerical methods, one and two dimensional flows, phase space, limit cycles, PoincareBendixson theorem, bifurcations, Hopf bifurcation, the Lorenz equations and chaos.
Offered by: Mathematics and Statistics
 Fall
 Prerequisites: MATH 222, MATH 223
 Restriction: Not open to students who have taken or are taking MATH 376
 Symbols:
 Terms
 Fall 2019
 Instructors
 Antony Raymond Humphries

MATH 327 Matrix Numerical Analysis 3 Credits
 Fall
 Winter
 Summer
Offered in the:Mathematics & Statistics (Sci): An overview of numerical methods for linear algebra applications and their analysis. Problem classes include linear systems, least squares problems and eigenvalue problems.
Offered by: Mathematics and Statistics
 Winter
 Prerequisites: MATH 223 or MATH 236 or MATH 247 or MATH 251, COMP 202 or consent of instructor.
 Symbols:
 Terms
 This course is not scheduled for the 20192020 academic year
 Instructors
 There are no professors associated with this course for the 20192020 academic year

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:
 Terms
 Winter 2020
 Instructors
 There are no professors associated with this course for the 20192020 academic year

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:
 Terms
 Fall 2019
 Instructors
 There are no professors associated with this course for the 20192020 academic year

MATH 346 Number Theory 3 Credits
 Fall
 Winter
 Summer
Offered in the:Mathematics & Statistics (Sci): Divisibility. Congruences. Quadratic reciprocity. Diophantine equations. Arithmetical functions.
Offered by: Mathematics and Statistics
 Winter
 Prerequisite: MATH 235 or consent of instructor
 Restriction: Not open to students who have taken or are taking MATH 377.
 Symbols:
 Terms
 This course is not scheduled for the 20192020 academic year
 Instructors
 There are no professors associated with this course for the 20192020 academic year

MATH 348 Euclidean Geometry 3 Credits
 Fall
 Winter
 Summer
Offered in the:Mathematics & Statistics (Sci): 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.
 Restriction: Not open to students who have taken MATH 398.
 Symbols:
 Terms
 Fall 2019
 Instructors
 Michael Lipnowski

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:
 Terms
 Fall 2019
 Instructors
 Sergey Norin

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 20192020 academic year
 Instructors
 There are no professors associated with this course for the 20192020 academic year

MATH 410 Majors Project 3 Credits
 Fall
 Winter
 Summer
Offered in the:Mathematics & Statistics (Sci): A supervised project.
Offered by: Mathematics and Statistics
 Prerequisite: Students must have 21 completed credits of the required mathematics courses in their program, including all required 200 level mathematics courses.
 Requires departmental approval.
 Symbols:
 Terms
 Fall 2019
 Winter 2020
 Instructors
 Djivede A Kelome, Russell Steele
 Djivede A Kelome

MATH 417 Linear Optimization 3 Credits
 Fall
 Winter
 Summer
Offered in the:Mathematics & Statistics (Sci): An introduction to linear optimization and its applications: Duality theory, fundamental theorem, sensitivity analysis, convexity, simplex algorithm, interiorpoint methods, quadratic optimization, applications in game theory.
Offered by: Mathematics and Statistics
 Prerequisites: COMP 202, and MATH 223 or MATH 236, and MATH 314 or equivalent
 Restriction: Not open to students who have taken or are taking MATH 487 or MATH 517.
 Symbols:
 Terms
 Fall 2019
 Instructors
 There are no professors associated with this course for the 20192020 academic year

MATH 423 Regression&Anal of Variance 3 Credits
 Fall
 Winter
 Summer
Offered in the:Mathematics & Statistics (Sci): Leastsquares estimators and their properties. Analysis of variance. Linear models with general covariance. Multivariate normal and chisquared distributions; quadratic forms. General linear hypothesis: Ftest and ttest. Prediction and confidence intervals. Transformations and residual plot. Balanced designs.
Offered by: Mathematics and Statistics
 Fall
 Prerequisites: MATH 324, and MATH 223 or MATH 236
 Restriction: Not open to students who have taken or are taking MATH 533.
 Symbols:
 Terms
 Fall 2019
 Instructors
 Yi Yang

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
 Winter 2020
 Instructors
 Djivede A Kelome

MATH 447 Intro. to Stochastic Processes 3 Credits
 Fall
 Winter
 Summer
Offered in the: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.
Offered by: Mathematics and Statistics
 Winter
 Prerequisite: MATH 323
 Restriction: Not open to students who have taken or are taking MATH 547.
 Symbols:
 Terms
 Winter 2020
 Instructors
 Russell Steele

MATH 523 Generalized Linear Models 4 Credits
 Fall
 Winter
 Summer
Offered in the:Mathematics & Statistics (Sci): Modern discrete data analysis. Exponential families, orthogonality, link functions. Inference and model selection using analysis of deviance. Shrinkage (Bayesian, frequentist viewpoints). Smoothing. Residuals. Quasilikelihood. Contingency tables: logistic regression, loglinear models. Censored data. Applications to current problems in medicine, biological and physical sciences. R software.
Offered by: Mathematics and Statistics
 Symbols:
 Terms
 Winter 2020
 Instructors
 Johanna Neslehova

MATH 524 Nonparametric Statistics 4 Credits
 Fall
 Winter
 Summer
Offered in the:Mathematics & Statistics (Sci): Distribution free procedures for 2sample problem: Wilcoxon rank sum, SiegelTukey, Smirnov tests. Shift model: power and estimation. Single sample procedures: Sign, Wilcoxon signed rank tests. Nonparametric ANOVA: KruskalWallis, Friedman tests. Association: Spearman's rank correlation, Kendall's tau. Goodness of fit: Pearson's chisquare, likelihood ratio, KolmogorovSmirnov tests. Statistical software packages used.
Offered by: Mathematics and Statistics
 Symbols:
 Terms
 This course is not scheduled for the 20192020 academic year
 Instructors
 There are no professors associated with this course for the 20192020 academic year

MATH 525 Sampling Theory & Applications 4 Credits
 Fall
 Winter
 Summer
Offered in the: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.
Offered by: Mathematics and Statistics
 Symbols:
 Terms
 This course is not scheduled for the 20192020 academic year
 Instructors
 There are no professors associated with this course for the 20192020 academic year

MATH 545 Intro to Time Series Analysis 4 Credits
 Fall
 Winter
 Summer
Offered in the:Mathematics & Statistics (Sci): Stationary processes; estimation and forecasting of ARMA models; nonstationary and seasonal models; statespace models; financial time series models; multivariate time series models; introduction to spectral analysis; long memory models.
Offered by: Mathematics and Statistics
 Symbols:
 Terms
 Winter 2020
 Instructors
 Russell Steele
Program Requirement:
Students may complete this program with a minimum of 60 credits or a maximum of 63 credits depending if they are exempt from MATH 222.
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; quadratic loci in two and three dimensions.
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, 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.
 Symbols:
 Terms
 Fall 2019
 Winter 2020
 Instructors
 Rosalie BélangerRioux

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 or MATH 130 or MATH 131, 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
 Symbols:
 Terms
 Fall 2019
 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 or MATH 130 or MATH 131, except by permission of the Department of Mathematics and Statistics
 Restriction: Not open to students who have taken MATH 152
 Symbols:
 Terms
 Winter 2020
 Instructors
 Charles Roth
In particular, MATH 150/151 and MATH 140/141/222 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 150/1151 are not required to take MATH 222.
Students who transfer to Honours in 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 (48 credits)
4548 credits
+ 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.
* 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.

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 2019
 Winter 2020
 Instructors
 Jeremy D Macdonald
 Jérôme Fortier

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:
 Terms
 Fall 2019
 Instructors
 Daniel T Wise

MATH 248 Honours Vector Calculus 3 Credits*
 Fall
 Winter
 Summer
Offered in the:Mathematics & Statistics (Sci): Partial derivatives and differentiation of functions in several variables; Jacobians; maxima and minima; implicit functions. Scalar and vector fields; orthogonal curvilinear coordinates. Multiple integrals; arc length, volume and surface area. Line and surface integrals; irrotational and solenoidal fields; Green's theorem; the divergence theorem. Stokes' theorem; and applications.
Offered by: Mathematics and Statistics
 Fall and Winter and Summer
 Prerequisites: MATH 133 and MATH 222 or consent of Department.
 Restriction: Intended for Honours Physics, Computer Science, Physiology and Engineering students.
 Restriction: Not open to students who have taken or are taking MATH 314 or MATH 358.
 Symbols:
 *
 Terms
 Fall 2019
 Instructors
 Gantumur Tsogtgerel

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 2020
 Instructors
 Henri Darmon

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:
 Terms
 Winter 2020
 Instructors
 Pengfei Guan

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:
 Terms
 Winter 2020
 Instructors
 JeanPhilippe Lessard

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:
 Terms
 Fall 2019
 Instructors
 Abbas Khalili Mahmoudabadi

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
 Corequisite(s): MATH 255 Honours Analysis 2
 Restriction: Not open to students who have taken or are taking MATH 324
 Symbols:
 Terms
 Winter 2020
 Instructors
 Johanna Neslehova

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 2019
 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:
 Terms
 Winter 2020
 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:
 Terms
 Fall 2019
 Instructors
 Michael Y Pichot

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:
 Terms
 Winter 2020
 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.
 Restriction: Not open to students who have taken MATH 380.
 Symbols:
 Terms
 Winter 2020
 Instructors
 Jacques Claude Hurtubise

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 2019
 Instructors
 Sarah Harrison

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:
 Terms
 Fall 2019
 Winter 2020
 Instructors
 Djivede A Kelome, Michael Lipnowski, Johanna Neslehova, Peter Bartello, Marcin Sabok
 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 2019
 Instructors
 Jessica Lin
Complementary Courses (15 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 2019
 Instructors
 Jerome Vetois

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 2019
 Instructors
 Axel W Hundemer
*** It is strongly recommended that students take MATH 254.
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:
 Terms
 Winter 2020
 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:
 Terms
 Fall 2019
 Instructors
 Russell Steele

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:
 Terms
 Winter 2020
 Instructors
 There are no professors associated with this course for the 20192020 academic year

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:
 Terms
 Fall 2019
 Instructors
 There are no professors associated with this course for the 20192020 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 20192020 academic year
 Instructors
 There are no professors associated with this course for the 20192020 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
 Winter 2020
 Instructors
 Djivede A Kelome
612 credits selected from:

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 2019
 Winter 2020
 Instructors
 Michael Langer, Giulia Alberini
 Reihaneh Rabbany, 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:
 Terms
 Winter 2020
 Instructors
 Luc P Devroye

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:
 Terms
 Fall 2019
 Instructors
 Sergey Norin

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:
 Terms
 Fall 2019
 Instructors
 Sergey Norin

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:
 Terms
 Fall 2019
 Instructors
 Antony Raymond Humphries

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:
 Terms
 This course is not scheduled for the 20192020 academic year
 Instructors
 There are no professors associated with this course for the 20192020 academic year

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
 Winter 2020
 Instructors
 Antony Raymond Humphries

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:
 Terms
 This course is not scheduled for the 20192020 academic year
 Instructors
 There are no professors associated with this course for the 20192020 academic year

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:
 Terms
 Fall 2019
 Instructors
 Michael Lipnowski

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:
 Terms
 Fall 2019
 Winter 2020
 Instructors
 Johanna Neslehova
 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
 This course is not scheduled for the 20192020 academic year
 Instructors
 There are no professors associated with this course for the 20192020 academic year
all MATH 500level courses.
++ Students with limited programming experience should take COMP 202 or equivalent before COMP 250.
Students may select other courses with the permission of the Department.