[[sums:courses]]

Students in the Faculty of Science may additionally take up to 6 credits of courses of level 600 and more. Please see SOUSA and the instructor for more information. An updated list of courses can be found on the departmental website.

Undergraduate students in U3 who want to enroll in graduate level courses may enroll in MATH 595-MATH 599. Courses listed as MATH 100- MATH 199 are U0 courses. Courses above level 500 are 4 credit courses.

# Courses

MATH 111 - Mathematics for Education Students
Sets and functions. Numeration systems. Whole numbers and integers, algorithms for whole-number computations, elementary number theory. Fractions and proportional reasoning. Real numbers, decimals and percents. A brief introduction to probability and statistics.

Education students only.

Not open to students who have successfully completed CEGEP course 201-101 or an equivalent. Not available for credit with MATH 112

MATH 112 - Fundamentals of Mathematics
Equations and inequalities, graphs, relations and functions, exponential and logarithmic functions, trigonometric functions and their use, mathematical induction, binomial theorem, complex numbers.

Education students only.

Not open to students who have successfully completed CEGEP course 201-101 or an equivalent.

Restriction: Open only to those students who are deficient in a pre-calculus background

MATH 122 - Calculus for Management
Review of functions, exponents and radicals, exponential and logorithm. Examples of functions in business applications. Limits, continuity and derivatives. Differentiation of elementary functions. Antiderivatives. The definite integral. Techniques of Integration. Applications of differentiation and integration including differential equations. Trigonometric functions are not discussed in this course.

Students intending to pursue one of the major or minor concentrations in Mathematics and Statistics in the Faculty of Management should take MATH 140 [or MATH 139] and MATH 141 instead.

Management students only

MATH 123 - Linear Algebra and Probability
Geometric vectors in low dimensions. Lines and planes. Dot and cross product. Linear equations and matrices. Matrix operations, properties and rank. Linear dependence and independence. Inverses and determinants. Linear programming and tableaux. Sample space, probability, combination of events. Conditional probability and Bayes Law. Random sampling. Random variables and common distributions.

Students intending to pursue one of the major or minor concentrations in Mathematics and Statistics in the Faculty of Management should take MATH 140 [or MATH 139] and MATH 141 instead.

Management students only

MATH 133 - Linear Algebra and Geometry
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.

MATH 134 - Enriched Linear Algebra and Geometry
Complex numbers. Systems of linear equations, matrix algebra, determinants. Subspaces of euclidean space, linear dependence and independence, bases. Bilinear and quadratic forms. The Gram-Schmidt process. Eigenvalues and eigenvectors, diagonalization. Orthogonal diagonalization of symmetric matrices. This course is intended for students in mathematics and physical sciences.

MATH 139 - Calculus 1 with Precalculus
Review of trigonometry and other Precalculus topics. Limits, continuity, derivative. Differentiation of elementary functions. Antidifferentiation. Applications.

MATH 140 - Calculus 1
Review of functions and graphs. Limits, continuity, derivative. Differentiation of elementary functions. Antidifferentiation. Applications.

MATH 141 - Calculus 2
The definite integral. Techniques of integration. Applications. Introduction to sequences and series.

MATH 150 - Calculus A
Functions, limits and continuity, differentiation, L'Hospital's rule, applications, Taylor polynomials, parametric curves, functions of several variables.

Advanced section of MATH 140, MATH 141. Students who complete MATH 150 and MATH 151 do not have to take Calculus 3

MATH 151 - Calculus B
Integration, methods and applications, infinite sequences and series, power series, arc length and curvature, multiple integration.

Advanced section of MATH 141 and MATH 222. Students who complete MATH 150 and MATH 151 do not have to take Calculus 3

MATH 180 - The Art of Mathematics
An overview of what mathematics has to offer. This course will let you discover the beauty of mathematical ideas while only requiring a high school background in mathematics. The topics of the course may include: prime numbers, modular arithmetic, complex numbers, matrices, permutations and combinations, probability, set theory, game theory, logic, chaos. Additional topics may be covered depending on the instructor.

Intended for students not enrolled in Mathematics; must be taken as a U0 course.

MATH 203 - Principles of Statistics 1
Examples of statistical data and the use of graphical means to summarize the data. Basic distributions arising in the natural and behavioural sciences. The logical meaning of a test of significance and a confidence interval. Tests of significance and confidence intervals in the one and two sample setting (means, variances and proportions). No calculus prerequisites

Potential course overlap. Check under Faculty degree requirements. You may not be able to receive credit for this course and other statistic courses.

Students may receive transfer credits for this course from College or CEGEP

MATH 204 - Principles of Statistics 2
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.

Potential course overlap. Check under Faculty degree requirements. You may not be able to receive credit for this course and other statistic courses.

MATH 222 - Calculus 3
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.

Students may receive transfer credits for this course from College or CEGEP

MATH 223 - Linear Algebra
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.

Open to Minors and Majors students

Students switching to Majors Mathematics or any Honours program and who completed MATH 223 must consult advisor.

MATH 235 - Algebra 1
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.

Open to Majors and Honours students

MATH 236 - Algebra 2
Linear equations over a field. Introduction to vector spaces. Linear mappings. Matrix representation of linear mappings. Determinants. Eigenvectors and eigenvalues. Diagonalizable operators. Cayley-Hamilton theorem. Bilinear and quadratic forms. Inner product spaces, orthogonal diagonalization of symmetric matrices. Canonical forms.

Open to Majors students

MATH 240 - Discrete Structures 1
Mathematical foundations of logical thinking and reasoning. Mathematical language and proof techniques. Quantifiers. Induction. Elementary number theory. Modular arithmetic. Recurrence relations and asymptotics. Combinatorial enumeration. Functions and relations. Partially ordered sets and lattices. Introduction to graphs, digraphs and rooted trees.

For students in any Computer Science program.

Restriction: Not open to students who have taken or are taking MATH 235.

MATH 242 - Analysis 1
A rigorous presentation of sequences and of real numbers and basic properties of continuous and differentiable functions on the real line.

Open to Majors and Honours students

Honours and Majors sections available

MATH 243 - Analysis 2
Infinite series; series of functions; power series. The Riemann integral in one variable. A rigorous development of the elementary functions.

Open to Majors students

MATH 247 - Honours Applied Linear Algebra
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.

Open to Honours students in Engineering, Computer Science. Honours Probability and Statistics and Honours Applied Mathematics may take either MATH 247 or MATH 251. Students who wish to take MATH 370 are advised to choose the latter

MATH 248 - Honours Advanced Calculus
Partial derivatives; implicit functions; Jacobians; maxima and minima; Lagrange multipliers. Scalar and vector fields; orthogonal curvilinear coordinates. Multiple integrals; arc length, volume and surface area. Line integrals; Green's theorem; the divergence theorem. Stokes' theorem; irrotational and solenoidal fields; applications.

Open to Honours students

MATH 249 - Honours Complex Variables
Functions of a complex variable; Cauchy-Riemann 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; Schwarz-Christoffel transformation; Poisson's integral formulas; applications.

Open to Honours students in Physics and Mathematical Physics

Honours Applied Mathematics may take either MATH 249 or MATH 366

MATH 251 - Honours Algebra 2
Linear equations over a field. Introduction to vector spaces. Linear maps and their matrix representation. Determinants. Canonical forms. Duality. Bilinear and quadratic forms. Real and complex inner product spaces. Diagonalization of self-adjoint operators.

Open to Honours students

MATH 255 - Honours Analysis 2
Series of functions including power series. Riemann integration in one variable. Elementary functions.

Open to Honours students

MATH 262 - Intermediate Calculus
Series and power series, including Taylor's theorem. Brief review of vector geometry. Vector functions and curves. Partial differentiation and differential calculus for vector valued functions. Unconstrained and constrained extremal problems. Multiple integrals including surface area and change of variables.

Engineering students only

MATH 263 - Ordinary Differential Equations for Engineers
First order ODEs. Second and higher order linear ODEs. Series solutions at ordinary and regular singular points. Laplace transforms. Linear systems of differential equations with a short review of linear algebra.

Corequisite: MATH 262.

Restrictions: Not open to students who are taking or have taken MATH 315 or MATH 325.

Engineering students only

MATH 264 - Advanced Calculus for Engineers
Review of multiple integrals. Differential and integral calculus of vector fields including the theorems of Gauss, Green, and Stokes. Introduction to partial differential equations, separation of variables, Sturm-Liouville problems, and Fourier series.

Prerequisite: MATH 262 or MATH 151 or MATH 152 or equivalent.

Corequisite: MATH 263

Restrictions: Not open to students who are taking or have taken MATH 319 or MATH 375.

Engineering students only

MATH 270 - Applied Linear Algebra
Introduction. Review of basic linear algebra. Vector spaces. Eigenvalues and eigenvectors of matrices. Linear operators.

Engineering students only

Prerequisite: MATH 263

MATH 271 - Linear Algebra and Partial Differential Equations
Applied Linear Algebra. Linear Systems of Ordinary Differential Equations. Power Series Solutions. Partial Differential Equations. Sturm-Liouville Theory and Applications. Fourier Transforms.

Prerequisites: MATH 263, MATH 264.

Not open to students who have taken MATH 266.

Engineering students only

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.

Prerequisites: MATH 133, MATH 222

Restriction: Not open to students who have taken or are taking MATH 248

Open to Majors and minors students - Honours students may take this course in place of MATH 248 if they have to take MATH 222 in the Fall

MATH 315 - Ordinary Differential Equations
First order ordinary differential equations including elementary numerical methods. Linear differential equations. Laplace transforms. Series solutions.

Prerequisite: MATH 222.

Corequisite: MATH 133.

Restriction: Not open to students who have taken or are taking MATH 325.

Open to Majors students

MATH 316 - Complex Variables
Algebra of complex numbers, Cauchy-Riemann equations, complex integral, Cauchy's theorems. Taylor and Laurent series, residue theory and applications.

Prerequisites: MATH 314 and MATH 243

Restriction: Not open to students who have taken or are taking MATH 249, MATH 366, MATH 381 or MATH 466.

Open to Majors students

MATH 317 - Numerical Analysis
Error analysis. Numerical solutions of equations by iteration. Interpolation. Numerical differentiation and integration. Introduction to numerical solutions of differential equations.

Prerequisites: MATH 315 or MATH 325 or MATH 263, and COMP 202 or permission of instructor.

Open to Majors students

MATH 318 - Mathematical Logic
Propositional calculus, truth-tables, switching circuits, natural deduction, first order predicate calculus, axiomatic theories, set theory.

Restriction: Not open to students who are taking or have taken PHIL 210

Not offered 2013-2014

The Department plans on offering this course next in 2014-2015

MATH 319 - Introduction to Partial Differential Equations
First order equations, geometric theory; second order equations, classification; Laplace, wave and heat equations, Sturm-Liouville theory, Fourier series, boundary and initial value problems.

Open to Majors students

MATH 320 - Differential Geometry
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 Gauss-Codazzi equations, rigidity.

Taught in alternate years

Prerequisites: MATH 236 or MATH 223 or MATH 247, and MATH 314 or MATH 248

Last offered Fall 2007. Not offered 2013-2014

Open to Majors students

MATH 323 - Probability
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.

Prerequisites: MATH 141 or equivalent.

Restriction: Not open to students who have taken or are taking MATH 356

Open to Majors students

MATH 324 - Statistics
Sampling distributions, point and interval estimation, hypothesis testing, analysis of variance, contingency tables, nonparametric inference, regression, Bayesian inference.

Open to Majors students

MATH 325 - Honours Ordinary Differential Equations
First and second order equations, linear equations, series solutions, Frobenius method, introduction to numerical methods and to linear systems, Laplace transforms, applications.

Prerequisite: MATH 222.

Restriction: Intended for Honours Mathematics, Physics and Engineering programs.

Open to Honours students

MATH 326 - Nonlinear Dynamics and Chaos
Linear systems of differential equations, linear stability theory. Nonlinear systems: existence and uniqueness, numerical methods, one and two dimensional flows, phase space, limit cycles, Poincare-Bendixson theorem, bifurcations, Hopf bifurcation, the Lorenz equations and chaos.

Prerequisites: MATH 222, MATH 223

Cross-listed with MATH 376. Open to Majors students

MATH 327 - Matrix Numerical Analysis
An overview of numerical methods for linear algebra applications and their analysis. Problem classes include linear systems, least squares problems and eigenvalue problems.

Taught in alternate years

Prerequisites: MATH 223 or MATH 236 or MATH 247 or MATH 251, COMP 202 or consent of instructor.

Cross-listed with MATH 397. Open to Majors students

Not offered 2013-2014

MATH 329 - Theory of Interest
Simple and compound interest, annuities certain, amortization schedules, bonds, depreciation.

Prerequisite: MATH 141

MATH 338 - History and Philosophy of Mathematics
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.

MATH 340 - Discrete Structures 2
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.

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.

Open to Majors students

MATH 346 - Number Theory
Divisibility. Congruences. Quadratic reciprocity. Diophantine equations. Arithmetical functions.

Taught in alternate years

Prerequisite: MATH 235 or consent of instructor

Cross-listed with MATH 377. Open to Majors students

Not offered 2013-2014

Mathematical maturity required. Students should consider taking this course as U2 or U3.

MATH 348 - Topics in Geometry
Selected topics - the particular selection may vary from year to year. Topics include: isometries in the plane, symmetry groups of frieze and ornamental patterns, equidecomposibility, non-Euclidean geometry and problems in discrete geometry.

Prerequisite: MATH 133 or equivalent or permission of instructor.

MATH 350 - Graph Theory and Combinatorics
Graph models. Graph connectivity, planarity and colouring. Extremal graph theory. Matroids. Enumerative combinatorics and listing.

Prerequisites: MATH 235 or MATH 240 and MATH 251 or MATH 223.

Restrictions: Not open to students who have taken or are taking MATH 343 or MATH 340.

Open to Honours Mathematics and Computer science students

MATH 352 - Problem Seminar
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.

This is a 1 credit course. Enrolment in a math related program or permission of the instructor. Requires departmental approval. Students may be asked to do the Putnam.

MATH 354 - Honours Analysis 3
Introduction to metric spaces. Multivariable differential calculus, implicit and inverse function theorems.

Prerequisite: MATH 255 or equivalent

MATH 355 - Honours Analysis 4
Lebesque measure, integration and Fubini's theorem. Abstract measure and integration. Convergence theorems. Introduction to Hilbert spaces, $L_2$ spaces, Fourier series. Fourier integrals (if time allows).

Prerequisite: MATH 354 or equivalent.

MATH 356 - Honours Probability
Sample space, probability axioms, combinatorial probability. Conditional probability, Bayes' Theorem. Distribution theory with special reference to the Binomial, Poisson, and Normal distributions. Expectations, moments, moment generating functions, uni-variate transformations. Random vectors, independence, correlation, multivariate transformations. Conditional distributions, conditional expectation. Modes of stochastic convergence, laws of large numbers, Central Limit Theorem.

Prerequisite: MATH 255 or MATH 243

Restriction: Not open to students who have taken or are taking MATH 323

Open to Honours students

MATH 357 - Honours Statistics
Data analysis. Estimation and hypothesis testing. Power of tests. Likelihood ratio criterion. The chi-squared goodness of fit test. Introduction to regression analysis and analysis of variance.

Prerequisite: MATH 356 or equivalent

Restriction: Not open to students who have taken or are taking MATH 324

Open to Honours students

MATH 363 - Discrete Mathematics
Logic and combinatorics. Mathematical reasoning and methods of proof. Sets, relations, functions, partially ordered sets, lattices, Boolean algebra. Propositional and predicate calculi. Recurrences and graph theory.

Engineering students only

MATH 366 - Honours Complex Analysis
Functions of a complex variable, Cauchy-Riemann equations, Cauchy's theorem and its consequences. Uniform convergence on compacta. Taylor and Laurent series, open mapping theorem, Rouché's theorem and the argument principle. Calculus of residues. Fractional linear transformations and conformal mappings.

Prerequisite: MATH 248.

Corequisite: MATH 354.

Restriction: Not open to students who have taken or are taking MATH 466, MATH 249, MATH 316, MATH 381.

Open to Honours students

Mandatory for Honours Mathematics students. Complementary course for Honours Probability and Statistics students. Honours Applied Mathematics may take either MATH 249 or MATH 366

MATH 370 - Honours Algebra 3
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.

Prerequisite: MATH 235 and MATH 251 or MATH 247

MATH 371 - Honours Algebra 4
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.

Prerequisite: MATH 370

MATH 375 - Honours Partial Differential Equations
First order partial differential equations, geometric theory, classification of second order linear equations, Sturm-Liouville problems, orthogonal functions and Fourier series, eigenfunction expansions, separation of variables for heat, wave and Laplace equations, Green's function methods, uniqueness theorems.

Prerequisites: MATH 247 or MATH 251 or equivalent, MATH 248 or equivalent, MATH 325

Open to Honours students

MATH 376 - Honours Nonlinear Dynamics
Linear systems of differential equations, linear stability theory. Nonlinear systems: existence and uniqueness, numerical methods, one and two dimensional flows, phase space, limit cycles, Poincare-Bendixson theorem, bifurcations, Hopf bifurcation, the Lorenz equations and chaos. Note: Additionally, a special project or projects may be assigned.

Prerequisites: MATH 222, MATH 223

Cross-listed with MATH 326. Open to Honours students

MATH 377 - Honours Number Theory
Divisibility. Congruences. Quadratic reciprocity. Diophantine equations. Arithmetical functions. Note: Additionally, a special project or projects may be assigned.

Cross-listed with MATH 346. Open to Honours students

Not offered 2013-2014

MATH 380 - Honours Differential Geometry
In addition to the topics of MATH 320, topics in the global theory of plane and space curves, and in the global theory of surfaces are presented. These include: total curvature and the Fary-Milnor theorem on knotted curves, abstract surfaces as 2-d manifolds, the Euler characteristic, the Gauss-Bonnet theorem for surfaces.

Prerequisites: MATH 251 or MATH 247, and MATH 248 or MATH 314

Topics of MATH 320: 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 Gauss-Codazzi equations, rigidity.

MATH 381 - Complex Variables and Transforms
Analytic functions, Cauchy-Riemann equations, simple mappings, Cauchy's theorem, Cauchy's integral formula, Taylor and Laurent expansions, residue calculus. Properties of one and two-sided Fourier and Laplace transforms, the complex inversion integral, relation between the Fourier and Laplace transforms, application of transform techniques to the solution of differential equations. The Z-transform and applications to difference equations.

Prerequisite: MATH 264

Engineering students only

MATH 387 - Honours Numerical Analysis
Error analysis. Numerical solutions of equations by iteration. Interpolation. Numerical differentiation and integration. Introduction to numerical solutions of differential equations.

Taught in alternate years

Prerequisites: MATH 325 or MATH 315, COMP 202 or permission of instructor.

Corequisites: MATH 255 or MATH 243.

MATH 396 - Undergraduate Research Project
Independent research project with a final written report.

Open to students in programs offered by the Faculty of Science only.

Students enrolled in Mathematics program can take MATH 410 and 420 (Majors) or MATH 470 and MATH 480 (Honours) in place of MATH 396.

MATH 397 - Honours Matrix Numerical Analysis
An overview of numerical methods for linear algebra applications and their analysis. Problem classes include linear systems, least squares problems and eigenvalue problems.

Taught in alternate years

Prerequisites: MATH 223 or MATH 236 or MATH 247 or MATH 251, COMP 202 or consent of instructor.

Cross-listed with MATH 327. Open to Honours students

Not offered 2013-2014

MATH 407 - Dynamic Programming
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.

Taught in alternate years

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

MATH 410 - Majors Project
A supervised project.

Requires departmental approval

Prerequisite: Students must have 21 completed credits of the required mathematics courses in their program, including all required 200 level mathematics courses.

Open to Majors students.

MATH 417 - Mathematical Programming
An introductory course in optimization by linear algebra, and calculus methods. Linear programming (convex polyhedra, simplex method, duality, multi-criteria problems), integer programming, and some topics in nonlinear programming (convex functions, optimality conditions, numerical methods). Representative applications to various disciplines.

Prerequisites: COMP 202, and MATH 223 or MATH 236, and MATH 314 or equivalent

Cross-listed with MATH 387. Open to Majors students

Not offered 2013-2014

MATH 420 - Independent Study
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.

Open to Majors students

Students may not take more than once MATH 420. Please check MATH 595 - MATH 599

MATH 423 - Regression and Analysis of Variance
Least-squares estimators and their properties. Analysis of variance. Linear models with general covariance. Multivariate normal and chi-squared distributions; quadratic forms. General linear hypothesis: F-test and t-test. Prediction and confidence intervals. Transformations and residual plot. Balanced designs.

Prerequisites: MATH 324, and MATH 223 or MATH 236

Cross-listed with MATH 533. Open to Majors students

MATH 427 - Statistical Quality Control
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.

Prerequisites: MATH 323 and MATH 324

MATH 430 - Mathematical Finance
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.

Although not listed, mathematical maturity and MATH 323 and MATH 324 or MATH 356 and MATH 357 are considered prerequisites. Intended for Mathematics students; this courses provides a rigourous mathematical treatment of finance.

MATH 437 - Mathematical Methods in Biology
The formulation and treatment of realistic mathematical models describing biological phenomena through qualitative and quantitative mathematical techniques (e.g. local and global stability theory, bifurcation analysis and phase plane analysis) and numerical simulation. Concrete and detailed examples will be drawn from molecular and cellular biology and mammalian physiology.

Taught in alternate years

Prerequisites: MATH 315 or MATH 325, and MATH 323 or MATH 356, a CEGEP or higher level computer programming course

Corequisite: MATH 326 or MATH 376

Cross-listed with MATH 537. Open to Majors students. Limited enrolment.

Not offered 2013-2014

MATH 447 - Introduction to Stochastic Processes
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.

Prerequisite: MATH 323

Cross-listed with MATH 547. Open to Majors students

Students should not consider taking this course as U1 students.

MATH 470 - Honours Research Project
The project will contain a significant research component that requires substantial independent work consisting of a written report and oral examination or presentation.

Requires Departmental Approval

Open to Honours students

MATH 480 - Honours Independent Study
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.

Requires Departmental Approval

Open to Honours students

Students may not take more than once MATH 480. Please check MATH 595 - MATH 599

MATH 487 - Honours Mathematical Programming
An introductory course in optimization by linear algebra, and calculus methods. Linear programming (convex polyhedra, simplex method, duality, multi-criteria problems), integer programming, and some topics in nonlinear programming (convex functions, optimality conditions, numerical methods). Representative applications to various disciplines. Note: Additionally, a special project or projects may be assigned.

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

Cross-listed with MATH 417. Open to Honours students

Not offered 2013-2014

MATH 488 - Honours Set Theory
Axioms of set theory. Operations on sets. Ordinal and cardinal numbers. Well-orderings, transfinite induction and recursion. Consequences of the axiom of choice. Boolean algebras. Cardinal arithmetic.

Taught in alternate years

Prerequisites: MATH 251 or MATH 255 or permission of instructor

Not offered 2012-2013 and 2013-2014. The department does plan to offer this course in a nearby future.

MATH 523 - Generalized Linear Models
Modern discrete data analysis. Exponential families, orthogonality, link functions. Inference and model selection using analysis of deviance. Shrinkage (Bayesian, frequentist viewpoints). Smoothing. Residuals. Quasi-likelihood. Sliced inverse regression. Contingency tables: logistic regression, log-linear models. Censored data. Applications to current problems in medicine, biological and physical sciences. GLIM, S, software.

Prerequisite: MATH 423 or EPIB 697

MATH 524 - Nonparametric Statistics
Distribution free procedures for 2-sample problem: Wilcoxon rank sum, Siegel-Tukey, Smirnov tests. Shift model: power and estimation. Single sample procedures: Sign, Wilcoxon signed rank tests. Nonparametric ANOVA: Kruskal-Wallis, Friedman tests. Association: Spearman's rank correlation, Kendall's tau. Goodness of fit: Pearson's chi-square, likelihood ratio, Kolmogorov-Smirnov tests. Statistical software packages used.

Prerequisite: MATH 324 or equivalent

Not offered 2013-2014

MATH 525 - Sampling Theory and Applications
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.

Prerequisite: MATH 324 or equivalent

MATH 533 - Honours Regression and Analysis of Variance
Least-squares estimators and their properties. Analysis of variance. Linear models with general covariance. Multivariate normal and chi-squared distributions; quadratic forms. General linear hypothesis: F-test and t-test. Prediction and confidence intervals. Transformations and residual plot. Balanced designs.

Note: An additional project or projects assigned by the instructor that require a more detailed treatment of the major results and concepts covered in MATH 423.

Prerequisites: MATH 357, MATH 247 or MATH 251.

Cross-listed with MATH 423. Open to Honours students

MATH 537 - Honours Mathematical Models in Biology
The formulation and treatment of realistic mathematical models describing biological phenomena through such qualitative and quantitative mathematical techniques as local and global stability theory, bifurcation analysis, phase plane analysis, and numerical simulation. Concrete and detailed examples will be drawn from molecular, cellular and population biology and mammalian physiology.

Taught in alternate years

Prerequisite(s): MATH 325, MATH 356, MATH 376, a CEGEP or higher-level computer programming course.

Cross-listed with MATH 437. Open to Honours students. Limited enrolment.

Not offered 2013-2014

MATH 540 - Life Actuarial Mathematics
Life tables and distributions; force of mortality; premium, net premium, and reserve valuation for life insurance and annuity contracts (discrete and continuous case); cash flow analysis for portfolios of life insurance and annuities; asset liability management; numerical techniques for multiple decrement and state models; portfolio valuation of aggregate risks.

Prerequisites: MATH 323 or equivalent and MATH 329

Not offered 2012-2013 and 2013-2014. The department does not plan to offer this course in a nearby future.

MATH 541 - Nonlife Actuarial Models
Stochastic models and inference for loss severity and claim frequency distributions; computational techniques for the aggregation of independent risks (Panjer's algorithm, FFT, etc.); risk measures and quantitative risk management applications; models and inference for multivariate data, heavy-tail distributions, and extremes; dynamic risk models based on stochastic processes and ruin theory.

Prerequisites: MATH 323 and MATH 324 or equivalent

Not offered 2012-2013 and 2013-2014. The department does not plan to offer this course in a nearby future.

MATH 545 - Introduction to Time Series Analysis
Stationary processes; estimation and forecasting of ARMA models; non-stationary and seasonal models; state-space models; financial time series models; multivariate time series models; introduction to spectral analysis; long memory models.

Taugh in alternate years.

Prerequisite: MATH 324 or MATH 357 or equivalent

Not offered 2013-2014

MATH 547 - Stochastic Processes
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.

Prerequisites: MATH 356 and either MATH 247 or MATH 251.

Cross-listed with MATH 447. Open to Honours students

MATH 550 - Combinatorics
Enumerative combinatorics: inclusion-exclusion, generating functions, partitions, lattices and Moebius inversion. Extremal combinatorics: Ramsey theory, Turan's theorem, Dilworth's theorem and extremal set theory. Graph theory: planarity and colouring. Applications of combinatorics.

Taught in alternate years Intended primarily for honours and graduate students in mathematics. Restriction: Permission of instructor.

Not offered 2013-2014

MATH 552 - Combinatorial Optimization
Algorithmic and structural approaches in combinatorial optimization with a focus upon theory and applications. Topics include: polyhedral methods, network optimization, the ellipsoid method, graph algorithms, matroid theory and submodular functions.

Prerequisite: MATH 350 or COMP 362 (or equivalent).

Cross-listed with COMP 552. Open to Mathematics students

MATH 553 - Algorithmic Game Theory
Foundations of game theory. Computation aspects of equilibria. Theory of auctions and modern auction design. General equilibrium theory and welfare economics. Algorithmic mechanism design. Dynamic games.

Prerequisite: COMP 362 or MATH 350 or MATH 354 or MATH 487, or instructor permission.

Cross-listed with COMP 553. Open to Mathematics students

MATH 555 - Fluid Dynamics
Kinematics. Dynamics of general fluids. Inviscid fluids, Navier-Stokes equations. Exact solutions of Navier-Stokes equations. Low and high Reynolds number flow.

Taught in alternate years

Prerequisite (Undergraduate): MATH 315 and MATH 319 or equivalent

Not offered 2012-2013 and 2013-2014

MATH 556 - Mathematical Statistics 1
Distribution theory, stochastic models and multivariate transformations. Families of distributions including location-scale families, exponential families, convolution families, exponential dispersion models and hierarchical models. Concentration inequalities. Characteristic functions. Convergence in probability, almost surely, in Lp and in distribution. Laws of large numbers and Central Limit Theorem. Stochastic simulation.

Prerequisite: MATH 357 or equivalent

MATH 557 - Mathematical Statistics 2
Sampling theory (including large-sample theory). Likelihood functions and information matrices. Hypothesis testing, estimation theory. Regression and correlation theory.

Prerequisite: MATH 556

MATH 560 - Optimization
Line search methods including steepest descent, Newton's (and Quasi-Newton) methods. Trust region methods, conjugate gradient method, solving nonlinear equations, theory of constrained optimization including a rigorous derivation of Karush-Kuhn-Tucker conditions, convex optimization including duality and sensitivity. Interior point methods for linear programming, and conic programming.

Prerequisite: Undergraduate background in analysis and linear algebra, with instructor's approval

Not offered 2011-2012, 2012-2013 and 2013-2014

MATH 564 - Advanced Real Analysis 1
Review of theory of measure and integration; product measures, Fubini's theorem; $L_p$ spaces; basic principles of Banach spaces; Riesz representation theorem for $C(X)$; Hilbert spaces; part of the material of MATH 565 may be covered as well.

Prerequisites: MATH 354, MATH 355 or equivalents

MATH 565 - Advanced Real Analysis 2
Continuation of topics from MATH 564. Signed measures, Hahn and Jordan decompositions. Radon-Nikodym theorems, complex measures, differentiation in $\mathbb{R}^n$, Fourier series and integrals, additional topics.

Prerequisite: MATH 564

MATH 566 - Advanced Complex Analysis
Simple connectivity, use of logarithms; argument, conservation of domain and maximum principles; analytic continuation, monodromy theorem; conformal mapping; normal families, Riemann mapping theorem; harmonic functions, Dirichlet problem; introduction to functions of several complex variables.

Prerequisites: MATH 366, MATH 564.

MATH 567 - Introduction to Functional Analysis
Banach and Hilbert spaces, theorems of Hahn-Banach and Banach-Steinhaus, open mapping theorem, closed graph theorem, Fredholm theory, spectral theorem for compact self-adjoint operators, spectral theorem for bounded self-adjoint operators.

Prerequisite: MATH 355 or equivalent.

Not offered 2012-2013 and 2013-2014

MATH 570 - Higher Algebra 1
Review of group theory; free groups and free products of groups. Sylow theorems. The category of R-modules; chain conditions, tensor products, flat, projective and injective modules. Basic commutative algebra; prime ideals and localization, Hilbert Nullstellensatz, integral extensions. Dedekind domains. Part of the material of MATH 571 may be covered as well.

Prerequisite: MATH 371 or equivalent

MATH 571 - Higher Algebra 2
Completion of the topics of MATH 570. Rudiments of algebraic number theory. A deeper study of field extensions; Galois theory, separable and regular extensions. Semi-simple rings and modules. Representations of finite groups.

Prerequisites: MATH 570 or consent of instructor

MATH 574 - Dynamical Systems
Dynamical systems, phase space, limit sets. Review of linear systems. Stability. Liapunov functions. Stable manifold and Hartman-Grobman theorems. Local bifurcations, Hopf bifurcations, global bifurcations. Poincare Sections. Quadratic maps: chaos, symbolic dynamics, topological conjugacy. Sarkovskii's theorem, periodic doubling route to chaos. Smale Horseshoe.

Taught in alternate years

Prerequisites: MATH 325 and MATH 354 or permission of the instructor.

Not offered 2011-2012, 2012-2013 and 2013-2014

MATH 576 - Geometry and Topology 1
Basic point-set topology, including connectedness, compactness, product spaces, separation axioms, metric spaces. The fundamental group and covering spaces. Simplicial complexes. Singular and simplicial homology. Part of the material of MATH 577 may be covered as well.

Prerequisite: MATH 354

MATH 577 - Geometry and Topology 2
Basic properties of differentiable manifolds, tangent and cotangent bundles, differential forms, de Rham cohomology, integration of forms, Riemannian metrics, geodesics, Riemann curvature.

Prerequisite: MATH 576

MATH 578 - Numerical Analysis 1
Development, analysis and effective use of numerical methods to solve problems arising in applications. Topics include direct and iterative methods for the solution of linear equations (including preconditioning), eigenvalue problems, interpolation, approximation, quadrature, solution of nonlinear systems.

Prerequisites: MATH 247 or MATH 251; and MATH 387; or permission of the instructor.

MATH 579 - Numerical Differential Equations
Numerical solution of initial and boundary value problems in science and engineering: ordinary differential equations; partial differential equations of elliptic, parabolic and hyperbolic type. Topics include Runge Kutta and linear multistep methods, adaptivity, finite elements, finite differences, finite volumes, spectral methods.

Prerequisites: MATH 375 and MATH 387 or permission of the instructor.

MATH 580 - Partial Differential Equations 1
Classification and wellposedness of linear and nonlinear partial differential equations; energy methods; Dirichlet principle. Brief introduction to distributions; weak derivatives. Fundamental solutions and Green's functions for Poisson equation, regularity, harmonic functions, maximum principle. Representation formulae for solutions of heat and wave equations, Duhamel's principle. Method of Characteristics, scalar conservation laws, shocks.

Prerequisites: MATH 375 or equivalent

MATH 581 - Partial Differential Equations 2
Systems of conservation laws and Riemann invariants. Cauchy- Kowalevskaya theorem, powers series solutions. Distributions and transforms. Weak solutions; introduction to Sobolev spaces with applications. Elliptic equations, Fredholm theory and spectra of elliptic operators. Second order parabolic and hyperbolic equations. Further advanced topics may be included.

Prerequisite(s): MATH 355 or equivalent, MATH 580.

MATH 587 - Advanced Probability Theory 1
Probability spaces. Random variables and their expectations. Convergence of random variables in Lp. Independence and conditional expectation. Introduction to Martingales. Limit theorems including Kolmogorov's Strong Law of Large Numbers.

Prerequisite: MATH 356 or equivalent and approval of instructor

Honours Probability and Statistics students may take this in replacement of MATH 355. Taking MATH 355 is strongly recommended.

MATH 589 - Advanced Probability Theory 2
Characteristic functions: elementary properties, inversion formula, uniqueness, convolution and continuity theorems. Weak convergence. Central limit theorem. Additional topic(s) chosen (at discretion of instructor) from: Martingale Theory; Brownian motion, stochastic calculus.

Prerequisites: MATH 587 or equivalent

MATH 590 - Advanced Set Theory
Students will attend the lectures and fulfill all the requirements of MATH 488. In addition, they will study an advanced topic agreed on with the instructor. Topics may be chosen from combinatorial set theory, Goedel's constructible sets, forcing, large cardinals.

Taught in alternate years

Prerequisites: MATH 318, either MATH 355 or MATH 371, or permission of the instructor.

Cross-listed with MATH 488. Open to Honours students and graduate students

Not offered 2011-2012, 2012-2013 and 2013-2014. The department does plan to offer this course in a nearby future.

MATH 591 - Mathematical Logic 1
Propositional logic and first order logic, completeness, compactness and Löwenheim-Skolem theorems. Introduction to axiomatic set theory. Some of the following topics: introduction to model theory, Herbrand's and Gentzen's theories, Lindström's characterization of first order logic.

Taught in alternate years

Prerequisites: MATH 488 or equivalent or consent of instructor

Not offered 2011-2012, 2012-2013 and 2013-2014. The department does plan to offer this course in a nearby future.

MATH 592 - Mathematical Logic 2
Introduction to recursion theory; recursively enumerable sets, relative recursiveness. Incompleteness, undecidability and undefinability theorems of Gödel, Church, Rosser and Tarski. Some of the following topics: Turing degrees, Friedberg-Muchnik theorem, decidable and undecidable theories.

Taught in alternate years

Prerequisites: MATH 488 or equivalent or consent of instructor

Not offered 2012-2013 and 2013-2014. The department does plan to offer this course in a nearby future.

MATH 595 - Topics in Analysis
This course covers a topic in analysis.

Prerequisite(s):At least 30 credits in required or complementary courses from the Honours in Mathematics program including MATH 354 or MATH 366. Additional prerequisites may be imposed by the Department of Mathematics and Statistics depending on the nature of the topic.

Restriction: Requires permission of the Department of Mathematics and Statistics.

MATH 596 - Topics in Algebra & Number Theory
This course covers a topic in algebra and/or number theory.

Prerequisite(s): At least 30 credits in required or complementary courses from the Honours in Mathematics program including MATH 370 or MATH 377. Additional prerequisites may be imposed by the Department of Mathematics and Statistics depending on the nature of the topic.

Restriction(s): Requires permission of the Department of Mathematics and Statistics.

MATH 597 - Topics in Applied Mathematics
This course covers a topic in applied mathematics.

Prerequisite(s): At least 30 credits in required or complementary courses from the Honours in Applied Mathematics program. Additional prerequisites may be imposed by the Department of Mathematics and Statistics depending on the nature of the topic.

Restriction(s): Requires permission of the Department of Mathematics and Statistics.

MATH 598 - Topics in Probability & Statistics
This course covers a topic in probability and/or statistics.

Prerequisite(s): At least 30 credits in required or complementary courses from the Honours in Probability and Statistics program including MATH 356. Additional prerequisites may be imposed by the Department of Mathematics and Statistics depending on the nature of the topic.

Restriction(s): Requires permission of the Department of Mathematics and Statistics.

MATH 599 - Topics in Geometry & Topology
This course covers a topic in geometry and/or topology.

Prerequisites: At least 30 credits in required or complementary courses from the Honours in Mathematics program including MATH 354 and MATH 380. Additional prerequisites may be imposed by the Department of Mathematics and Statistics depending on the nature of the topic.

Restriction(s): Requires permission of the Department of Mathematics and Statistics.